In TSP a hypothetical salesman has to visit a set of cities. " It can be tough. Mathematical literature is full of ideas for finding good solutions to the Traveling Salesman Problem, but each method comes with the caveat: the solution given is never guaranteed to be the best. And now, Traveling Salesman becomes clear: let [the postal service, UPS, FedEx, other carrier] do the traveling for you and let someone else take care of a far simpler problem. In this problem, a traveling salesman has to visit all the cities in a given list. net dictionary. Given a set of cities, one depot where \(m\) salesmen are located, and a cost metric, the objective of the \(m\)TSP is to determine a tour for each salesman such that the total tour. The applet below lets you practice with three algorithms used for solving the TSP: the Brute-Force, Nearest-Neighbor. Three implementations of the traveling salesman problem are provided: Top-down with a run time of ; Top-down using memoization with a run time of ; Bottom up with a run time of ; We will solve the problem as follows: define tsp( S, k ) to be the minimum path from vertex v 0 to vertex v k passing through the intermediate vertices in the set S. 1 Multiterminal cut In this chapter, we describe a methodology that can be used for some problems for which the previous chapter's methodology fails. TSP (Travelling Salesman Problem) on CUDA. Chapter 10 The Traveling Salesman Problem 10. 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?. This is the travelling salesman problem. > This. A combinatorial problem is one where the goal is to place discrete items into a correct order. Result: TSP- A Logistic Problem Consider the following Travelling Salesman Problem.
In fact, it's not even in NP. In this video lesson, we talk about the traveling salesman problem. Wiener, Thora Tenbrink In the ﬁeld of human cognition, performance and optimization behavior in the TSP has mainly been investigated by means of visual versions in which humans are confronted with a number of dots on a computer monitor. (It doesn't actually matter which city is the starting point. CASQUILHO Technical University of Lisbon, Ave. Chinchón made an interesting post showing how to create a traveling salesman portrait in R. Predict solutions to the Traveling Salesman Problem with a Graph Neural Network graph-neural-networks neural-network traveling-salesman-problem graph-theory tensorflow HTML Updated May 24, 2019. Approach to the Traveling Salesman Problem Marco Dorigo, Senior Member, IEEE, and Luca Maria Gambardella, Member, IEEE Abstract— This paper introduces the ant colony system (ACS), a distributed algorithm that is applied to the traveling salesman problem (TSP). prolog travelling salesman problem, Search on prolog travelling salesman problem. The book "The Travehng Sales man Problem: A guided tour of combinatorial optimization" edited by Lawler, Lenstra, Rinoo Ka y n and Shmoys provides the state of the art description of the topi u cp to 1985. The Traveling Salesman Problem: A Case Study in Local Optimization David S. The input, very simple, just a complete. One interesting way to solve the mTSP is to transform it in a TSP and solve it using any TSP algorithm/heuristic. "In Pursuit of the Traveling Salesman: Mathematics at the Limits of Computation, does a wonderful job presenting the history and significance of the TSP and an overview of cutting-edge research. They have been used successfully in a variety of different problems, including the trav-eling salesman. In this example, we consider a salesman traveling in the US. The Hamiltoninan cycle. What is the cheapest way to hit them all exactly once and then return to the headquarters? The computation of the single best answer for what is known as the traveling salesman problem is famously infeasible. un-directed graph, and each of the end choose two edges has a non-negative cost.
Comparison of Neural Networks for Solving the Travelling Salesman Problem approach for approximately solving the Travelling Salesman Problem on 2D Euclidean graphs. 5 The Travelling Salesman Problem The Travelling Salesman Problem A travelling salesman, starting in his own town, has to visit each of towns where he should go to precisely or at least once and return his home by the shortest route. TSP (Travelling Salesman Problem) on CUDA. Wikipedia succinctly states the problem like so: Given a list of cities and the distances between each pair. Abstract: This paper introduces the ant colony system (ACS), a distributed algorithm that is applied to the traveling salesman problem (TSP). The Traveling Salesman Problem (TSP) consists in finding a Hamilton Circuit on a weighted graph with the least total weight. Gutin & Punnen, (2004) explain that TSP is dealing with determining the optimum geographic route, in which the salesman begins from his domicile, visits a prescribed set of locations and returns to the initial point. A Hamiltonian cycle is a tour that contains every node precisely once. Form the convex hull of the set of nodes and use this as an initial sub-tour Step 2. Applying a genetic algorithm to the travelling salesman problem - tsp. The concept of convex hull is illustrated in the next figure: The convex hull algorithm is as follows: Step 1. Traveling salesman problem: a worst case scenario. So the logical thing to do would be for him to either choose the shortest possible route, or the cheapest. The travelling salesman problem may be a fun puzzle to solve at home with about six nodes. This problem involves finding the shortest closed tour (path) through a set of stops (cities). If the solution were to be a proof that it cannot be solved in polynomial time, this is already expected, so it wouldn't have significant ramifications outside the academic community. Given a number of cities and the costs of travelling from any city to any other city, find the least-cost round-trip route that visits each city exactly once and then returns to the starting city. The origins of the travelling salesman problem are unclear.
Computation of the travelling salesman problem by a shrinking blob Jeff Jones • Andrew Adamatzky Published online: 16 October 2013 Springer Science+Business Media Dordrecht 2013 Abstract The travelling salesman problem (TSP) is a well known and challenging combinatorial optimisation problem. Four mathematicians are hired by the US government to solve the most powerful problem in computer science history. A network problem that can be formulated as a combinatorial optimization problem. The TSPB is an extension of the traveling salesman problem in which a set of customers is partitioned into a set of linehaul customers to be visited contiguously at the beginning of the route and a set of backhaul customers to be visited once all. If you can find a fast way to solve it, you have proved P=NP and changed the face of computation. The function. Travelling Sales Person Problem. Travelling salesman using brute-force and heuristics. Traveling Salesman Problem is an extremely important problem in operational research. Johnson1 Lyle A. APPLICATION OF GENETIC ALGORITHM TO SOLVE TRAVELING SALESMAN PROBLEM Oloruntoyin Sefiu Taiwo, Olukehinde Olutosin Mayowa & Kolapo Bukola Ruka Department of Computer Science & Engineering Ladoke Akintola University of Technology, Ogbomoso E‐mail: oloruntoyin86@gmail. You can search forum titles, topics, open questions, and answered questions. ir Abstract. Bumblebees aren’t just hard workers, they’re efficient, too. Notebook of an Industrial Enginee. By adding tag words that describe for Games&Apps, you're helping to make these Games and Apps be more discoverable by other APKPure users. It's the poster child for the world of complexity, explaining that, despite what we may hope, computer speed alone will never solve all the problems dished out by business, engineering, and science. This "easy to state" and "difficult to solve" problem has attracted the attention of both academicians and practitioners who have been attempting to solve and use the results in practice. The travelling salesman problem (TSP) asks the following question: 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?. He also knows the associated cost of travelling between the cities.
Applying a genetic algorithm to the traveling salesman problem To understand what the traveling salesman problem (TSP) is, and why it's so problematic, let's briefly go over a classic example of the problem. My goal with this project was to create Traveling Salesman Art. Note the difference between Hamiltonian Cycle and TSP. image:pixabay. That’s why different heuristics are generally applied to solve. The ﬁnal score of the game is used as a comparison metric for how close of an approximation our heuristic is to the true solution, determined by the breadth-ﬁrst search in our tests. 1 is a GPU-accelerated heuristic solver for the symmetric Traveling Salesman Problem with up to 32767 cities, based on iterative hill climbing with 2-opt local search. The order of city doesn’t matter. For example, if the terrain from A to B was uphill, the energy required to travel from A. Traveling salesman problem (TSP) is a basis for many bigger problems. (It doesn't actually matter which city is the starting point. If there is a way to break this problem into smaller component problems, the components will be at least as complex as the original one. 1 Introduction The Traveling Salesman Problem (TSP) is a problem in combinatorial optimization studied in operations research and theoretical computer science. Due to complexity involved with exact solution approaches it is hard to solve TSP within feasible time. The travelling salesman problem (TSP), or in recent years, the travelling salesperson problem, asks the following question: "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?". Traveling Salesman Problem Using Genetic Algorithm: A Survey Pooja Vaishnav, Dr. Many people have studied this problem. "It shows that bumblebees, with their diminutive 1 milligram brains, are capable of finding a nearly perfect solution to the traveling salesman problem, with relatively few attempts and in a.
A simulated bee colony (SBC) algorithm models the behavior of a hive of honeybees to solve combinatorial optimization problems. travellingsalesmanmovie. An App That Solves the Famed 'Traveling Salesman Problem' if you enter any list of cities—in the U. Given a set of cities, one depot where \(m\) salesmen are located, and a cost metric, the objective of the \(m\)TSP is to determine a tour for each salesman such that the total tour. It's the poster child for the world of complexity, explaining that, despite what we may hope, computer speed alone will never solve all the problems dished out by business, engineering, and science. As Travelling Salesman Problem is ordering problem so we have used permutation encoding. Abstract: This paper introduces the ant colony system (ACS), a distributed algorithm that is applied to the traveling salesman problem (TSP). We can say that salesman wishes to make a tour or Hamiltonian cycle, visiting each city exactly once and finishing at the city he starts from. Since this problem was posed in 1971 no one has managed to prove definitively if P equals NP. " It can be tough. We had a friendly competition at Jayway where I work which was: who could get the best result in different instances of the Traveling Salesman Problem. Postgres, SQL Server, and several others have the next best thing — recursive CTEs! We’ll use them to solve the Traveling Salesman Problem and find the shortest round-trip route through several US cities. He has to visit every city once. 1 Introduction The Traveling Salesman Problem (TSP) is a problem in combinatorial optimization studied in operations research and theoretical computer science. ic Specif focus is given to developing a generalized framework for this problem that can be applied to any number of variants on the basic formulation.
I stumbled upon this submission purely by accident while looking for something completely unrelated. Explain why this problem is equivalent to the travelling salesman problem. - free book at FreeComputerBooks. So basically some scientists whose has access to this software are using a tool developed by a company to solve the T. One might be surprised to ﬁnd, how-ever, that even the TSP is too simpliﬁed to encompass any time-dependent. 2018 I'm currently working on a genetic algorithm for the Travelling Salesman Problem. Travelling Salesman Problem - Nearest Neighbor Algorithm. Directed by Timothy Lanzone. The Problem. In this paper we use marker method and propose a new mutation operator that selects. The drop rate for this item is 2%. There should be an interface to input the cities for the salesman to visit. CASQUILHO Technical University of Lisbon, Ave. In simple words, it is a problem of finding optimal route between nodes in the graph. "It shows that bumblebees, with their diminutive 1 milligram brains, are capable of finding a nearly perfect solution to the traveling salesman problem, with relatively few attempts and in a. This is the third part in my series on the "travelling salesman problem" (TSP).
1 Solution of a Large-Scale Traveling-Salesman Problem 9 Great new ideas may transform the discipline they came from so profoundly that they become hard to discern against the changed background. This problem is known to be NP-hard, and cannot be solved exactly in polynomial time. $\begingroup$ Why do you think that it is possible to transform traveling salesman problem into subgraph isomorphism problem? $\endgroup$ - Boris Novikov Apr 7 '13 at 17:32 $\begingroup$ I read, that if you could solve one NP-complete problem in constant time, you can solve them all, so I think that all NP-complete problems are transferable. He tries to find the shortest path that takes him to each of the red cities, without ever visiting the same city twice. APPLICATION OF GENETIC ALGORITHM TO SOLVE TRAVELING SALESMAN PROBLEM Oloruntoyin Sefiu Taiwo, Olukehinde Olutosin Mayowa & Kolapo Bukola Ruka Department of Computer Science & Engineering Ladoke Akintola University of Technology, Ogbomoso E‐mail: oloruntoyin86@gmail. Choose the best route available for one or more vehicles by using this application that lets you load multiple checkpoints and provides you with. A tour is a connected subgraph for which each vertex has degree two. Now, not only does. The problem is the first statement of the Traveling Salesman to find the shortest tour of a given number of cities Problem (TSP) as we know it today in 1930. To start with, we consider the multiterminal cut problem : given a graph G with edge-costs and. NP(TSP) -hard problem in which, given a list of cities and their pairwise distances, the task is to find a shortest possible tour that visits each place exactly once. The OTSPTW is an extension of classical traveling salesman problem that is well known in optimization. The Travelling Salesman Problem (TSP) This is the most interesting and the most researched problem in the field of Operations Research. With Danny Barclay, Eric Bloom, David John Cole, Malek Houlihan. 2 THE TRAVELING SALESMAN PROBLEM AND ITS VARIATIONS 1.
34 thoughts on “ Travelling Salesman Problem in C and C++ ” Mohit D May 27, 2017. Genetic Algorithm: The Travelling Salesman Problem via Python, DEAP. At the same time, in terms of algorithms, these two versions of this problem. Solutions that are “good enough” for practical applications. The method used here is based on an article named, A combination of genetic algorithm and particle swarm optimization method for solving traveling salesman problem. Convex Hull Algorithm (Stewart, Bodin) The convex hull is the smallest convex polygon completely enclosing a set of points. Until now, researchers have not found a polynomial time algorithm for traveling salesman problem. I am hoping that i can do a good job with at least a rough version of the project in the 10 days i have[its not really limited to 10 days, could probably get a whole month to do this. Focused on a variation of the Euclidean traveling salesman problem (TSP), namely the prize-collecting traveling salesman problem with time windows (PCTSPTW), this paper presents a novel ant colony optimization solving method. He tries to find the shortest path that takes him to each of the red cities, without ever visiting the same city twice. The code implemented here is a simple version to Tabu search, but should cover all the basics. Travelling Salesman Problem (TSP) Created by Alex P. I wrote my solver in C++ to refresh my knowledge there an it worked fairly well - although my theory in the subject wasn’t the best. The diﬀerence between the problem studied in the former paper and the Steiner Ring Star Problem is that there is no distinction between facility and customer vertices, 3 The Attractive Traveling Salesman Problem CIRRELT-2007-33. IEOR 4418: Transportation Analytics and Logistics Traveling Salesman Problem Lecturer: Adam N. TRAVELING SALESMAN PROBLEM Insertion Algorithms (Rosenkrantz, Stearns, Lewis, 1974) An insertion procedure takes a sub-tour on k nodes at iteration k and determines which of the remaining n-k nodes shall be inserted to the sub-tour next (the selection step) and where (between which two nodes) it should be inserted (the insertion step). Koether Hampden-Sydney College Mon, Nov 10, 2014 Robb T.
Cook is professor of combinatorics and optimization at the University of Waterloo. Abstract: Traveling salesman problem is a NP-hard problem. Travelling salesman problem is the most notorious computational. After a certain number of iterations, this term does not suffer substantial changes in its value, evidencing the fact that problem s restrictions are almost satisfied. Skip to content. 2010040104: The Traveling Salesman Problem (TSP) and the Vehicle Routing Problem (VRP) are two of the most popular problems in the field of combinatorial optimization. In this article we will restrict attention to TSPs in which cities are on a plane and a path (edge) exists between each pair of cities (i. The Traveling Salesman Problem: A Computational Study is a good book, completely covering the implementation. travelling-salesman-problem definition: Noun (uncountable) 1. If you can find a fast way to solve it, you have proved P=NP and changed the face of computation. For more details on TSP please take a look here. Solving the Traveling Salesmans Problem Using the African Buffalo 27 Aug 2015 This paper proposes the African Buffalo Optimization (ABO) which is a new The Traveling Salesmans Problem (TSP) is the problem faced by a are generally stochastic became the hotbed of several researchers due to the. Examples are shown and solved. Shortest round trips Welcome to the TSP game! This website is about the so-called "Traveling Salesman Problem". The traveling salesman problems abide by a salesman and a set of cities. No general method of solution is known, and the problem is NP-hard. Definition of travelling salesman problem in the Definitions. , least total distance) Hamiltonian cycle a salesman can take through each of cities. As in "Spın̈al Tap". It which visits each city exactly once and returns to arose in connection with "A new definition of curve the starting city [3] length" that Menger proposed.
Four mathematicians are hired by the US government to solve the most powerful problem in computer science history. Win a trip around the world based on an algorithm you write! This is your chance to get your hands on something that’s normally purely theoretical and have some fun with it. Notebook of an Industrial Enginee. Currently, I’m dealing with the multiobjective part of the problem. Travelling salesman problem is the most notorious computational. optimization optimization-algorithms combinatorial-optimization combinatorics integer-programming travelling-salesman-problem traveling-salesman travelling-salesman Python Updated Jul 29, 2018 AbraaoHonorio / Design-and-Analysis-of-Algorithms. Essentially, the idea is to sample a bunch of dark pixels in an image, solve the well-known traveling salesman problem for those pixels, then draw the optimized route between the pixels. Synonyms for Travelling salesman problem in Free Thesaurus. Kookaburra has last laugh to solve Traveling Salesman Problem Research & Development. The Traveling Salesman Problem (TSP) is one of the most famous problems in computer science. The Traveling Salesman Problem De nition: A complete graph K N is a graph with N vertices and an edge between every two vertices. Solve Later ; Find a short way through given points. A General VNS heuristic for the traveling salesman problem with time windows. 260n and linear space. Gutin & Punnen, (2004) explain that TSP is dealing with determining the optimum geographic route, in which the salesman begins from his domicile, visits a prescribed set of locations and returns to the initial point. Skip to content. In TSP, you. These are all greedy algorithms that give an approximate result. ir 2 Department of Industrial Management, Persian Gulf University, Bushehr 75168, Iran salimifard@pgu. It couldn't be easier to state: Given a list of cities and their locations (usually specified as Cartesian co-ordinates on a plane), what is the shortest itinerary which will visit every city exactly.
Wikipedia succinctly states the problem like so: Given a list of cities and the distances between each pair. Apply now for jobs that are hiring near you. 0 for Android. The problem is, 99% of the time people discuss Traveling Salesperson being NP-Complete, they are wrong. This video shows how the “obvious” solution — “well, just start somewhere and. A salesperson must visit n cities, passing through each city only once, beginning from one of the city that is considered as a base or starting city and returns to it. The traveling salesman problem is a classic of Computer Science. 85,900 cities was in fact an electronic chip (AFAIK) where holes had to be drilled in smallest amount of time. Traveling salesman problem, Monte Carlo optimization, importance sampling, I. It should accept data as triples in the format: (city #1, city #2, distance) , where distance is the distance in a standard unit (like miles or kilometers) between. At the same time, in terms of algorithms, these two versions of this problem. After a certain number of iterations, this term does not suffer substantial changes in its value, evidencing the fact that problem s restrictions are almost satisfied. Solve travelling salesman problem using any ai technique. Part one covered defining the TSP and utility code that will be used for the various optimisation algorithms I shall discuss. Traveling Salesman Art. Bumblebees aren’t just hard workers, they’re efficient, too. The multi traveling salesman problem is the extension of the well-known problem of traveling salesman and considered as a NP-Complete problem having exponential solution space. The Travelling Salesman Problem (TSP) This is the most interesting and the most researched problem in the field of Operations Research. Find descriptive alternatives for traveling salesman.
The Traveling salesman problem : a guided tour of combinatorial optimization Item Preview remove-circle Share or Embed This Item. Hamilton and by the British mathematician Thomas Kirkman. After a certain number of iterations, this term does not suffer substantial changes in its value, evidencing the fact that problem s restrictions are almost satisfied. In this post here, you may read in detail how the simulation process works and you may also play trying to find the shortest route through some world cities or through all of the US State capitals. Traveling salesman problem, Monte Carlo optimization, importance sampling, I. Ultimate writing & creativity center reviews assigned task list,. Ant Colony Optimization Techniques applied on Travelling Salesman Problem. Last week, Antonio S. A tour is a connected subgraph for which each vertex has degree two. ingsalesmanproblem. For every >0 there is an integer k. To start with, we consider the multiterminal cut problem : given a graph G with edge-costs and. In the TSP a salesman is given a list of cities, and the distance between each pair. The traveling salesperson problem is a notoriously difficult combinatorial optimization problem, In principle, one can enumerate all possible tours and pick the shortest one; in practice, the number of tours is so staggeringly large (roughly N factorial) that this approach is useless. This paper is a survey of genetic algorithms for the traveling salesman problem. The Traveling Salesman Problem is a well known challenge in Computer Science: it consists on finding the shortest route possible that traverses all cities in a given map only once.
JASA PEMBUATAN TESIS INFORMATIKA Travelling Salesman Problem (TSP) dynamic programming dan algoritma genetika - Source Code Program Tesis Skripsi Tugas Akhir , Source Code Travelling Salesman Problem (TSP) dynamic programming dan algoritma genetika - Source Code Program Tesis Skripsi Tugas Akhir , Gratis download Travelling Salesman Problem (TSP) dynamic programming dan algoritma genetika. Now, not only does. 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?. The ﬁnal score is a. Many SQL implementations don’t have loops, making some kinds of analysis very difficult. This is a problem that, even when broken down into its components, remains complex and difficult to solve. METHODOLOGY As we know, the Traveling salesman problem is a NP-hard problem, consisting of vast search spaces and finding its exact or optimal result usually requires. Excerpt from The Algorithm Design Manual: The traveling salesman problem is the most notorious NP-complete problem. Intuitively we see 2 comes after 5, but how could computer calculate it? I don't know if the "Travelling Salesman Problem" gives the same answer ( 5 2 4 1 6 3 ), but I guess usually it does. simulatedannealing() is an optimization routine for traveling salesman problem. The travelling salesman problem consists in finding the shortest (or a nearly shortest) path connecting a number of locations (perhaps hundreds), such as cities visited by a travelling salesman on his sales route. This Traveling Salesman Problem appears in some form in astronomical observation, DNA sequencing, and many other applications besides road-trip planning. The travelling salesman problem may be a fun puzzle to solve at home with about six nodes. Notebook of an Industrial Enginee. A Constraint Programming Approach for Solving Multiple Traveling Salesman Problem Masoumeh Vali1, Khodakaram Salimifard2 1 Department of Industrial Management, Persian Gulf University, Bushehr 75168, Iran m. Travelling Salesman Problem using Branch and Bound Approach Chaitanya Pothineni December 13, 2013 Abstract To ﬁnd the shortest path for a tour using Branch and Bound for ﬁnding the optimal solutions.
Travelling Salesman Problem An implementation of a branch and bound algorithm to solve the Travelling Salesman Problem (TSP). Given a set of towns and the distances between them, determine the shortest path starting from a given town, passing through all the other towns and Explanation of travelling salesman problem. As the number of nodes increases the number of possible Hamiltonian cycles increases very rapidly. Given a list of cities and their pair wise distances, the task is to find a shortest possible tour that visits each city exactly once. We start from the following important result, paraphrased from [ 8]to suitourpurposes. GitHub Gist: instantly share code, notes, and snippets. Implementation of Travelling Salesman problem using Oracle Locator and Pl/Sql only. These are all greedy algorithms that give an approximate result. Hi, Nicely explained. The traveling salesman problem is a problem in graph theory requiring the most efficient (i. A standalone navigation-program utilizing OSMNavigation. the traveling salesman. We investigate the solution of the traveling salesman problem with proﬁts (TSPP) [7] by means of an ejection chain procedure combined with a multi-objective evolution-ary algorithm. java python array AI ComputerGraphics Group Problem WT pattern DAA android inheritance conversion matrix stack HTML class linkedlist matrices string ADS lab PL/SQl code club node object polymorphism CNLAB OSLAB color commands machine learning math oops switch. The problem is, 99% of the time people discuss Traveling Salesperson being NP-Complete, they are wrong. The Traveling Salesman Problem (TSP) consists in finding a Hamilton Circuit on a weighted graph with the least total weight. At the same time, in terms of algorithms, these two versions of this problem. There are also necessary and su cient conditions to determine if a possible solution does exist when one is not given a.
This page was last edited on 12 May 2019, at 09:26. The set of all tours (feasible solutions) is broken up into increasingly small subsets by a procedure called. The Traveling Salesman Problem is a well known challenge in Computer Science: it consists on finding the shortest route possible that traverses all cities in a given map only once. traveling salesma tsp. What I was not able to understand is why we are adding the return to the same node as well for the minimum comparison. A handbook for travelling salesmen from 1832. The travelling salesman problem is possibly the most famous and probably the most easy to understand of the so-called "NP-hard" problems computer scientists (and mathematicians) have found. The MTSP can be generalized to a wide variety of routing and scheduling problems. A Recurrent Neural Network to Traveling Salesman Problem 139 The second term of equation (10), Wx(t) − θ, measures the violation of the constraints to the Assignment Problem. The travelling salesman problem (TSP) asks the following 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?". The algorithm is based on the use of the Hopfield recurrent neural network, the “Winner takes all” (WTA) method for the cycle formation, and the 2-opt optimization method. It which visits each city exactly once and returns to arose in connection with "A new definition of curve the starting city [3] length" that Menger proposed. After a certain number of iterations, this term does not suffer substantial changes in its value, evidencing the fact that problem's restrictions are almost satisfied. The Traveling Salesman Problem: A Case Study in Local Optimization David S. Scientists are still trying to explore the new ways which are more efficient to find the shortest route for a travelling salesman. The objective of this work is developing a generic simulated annealing (SA) algorithm to solve the traveling salesman problem (TSP), which is find the shortest route through N given cities such that every city is visited exactly once. Genetic algorithms are randomized search techniques that simulate some of the processes observed in natural evolution. This paper discusses a highly effective heuristic procedure for generating optimum and near-optimum solutions for the symmetric traveling-salesman problem. O'Neil, Dan Tamir and Martin Burtscher Presented By Rukshan Siriwardhane (148208V) Vimukthi Wickramasinghe (148245F).