travelling salesman calculator

Traveling Salesman Problem Calculator Online

The Traveling Salesman Problem Calculator is a sophisticated tool designed to solve the TSP by determining the most efficient route that connects multiple points or cities. It utilizes algorithms to process the distances between various points and computes the shortest possible itinerary that visits each point once before returning to the start. This calculator is invaluable for logistics, delivery services, and anyone needing to optimize travel paths over multiple locations.

Formula of Traveling Salesman Problem Calculator

To understand the basic calculations underlying the TSP, consider the formula for calculating the distance between two cities:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

• (x1, y1) and (x2, y2) are the coordinates of the two cities.

This formula, rooted in the Pythagorean theorem, calculates the Euclidean distance between any two points on a plane. Providing a foundational step for the TSP calculator to evaluate all possible routes.

Table for General Terms

To aid in understanding and utilizing the TSP calculator, below is a table of general terms commonly searched or related to the problem. Alongside their meanings or relevant conversions:

This table serves as a quick reference for newcomers to grasp essential concepts related to the TSP and its calculator.

Example of Traveling Salesman Problem Calculator

Consider a delivery company needing to plan a route through cities A, B, and C, with their coordinates on a map as follows: A(1,1), B(4,5), and C(7,2). Using the TSP calculator with the given distance formula. It computes the shortest route that minimizes travel distance while ensuring each city is visited once before returning to the starting point.

Most Common FAQs

The Traveling Salesman Problem is a famous optimization challenge that seeks to find the shortest possible route visiting a set of points exactly once and returning to the original point.

The TSP calculator uses algorithms to compute the distances between all points and iteratively explores permutations of routes to find the one with the least total distance.

Absolutely. The TSP calculator is use in logistics, route planning for deliveries. Any scenario where efficient travel across multiple points is required, saving time and resources.

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Traveling Salesman Problem

The traveling salesman problem (TSP) asks the question, "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city and returns to the origin city?".

This project

• The goal of this site is to be an educational resource to help visualize, learn, and develop different algorithms for the traveling salesman problem in a way that's easily accessible
• As you apply different algorithms, the current best path is saved and used as input to whatever you run next. (e.g. shortest path first -> branch and bound). The order in which you apply different algorithms to the problem is sometimes referred to the meta-heuristic strategy.

Heuristic algorithms

Heuristic algorithms attempt to find a good approximation of the optimal path within a more reasonable amount of time.

Construction - Build a path (e.g. shortest path)

• Shortest Path

Arbitrary Insertion

Furthest insertion.

• Nearest Insertion
• Convex Hull Insertion*
• Simulated Annealing*

Improvement - Attempt to take an existing constructed path and improve on it

• 2-Opt Inversion
• 2-Opt Reciprcal Exchange*

Exhaustive algorithms

Exhaustive algorithms will always find the best possible solution by evaluating every possible path. These algorithms are typically significantly more expensive then the heuristic algorithms discussed next. The exhaustive algorithms implemented so far include:

• Random Paths

Depth First Search (Brute Force)

• Branch and Bound (Cost)
• Branch and Bound (Cost, Intersections)*

Dependencies

These are the main tools used to build this site:

• web workers
• material-ui

Contributing

Pull requests are always welcome! Also, feel free to raise any ideas, suggestions, or bugs as an issue.

This is an exhaustive, brute-force algorithm. It is guaranteed to find the best possible path, however depending on the number of points in the traveling salesman problem it is likely impractical. For example,

• With 10 points there are 181,400 paths to evaluate.
• With 11 points, there are 1,814,000.
• With 12 points there are 19,960,000.
• With 20 points there are 60,820,000,000,000,000, give or take.
• With 25 points there are 310,200,000,000,000,000,000,000, give or take.

This is factorial growth, and it quickly makes the TSP impractical to brute force. That is why heuristics exist to give a good approximation of the best path, but it is very difficult to determine without a doubt what the best path is for a reasonably sized traveling salesman problem.

This is a recursive, depth-first-search algorithm, as follows:

• From the starting point
• For all other points not visited
• If there are no points left return the current cost/path
• Else, go to every remaining point and
• Mark that point as visited
• " recurse " through those paths (go back to 1. )

Implementation

Nearest neighbor.

This is a heuristic, greedy algorithm also known as nearest neighbor. It continually chooses the best looking option from the current state.

• sort the remaining available points based on cost (distance)
• Choose the closest point and go there
• Chosen point is no longer an "available point"
• Continue this way until there are no available points, and then return to the start.

Two-Opt inversion

This algorithm is also known as 2-opt, 2-opt mutation, and cross-aversion. The general goal is to find places where the path crosses over itself, and then "undo" that crossing. It repeats until there are no crossings. A characteristic of this algorithm is that afterwards the path is guaranteed to have no crossings.

• While a better path has not been found.
• For each pair of points:
• Reverse the path between the selected points.
• If the new path is cheaper (shorter), keep it and continue searching. Remember that we found a better path.
• If not, revert the path and continue searching.

This is a heuristic construction algorithm. It select a random point, and then figures out where the best place to put it will be.

• First, go to the closest point
• Choose a random point to go to
• Find the cheapest place to add it in the path
• Continue from #3 until there are no available points, and then return to the start.

This is an impractical, albeit exhaustive algorithm. It is here only for demonstration purposes, but will not find a reasonable path for traveling salesman problems above 7 or 8 points.

I consider it exhaustive because if it runs for infinity, eventually it will encounter every possible path.

• From the starting path
• Randomly shuffle the path
• If it's better, keep it
• If not, ditch it and keep going

Two-Opt Reciprocal Exchange

This algorithm is similar to the 2-opt mutation or inversion algorithm, although generally will find a less optimal path. However, the computational cost of calculating new solutions is less intensive.

The big difference with 2-opt mutation is not reversing the path between the 2 points. This algorithm is not always going to find a path that doesn't cross itself.

It could be worthwhile to try this algorithm prior to 2-opt inversion because of the cheaper cost of calculation, but probably not.

• Swap the points in the path. That is, go to point B before point A, continue along the same path, and go to point A where point B was.

Branch and Bound on Cost

This is a recursive algorithm, similar to depth first search, that is guaranteed to find the optimal solution.

The candidate solution space is generated by systematically traversing possible paths, and discarding large subsets of fruitless candidates by comparing the current solution to an upper and lower bound. In this case, the upper bound is the best path found so far.

While evaluating paths, if at any point the current solution is already more expensive (longer) than the best complete path discovered, there is no point continuing.

For example, imagine:

• A -> B -> C -> D -> E -> A was already found with a cost of 100.
• We are evaluating A -> C -> E, which has a cost of 110. There is no point evaluating the remaining solutions.

Instead of continuing to evaluate all of the child solutions from here, we can go down a different path, eliminating candidates not worth evaluating:

• A -> C -> E -> D -> B -> A
• A -> C -> E -> B -> D -> A

Implementation is very similar to depth first search, with the exception that we cut paths that are already longer than the current best.

This is a heuristic construction algorithm. It selects the closest point to the path, and then figures out where the best place to put it will be.

• Choose the point that is nearest to the current path

Branch and Bound (Cost, Intersections)

This is the same as branch and bound on cost, with an additional heuristic added to further minimize the search space.

While traversing paths, if at any point the path intersects (crosses over) itself, than backtrack and try the next way. It's been proven that an optimal path will never contain crossings.

Implementation is almost identical to branch and bound on cost only, with the added heuristic below:

This is a heuristic construction algorithm. It selects the furthest point from the path, and then figures out where the best place to put it will be.

• Choose the point that is furthest from any of the points on the path

Convex Hull

This is a heuristic construction algorithm. It starts by building the convex hull , and adding interior points from there. This implmentation uses another heuristic for insertion based on the ratio of the cost of adding the new point to the overall length of the segment, however any insertion algorithm could be applied after building the hull.

There are a number of algorithms to determine the convex hull. This implementation uses the gift wrapping algorithm .

In essence, the steps are:

• Determine the leftmost point
• Continually add the most counterclockwise point until the convex hull is formed
• For each remaining point p, find the segment i => j in the hull that minimizes cost(i -> p) + cost(p -> j) - cost(i -> j)
• Of those, choose p that minimizes cost(i -> p -> j) / cost(i -> j)
• Add p to the path between i and j
• Repeat from #3 until there are no remaining points

Simulated Annealing

Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem.

For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to exact algorithms

Visualize algorithms for the traveling salesman problem. Use the controls below to plot points, choose an algorithm, and control execution. (Hint: try a construction alogorithm followed by an improvement algorithm)

Traveling Salesperson Problem : TSP is a problem that tries to find a tour of minimum cost that visits every city once. In this visualization, it is assumed that the underlying graph is a complete graph with (near-)metric distance (meaning the distance function satisfies the triangle inequality) by taking the distance of two points and round it to the nearest integer.

Remarks : By default, we show e-Lecture Mode for first time (or non logged-in) visitor. If you are an NUS student and a repeat visitor, please login .

View the visualisation of TSP algorithm here.

Originally, all edges in the input graph are colored with the grey .

Throughout the visualization, traversed edge will be highlighted with orange .

Pro-tip 1: Since you are not logged-in , you may be a first time visitor (or not an NUS student) who are not aware of the following keyboard shortcuts to navigate this e-Lecture mode: [PageDown] / [PageUp] to go to the next/previous slide, respectively, (and if the drop-down box is highlighted, you can also use [→ or ↓/← or ↑] to do the same),and [Esc] to toggle between this e-Lecture mode and exploration mode.

There are two different sources for specifying an input graph:

• Draw Graph : You can put several points on the drawing box, but you must not draw any edge to ensure the (near-)metric property of the graph. After you have finished putting the points, the edges will be drawn automatically for you after.
• Example Graphs : You can select from the list of graphs to get you started.

Pro-tip 2: We designed this visualization and this e-Lecture mode to look good on 1366x768 resolution or larger (typical modern laptop resolution in 2021). We recommend using Google Chrome to access VisuAlgo. Go to full screen mode ( F11 ) to enjoy this setup. However, you can use zoom-in ( Ctrl + ) or zoom-out ( Ctrl - ) to calibrate this.

Bruteforce : It tries all (V-1)! permutation of vertices (not all V! since it does not matter where we start from). It enumerates all possibilities by doing a dfs search with parameters similar to those of Held-Karp algorithm, that is, the DFS search will return the value of the tour starting from current vertex to all vertices that we have not already visited.

Time complexity: O(V * (V - 1)!) = O(V!).

Pro-tip 3: Other than using the typical media UI at the bottom of the page, you can also control the animation playback using keyboard shortcuts (in Exploration Mode): Spacebar to play/pause/replay the animation, ← / → to step the animation backwards/forwards, respectively, and - / + to decrease/increase the animation speed, respectively.

Dynamic Programming : It uses a widely known algorithm called Held-Karp . In this visualization, it is implemented as a DFS search that is the same with the bruteforce algorithm, but with memoization to cache the answers. This dramatically brings down the run time complexity to O(2^V * V^2).

Time complexity: O(2^V * V^2).

Note that for N = 10, this algorithm takes roughly ~(100 * 2^10) = 102K operations while the bruteforce algorithm takes roughly ~(10!) = 3628800 operations, around 30 times faster.

Approximation : There are two approximation algorithms available, a 2-approximation algorithm and a 1.5-approximation algorithm that is also well known as Christofides Algorithm.

You have reached the last slide. Return to 'Exploration Mode' to start exploring!

Note that if you notice any bug in this visualization or if you want to request for a new visualization feature, do not hesitate to drop an email to the project leader: Dr Steven Halim via his email address: stevenhalim at gmail dot com.

Visualisation Scale

Example Graphs

Dynamic Programming

Approximation

Bitonic TSP

Local Search

1.0x (Default)

0.5x (Minimal Details)

Small Graph

TSPLIB Ulysses 22

TSPLIB Burma 14

TSPLIB Bays 29

TSPLIB Fri 26

CS4234 Tutorial Three

2-approximation TSP

1.5-approximation TSP

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Traveling Salesman Problem Calculator

The Traveling salesman problem is the problem that demands the shortest possible route to visit and come back from one point to another. It is important in theory of computations. This page contains the useful online traveling salesman problem calculator which helps you to determine the shortest path using the nearest neighbour algorithm. This TSP solver online will ask you to enter the input data based on the size of the matrix you have entered.

TSP Solver Online

The above travelling salesman problem calculator will be a highly useful tool for the computer science engineering students, as they have TSP problem in their curriculum. TSP solver online tool will fetch you reliable results.

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Traveling Salesperson Problem

This section presents an example that shows how to solve the Traveling Salesperson Problem (TSP) for the locations shown on the map below.

The following sections present programs in Python, C++, Java, and C# that solve the TSP using OR-Tools

Create the data

The code below creates the data for the problem.

The distance matrix is an array whose i , j entry is the distance from location i to location j in miles, where the array indices correspond to the locations in the following order:

The data also includes:

• The number of vehicles in the problem, which is 1 because this is a TSP. (For a vehicle routing problem (VRP), the number of vehicles can be greater than 1.)
• The depot : the start and end location for the route. In this case, the depot is 0, which corresponds to New York.

Other ways to create the distance matrix

In this example, the distance matrix is explicitly defined in the program. It's also possible to use a function to calculate distances between locations: for example, the Euclidean formula for the distance between points in the plane. However, it's still more efficient to pre-compute all the distances between locations and store them in a matrix, rather than compute them at run time. See Example: drilling a circuit board for an example that creates the distance matrix this way.

Another alternative is to use the Google Maps Distance Matrix API to dynamically create a distance (or travel time) matrix for a routing problem.

Create the routing model

The following code in the main section of the programs creates the index manager ( manager ) and the routing model ( routing ). The method manager.IndexToNode converts the solver's internal indices (which you can safely ignore) to the numbers for locations. Location numbers correspond to the indices for the distance matrix.

The inputs to RoutingIndexManager are:

• The number of rows of the distance matrix, which is the number of locations (including the depot).
• The number of vehicles in the problem.
• The node corresponding to the depot.

Create the distance callback

To use the routing solver, you need to create a distance (or transit) callback : a function that takes any pair of locations and returns the distance between them. The easiest way to do this is using the distance matrix.

The following function creates the callback and registers it with the solver as transit_callback_index .

The callback accepts two indices, from_index and to_index , and returns the corresponding entry of the distance matrix.

Set the cost of travel

The arc cost evaluator tells the solver how to calculate the cost of travel between any two locations — in other words, the cost of the edge (or arc) joining them in the graph for the problem. The following code sets the arc cost evaluator.

In this example, the arc cost evaluator is the transit_callback_index , which is the solver's internal reference to the distance callback. This means that the cost of travel between any two locations is just the distance between them. However, in general the costs can involve other factors as well.

You can also define multiple arc cost evaluators that depend on which vehicle is traveling between locations, using the method routing.SetArcCostEvaluatorOfVehicle() . For example, if the vehicles have different speeds, you could define the cost of travel between locations to be the distance divided by the vehicle's speed — in other words, the travel time.

Set search parameters

The following code sets the default search parameters and a heuristic method for finding the first solution:

The code sets the first solution strategy to PATH_CHEAPEST_ARC , which creates an initial route for the solver by repeatedly adding edges with the least weight that don't lead to a previously visited node (other than the depot). For other options, see First solution strategy .

Add the solution printer

The function that displays the solution returned by the solver is shown below. The function extracts the route from the solution and prints it to the console.

The function displays the optimal route and its distance, which is given by ObjectiveValue() .

Solve and print the solution

Finally, you can call the solver and print the solution:

This returns the solution and displays the optimal route.

Run the programs

When you run the programs, they display the following output.

In this example, there's only one route because it's a TSP. But in more general vehicle routing problems, the solution contains multiple routes.

Save routes to a list or array

As an alternative to printing the solution directly, you can save the route (or routes, for a VRP) to a list or array. This has the advantage of making the routes available in case you want to do something with them later. For example, you could run the program several times with different parameters and save the routes in the returned solutions to a file for comparison.

The following functions save the routes in the solution to any VRP (possibly with multiple vehicles) as a list (Python) or an array (C++).

You can use these functions to get the routes in any of the VRP examples in the Routing section.

The following code displays the routes.

For the current example, this code returns the following route:

As an exercise, modify the code above to format the output the same way as the solution printer for the program.

Complete programs

The complete TSP programs are shown below.

Example: drilling a circuit board

The next example involves drilling holes in a circuit board with an automated drill. The problem is to find the shortest route for the drill to take on the board in order to drill all of the required holes. The example is taken from TSPLIB, a library of TSP problems.

Here's scatter chart of the locations for the holes:

The following sections present programs that find a good solution to the circuit board problem, using the solver's default search parameters. After that, we'll show how to find a better solution by changing the search strategy .

The data for the problem consist of 280 points in the plane, shown in the scatter chart above. The program creates the data in an array of ordered pairs corresponding to the points in the plane, as shown below.

Compute the distance matrix

The function below computes the Euclidean distance between any two points in the data and stores it in an array. Because the routing solver works over the integers, the function rounds the computed distances to integers. Rounding doesn't affect the solution in this example, but might in other cases. See Scaling the distance matrix for a way to avoid possible rounding issues.

Add the distance callback

The code that creates the distance callback is almost the same as in the previous example. However, in this case the program calls the function that computes the distance matrix before adding the callback.

Solution printer

The following function prints the solution to the console. To keep the output more compact, the function displays just the indices of the locations in the route.

Main function

The main function is essentially the same as the one in the previous example , but also includes a call to the function that creates the distance matrix.

Running the program

The complete programs are shown in the next section . When you run the program, it displays the following route:

Here's a graph of the corresponding route:

The OR-Tools library finds the above tour very quickly: in less than a second on a typical computer. The total length of the above tour is 2790.

Here are the complete programs for the circuit board example.

Changing the search strategy

The routing solver does not always return the optimal solution to a TSP, because routing problems are computationally intractable. For instance, the solution returned in the previous example is not the optimal route.

To find a better solution, you can use a more advanced search strategy, called guided local search , which enables the solver to escape a local minimum — a solution that is shorter than all nearby routes, but which is not the global minimum. After moving away from the local minimum, the solver continues the search.

The examples below show how to set a guided local search for the circuit board example.

For other local search strategies, see Local search options .

The examples above also enable logging for the search. While logging isn't required, it can be useful for debugging.

When you run the program after making the changes shown above, you get the following solution, which is shorter than the solution shown in the previous section .

For more search options, see Routing Options .

The best algorithms can now routinely solve TSP instances with tens of thousands of nodes. (The record at the time of writing is the pla85900 instance in TSPLIB, a VLSI application with 85,900 nodes. For certain instances with millions of nodes, solutions have been found guaranteed to be within 1% of an optimal tour.)

Scaling the distance matrix

Since the routing solver works over the integers, if your distance matrix has non-integer entries, you have to round the distances to integers. If some distances are small, rounding can affect the solution.

To avoid any issue with rounding, you can scale the distance matrix: multiply all entries of the matrix by a large number — say 100. This multiplies the length of any route by a factor of 100, but it doesn't change the solution. The advantage is that now when you round the matrix entries, the rounding amount (which is at most 0.5), is very small compared to the distances, so it won't affect the solution significantly.

If you scale the distance matrix, you also need to change the solution printer to divide the scaled route lengths by the scaling factor, so that it displays the unscaled distances of the routes.

Except as otherwise noted, the content of this page is licensed under the Creative Commons Attribution 4.0 License , and code samples are licensed under the Apache 2.0 License . For details, see the Google Developers Site Policies . Java is a registered trademark of Oracle and/or its affiliates.

Last updated 2023-01-16 UTC.

Traveling Salesman Problem

The traveling salesman problem is mentioned by the character Larry Fleinhardt in the Season 2 episode " Rampage " (2006) of the television crime drama NUMB3RS .

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Weisstein, Eric W. "Traveling Salesman Problem." From MathWorld --A Wolfram Web Resource. https://mathworld.wolfram.com/TravelingSalesmanProblem.html

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Travelling Salesman

Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city?

Touch the canvas in order to add a point. You cannot add points when solution is being calculated.

• Nearest Neighbour: Start at a particular node. Travel to the nearest node. Repeat. This algorithm is very simple to implement.
• Greedy Heuristic: Form the initial path with shorter edges, and connect them.
• Simulated Annealing: Inspired by the way crystals cool, this method tries to converge to a local minima while implementing a cooling schedule. In every step, two nodes from the path are switched, and the resulting path is accepted or rejected using Metropolis algorithm (please find intricate details here ).
• Genetic Algorithm: A poplation of entities whose genes comprise of paths, and whose fitness is based on how short the paths are. Fitter entities have greater chance of their genes making it into the offspring. Also uses mutation (to explore prospectively better avenues) and recombination (to combine the best of two genes).
• Ant Colony Optimization: Initially, a population of ants randomly traverse the graph. By gauging the shortness of each edge, they leave more pheromones along that edge. In the next iteration, at every node, the ants choose the edge on a probabilistic manner, weighted by pheromone strength. Both, genetic algorithm and ant colony optimization are called metaheuristic methods because they solve the problem at hand by working at a higher level, instead of directly tackling the problem.
• Christofides' Algorithm Considered the gold standard of solving the Travelling Salesman Problem, this algorithm utilizes insights from an easily solvable problem in graph theory (constructing a minimal spanning tree from a given graph) and manipulates it to arrive at (on average) comparatively shorter paths.
• I will try to make simulations of the optimized algorithms above, if time permits.
• When there are 8+ points, then an initial lag is expected before the solving process starts
• With 10 points, an average time of 49 minutes was required to find the solution to the route
• Simulation may lag on lower-end computers and phones
• Related: Ant Colony Optimization

Developed by ChanRT | Fork me at GitHub

TSPSG TSP Solver and Generator

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About TSPSG

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This software is intended to generate and solve Travelling Salesman Problem ( TSP ) tasks. It uses Branch and Bound method for solving. An input is a number of cities and a matrix of city-to-city travel prices. The matrix can be populated with random values in a given range (useful for generating tasks). The result is an optimal route, its price, step-by-step matrices of solving and solving graph. The task can be saved in internal binary format and opened later. The result can be printed or saved as PDF , HTML , or  ODF .

TSPSG may be useful for teachers to generate test tasks or just for regular users to solve TSPs. Also, it may be used as an example of using Branch and Bound method to solve a particular task.

• 75015 reads

TSPSG v0.1 beta 2

The second beta of TSP Solver and Generator is out! This beta mainly features bugfixes but has some new features, too. One of them is the support for embedding solution graph into HTML when saving a solution (using data URI scheme , not supported by IE 7 and earlier, supported by all other major browsers). Also, see Ticket #5 and Ticket #8 for the description of other new features.

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Some Symbian love

As you may already know, recently TSPSG was accepted to Qt Ambassador Program . As part of this program I've been sent some merchandise that included a Nokia C7-00 device powered by Symbian^3 . This gave me the ability to test TSPSG on a real Symbian device.

As a result of this, I've made a Symbian build of TSPSG v0.1 beta 1 release source code, found some slight (mostly UI ) problems, fixed them and submitted the result to Nokia OVI Store for Symbian^1 (a.k.a S60 5th Edition ) and Symbian^3 devices. Several days ago Symbian^3 version has passed the QA and is now available for download from the store. Symbian^1 is yet in the process. Update: Symbian^1 version is now live, too.

• 42574 reads

TSPSG was accepted to Qt Ambassador Program

Great news, everyone!

At the beginning of this year I have applied with TSPSG to Qt Ambassador Program . Recently, my application was accepted and now TSPSG is featured in Qt Ambassador Showcase . You can find it here: http://qt.nokia.com/qt-in-use/ambassadors/project?id=a0F20000006KW1cEAG .

• 49791 reads

TSPSG v0.1 beta 1 released

The first beta of TSP Solver and Generator has been released during this weekend. Feel free to download its source and binary builds from the project's SourceForge.net Files section . The binary builds are available for Windows , Windows Mobile and FreeBSD  (expeimental).

The main new feature of this release is the solution graph generation . Also, it features toolbar customization (only on desktop platforms), drag-an-drop , support for switching between available Qt styles , an improved solution output generation algorithm , and some other improvements and bugfixes. See the attached ChangeLog for more details.

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Issue Tracker launch

The official TSPSG issue tracker has been launched today. You can always find it by this link: http://tspsg.info/goto/bugtracker .

Also, this means that the beta release is coming soon. So keep tuned…

• 28387 reads

Welcome to TSPSG website!

The official TSPSG website has been launched today.

There isn't much information here at this moment, but this site will be the main source for TSPSG news and support.

• 34758 reads

TSPSG v0.1 alpha 2 is out!

The second alpha of TSPSG is here . You can download the binary builds for Windows , Windows Mobile and Symbian or compile it form the source code yourself right now.

The new version features symmetric mode, improved solution algorithm, support for tasks with up to 50 cities, printing of solution results and many more. Just read the attached ChangeLog.

• 46050 reads

TSPSG v0.1 alpha 1 is here

This build is alpha and is intended only to see what's going on and test TSPSG . It does contain bugs. No bug tracker or feature request facilities will be available until the first beta.

For those who are still interested: download TSPSG v0.1 alpha 1 . Only Windows and Windows Mobile binary builds are available at this moment. Linux , FreeBSD and other supported platforms users have to download source, unpack, run qmake then make from the unpacked directory (note, that you will need Qt 4.5 or later to build this release of  TSPSG ).

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Multiple Traveling Salesman Problem Using Genetic Algorithms

Travelling Salesman Problem

• Travelling salesman problem

The travelling salesman problem (often abbreviated to TSP) is a classic problem in graph theory . It has many applications, in many fields. It also has quite a few different solutions.

The problem

The problem is usually stated in terms of a salesman who needs to visit several towns before eventually returning to the starting point. There are various routes he could take, visiting the different towns in different orders. Here is an example:

There are several different routes that will visit every town. For example, we could visit the towns in the order A , B , C , D , E , then back to A . Or we could use the route A , D , C , E , B then back to A .

But not all routes are possible. For example, we cannot use a route A , D , E , B , C and then back to A , because there is no road from C to A .

The aim is to find the route that visits all the towns with the minimum cost . The cost is shown as the weight of each edge in the graph. This might be the distance between the towns, or it might be some other measure. For example, it might be the time taken to travel between the towns, which might not be proportionate to the distance because some roads have lower speed limits or are more congested. Or, if the salesman was travelling by train, it might be the price of the tickets.

The salesman can decide to optimise for whatever measure he considers to be most important.

Alternative applications and variants

TSP applies to any problem that involves visiting various places in sequence. One example is a warehouse, where various items need to be fetched from different parts of a warehouse to collect the items for an order. In the simplest case, where one person fetches all the items for a single order and then packs and dispatches the items, a TSP algorithm can be used. Of course, a different route would be required for each order, which would be generated by the ordering system.

Another interesting example is printed circuit board (PCB) drilling. A PCB is the circuit board you will find inside any computer or other electronic device. They often need holes drilled in them, including mounting holes where the board is attached to the case and holes where component wires need to pass through the board. These holes are usually drilled by a robot drill that moves across the board to drill each hole in the correct place. TSP can be used to calculate the optimum drilling order.

The TSP algorithm can be applied to directed graphs (where the distance from A to B might be different to the distance from B to A ). Directed graphs can represent things like one-way streets (where the distance might not be the same in both directions) or flight costs (where the price of a single airline ticket might not be the same in both directions).

There are some variants of the TSP scenario. The mTSP problem covers the situation where there are several salesmen and exactly one salesman must visit each city. This applies to delivery vans, where there might be several delivery vans. The problem is to decide which parcels to place on each van and also to decide the route of each van.

The travelling purchaser problem is another variant. In that case, a purchaser needs to buy several items that are being sold in different places, potentially at different prices. The task is to purchase all the items, minimising the total cost (the cost of the items and the cost of travel). A simple approach would be to buy each item from the place where it is cheapest, in which case this becomes a simple TSP. However, it is not always worth buying every item from the cheapest place because sometimes the travel cost might outweigh the price difference.

In this article, we will only look at the basic TSP case.

Brute force algorithm

We will look at 3 potential algorithms here. There are many others. The first, and simplest, is the brute force approach.

We will assume that we start at vertex A . Since we intend to make a tour of the vertices (ie visit every vertex once and return to the original vertex) it doesn't matter which vertex we start at, the shortest loop will still be the same.

So we will start at A , visit nodes B , C , D , and E in some particular order, then return to A .

To find the shortest route, we will try every possible ordering of vertices B , C , D , E , and record the cost of each one. Then we can find the shortest.

For example, the ordering ABCDEA has a total cost of 7+3+6+7+1 = 24.

The ordering ABCEDA (i.e. swapping D and E ) has a total cost of 7+3+2+7+1 = 20.

Some routes, such as ADEBCA are impossible because a required road doesn't exist. We can just ignore those routes.

After evaluating every possible route, we are certain to find the shortest route (or routes, as several different routes may happen to have the same length that also happens to be the shortest length). In this case, the shortest route is AECBDA with a total length of 1+8+3+6+1 = 19.

The main problem with this algorithm is that it is very inefficient. In this example, since we have already decided that A is the start/end point, we must work out the visiting order for the 4 towns BCDE . We have 4 choices of the first town, 3 choices for the second town, 2 choices for the third town, and 1 choice for the fourth town. So there are 4! (factorial) combinations. That is only 24 combinations, which is no problem, you could even do it by hand.

If we had 10 towns (in addition to the home town) there would be 10! combinations, which is 3628800. Far too many to do by hand, but a modern PC might be able to do that in a fraction of a second if the algorithm was implemented efficiently.

If we had 20 towns, then the number of combinations would be of order 10 to the power 18. If we assume a computer that could evaluate a billion routes per second (which a typical PC would struggle to do, at least at the time of writing), that would take a billion seconds, which is several decades.

Of course, there are more powerful computers available, and maybe quantum computing will come into play soon, but that is only 20 towns. If we had 100 towns, the number of combinations would be around 10 to the power 157, and 1000 towns 10 to the power 2568. For some applications, it would be quite normal to have hundreds of vertices. The brute force method is impractical for all but the most trivial scenarios.

Nearest neighbour algorithm

The nearest neighbour algorithm is what we might call a naive attempt to find a good route with very little computation. The algorithm is quite simple and obvious, and it might seem like a good idea to someone who hasn't put very much thought into it. You start by visiting whichever town is closest to the starting point. Then each time you want to visit the next town, you look at the map and pick the closest town to wherever you happen to be (of course, you will ignore any towns that you have visited already). What could possibly go wrong?

Starting at A , we visit the nearest town that we haven't visited yet. In this case D and E are both distance 1 from A . We will (completely arbitrarily) always prioritise the connections in alphabetical order. So we pick D .

As an aside, if we had picked E instead we would get a different result. It might be better, but it is just as likely to be worse, so there is no reason to chose one over the other.

From D , the closest town is C with a distance of 6 (we can't pick A because we have already been there).

From C the closest town is E with distance 2. From E we have to go to B because we have already visited every other town - that is a distance of 8. And from B we must return to A with a distance of 7.

The final path is ADCEBA and the total distance is 1+6+2+8+7 = 24.

The path isn't the best, but it isn't terrible. This algorithm will often find a reasonable path, particularly if there is a natural shortest path. However, it can sometimes go badly wrong.

The basic problem is that the algorithm doesn't take account of the big picture. It just blindly stumbles from one town to whichever next town is closest.

In particular, the algorithm implicitly decides that the final step will be B to A . It does this based on the other distances, but without taking the distance BA into account. But what if, for example, there is a big lake between B and A that you have to drive all the way around? This might make the driving distance BA very large. A more sensible algorithm would avoid that road at all costs, but the nearest neighbour algorithm just blindly leads us there.

We can see this with this revised graph where BA has a distance of 50:

The algorithm will still recommend the same path because it never takes the distance BA into account. The path is still ADCEBA but the total distance is now 1+6+2+8+50 = 67. There are much better routes that avoid BA .

An even worse problem can occur if there is no road at all from B to A . The algorithm would still guide us to town B as the final visit. But in that case, it is impossible to get from B to A to complete the journey:

Bellman–Held–Karp algorithm

The Bellman–Held–Karp algorithm is a dynamic programming algorithm for solving TSP more efficiently than brute force. It is sometimes called the Held–Karp algorithm because it was discovered by Michael Held and Richard Karp, but it was also discovered independently by Richard Bellman at about the same time.

The algorithm assumes a complete graph (ie a graph where every vertex is connected to every other). However, it can be used with an incomplete graph like the one we have been using. To do this, we simply add extra the missing connections (shown below in grey) and assign them a very large distance (for example 1000). This ensures that the missing connections will never form part of the shortest path:

The technique works by incrementally calculating the shortest path for every possible set of 3 towns (starting from A ), then for every possible set of 4 towns, and so on until it eventually calculates the shortest path that goes from A via every other town and back to A .

Because the algorithm stores its intermediate calculations and discards non-optimal paths as early as possible, it is much more efficient than brute force.

We will use the following notation. We will use this to indicate the distance between towns A and B :

And we will use this to indicate the cost (ie the total distance) from A to C via B :

Here are some examples:

The first example is calculated by adding the distance AB to BC , which gives 10. The second example is calculated by adding AC to CB . But since there is no road from A to C , we give that a large dummy distance of 1000, so that total cost is 1003, which means it is never going to form a part of the shortest route. The third example is calculated by adding the distance AD to DE , which gives 8.

In the first step, we will calculate the value of every possible combination of 2 towns starting from A . There are 12 combinations: AB(C) , AB(D) , AB(E) , AC(B) , AC(D) , AC(E) , AD(B) , AD(C) , AD(E) , AE(B) , AE(C) , AE(D) .

These values will be stored for later use.

For step 2 we need to extend our notation slightly. We will use this to indicate the lowest cost from A to D via B and C (in either order):

To be clear, this could represent one of two paths - ABCD or ACBD whichever is shorter. We can express this as a minimum of two values:

This represents the 2 ways to get from A to D via B and C :

• We can travel from A to C via B , and then from C to D .
• We can travel from A to B via C , and then from B to D .

We have already calculated A to C via B (and all the other combinations) in step 1, so all we need to do is add the values and find the smallest. In this case:

• A to C via B is 10, C to D is 6, so the total is 16.
• A to B via C is 1003, B to D is 1000, so the total is 2003.

Clearly, ABCD is the best route.

We need to repeat this for every possible combination of travelling from A to x via y and z . There are, again, 12 combinations: AB(CD) , AB(CE) , AB(DE) , AC(BD) , AC(BE) , AC(DE) , AD(BC) , AD(BE) , AD(CE) , AE(BC) , AE(BD) , AE(CD) .

We store these values, along with the optimal path, for later use.

In the next step, we calculate the optimal route for travelling from A to any other town via 3 intermediate towns. For example, travelling from A to E via B , C , and D (in the optimal order) is written as:

There are 3 paths to do this:

• A to D via B and C , then from D to E .
• A to C via B and D , then from C to E .
• A to B via C and D , then from B to E .

We will choose the shortest of these three paths:

Again we have already calculated all the optimal intermediate paths. This time there are only 4 combinations we need to calculate: AB(CDE) , AC(BDE) , AD(BCE) , and AE(BCD) .

We are now in a position to calculate the optimal route for travelling from A back to A via all 4 other towns:

We need to evaluate each of the 4 options in step 3, adding on the extra distance to get back to A :

We can then choose the option that has the lowest total cost, and that will be the optimal route.

Performance

The performance of the Bellman–Held–Karp algorithm can be expressed in big-O notations as:

The time performance is approximately exponential. As the number of towns increases, the time taken will go up exponentially - each time an extra town is added, the time taken will double. We are ignoring the term in n squared because the exponential term is the most significant part.

Exponential growth is still quite bad, but it is far better than the factorial growth of the brute-force algorithm.

It is also important to notice that the algorithm requires memory to store the intermediate results, which also goes up approximately exponentially. The brute force algorithm doesn't have any significant memory requirements. However, that is usually an acceptable trade-off for a much better time performance.

The stages above describe how the algorithm works at a high level. We haven't gone into great detail about exactly how the algorithm keeps track of the various stages. Over the years since its discovery, a lot of work has been put into optimising the implementation. Optimising the implementation won't change the time complexity, which will still be roughly exponential. However, it might make the algorithm run several times faster than a poor implementation.

We won't cover this in detail, but if you ever need to use this algorithm for a serious purpose, it is worth considering using an existing, well-optimised implementation rather than trying to write it yourself. Unless you are just doing it for fun!

Other algorithms

Even the Bellman–Held–Karp algorithm has poor performance for modestly large numbers of towns. 100 towns, for example, would be well beyond the capabilities of a modern PC.

There are various heuristic algorithms that are capable of finding a good solution, but not necessarily the best possible solution, in a reasonable amount of time. I hope to cover these in a future article.

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Traveling Salesman Problem: Solver-Based

This example shows how to use binary integer programming to solve the classic traveling salesman problem. This problem involves finding the shortest closed tour (path) through a set of stops (cities). In this case there are 200 stops, but you can easily change the nStops variable to get a different problem size. You'll solve the initial problem and see that the solution has subtours. This means the optimal solution found doesn't give one continuous path through all the points, but instead has several disconnected loops. You'll then use an iterative process of determining the subtours, adding constraints, and rerunning the optimization until the subtours are eliminated.

For the problem-based approach, see Traveling Salesman Problem: Problem-Based .

Problem Formulation

Formulate the traveling salesman problem for integer linear programming as follows:

Generate all possible trips, meaning all distinct pairs of stops.

Calculate the distance for each trip.

The cost function to minimize is the sum of the trip distances for each trip in the tour.

The decision variables are binary, and associated with each trip, where each 1 represents a trip that exists on the tour, and each 0 represents a trip that is not on the tour.

To ensure that the tour includes every stop, include the linear constraint that each stop is on exactly two trips. This means one arrival and one departure from the stop.

Generate Stops

Generate random stops inside a crude polygonal representation of the continental U.S.

Calculate Distances Between Points

Because there are 200 stops, there are 19,900 trips, meaning 19,900 binary variables (# variables = 200 choose 2).

Generate all the trips, meaning all pairs of stops.

Calculate all the trip distances, assuming that the earth is flat in order to use the Pythagorean rule.

With this definition of the dist vector, the length of a tour is

dist'*x_tsp

where x_tsp is the binary solution vector. This is the distance of a tour that you try to minimize.

Create Graph and Draw Map

Represent the problem as a graph. Create a graph where the stops are nodes and the trips are edges.

Display the stops using a graph plot. Plot the nodes without the graph edges.

Constraints

Create the linear constraints that each stop has two associated trips, because there must be a trip to each stop and a trip departing each stop. This formulation works when the problem has at least three stops.

Binary Bounds

All decision variables are binary. Now, set the intcon argument to the number of decision variables, put a lower bound of 0 on each, and an upper bound of 1.

Optimize Using intlinprog

The problem is ready for solution. To suppress iterative output, turn off the default display.

Create a new graph with the solution trips as edges. To do so, round the solution in case some values are not exactly integers, and convert the resulting values to logical .

Visualize Solution

As can be seen on the map, the solution has several subtours. The constraints specified so far do not prevent these subtours from happening. In order to prevent any possible subtour from happening, you would need an incredibly large number of inequality constraints.

Subtour Constraints

Because you can't add all of the subtour constraints, take an iterative approach. Detect the subtours in the current solution, then add inequality constraints to prevent those particular subtours from happening. By doing this, you find a suitable tour in a few iterations.

Eliminate subtours with inequality constraints. An example of how this works is if you have five points in a subtour, then you have five lines connecting those points to create the subtour. Eliminate this subtour by implementing an inequality constraint to say there must be less than or equal to four lines between these five points.

Even more, find all lines between these five points, and constrain the solution not to have more than four of these lines present. This is a correct constraint because if five or more of the lines existed in a solution, then the solution would have a subtour (a graph with n nodes and n edges always contains a cycle).

Detect the subtours by identifying the connected components in Gsol , the graph built with the edges in the current solution. conncomp returns a vector with the number of the subtour to which each edge belongs.

Include the linear inequality constraints to eliminate subtours, and repeatedly call the solver, until just one subtour remains.

Solution Quality

The solution represents a feasible tour, because it is a single closed loop. But is it a minimal-cost tour? One way to find out is to examine the output structure.

The smallness of the absolute gap implies that the solution is either optimal or has a total length that is close to optimal.

Related Topics

• Traveling Salesman Problem: Problem-Based

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• Introduction
• Create game
• Optimal tour
• Description of the algorithm
• Calculation steps

Shortest round trips

Welcome to the tsp game.

This website is about the so-called "Traveling Salesman Problem".

It deals with the question, how to plan a complete round trip through a certain number of cities to obtain the shortest tour possible. This question can be answered quite easily for four cities. However, it gets complicated when the number of cities is increased. There exist for example 181.440 different tours through just ten cities.

How can one find the shortest tour on twenty or even more cities?

For this reason, various algorithms have been invented, which try to solve the Traveling Salesman Problem as fast as possible.

And now it is your turn!

Create a new game in the next tab and try to find a shortest tour yourself! Afterwards, you may have a look at the solution and the calculation steps of the applied algorithms.

What would you like to do first?

Repeat game

On this page you can create a new game, find your tour, see the solution, repeat the current game, test your logistic skills and draw the shortest round trip you can find..

Do not forget to visit every city exactly once!

By changing the tab, the drawing mode will be terminated.

There is no way back to the "Play game" tab.

Congratulations! Your tour is optimal.

Too bad unfortunately, your tour is not optimal., too bad unfortunately, your tour does not visit all nodes., too bad unfortunately, your tour contains subtours., how has the solution been calculated.

In this tab you may have a look at the optimal tour and the corresponding calculation steps.

In the Description of the algorithm you may find more details on the applied algorithms of the different steps.

Graphs and algorithms

• 'Heuristics', which find a round trip, but do not indicate its optimality in relation to an optimal solution. Its length is always larger than the length of an optimal tour. It is than called 'upper bound'.
• "Exact solver", which converge to an optimal round trip slowly. Found paths are never longer than an optimal solution. Therefore, their length is called 'lower bound'. Their result is rarely a round trip through all nodes.

Nearest neighbour algorithm

Multiple fragment algorithm.

• There are no more than two incident edges allowed for each node.
• No circles are allowed.

Lagrangian relaxation

• Remove one node from the graph.
• Add edges between the remaining nodes in ascending order, like in the Multiple Fragment algorithm. There may be more than two edges incident to one node. However, circles are not allowed.
• Now add the removed node together with its two shortest incident edges to the graph. If a round trip is obtained, stop. There is no shorter round trip. Otherwise, one continues as follows.
• The aim is to have exactly two edges incident to one node. Therefore, find out by which number the number of incident edges differs from 2. Say four edges are incident to a node, then the result is 2. One incident edge leads to -1. Add the result to the length of all incident edges.
• Return to the first step.

Branch and Bound

• e and f are forced edges. All other edges are permitted.
• e is forced and f permitted. Edges that have been free before this step will stay free.
• e is permitted. All other edges stay free, if they have been before.

Origins of the Traveling Salesman Problem

The application, studying mathematics at the tum, a last remark about this page's goal and citations.

Chair M9 of Technische Universität München does research in the fields of discrete mathematics, applied geometry and the optimization of mathematical problems. The problem and corresponding algorithms presented here are a famous example for the application of mathematics on an applied problem (and can be assigned to the field of combinatorial optimization). This page shall help the reader to recognize the application of mathematics to real life problems and to understand easy mathematical solution methods used. The algorithms presented were chosen according to understandability, they do not represent fields of research of the chair.

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Free Geography Tools

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Online Traveling Salesman Problem Solver

Wikipedia defines the “Traveling Salesman Problem” this way:

… given a number of cities and the costs of travelling from any city to any other city, what is the least-cost round-trip route that visits each city exactly once and then returns to the starting city?

You can substitute “address” for “city”, making this an intra-urban travel problem. The OptiMap website solves this problem automatically for up to 24 locations (“nodes”). You can enter the nodes by clicking in a Google Maps interface:

You can also enter address nodes individually using the “Add Location By Address” box. Even better, you can add text lists of addresses or coordinates (latitude/longitude) by clicking on the “Bulk add by address or (lat, lng).” link, then copying and pasting the list into the text box that shows up. Latitude/longitude should be in decimal format, one set on each line, separated by commas and surrounded by parentheses, e.g. (35.333, –110.254). You can also specify only walking directions, and avoiding highways. The first node or address entered is always considered to be the starting point.

When you’re done entering nodes, click on “Calculate Fastest Roundtrip” to solve the problem for a round-trip that ends where you started:

You’ll also get a set of Google Maps driving directions for the trip shown in the solution map. By clicking on the “Toggle raw path output” button, you’ll also get a text list of latitude/longitude coordinates in sequence for this route that you could convert into a GPS route:

The “Calculate Fastest A-Z Trip” works in a similar fashion, but for a one-way trip, where the first address/node you entered is taken as the start “A”, and the last address/node is the destination “Z”.

The technical background and source code are available on the OptiMap website , as are instructions on how to use this on your own website.

Related posts:

• Another Google Maps Geocoder/Reverse Geocoder
• Drawing Lines Between Points In Google Maps, Straight And Great Circle
• Coordinate Data From Google Maps
• Easy Google Maps Route Creation With NetKvik
• Compare Point Latitudes And Longitudes With Iso-Longitude-Latitude

2 Responses to “Online Traveling Salesman Problem Solver”

Hi – Here’s an entry with additional info on the traveling salesman: http://technology.slashgeo.org/article.pl?sid=08/01/17/2258255 Cheers and thanks for your useful blog! :-)

• 1 Online Geocoding, Address Verification And Shortest Path Utilities From the USC GIS Research Laboratory | Free Geography Tools Pingback on Feb 10th, 2009 at 6:23 am

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Plus.Maths.org

The travelling salesman

On 20th November 2012 Plus hosted the first UK screening of Travelling Salesman , an intellectual thriller imagining the consequences of solving the P vs NP problem, at the Centre for Mathematical Sciences in Cambridge. Here you can find out what this problem is all about.

We're hosting another screening of the film on 14 March 2013, Pi Day, as part of the Cambridge Science Festival

Get cash from the cash point, go to the supermarket, pick up kids from school and prescription from doctor. In what order should you do these things so that the distance you've got to drive is as short as possible? Not a particularly exciting problem, you might think, but it's one that fascinates mathematicians. That's because in general it's very hard to solve and opens the door on one of the trickiest unanswered questions in mathematics.

The problem is called the travelling salesman problem and the general form goes like this: you've got a number of places to visit, you're given the distances between them, and you have to work out the shortest route that visits every place exactly once and returns to where you started. If it's a small number of places, you can find the answer quite easily simply by looking at all the possible routes. As the number of places grows, this becomes incredibly tedious. Is there a better method for doing this, an algorithm, that can give you an answer in a reasonable amount of time even if the number of places is huge?

The functions 2 n (black), n 3 (red) and n 2 plotted against n. You can see that 2 n grows fastest for larger n.

This leads us to the big question: are there any polynomial-time algorithms for problems in the NP class that simply haven't been discovered yet? The question is known as the P versus NP problem because the class of problems that can be solved in polynomial time is called P. P versus NP is one of the hardest open problems in maths. Anyone who manages to answer it will win $1 million from the Clay Mathematics Institute (see How maths can make you rich and famous ). Not everyone agrees, but most mathematicians seem to think that P is not equal to NP: this would mean that NP problems really are very difficult, they cannot be solved in polynomial time.

Answers to NP problems can be used as the key to encrypted messages.

And there's another twist to the story: any problem in the NP class can actually be reduced to the decision version of the travelling salesman problem. This means that any algorithm that solves the decision travelling salesman problem can be translated into one that solves all other problems in the NP class. So imagine you find a polynomial-time algorithm for the decision travelling salesman problem. This would then mean that every problem in NP could be solved in polynomial time, you would have proved that P=NP and could go and collect your $1 million. (And the same would be true if you found such an algorithm for the harder, general version of the travelling salesman problem.)

But there are other implications too. Problems from the NP class are often used in cryptography, for example in the RSA system that's used to make internet transactions secure. Essentially, the answer to an NP problem (say the prime factors of a large number) is used as the key you need to decode a message. The fact that there are no known algorithms to solve NP problems quickly means that the key is very hard to crack. (See Safety in numbers for more.)

So imagine you did manage to find an efficient algorithm to solve the travelling salesman problem. You'd get your million dollars, a key to the world's most secret codes and your life would probably no longer be safe. Someone should make a movie about this...

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A new 'Shrink' algorythm resolves the TSP problem at a rate of n^3*7E-5 secs. 100 nodes take 2 seconds on a 1.8Ghz PC running on a QPC2 emulator with a procedural basic. Timings were done by a Professor of mathematics at Delaware State university. The code can surely be optimised, and produces a 94% accurate result as things stand, but this will be improved on. The maths are very simple, but the logic is quite complex. The program was published by the English 'Quanta' QL users group, and is available for programmers to work on.

The travelling salesman problem

TSP solved? I am not sure! I believe tha I have found the effective algoritm for the shortest route to take. I have contacted The Clay Mathematics Institute for how to present my solution. Sincerely, Dr Lars Hellström, Uppsala, Sweden

Travelling caregiver problem

Real world gets more complicated than the salesman pitch.

In the real world, the factors influencing the optimal outcome: * is it faster to do tasks without kids (or persons cared for), * how much time do you have to complete all tasks, * is it cheaper to be quick, or take shortest route?

I have no algorithm but these factors affect my decision-making every day to maximise my 24 hours.

Traveling Caregiver Problem

1. "Mum" has scientifically reduced the problem to its essence. Never take the kids to the grocery store if efficiency is your first concern. So go there first. 2. Solve as much of the problem once and for all in advance as possible. Never go to an ATM (if that's what a pay point is). Get a Paypal account, move cash into it online, and use the Paypal card instead of cash. Easier, more secure, eliminates one stop on the trip, and gives you a record of what you spent and where, making budgeting simpler (thus reducing another set of math and tracking problems). 3. Change your prescriptions to three-month refills or better, delivered by mail. There -- two trips out of three to the pharmacy, or all of them, eliminated. 4. The Law of Scientific Parsimony absolutely dictates: Never give a problem to a mathematician if a Mum can solve it. This approach has been proven by experience to work for up to whatever number of children are in your family.

And if you really need to pretend this is a math/geography problem: It is not. It's a management question. The first parameter to plug in is the likelihood of the traveling salesman closing a deal, and how big, at each destination. Send him to the likeliest big deals first and hit the marginal ones up with a phone call. Be very wary of trying to apply math to social-interaction questions with small sample sizes.

Glad to be of assistance.

Programming Assignment Help

I really appreciate your effort in providing this kind of content to us.

Agreed - avoid it if possible

"Mum" has it spot on, as usual. I teach advanced server performance tuning, and the first thing I ask new students is "what's the fastest way to get from London to Glasgow ?" (I live in UK). Answer: don't go to Glasgow, have a video call instead. In IT you can't make the hardware go faster (e.g. if a disk spins round at 10,000rpm, that's what it does, no amount of blowing on it will make it spin round faster) so the only way to "speed up" disk IOs is … you can't. You have to eliminate some of them. Just like Mum's Paypal account.

TSP Solution

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Travelling Salesman Problem using Branch and Bound

Given a set of cities and the distance between every pair of cities, the problem is to find the shortest possible route that visits every city exactly once and returns to the starting point.

For example, consider the following graph . A TSP tour in the graph is A —> B —> C —> D —> B —> A . The cost of the tour is 10 + 25 + 40 + 25 + 10 = 100 .

This post discusses the Travelling Salesman Problem using Branch and Bound.

  The term Branch and Bound refer to all state-space search methods in which all the children of an E–node are generated before any other live node can become the E–node. E–node is the node, which is being expended. State–space tree can be expended in any method, i.e., BFS or DFS . Both start with the root node and generate other nodes. A node that has been generated and whose children are not yet been expanded is called a live-node. A node is called a dead node, which has been generated, but it cannot be expanded further. In this method, we expand the most promising node, which means the node which promises that expanding or choosing it will give us the optimal solution. So, we prepare the tree starting from the root and then expand it.

We have a cost matrix defined by:

For example, consider the following cost matrix M ,

Following is the state-space tree for the above TSP problem, which shows the optimal solution marked in green:

As we can see from the above diagram, every node has a cost associated with it. When we go from the city i to city j , the cost of a node j will be the sum of the parent node i , the cost of an edge (i, j) , and the lower bound of the path starting at node j .

As the root node is the first node to be expanded, it doesn’t have any parent. So, the cost will be only the lower bound of the path starting at the root.

Now, how do we calculate the lower bound of the path starting at any node?

In general, to get the lower bound of the path starting from the node, we reduce each row and column so that there must be at least one zero in each row and Column. We need to reduce the minimum value from each element in each row and column.

Let’s start from the root node.

We reduce the minimum value in each row from each element in that row. The minimum in each row of cost matrix M is marked by blue [10 2 2 3 4] below.

After reducing the row, we get the below reduced matrix.

We then reduce the minimum value in each column from each element in that column. Minimum in each column is marked by blue [1 0 3 0 0] . After reducing the column, we get below the reduced matrix. This matrix will be further processed by child nodes of the root node to calculate their lower bound.

The total expected cost at the root node is the sum of all reductions.

Since we have discovered the root node C0 , the next node to be expanded can be any node from C1 , C2 , C3 , C4 . Whichever node has a minimum cost will be expanded further. So, we have to find out the expanding cost of each node.

The parent node C0 has below reduced matrix:

Let’s consider an edge from 0 —> 1 .

1. As we add an edge (0, 1) to our search space, set outgoing edges for city 0 to INFINITY and all incoming edges to city 1 to INFINITY . We also set (1, 0) to INFINITY .

So in a reduced matrix of the parent node, change all the elements in row 0 and column 1 and at index (1, 0) to INFINITY (marked in red).

The resulting cost matrix is:

2. We try to calculate the lower bound of the path starting at node 1 using the above resulting cost matrix. The lower bound is 0 as the matrix is already in reduced form, i.e., all rows and all columns have zero value.

Therefore, for node 1, the cost will be:

Let’s consider an edge from 0 —> 2

1. Change all the elements in row 0 and column 2 and at index (2, 0) to INFINITY (marked in red).

2. Now calculate the lower bound of the path starting at node 2 using the approach discussed earlier. The resultant matrix will be:

Therefore, for node 2, the cost will be

Let’s consider an edge from 0 —> 3 .

1. Change all the elements in row 0 and column 3 and at index (3, 0) to INFINITY (marked in red).

2. Now calculate the lower bound of the path starting at node 3 using the approach discussed earlier. The lower bound of the path starting at node 3 is 0 as it is already in reduced form, i.e., all rows and all columns have zero value.

Therefore, for node 3, the cost will be

Similarly, we calculate the cost of 0 —> 4 . Its cost will be 31 .

Now find a live node with the least estimated cost. Live nodes 1 , 2 , 3 , and 4 have costs 35 , 53 , 25 , and 31 , respectively. The minimum among them is node 3 , having cost 25 . So, node 3 will be expanded further, as shown in the state-space tree diagram. After adding its children to the list of live nodes, find a live node with the least cost and expand it. Continue the search till a leaf is encountered in the space search tree. If a leaf is encountered, then the tour is completed, and we will return to the root node.

  Following is the C++ implementation of the above idea:

Download    Run Code

Output: 1 —> 3 3 —> 4 4 —> 2 2 —> 5 5 —> 1   Total cost is 34

  The proposed method, which uses Branch and Bound, is better because it prepares the matrices in different steps. At each step, the cost matrix is calculated. From the initial point, we know that what can be the minimum cost of the tour. The cost of the initial stages is not an exact cost, but it gives some idea because it is the approximated cost. At each step, it gives us a strong reason for which node we should travel the next and which one not. It gives this fact in terms of the cost of expanding a particular node.

  References:

1. https://www.seas.gwu.edu/~bell/csci212/Branch_and_Bound.pdf 2. http://research.ijcaonline.org/volume65/number5/pxc3885866.pdf

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Seeking the ideal traveling salesman problem solution for business

The task of optimal route finding is crucial for many businesses. It is known as the Traveling Salesman Problem or TSP and is of particular relevance in situations when the supply expenses are nearly compared to the cost of the product itself, and the speed of delivery is one of the main priorities. Let's take a look at the insight of this traveling salesmen issue in more detail and learn what helpful solutions have been developed.

What is the Traveling Salesman Problem?

It is a well-known and intensely investigated issue. Challenge is to find the traveling salesman problem solver to create the most optimal route passing through all specified points or cities only once and coming back to the beginning point. The traveling salesman problem solution also should contain optimality route criteria: the shortest, the fastest, the cheapest, or all together and initial data of the route such as distance, cost, time, etc.

The TSP is based on the Hamilton cycle, which deals with finding a path visiting every node once, and returning to the beginning within the graph, but TSP is concerned with a Hamiltonian circuit as a traveling salesman calculator with the lowest cost. The peculiarity of the TSP is that it is simple enough to formulate, and it is also relatively easy to get a good decision for it, but finding an optimal route for a large data set is not an easy and resource-intensive process.

Approaches for the traveling salesman problem solution

There are many different ways to find the best traveling salesman problem solver, which can be divided into several groups: exact, heuristic, and metaheuristic algorithms.

Exact algorithms

Exact algorithms find an assured optimal solution. This group includes: The brute force method – is a sequential consideration of all possible routes and choosing the optimal one. The branch-and-bound method is a variation of the exhaustive search that differs by screening out from the calculating process subsets of ineffective solutions. The key idea of dynamic programming is to be a reliable TSP solver to calculate and memorize the distance traveled from the original city to all the others, then add to them the distances from the current cities to the remaining ones, and so on. The first TSP application of dynamic programming is the Held-Karp Algorithm. Compared to exhaustive search, this traveling salesman problem tool can significantly reduce the amount of computation. The main advantage of the group techniques is that they assure to find the right solution for TSP problem, which is not possible for algorithms from other groups. However, in practice, these algorithms are rarely applied due to the enormous time spent even for small values of N.

Heuristic algorithms

Heuristic algorithms determine good or near-optimal solutions but are sufficient to solve the traveling salesman problem. Examples: The wooden algorithm is a procedure for solving through the construction of the shortest spanning tree. Greedy algorithms are based on finding locally optimal solutions at each stage of computations and assume that the final found TSP solver will be globally optimal. So at each iteration, the best section of the path is selected, which is included in the final route. The most popular application of greedy algorithms is the Nearest Neighbor algorithm that builds a path by finding the vertex closest to a given vertex.

The 2-opt algorithm reduces to removing two intersecting edges and inserting new edges that do not break the correctness of the solution.

The advantages of these algorithms to solve the TSP problem are the speed strict dependence of a solution finding on the initial data size. They also have the disadvantages – the low quality of the response with an increase in the number of cities.

Metaheuristic algorithms

Metaheuristic algorithms – generalized traveling salesman problem strategies for finding the optimum in the space of solutions, depending on randomness. They include: Ant algorithm – an algorithm that mimics the behavior of an ant colony seeking a path to a food source. Simulated annealing is an algorithm that simulates the physical process of substance crystallization at a decreasing temperature. A genetic algorithm mimics the evolutionary process in nature. The algorithm of cloning selection is a form of a genetic algorithm that does not use inheritance from multiple ancestors.

The advantages of these algorithms are implementation simplicity, finding more optimal paths in comparison with heuristic algorithms. The disadvantages of these algorithms include the dependence on hyperparameters, which are selected individually for different sets of initial data, as well as the complexity of the asymptotic analysis due to differing hyperparameters.

What approach to deal with the problem is better?

The choice of one or another approach to the traveling salesman problem solving is due to the initial data size, available production information, the definite implementing time, and the required goals. For example, use navigators require accuracy on a small amount of the original data with low performance and limited time. So it is justified to use precise algorithms. In the case of selecting the optimal routes for the goods delivery, the best TSP solution is using heuristic algorithms that have predictable enough speed and no need to tune hyperparameters, also have good results with an insignificant amount of the initial data. If reliability is required for a significant number of points combined with high performance and limited time, it is worth using the metaheuristic algorithms to get the TSP solver optimap.

How to Solve Traveling Salesman Problem. Different Programming Languages

Distancematrix API understands how the TSP problems are important in transportation logistics, an industry that cooperates with transportation planning. Traveling salesman should go around N points and eventually return to the origin place to sell products and goods. And to select the excellent path, you may apply traveling salesman problem Java, TSP python, and other programming languages.

Given a number of places and the current distance between them, the TSP problem is in detection of the shortest way where each place will be visited only once and then return to the origin point. To simplify it, remember about the Hamiltonian Cycle. You might use a naive TSP variant for the counting or apply a programming language. Traveling salesman problem Java, Python TSP, C++, or C# is dynamic programming to receive the shortest way.

Let's try to solve the TSP, define the best path for the following scheme:

We see that the best path here is 1-2-4-3-1. The cost here is defined as 10+25+30+15 and equals 80. Using TSP coding with dynamic programming, we define i as the price, and 1 will be our start and end point. Everything here seems simple [cost(i) + dist(i, 1)] . Our aim is to calculate the cost, that is, to receive the value of i. It is better to take the traveling salesman algorithm on any programming language to find out the price of the less expensive route.

The programming language needs you to define variables for correct computation. The program makes calculations with higher accuracy and this is convenient if you need to calculate large numbers of places and distances. The programming language simplifies the calculations and provides you with several options for the fastest and least expensive TSP routes. Our traveling salesman problem solver will be, for example, Java.

The target of the Distancematrix API is to find the fastest, shortest, and least expensive way to implement on traveling salesman problem Python, TSP Java source code, or using C++.

Practical Significance of the Traveling Salesman Problem

The application of the TSP is quite extensive. The task is used in logistics, transport, various communication systems designing, even in psychology and pedagogy. Examples of the possible options for using the traveling salesman problem in logistic practices are determining the optimal route for cargo transportation; calculation of the best traveling salesman map for couriers, in telecommunications and communications – satellite management, telecommunication systems design, informatics – data array clustering, energy and utilities – connecting settlements with power lines and gas supply), electronics (designing microcircuit topologies). In addition to logistics, the TSP task is also applied in the economy and human activity: finance (optimization of cash flows, for example, finding ways to transfer funds with minimal transaction costs), tourism (traveling salesman calculator of routes for excursions and tours), show business (organizing tours of music groups), biology (genome assembly), etc.

In this regard, developing algorithms and methods for successful TSP solutions are in great demand.

Where is Travelling salesman problem calculator used?

Traveling salesman calculator has become increasingly popular in recent years due to its ability to optimize complex routing problems in a fraction of the time it would take a human to solve them manually. It has practical applications in a wide range of fields, from logistics and transportation to finance and biology. TSP calculators use advanced algorithms to find the shortest possible route that visits a set of locations and returns to the starting point. This can be a valuable tool for businesses looking to optimize their delivery or sales routes, as well as for researchers looking to solve complex routing problems in their fields. By leveraging the power of a traveling salesman problem solver, organizations can save time, reduce costs, and increase efficiency.

What is the best tsp solver?

The best TSP solver depends on various factors, such as the size of the problem, the required accuracy, and the available computational resources. There are many algorithms available to solve the TSP, including exact methods such as branch and bound and cutting plane, and heuristic methods such as ant colony optimization, simulated annealing, and genetic algorithms. The choice of the best tsp problem solver also depends on the specific requirements of the problem and the preferences of the user. Some solvers may be more suitable for small instances, while others may be better suited for large-scale problems. Nowadays, you can find the best tsp solver online. It is recommended to test different solvers on a particular problem to determine which one provides the best results.

Popular solution in business practice — Distancematrix.ai API

Academic TSP solutions try to generate an ideal one for this vital issue but the vast majority is not suitable as real-life decisions. The reason is that creating the best Google maps traveling salesman is time-consuming. In real life, time frequently is a crucial choice factor. For instance, a logistics company needs to figure out a route in minutes when planning its daily schedule because its results depend on both these shipping route planning decisions and avoiding drivers' downtime. So the business world requires not optimal salesman traveling problem solutions but near-optimal ones in the shortest possible time, providing companies with the opportunity to plan routes without any problem, quickly and efficiently. There are different ways to solve the TSP problem other than the academic approaches. There are a lot of API solutions for optimization, but they are significantly limited by the number of waypoints to be optimized, with no time windows, no round trips, no capacity constraints, etc. Applying the Distance Matrix API , you can calculate the distance and the route time between each pair of locations taking into account real-time data. Keep in mind that depending on the particular traveling salesperson problem task, you can make calculations taking into account the real-time traffic or not. Besides, the request calculation time is up to 50 elements per second, and you can get the API response in less than a second. Distancematrix.ai API tool supports roads all over the world. Using it as a traveling salesman solver, you can assign the nearest driver based on proximity, provide job opportunities only for a particular drive time, and determine the nearest goods delivery point to a customer. Also, you can create a standard distance matrix or use a single origin with multiple destinations.

Distancematrix.ai also considerably facilitates the travel salesman process when it is required to request a big matrix.

As you can see, efficient TSP solver in your business practice can help you reduce the cost of the order and the delivery time, optimize trips and delivery for suppliers and distributors, etc. You can choose any of the many different TSP tools for this purpose, but remember that Distancematrix.ai is a reliable one that can make things easier as it was designed as the TSP solver. We strongly believe it's a great option to enhance the effectiveness of your business performance.

Do you need more information about the Distance Matrix API?

• Weiqi Li (February 9th 2021). How to Solve the Traveling Salesman Problem, Theory of Complexity – Definitions, Models, and Applications, Ricardo López-Ruiz, IntechOpen, DOI: 10.5772/intechopen.96129. Available from: https://www.intechopen.com/chapters/75156
• Ćwik, M., & Józefczyk, J. (2018). Heuristic algorithms for the minmax regret flow-shop problem with interval processing times. Central European journal of operations research , 26(1), 215–238. https://link.springer.com/article/10.1007/s10100-017-0485-8

About Speedy Route

Speedy Route calculates the best route when visiting multiple locations and then returning back to the start. It is ideal for delivery drivers, sales people on the road, or anyone who needs to make multiple stops. Speedy Route re-orders the locations you enter into the best optimal order, so that every location is visited once before returning to your start location in the shortest and quickest way possible.

Speedy Route is available in the United States and also world-wide, e.g. in the United Kingdom and the rest of Europe, as well as in Canada, Australia and New Zealand, the Far East, South America, and the rest of the World. Find the best route with Speedy Route.

Single or Multiple Delivery Vehicles

Speedy Route can plan your route for a single vehicle or multiple delivery vehicles, and will produce the optimal route for the number of delivery vehicles you have available. If you set the number of available delivery vehicles to be more than one, the calculated route may use any number of vehicles up the maximum available. The calculated route might not use all the vehicles available if the optimal route can be achieved using fewer vehicles.

Calculating the optimal route is an example of the Travelling Salesman Problem solved by Route planning software, in which given a list of places to visit, and after having calculated the time to travel between each place, the optimal route is that which visits every location exactly once before returning to the start location by the fastest route.

Speedy Route is a charged subscription service for the calculation of routes containing more than 10 locations, and also for more than three calculations within a rolling 24 hour period for routes containing any number of locations. Subscription periods are activated immediately upon purchase, and are available on a monthly rolling basis. We only accept payments in U.S. Dollar ($).

$69/mo: Up to 5 drivers, 500 stops per route $99/mo: Up to 10 drivers, unlimited stops per route

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Speedy Route attempts to solve optimal route calculation requests as a 'best-effort' service. The time elapsed required to calculate a result is dependent on many factors, including route complexity, server load, internet connectivity, and the presence and performance of other consumed down-stream services. Some routes may not be solvable within a reasonable amount of time, and therefore may not be solvable by Speedy Route. The maximum number of locations in a route that Speedy Route will attempt to calculate is 500 (five hundred) locations, although we may increase this limit in the future.

We monitor our systems to maintain the performance and reliability of Speedy Route. All users of Speedy Route (both paid subscription and free users) agree to be abide by our 'Fair Use' policy. Users shall not maliciously attempt 'Denial-of-service' style attacks on Speedy Route, or repeatedly use the service to calculate the same route with no good reason. Users shall also not attempt to circumvent security features. Any user found to be in breach of these policies may have their registration and subscription with Speedy Route cancelled, and be blocked from using the service in the future.

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Implement Traveling Salesman Problem using the nearest-neighbor heuristic. Input: The input Graph is provided in the form of a 2-D matrix (adjacency matrix). Consider the first node as the starting point. Sample input: G = [ [0, 2, 3, 20, 1], [2, 0, 15, 2, 20], [3, 15, 0, 20, 13], [20, 2, 20, 0, 9], [1, 20, 13, 9, 0], ] Output: A list of indices indicating the path taken. You must return the sequence of nodes, the path taken starting from node 0. In this example,G is 5x5, indicating there are 5 nodes in this graph: 0-4. You will always begin with node 0, and your path should include every node exactly once, and only go between nodes with a nonzero edge between them. You path will end at the starting node. Sample output (For above graph G): [0, 4, 3, 1, 2, 0] Note: Not all graphs are fully connected: some rows in G may have more than one 0. These indicate absence of an edge. Name your function solve_tsp(G). Name your file TSP.py

The following code of traveling salesman problem are:

def solve_tsp(G):

   n = len(G)

   path = [0]

   visited = [False] * n

  visited [0] = True

   for _ in range(n - 1):

       min_dist = float('inf')

       for i in range (n):

           if visited[i] == False and min_dist > G[path[-1]][i]:

               min_dist = G[path[-1]][i]

               curr = i

       path.append(curr)

       visited[curr] = True

  path .append(0)

   return path

What is travelling salesman problem?

One of the most well-known issues in both mathematics and computer science is The Traveling Salesman Problem (TSP) . It entails determining the shortest path that makes a single stop at each destination before returning to a starting point. The TSP is a significant problem with both theoretical and real-world applications that has been explored for more than a century. The TSP has many versions, such as the Hamiltonian cycle question, that is similar to the TSP but does not need that the starting & ending points match. Finding an ideal solution to the TSP is computationally challenging since it is NP-hard. Numerous algorithms have been created in an effort to solve it as a result. These methods can be precise or a rough estimate.

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n desktop.h declare two exception classes: nopowerexception. this exception will be thrown when the user turns on a computer that does not connect to power outlet. this class is an empty class.

The exceptions class has two further derived classes for managing runtime exception handlers and other types of exceptions.

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PAssignment explanation In this assignment, you need to implement a Python program using a function that takes the expression as parameter and return the results. 1. Implements a calculator with the following functionality: O Can support the following operations: +- ***/ // %. O Do the math and find the result using the PEMDAS rules learned in the lecture and in high school calculus O Supports both integers and floats and returns the result in float format with a precision of 2 decimal places. 2. The program does NOT ask the user for inputs one after another! Rather, it asks the user to enter a string containing the entire mathematical operation he/she wishes to perform as follows: Calculator: User: Please enter the mathematical expression you want the program to evaluate: 2.5 +3-10/4 **3 // 2 +99.1-9% 3 3. Once user finishes the calculation, the calculator should ask the user if he has more operations to do or not. 4. If the user is done with calculations, the calculator should give a summary of the all the operations done in this calculation session along with the output results as follows: |Operation no. | |1 12 |3 I 1 CALCULATOR OPERATIONS HISTORY 1 2.5 +3-10/4 ** 3 // 2 +99.1-9% 3 | 98.1/3 +9-3.3 ** 2 +44 100 * 9+3** 8/9 operation expression 1 operation output | 104.6 74.81 1629.0 NOTE: the data above is JUST an example, your code MUST accept user input for different strings that follow the format mentioned in step 2 and successfully do the extraction and display of the output in a similar way to what is shown in step 4. The grader will enter different inputs to test your code to assure its success in accomplishing the assignment objective. IMPORTANT: you are NOT allowed to use any Python built-in (or even available online) module function that performs the above requirement, such as eval or similar. You MUST do it yourself PYTHON PROGRAM

Explanation:

program using a function that takes the expression as

parameter and return the results.

1. Implements a calculator with the following functionality:

Can support the following operations: +- ***/ // %.

Do the math and find the result using the PEMDAS rules learned in the lecture and in high

school calculus

O Supports both integers and floats and returns the result in float format with a

precision of 2 decimal places.

2. The program does NOT ask the user for inputs one after another! Rather, it asks the user to enter

a string containing the entire mathematical operation he/she wishes to perform as follows:

Calculator:

Please enter the mathematical expression you want the program to evaluate:

2.5 +3-10/4 **3 // 2 +99.1-9% 3

3. Once user finishes the calculation, the calculator should ask the user if he has more operations to

4. If the user is done with calculations, the calculator should give a summary of the all the operations

done in this calculation session along with the output results as follows:

|Operation no. |

CALCULATOR OPERATIONS HISTORY

2.5 +3-10/4 ** 3 // 2 +99.1-9% 3 |

98.1/3 +9-3.3 ** 2 +44

100 * 9+3** 8/9

operation expression

operation output |

NOTE: the data above is JUST an example, your code MUST accept user input for different strings that

follow the format mentioned in step 2 and successfully do the extraction and display of the output in a

similar way to what is shown in step 4. The grader will enter different inputs to test your code to assure

its success in accomplishing the assignment objective.

IMPORTANT: you are NOT allowed to use any Python built-in (or even available online)

module function that performs the above requirement, such as eval or similar. You MUST do

it yourself PYTHON PROGRAM

An ________ is a companywide network that is based on internet-like Technology, but is closed to public access.

An intranet is a companywide network that is based on internet-like technology, but is closed to public access. It is used for communication and collaboration within an organization, and typically includes a variety of resources such as internal websites, databases, and file servers that are only accessible to authorized users within the organization.

An intranet can be a useful tool for improving efficiency and productivity within a company, as it allows employees to access important information and resources quickly and easily, and facilitates communication and collaboration among team members. An intranet is used to facilitate communication and collaboration within an organization. It is a companywide network that is based on internet-like technology, but is closed to public access. Some common uses of an intranet include:

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True or False Real-time systems are used for process control in manufacturing plants, assembly lines, robotics, andcomplex physical systems.

True. Real-time systems are used for process control in manufacturing plants, assembly lines, robotics, and complex physical systems.

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During the current month, Grey Company sold 60,000 units for $10 each. Each unit had an equivalent cost of $6 each. The journal entry to record the sale would include which of the following? a. Finished Goods600,000 Cost of Goods Sold600,000 b. Cost of Goods Sold360,000 Finished Goods360,000 c. Cost of Goods Sold600,000 Finished Goods600,000 d. Finished Goods360,000 Cost of Goods Sold360,000

The finished goods would be listed as part of the sale's journal entry at 360,000 and cost of goods sold at 360,000.

Hence, The finished goods would be listed as part of the sale's journal entry at 360,000 and cost of goods sold at 360,000.

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Summarize the history of artificial intelligence detailing its origin and future state in technology today. Wrong answer will get reported

Scaled AI implementation can enhance team performance and strengthen corporate culture. Discover how BCG's AI-driven projects have aided in maximizing value for our clients. Learn About Our AI Products.

The replication of human intelligence functions by machines , particularly computer systems, is known as artificial intelligence. Expert systems, language processing, speech recognition, and machine vision are some examples of specific AI applications.

Artificial intelligence is founded on the idea that intellect can be described in a way that makes it simple for a computer to duplicate it and carry out activities of any complexity. Artificial intelligence aims to emulate cognitive processes in humans.

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select all the statements about beethoven's adult career. multiple select question. beethoven received an annual income from three noblemen so he would stay in vienna. beethoven received an annual income from napoleon after dedicating his third symphony, eroica, to him. beethoven began to lose his hearing in his late twenties but found a new determination to be a composer in his heiligenstadt testament (1802). in vienna, beethoven became popular with the public and nobility alike.

Beethoven received an annual income from three noblemen so he would stay in Vienna.

What annual income?

The annual income that an individual earns depends on a variety of factors, such as their occupation, skills, experience, and the level of demand for their labor. Generally speaking, the higher the skill level, experience, or demand for a particular job , the higher the salary level. For example, the median annual income of a doctor in the United States is approximately $208,000; whereas the median annual income of a retail salesperson is approximately $25,000. Additionally, one's geographical location can also affect their annual salary. For example, the median annual income for an administrative assistant in New York City is $48,500, whereas the median annual income for an administrative assistant in Houston, Texas is $38,000.

- Beethoven received an annual income from three noblemen so he would stay in Vienna.

- Beethoven began to lose his hearing in his late twenties but found a new determination to be a composer in his Heiligenstadt Testament (1802).

- In Vienna, Beethoven became popular with the public and nobility alike.

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most mobile phones use a(n) card to identify the phone, account information, and cellular carrier. group of answer choices subscriber identity module mobile identity module mobile device card subscriber device card

A Subscriber Identity Module card is used by the majority of mobile phones to identify the device, the account, and the cellular carrier.

The SIM (subscriber identity module) is a memory device that keeps data like the subscriber's identification number, the networks and nations where the customer is eligible for service, privacy keys, and other user-specific data.

The Global System for Mobiles' "heart" is known as the NSS, or Network Switching Subsystem. HLR, or Home Location Register, is a sort of database used in mobile computing that stores details about authorized users via the GSM core network.

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Write the sentence "If it's sunny, OR if the temperature is greater than 80 and it's not raining, I will go to the beach." as a Java if statement using an int variable temperature and boolean variables sunny and raining. If the conditional is true, print out "Go to the beach!" So, you will go to beach on days that it is sunny in any temperature, or you will go to the beach on days when the temperature is over 80 degrees and it's not raining

The words If it is sunny OR if the temperature is more than 80 degrees and it is not raining. I'll go to the coast. the two Boolean expressions, either one or both, are true.

They are connected by a logical or, after which the condition's body is carried out. For instance, your parents could say that they don't need the car and you can go outdoors if you can walk. If two boolean values or expressions are combined with a logical and, and the first expression returns false, the second expression won't be performed. Since the first statement must be true for the result to be true and both sides of the must be true for the result to be true.

math algebra  is fundamentally more complicated t han boolean algebra. Only two boolean values exist.

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atch each description on the left with the appropriate cloud technology on the right. drag drop public cloud provides cloud services to just about anyone. press delete to clear private cloud allows cloud services to be shared by several organizations. press delete to clear community cloud provides cloud services to a single organization. press delete to clear hybrid cloud integrates one cloud service with other cloud services.

According to the question, the correct match is a: 1. Public cloud, b: 3. Community cloud, c: 4. Private cloud, d: 2. Hybrid cloud.

A cloud service is any service that is made available to users who are on demand via internet from the cloud computing service providers.  These service providers have servers in their company premises where they offer the services from.

The service known as “cloud computing” operates via internet technologies. Software-as-a-service ( SaaS ) is a notion that is part of cloud computing that is used to host applications by any third party and offer them to users as services.

Platform-as-a-service (PaaS) is a model where a third party offers the user the tool for application development .

Therefore, the correct match is a: 1. Public cloud , b: 3. Community cloud, c: 4. Private cloud, d: 2. Hybrid cloud.

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this twentieth-century artist, and creator of fountain (a factory-made urinal), was very influential for later artists working in alternative media. question 2 options: marcel duchamp jackson pollock john cage claes oldenburg all of the other answers

This twentieth-century artist , and creator of fountain (a factory-made urinal), was very influential for later artists working in alternative media is Marcel Duchamp . The correct option is a .

Dada , a movement that challenged long-held beliefs about what and how art should be created, was founded by Marcel Duchamp .

Duchamp set the path for later movements including Pop (Andy Warhol), Minimalism ( Robert Morris ), and Conceptualism . He is linked to numerous aesthetic movements, including Cubism , Dada, and Surrealism (Sol LeWitt).

Marcel Duchamp , a 20th-century artist and the designer of the fountain (a manufactured urinal ), had a significant impact on succeeding artists working in alternative media .

Thus, the correct option is a .

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You are running windows 7 pro and want to use a virtualization program so you can test out windows 10 and also work with other operating systems. what should you install?

Microsoft's proprietary Hyper-V hypervisor, which controls Windows 10 virtualization, is used. This hypervisor is sufficient for even the largest enterprise deployments because it powers the whole Azure cloud stack.

You can get some extremely excellent features from Oracle VM Virtual Box without paying a penny.

Therefore, The most recent virtualization technology from Microsoft is called Windows Virtual PC. It enables you to launch numerous productivity programs with a single click from a PC running Windows 7 in a virtual environment.

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Field refers to a collection of related records. a. True b. False

becayse it is collectionof realeted records

Field refers to a collection of related records is True thus option (a) is correct.

The field is the collection of data or a set of data in which the same kind of data or the data for the same purpose is stored.

For example, the collection of email addresses could be a field because in the column the data type is the same.

As per the given,

Field refers to a collection of related records.

A field is a group of data or a set of data that contains the same type of data or data used for the same purpose .

For instance, because the data type in the column is the same , the collection of email addresses may be a field.

Hence"True if the field refers to a group of connected records".

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which one of the following javascript keywords is not usually used initeration? a. do b. switch c. for d. while

From the following keywords Do keyword in javascript is not usually used in iteration .

The acts or procedure of iterating or reiterating: for example, a process where the repetition of a series of actions produces outcomes that get progressively closer to the preferred result.

There are primarily two kinds of loops: When a sequence of instructions is repeated dependent on whether a condition evaluates as True or False, this process is known as condition-controlled iteration (also known as endless iteration). While loops , do-while loops, and repeat-till loops are a few examples of condition-controlled iteration.

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question 1 a data analyst is analyzing medical data for a health insurance company. the dataset contains billions of rows of data. which of the following tools will handle the data most efficiently? 1 point a word processor a spreadsheet sql a presentation

The data will be handled most effectively by SQL tools .

Hence, The data will be handled most effectively by SQL tools .

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________ refers to the way that sensory information is interpreted and consciously experienced; ________ refers to what happens when sensory information is detected by a sensory receptor. a. perception; reception b. perception; sensation c. sensation; perception d. preception; postception

Option B. " Perception " refers to the way that sensory information is interpreted and consciously experienced; " sensation " refers to what happens when sensory information is detected by a sensory receptor.

Perception is the interpretation and conscious experience of the information that is detected by our senses. Our senses, such as:

Detect the information around us and send it to our brains to be processed and interpreted . This processing and interpretation of sensory information is known as perception. On the other hand, sensation is the initial process of detecting sensory information . Our senses act as receptors to detect the sensory information around us, such as the sound of someone speaking or the taste of food.

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which of the following best defines the concept of a message digest in the public/private key encryption world?

TZ environmental factor The time zone is set via the TZ environment variable . Different time functions use it to calculate times in relation to Coordinated Universal Time (UTC).

The operating system specifies the format. A process receives the SIGKILL signal, which causes it to end instantly (kill). This signal cannot be captured or ignored, thus the recipient process cannot undertake any cleanup after receiving it, unlike SIGTERM and SIGINT. You can leverage the built-in variables provided by ALM to make use of the most recent data regarding the test or programmed component, as well as the UFT One computer that is running your test or component. These can contain the name and path of the test or component , the type and version of the operating system, and the localhostname.

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use the necessary commands from the command line interface (cli) to answer the following questions: of the shells listed below, which is not available on the system? what percentage of space is used on /dev/sda1? which disk partition is the boot partition?

Operating systems and software are controlled through a text-based interface known as the command line interface (CLI).

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the alliance between nokia and microsoft calls for nokia to transition its smartphone portfolio to microsoft's windows phone platform. this is an example of using an alliance in a new products and services. (1 mark)

The alliance between Nokia and Microsoft calls for Nokia to transition its smartphone portfolio to Microsoft's Windows Phone platform ; This is an example of using an alliance to fast cycle market in new products and services.

A fast cycle market refers to a trading strategy that acquires the advantage of different market cycles. In the fast cycle, market prices trend quickly. If we talk about the competitive advantages of fast cycle market, it facilitates in organizing and leading an enterprise or product in order to gain real advantages over competitors.

Thus, in the given phenomenon an alliance to fast cycle market is used where Nokia's new smartphone is going to have a transition to  Microsoft's Windows Phone platform.

Complete question:

The alliance between Nokia and Microsoft calls for Nokia to transition its smartphone portfolio to Microsoft's Windows Phone platform; This is an example of using an alliance to _________  in new products and services.

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FILL IN THE BLANK. The _____ aesthetic makes some points on a plot more transparent, or see-through, than others.

The transparency aesthetic makes some points on a plot more transparent, or see-through, than others.

Explanation in Detail:

In a plot or graph, the transparency aesthetic is used to control the level of transparency of different data points or elements. This can be useful for visualizing data that is overlapping or stacked on top of each other, as it allows the underlying data to be seen through the more transparent points.

The transparency aesthetic is often used in combination with other aesthetics, such as color, shape, and size, to create more complex and visually appealing plots. It can be controlled using various graphical parameters or functions in the plotting software or library being used.

For example, in the R programming language , the transparency aesthetic can be controlled using the "alpha" parameter in the "geom_point" function of the ggplot2 package. In Python, the transparency aesthetic can be controlled using the "alpha" parameter in the "scatter" function of the Matplotlib library.

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As a windows administrator for a large company, you are asked to grant temporary software installation permissions to the sales department. which of the following would be the most efficient method for accomplishing this task?

Create a new user group specifically for the sales department, and then grant the necessary permissions to that group.

To do this, you would need to follow these steps:

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identify the kind of exception that occurs in each of the following scenarios: group of answer choices a user process dereferences a null pointer. a linux command shell creates a new process. a network adaptor card receives a data packet. the system's main memory malfunctions.

Dereferencing a null pointer typically results in a null reference exception.

Creating a new process in a Linux command shell does not typically result in an exception. Receiving a data packet on a network adapter card does not typically result in an exception. A malfunction in the system's main memory could potentially result in a hardware exception or a memory access violation exception, depending on the specifics of the malfunction and how it is handled by the system.

An exception is a runtime error that occurs when a program encounters an unexpected condition. There are many different types of exceptions that can occur, depending on the nature of the error and the context in which it occurs. Some common types of exceptions include:

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angela uses the mobile device management (mdm) tools to allow users to enroll different devices and manage their intune accounts. which of the following are other benefits provided by this tool?

The endpoint management program Microsoft Intune is hosted in the cloud. It controls user access and streamlines app and device management across all of your different endpoints, such as mobile phones, desktop PCs , and virtual endpoints. On both company-owned and user-owned devices, you can restrict access and data.

Between MDM and Intune, what is the difference?

The primary distinction between MDM for Office 365 and Intune is that the latter is not just applicable in Office 365-related scenarios. For the majority of enterprises, the management boundaries must be expanded to include all applications on devices that may use modern authentication, as well as all data that can be exposed via AAD and applications.

How does an MDM function?

MDM software gathers various hardware and software data on devices, assisting businesses in monitoring and tracking both company-owned and Bring Your Own Device ( BYOD ) devices. For instance, among other things, you can view ownership details, installed settings and applications, warranty and security status, and current location.

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the algorithm runs in an unreasonable amount of time because it will use approximately n2 steps to draw

Algorithms that execute in an excessively long time include those with exponential or factorial efficiencies .

With larger datasets, an algorithm's efficiency frequently degrades quickly. Big data necessitates the development of novel algorithms, and speed is crucial to obtaining results in a timely manner. Time complexity and space complexity are the two primary indicators of an algorithm's effectiveness, although they cannot be directly compared . This means that algorithmic efficiency takes time and spatial complexity into account. One of the most popular sorting algorithms is quicksort since it is also one of the most effective. Time complexity and space complexity are the two primary indicators of an algorithm's effectiveness, although they cannot be directly compared.

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Uyen loves to think about palterns and systems. She enjoys learning new computer programming languages and finding out what they can do. How would a personality test MOST likely describe Uyen? O A. analytical OB. sociable O c. introverted OD. intuitive

Based on the information provided, it is most likely that a personality test would describe Uyen as analytical. This is because she enjoys thinking about patterns and systems, and learning about new programming languages, which suggests that she is analytical and logical in her thinking and approach to problem-solving. It is also possible that Uyen may be described as introverted, as she enjoys spending time learning and thinking on her own, rather than seeking out social activities. However, without more information it is difficult to accurately determine Uyen's personality traits.

here is a simple event driven program. what is missing from it? that is, what needs to be added to this program so that it compiles, runs, and noticeably responds to events? (note: do not delete any code from the program. only add code to it.)

Everything that needs to be added to this program so that it compiles , runs , and noticeably responds to events .

A computer programme is a collection of instructions that can be used as both a verb and a noun. As a verb, it refers to the process of writing a software programme using a programming language . An application, programme , or application software, as a noun, is used to perform a specific task on a computer.

Microsoft PowerPoint , for example, is a programme that allows you to create documents related to your presentation. A browser is also an application that allows us to navigate any website.

The programme instructs the computer to perform a specific task. A computer can operate with the operating system even if it lacks application software ( programmes ).

import java.awt.*;

import java.awt.event.*;

import javax.swing.*;

 class WhatIsMissing extends Frame implements KeyListener,ComponentListener {

  public WhatIsMissing()

  {     JFrame jf = new JFrame("WhatIsMissing");

        jf.setLayout(new FlowLayout());

 JTextField textField;

 textField  = new JTextField(10);

    JButton jb = new JButton("Hello");

   textField.addKeyListener(this);   //add key listener to handle keyboard events

    jb.addComponentListener(this);    //add component listener to handle component events

   jf.add(textField);

    jf.add(jb);

    jf.pack();

    jf.setSize(400, 400);

 jf.setVisible(true);

        //to show frame

  (atherate)Override

   public void keyTyped(KeyEvent e){

    System.out.println("Key Typed");

  (atherate)Override   public void keyReleased(KeyEvent e){

    System.out.println("Key Released");

  (atherate)Override   public void keyPressed(KeyEvent e){

    System.out.println("Key Pressed");

  (atherate)Override    public void componentMoved(ComponentEvent e){

    System.out.println("Component is Moved");

  (atherate)Override    public void componentResized(ComponentEvent e){

    System.out.println("Component is Resized");

  (atherate)Override    public void componentHidden(ComponentEvent e){

    System.out.println("Component is Hidden");

  (atherate)Override    public void componentShown(ComponentEvent e){

    System.out.println("Component is shown");

  public static void main(String args[])

   new WhatIsMissing();

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the compress utility preserves the original ownership, modification, and access time for each file that it compresses. T/F

True, for each file it compresses , the compress software keeps track of the original owner, modification date, and access time.

What is a File Compression?

A type of utility tool that compresses and decompresses uncommonly used files is known as a file compression utility. Most of them have the ability to compress rarely used files such that they take up between 40 and 90% less space on a hard drive . This frees up room for other, more often used items.

Some file compression utility software can only function with specific file kinds, like downloadable font files; others can compress all file types. Depending on the user, their setup, and their preferences, a certain type may be used. When something is compressed, these tools typically install a specific driver that stays active in memory . Rather than having to load the application from scratch each time, files can now be decompressed (and recompressed) as needed without being harmful or consuming excessive resources.

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Write a query that will return sales details of all customers and products. The query should return all customers, even customers without invoices and also all products, even those products that were not sold. Print "N/A" for a null customer or product name, and 0 for a null quantity. For each row return customer name, product name, and the quantity of the product sold. Order the result ascending by customer id, product id and invoice item id.

The query code for that requirement will be written use SQL.

The query code is,

SELECT IFNULL(customer_name, "N/A") customer_name,

IFNULL(product_name, "N/A") product_name, IFNULL(quantity, 0) quantity

FROM ((customer LEFT OUTER JOIN invoice ON customer.id = invoice.customer_id)

     LEFT OUTER JOIN invoice_item ON invoice_item.invoice_id = invoice.id)

LEFT OUTER JOIN product ON invoice_item.product_id = product.id

ORDER BY customer.id, product.id,invoice_item.id;

SELECT statement is for select the data.

IFNULL function is to return specific value for NULL expression, or return the expression if the expression is not NULL.

FROM statement is to specify the selected data.

LEFT OUTER JOIN statement to combine the data include unmatched row.

ORDER BY statement is to arrange the data in specific order.

You question is incomplete, but most probably your full question was

(images attached)

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SELECT IFNULL(customer_name, "N/A") AS customer_name,

      IFNULL(product_name, "N/A") AS product_name,

      IFNULL(quantity, 0) AS quantity

FROM customer

LEFT JOIN invoice ON customer.id = invoice.customer_id

LEFT JOIN invoice_item ON invoice_item.invoice_id = invoice.id

RIGHT JOIN product ON invoice_item.product_id = product.id

ORDER BY customer.id, product.id, invoice_item.id;

In MySQL, the keyword "AS" is used to alias column names or table names. Additionally, MySQL uses LEFT JOIN and RIGHT JOIN instead of LEFT OUTER JOIN and RIGHT OUTER JOIN. The functionality of the query remains the same, but it is adjusted to the syntax requirements of MySQL.

Word processing software includes tools to assist in the writing process such as:

Spell check: This tool checks the spelling of words in a document and suggests corrections if any mistakes are found.

Grammar check: This tool checks the grammar of a document and suggests corrections if any mistakes are found.

Thesaurus: This tool provides synonyms for words in a document, allowing the writer to find alternative words to use.

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Successful CPFR (Collaborative planning forecasting and replenishment) programs include all of the following except: The involvement of all key trading partners to help develop joint sales projections Incorporate trading partners' plans to manage any exceptions like factory shut downs for maintenance Focus on the impacts of special events like new store openings on inventory needs Joint efforts to assess the impacts that marketing promotions will have on production plans throughout the supply chain The focal firm planning production with limited input from trading partners

With the help of the CPFR business approach, several parties can participate in the planning and fulfillment of client demand.

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