## 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

11403 |
Computers and Intractability: A Guide to the Theory of NP-Completeness
- Garey, Johnson
- 1979
(Show Context)
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]... |

8156 |
Genetic Algorithms
- Goldberg
- 1989
(Show Context)
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... |

404 |
Simulated Annealing: Theory and Applications
- Laarhoven, Aarts
- 1987
(Show Context)
Citation Context ...mation techniques, typically based on deterministic or probabilistic search heuristics, have been proposed 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, ha... |

348 |
An effective heuristic algorithm for the traveling salesman problem
- Lin, Kernighan
- 1973
(Show Context)
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... |

282 |
TSPLIB—A traveling salesman problem library
- REINELT
- 1991
(Show Context)
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... |

279 |
The traveling salesman problem: a guided tour of combinatorial optimization
- Lawler, Lenstra, et al.
- 1985
(Show Context)
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... |

171 |
The Travelling Salesman. Computational Solutions for TSP Applications
- Reinelt
- 1994
(Show Context)
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... |

156 |
Local optimization and the traveling salesman problem
- JOHNSON
- 1990
(Show Context)
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... |

137 |
Fast Algorithms for Geometric Traveling Salesman Problems
- Bentley
- 1993
(Show Context)
Citation Context ...e asymmetric TSP is shown in Fig. 5. The approach for solving the ATSP starts with p nearestneighbor runs to create p individuals for the initial population. The fast-3-Opt tour improvement heuristic =-=[2]-=- is subsequently used to transform the individuals of the initial population into local optima. The reason why LK, used in the STSP, does not produce satisfactory results is that it includes 2-Opt mov... |

132 |
Parallel genetic algorithms, population genetics and combinatorial optimization
- Mühlenbein
- 1989
(Show Context)
Citation Context ...imum 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. The basic idea is to use a simple nearest-neighbor tour construction heuristic for creating t... |

119 |
A new adaptive multistart technique for combinatorial global optimization
- Boese, Kahng, et al.
- 1994
(Show Context)
Citation Context ...A) optimization methods which have been shown to produce high quality solutions to the STSP. For example, setting the number of generations to 0 is equivalent to performing a multi-start local search =-=[5]-=-, where the individual with the highest fitness represents the solution. Furthermore, the Large Step Markov Chains approach [20] and the Iterated-LK technique are special cases of our GA approach, sin... |

118 |
Incorporating problem specific knowledge in genetic algorithms
- Grefenstette
- 1987
(Show Context)
Citation Context ...otivated several researchers to build additional heuristic elements into GAs. The proposals for such "heuristic" GAs include tour construction heuristics for generating the initial populatio=-=n of a GA [13]-=-, tour improvement heuristics for producing local optima [15], [24], and special heuristic crossover operators tailored to the characteristics of the TSP [14], [21], [23], [28], [29]. Since these stud... |

110 | Evolution in Time and Space – The Parallel Genetic Algorithm
- Mühlenbein
- 1991
(Show Context)
Citation Context ... into GAs. The proposals for such "heuristic" GAs include tour construction heuristics for generating the initial population of a GA [13], tour improvement heuristics for producing local opt=-=ima [15], [24]-=-, and special heuristic crossover operators tailored to the characteristics of the TSP [14], [21], [23], [28], [29]. Since these studies seem to indicate that the only way to obtain results comparable... |

103 | Ant-Q: A reinforcement learning approach to the traveling salesman problem
- M, Marco
- 1995
(Show Context)
Citation Context ... 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 combined efforts of several meth... |

97 | Large-Step Markov Chains for the Traveling Salesman Problem
- Martin, Otto, et al.
- 1991
(Show Context)
Citation Context ...fforts 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. The bas... |

90 |
Evolution algorithms in combinatorial optimization
- Mühlenbein, Gorges-Schleuter, et al.
- 1988
(Show Context)
Citation Context ...r 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. The basic idea is to use a simple nearest-neighbor tour construction heuristic for creating the ini... |

63 | Genetic local search algorithms for the traveling salesman problem
- Ulder, Aarts, et al.
- 1990
(Show Context)
Citation Context ...mal 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. The basic idea is to use a simple nearest-neighbor tour construction heuristic for creating the initial p... |

55 |
An analysis of the elastic net approach to the travelling salesman problem. Neural Computation
- Durbin, Szeliski, et al.
- 1989
(Show Context)
Citation Context ...ilistic search heuristics, have been proposed 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, ... |

47 | Memetic algorithms for combinatorial optimization problems: Fitness landscapes and effective search strategies. Doctoral dissertation
- Merz
- 2000
(Show Context)
Citation Context ...ulation by the offspring produced is performed as described in the algorithm for the STSP. IV. Implementation and Results The algorithms were implemented in C++ on a DEC Alpha workstation under OSF/1 =-=[22]-=-, using some of the features provided by the GALIB library (version 2.3.2) [30]. Detailed information about the development of the solution qualities in each of the experiments conducted are given els... |

45 |
A parallel tabu search algorithm for large traveling salesman problems
- FIECHTER
- 1994
(Show Context)
Citation Context ...ministic or probabilistic search heuristics, have been proposed 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 qu... |

45 |
G.Liepins, A New Approach to the Traveling Salesman Problem by Genetic Algorithms
- Homaifar
- 1993
(Show Context)
Citation Context ...e 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 combined e... |

40 | Cost Versus Distance in the Traveling Salesman Problem
- Boese
- 1995
(Show Context)
Citation Context ...a "globally convex" or "big valley" character, such that the optimal solution can be found near the center of a single valley of near-optimum solutions with approximately equal dis=-=tance to each other [4]-=-. Furthermore, there is a novel mutation operator which performs random jumps within the neighborhood of a local optimum, and a new replacement scheme which attemps to avoid the emergence of highly si... |

37 | Genetic operators, the fitness landscape and the traveling salesman problem
- Mathias, Whitley
- 1992
(Show Context)
Citation Context ...ting the initial population of a GA [13], tour improvement heuristics for producing local optima [15], [24], and special heuristic crossover operators tailored to the characteristics of the TSP [14], =-=[21]-=-, [23], [28], [29]. Since these studies seem to indicate that the only way to obtain results comparable to good conventional local search techniques is to incorporate TSP specific knowledge into a GA,... |

10 |
A modified edge recombination operator for the travelling salesman problem
- Tang, Leung
- 1994
(Show Context)
Citation Context ...tial population of a GA [13], tour improvement heuristics for producing local optima [15], [24], and special heuristic crossover operators tailored to the characteristics of the TSP [14], [21], [23], =-=[28]-=-, [29]. Since these studies seem to indicate that the only way to obtain results comparable to good conventional local search techniques is to incorporate TSP specific knowledge into a GA, our approac... |

4 |
Gucht, "The Effects of Population Size, Heuristic Crossover and Local Improvement on a Genetic Algorithm for the Travelling Salesman Problem
- Jog, Suh, et al.
- 1989
(Show Context)
Citation Context ...ements into GAs. The proposals for such "heuristic" GAs include tour construction heuristics for generating the initial population of a GA [13], tour improvement heuristics for producing loc=-=al optima [15]-=-, [24], and special heuristic crossover operators tailored to the characteristics of the TSP [14], [21], [23], [28], [29]. Since these studies seem to indicate that the only way to obtain results comp... |

3 |
Neural Networks and the Travelling Salesman Problem
- Aarts, Stehouwer
- 1993
(Show Context)
Citation Context ...tics, have been proposed 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... |

3 |
GALIB 2.3.2
- Wall
- 1995
(Show Context)
Citation Context ...r the STSP. IV. Implementation and Results The algorithms were implemented in C++ on a DEC Alpha workstation under OSF/1 [22], using some of the features provided by the GALIB library (version 2.3.2) =-=[30]-=-. Detailed information about the development of the solution qualities in each of the experiments conducted are given elsewhere [3]. Table I summarizes the final results obtained by running the STSP-G... |

1 |
Combinatorial Optimizationwith Parallel Adaptive Threshold Accepting
- Freisleben, Schulte
- 1992
(Show Context)
Citation Context ...ly based on deterministic or probabilistic search heuristics, have been proposed 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 successfu... |

1 |
ASPARAGOS: An AsynchronousParallel Genetic Optimization Strategy
- Gorges-Schleuter
- 1989
(Show Context)
Citation Context ...ar-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. The basic idea is to use a simple nearest-neighbor tour construction heuristic for crea... |