Main Effect Fine-tuning of the Mutation Operator and the Neighbourhood Function for Uncapacitated Facility Location Problems

In both genetic algorithms (GAs) and simulated annealing (SA), solutions can be represented by gene representation. Mutation operator in GA and neighborhood function in SA are used to explore the solution space. They usually select genes for performing mutation. The rate of selection of genes can be called mutation rate. However, randomly selecting genes may not be the best way for both algorithms. This paper describes how to estimate the main effect in genes representation. The resulting estimates cannot only be used to understand the domination of gene representation, but also employed to fine-tune the mutation rate in both the mutation operator in the GA and the neighborhood function in the SA. It has been demonstrated the use of the proposed methods for solving uncapacitated facility location problems and discuss the examination of the proposed methods with some useful comparisons with both the latest developed GA and SA for solving this problem. For many well-known benchmark problems, the proposed methods yield better results in solution quality than the previously used methods.

[1]  J. Beasley,et al.  A genetic algorithm for the set covering problem , 1996 .

[2]  Colin R. Reeves,et al.  Genetic Algorithms for the Operations Researcher , 1997, INFORMS J. Comput..

[3]  Colin R. Reeves,et al.  Genetic Algorithms and Neighbourhood Search , 1994, Evolutionary Computing, AISB Workshop.

[4]  John M. Wilson,et al.  A genetic algorithm for the generalised assignment problem , 1997 .

[5]  R. Barton,et al.  Simulated annealing heuristics for the average flow-time and the number of tardy jobs bi-criteria identical parallel machine problem , 1997 .

[6]  Jozef Kratica,et al.  Solving the simple plant location problem by genetic algorithm , 2001, RAIRO Oper. Res..

[7]  Kit Yan Chan,et al.  An epistasis measure based on the analysis of variance for the real-coded representation in genetic algorithms , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[8]  Gilbert Syswerda,et al.  Uniform Crossover in Genetic Algorithms , 1989, ICGA.

[9]  H. Szu,et al.  Nonconvex optimization by fast simulated annealing , 1987, Proceedings of the IEEE.

[10]  John E. Beasley,et al.  Obtaining test problems via Internet , 1996, J. Glob. Optim..

[11]  Xin Yao,et al.  Simulated annealing with extended neighbourhood , 1991, Int. J. Comput. Math..

[12]  Orhan Türkbey,et al.  Evolutionary Simulated Annealing Algorithms for Uncapacitated Facility Location Problems , 2004 .

[13]  Scott Kirkpatrick,et al.  Optimization by Simmulated Annealing , 1983, Sci..

[14]  Terence C. Fogarty,et al.  Varying the Probability of Mutation in the Genetic Algorithm , 1989, ICGA.

[15]  Kit Yan Chan,et al.  Parameterisation of mutation in evolutionary algorithms using the estimated main effect of genes , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[16]  Jan Karel Lenstra,et al.  A local search template (extended abstract) , 1992 .

[17]  Jan Karel Lenstra,et al.  A local search template , 1998, Comput. Oper. Res..

[18]  John E. Beasley,et al.  A genetic algorithm for the generalised assignment problem , 1997, Comput. Oper. Res..

[19]  Mark S. Daskin,et al.  Network and Discrete Location: Models, Algorithms and Applications , 1995 .

[20]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[21]  S. Chatterjee,et al.  Genetic algorithms and traveling salesman problems , 1996 .

[22]  Mehmet Emin Aydin,et al.  A Distributed Evolutionary Simulated Annealing Algorithm for Combinatorial Optimisation Problems , 2004, J. Heuristics.

[23]  K. B. Haley,et al.  A comparative study of both standard and adaptive versions of threshold accepting and simulated annealing algorithms in three scheduling problems , 1995 .