## A Genetic Local Search Algorithm for Solving Symmetric and Asymmetric Traveling Salesman Problems (1996)

Venue: | In Proceedings of the 1996 IEEE International Conference on Evolutionary Computation |

Citations: | 78 - 12 self |

### BibTeX

@INPROCEEDINGS{Freisleben96agenetic,

author = {Bernd Freisleben and Peter Merz},

title = {A Genetic Local Search Algorithm for Solving Symmetric and Asymmetric Traveling Salesman Problems},

booktitle = {In Proceedings of the 1996 IEEE International Conference on Evolutionary Computation},

year = {1996},

pages = {616--621},

publisher = {IEEE Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

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 minimum--length closed tour that visits each city once and returns to its starting point. A symmetric TSP (STSP) is one where the distance between any...

### Citations

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Citation Context ... asymmetric TSP (ATSP) these distances are different. The TSP has become a standard testbed for combinatorial optimization methods which attempt to find nearoptimum solutions to this NP--hard problem =-=[10]-=-. Several such approximation techniques, typically based on deterministic or probabilistic search heuristics, have been proposed in the literature, including the classical local search algorithms [27]... |

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Citation Context ... in the literature, including the classical local search algorithms [27], simulated annealing [17], threshold acceptings[8], tabu search [7], elastic nets [6], neural networks [1], genetic algorithms =-=[11]-=-, [14], and ant colonies [9]. Although some of these approaches, when applied individually, have proven to be successful in producing quite good results, top quality solutions seem to require the comb... |

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Citation Context ...to p different randomly chosen starting points, is used for that purpose. Each of the p individuals of the initial GA population P is then exposed to the Lin-Kernighan (LK) tour improvement heuristic =-=[19]-=-. The result of the LK local search is a population of p individuals which represent locally optimal solutions. The LK heuristic, which is an efficient realization of a k-Opt procedure with k variable... |

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Citation Context ...ic 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 minimum--length closed tour that visits each city once and returns to its starting point. A symmetric TSP (S... |

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Citation Context ...ce the ATSP represents a generalization of the STSP, it is more difficult to solve. This is documented by the fact that optimal solutions are currently only available for instances with up 400 cities =-=[26]-=-. Although it is possible to transform (the directed graph of) a given ATSP into (an undirected graph of) an equivalent STSP, local search heuristics such as 2-Opt usually fail to produce satisfactory... |

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Citation Context ... 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 minimum--length closed tour that visits each city once and returns to its starting point. A symmetric TSP (STSP) i... |

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Citation Context ...ined efforts of several methods, particularly for large TSP instances. For example, near-optimum or optimal tours have been obtained by combinations of local search algorithms and simulated annealing =-=[16]-=-, [20] and by combinations of local search algorithms and genetic algorithms (GA) [12], [23], [25], [29]. In this paper, we present a new combined local search/genetic algorithm approach to the TSP. T... |

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