A Grouping Genetic Algorithm for the Multiple Traveling Salesperson Problem

The multiple traveling salesperson problem (MTSP) involves scheduling m > 1 salespersons to visit a set of n > m locations. Thus, the n locations must be divided into m groups and arranged so that each salesperson has an ordered set of cities to visit. The grouping genetic algorithm (GGA) is a type of genetic algorithm (GA) designed particularly for grouping problems. It has been successfully applied to a variety of grouping problems. This paper focuses on the application of a GGA to solve the MTSP. Our GGA introduces a new chromosome representation to indicate which salesperson is assigned to each tour and the ordering of the cities within each tour. We compare our method to standard GAs that employ either the one-chromosome or two-chromosome representation for MTSP. This research demonstrates that our GGA with its new chromosome representation is capable of solving a variety of MTSP problems from the literature and can outperform the traditional encodings of previously published GA methods.

[1]  Jarmo T. Alander,et al.  An Indexed Bibliography of Genetic Algorithms , 1995 .

[2]  Jano I. van Hemert,et al.  Graph Coloring with Adaptive Evolutionary Algorithms , 1998, J. Heuristics.

[3]  Colin R. Reeves,et al.  A genetic algorithm for flowshop sequencing , 1995, Comput. Oper. Res..

[4]  Emanuel Falkenauer,et al.  A hybrid grouping genetic algorithm for bin packing , 1996, J. Heuristics.

[5]  Victor B. Kreng,et al.  Modular product design with grouping genetic algorithm - a case study , 2004, Comput. Ind. Eng..

[6]  Kin Keung Lai,et al.  Forecasting Foreign Exchange Rates With Artificial Neural Networks: A Review , 2004, Int. J. Inf. Technol. Decis. Mak..

[7]  Yang-Byung Park,et al.  A hybrid genetic algorithm for the vehicle scheduling problem with due times and time deadlines , 2001 .

[8]  Lixin Tang,et al.  A multiple traveling salesman problem model for hot rolling scheduling in Shanghai Baoshan Iron & Steel Complex , 2000, Eur. J. Oper. Res..

[9]  Parag C. Pendharkar,et al.  A Hybrid Bayesian Network-Based Multi-Agent System And A Distributed Systems Architecture For The Drug Crime Knowledge Management , 2003, Int. J. Inf. Technol. Decis. Mak..

[10]  Evelyn C. Brown,et al.  CF-GGA: A grouping genetic algorithm for the cell formation problem , 2001 .

[11]  Lawrence J. Schmitt,et al.  Performance characteristics of alternative genetic algorithmic approaches to the traveling salesman problem using path representation: An empirical study , 1998, Eur. J. Oper. Res..

[12]  Fred Glover,et al.  Artificial intelligence, heuristic frameworks and tabu search , 1990 .

[13]  K. Katayama,et al.  The efficiency of hybrid mutation genetic algorithm for the travelling salesman problem , 2000 .

[14]  Larry J. Eshelman,et al.  Spurious Correlations and Premature Convergence in Genetic Algorithms , 1990, FOGA.

[15]  Liangsheng Qu,et al.  A Synergetic Approach to Genetic Algorithms for Solving Traveling Salesman Problem , 1999, Inf. Sci..

[16]  Charles J. Malmborg,et al.  A genetic algorithm for service level based vehicle scheduling , 1996 .

[17]  P. W. Poon,et al.  Genetic algorithm crossover operators for ordering applications , 1995, Comput. Oper. Res..