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A Genetic Local Search Algorithm for Solving Symmetric and Asymmetric Traveling Salesman Problems
 In Proceedings of the 1996 IEEE International Conference on Evolutionary Computation
, 1996
"... The combination of local search heuristics and genetic algorithms is a promising approach for finding nearoptimum solutions to the traveling salesman problem (TSP). In this paper, an approach is presented in which local search techniques are used to find local optima in a given TSP search space, and ..."
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Cited by 87 (12 self)
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The combination of local search heuristics and genetic algorithms is a promising approach for finding nearoptimum solutions to the traveling salesman problem (TSP). In this paper, an approach is presented in which local search techniques are used to find local optima in a given TSP search space, and genetic algorithms are used to search the space of local optima in order to find the global optimum. New genetic operators for realizing the proposed approach are described, and the quality and efficiency of the solutions obtained for a set of symmetric and asymmetric TSP instances are discussed. The results indicate that it is possible to arrive at high quality solutions in reasonable time. I. Introduction In the Traveling Salesman Problem (TSP) [18], [27], a number of cities with distances between them is given and the task is to find the minimumlength closed tour that visits each city once and returns to its starting point. A symmetric TSP (STSP) is one where the distance between any...
Genetic Algorithms for the Travelling Salesman Problem: A Review of Representations and Operators
 Artificial Intelligence Review
, 1999
"... This paper is the result of a literature study carried out by the authors. It is a review of the dierent attempts made to solve the Travelling Salesman Problem with Genetic Algorithms. We present crossover and mutation operators, developed to tackle the Travelling Salesman Problem with Genetic Alg ..."
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Cited by 87 (2 self)
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This paper is the result of a literature study carried out by the authors. It is a review of the dierent attempts made to solve the Travelling Salesman Problem with Genetic Algorithms. We present crossover and mutation operators, developed to tackle the Travelling Salesman Problem with Genetic Algorithms with dierent representations such as: binary representation, path representation, adjacency representation, ordinal representation and matrix representation. Likewise, we show the experimental results obtained with dierent standard examples using combination of crossover and mutation operators in relation with path representation. Keywords: Travelling Salesman Problem; Genetic Algorithms; Binary representation; Path representation; Adjacency representation; Ordinal representation; Matrix representation; Hybridation. 1 1 Introduction In nature, there exist many processes which seek a stable state. These processes can be seen as natural optimization processes. Over the last...
Genetic Local Search for the TSP: New Results
 In Proceedings of the 1997 IEEE International Conference on Evolutionary Computation
, 1997
"... The combination of local search heuristics and genetic algorithms has been shown to be an effective approach for finding nearoptimum solutions to the traveling salesman problem. In this paper, previously proposed genetic local search algorithms for the symmetric and asymmetric traveling salesman pr ..."
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Cited by 83 (13 self)
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The combination of local search heuristics and genetic algorithms has been shown to be an effective approach for finding nearoptimum solutions to the traveling salesman problem. In this paper, previously proposed genetic local search algorithms for the symmetric and asymmetric traveling salesman problem are revisited and potential improvements are identified. Since local search is the central component in which most of the computation time is spent, improving the efficiency of the local search operators is crucial for improving the overall performance of the algorithms. The modifications of the algorithms are described and the new results obtained are presented. The results indicate that the improved algorithms are able to arrive at better solutions in significantly less time. I. Introduction Consider a salesman who wants to start from his home city, visit each of a set of n cities exactly once, and then return home. Since the salesman is interested in finding the shortest possible r...
Combining Simulated Annealing with Local Search Heuristics
, 1993
"... We introduce a metaheuristic to combine simulated annealing with local search methods for CO problems. This new class of Markov chains leads to significantly more powerful optimization methods than either simulated annealing or local search. The main idea is to embed deterministic local search tech ..."
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Cited by 79 (7 self)
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We introduce a metaheuristic to combine simulated annealing with local search methods for CO problems. This new class of Markov chains leads to significantly more powerful optimization methods than either simulated annealing or local search. The main idea is to embed deterministic local search techniques into simulated annealing so that the chain explores only local optima. It makes large, global changes, even at low temperatures, thus overcoming large barriers in configuration space. We have tested this metaheuristic for the traveling salesman and graph partitioning problems. Tests on instances from public libraries and random ensembles quantify the power of the method. Our algorithm is able to solve large instances to optimality, improving upon state of the art local search methods very significantly. For the traveling salesman problem with randomly distributed cities in a square, the procedure improves on 3opt by 1.6%, and on LinKernighan local search by 1.3%. For the partitioni...
The Traveling Salesman Problem: An overview of exact . . .
, 1992
"... In this paper, some of the main known algorithms for the traveling salesman problem are surveyed. The paper is organized as follows: 1) definition; 2) applications; 3) complexity analysis; 4) exact algorithms; 5) heuristic algorithms; 6) conclusion. ..."
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Cited by 74 (0 self)
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In this paper, some of the main known algorithms for the traveling salesman problem are surveyed. The paper is organized as follows: 1) definition; 2) applications; 3) complexity analysis; 4) exact algorithms; 5) heuristic algorithms; 6) conclusion.
Chained LinKernighan for large traveling salesman problems
, 2000
"... We discuss several issues that arise in the implementation of Martin, Otto, and Felten's Chained LinKernighan heuristic for largescale traveling salesman problems. Computational results are presented for TSPLIB instances ranging in size from 11,849 cities up to 85,900 cities; for each of t ..."
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Cited by 70 (1 self)
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We discuss several issues that arise in the implementation of Martin, Otto, and Felten's Chained LinKernighan heuristic for largescale traveling salesman problems. Computational results are presented for TSPLIB instances ranging in size from 11,849 cities up to 85,900 cities; for each of these instances, solutions within 1% of the optimal value can be found in under 1 CPU minute on a 300 Mhz Pentium II workstation, and solutions within 0.5% of optimal can be found in under 10 CPU minutes. We also demonstrate the scalability of the heuristic, presenting results for randomly generated Euclidean instances having up to 25,000,000 cities. For the largest of these random instances, a tour within 1% of an estimate of the optimal value can be obtained in under 1 CPU day on a 64bit IBM RS6000 workstation.
Experimental Analysis of Heuristics for the STSP
 Local Search in Combinatorial Optimization
, 2001
"... In this and the following chapter, we consider what approaches one should take when one is confronted with a realworld application of the TSP. What algorithms should be used under which circumstances? We ..."
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Cited by 67 (1 self)
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In this and the following chapter, we consider what approaches one should take when one is confronted with a realworld application of the TSP. What algorithms should be used under which circumstances? We
Genetic local search algorithms for the traveling salesman problem
 IN PARALLEL PROBLEM SOLVING FROM NATURE, H.P. SCHWEFEL AND
, 1990
"... We briefly review previous attempts to generate nearoptimal solutions of the Traveling Salesman Problem by applying Genetic Algorithms. Following the lines of Johnson [1990] we discuss ome possibilities for speeding up classical Local Search algorithms by casting them into a genetic frame. In an ex ..."
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Cited by 66 (1 self)
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We briefly review previous attempts to generate nearoptimal solutions of the Traveling Salesman Problem by applying Genetic Algorithms. Following the lines of Johnson [1990] we discuss ome possibilities for speeding up classical Local Search algorithms by casting them into a genetic frame. In an experimental study two such approaches, viz. Genetic Local Search with 2Opt neighbourhoods and LinKernighan neighbourhoods, respectively, are compared with the corresponding classical multistart Local Search algorithms, as well as with Simulated Annealing and Threshold Accepting, using 2Opt neighbourhoods. As to be expected a genetic organization of Local Search algorithms can considerably improve upon performance though the genetic components alone can hardly counterbalance a poor choice of the neighbourhoods.
LargeStep Markov Chains for the TSP Incorporating Local Search Heuristics
 Operations Research Letters
, 1992
"... We consider a new class of optimization heuristics which combine local searches with stochastic sampling methods, allowing one to iterate local optimization heuristics. We have tested this on the Euclidean Traveling Salesman Problem, improving 3opt by over 1.6% and LinKernighan by 1.3%. This wo ..."
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Cited by 63 (5 self)
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We consider a new class of optimization heuristics which combine local searches with stochastic sampling methods, allowing one to iterate local optimization heuristics. We have tested this on the Euclidean Traveling Salesman Problem, improving 3opt by over 1.6% and LinKernighan by 1.3%. This work was supported in part by the grants DOEFG0385ER25009 and NSFECS8909127, and by a grant from the PSCCUNY Research Award Program. Correspondence regarding this work should be addressed to S. Otto. y This manuscript was published in Operation Research Letters, v. 11, pp. 21924, 1992. 1 Introduction Given N cities labeled by i = 1; N , separated by distances d ij , the Traveling Salesman Problem (TSP) consists in finding the shortest tour, i.e., the shortest closed path visiting every city exactly once. To be specific, we will consider the symmetric TSP where d ij = d ji , but our method generalizes to the asymmetric case also. The problem of finding the optimal tour is a difficult...