Node Histogram vs . Edge Histogram : A Comparison of PMBGAs in Permutation Domains

Previous papers have proposed an algorithm called the edge histogram sampling algorithm (EHBSA) that models the relative relation between two nodes (edge) of permutation strings of a population within the PMBGA framework for permutation domains. This paper proposes another histogram based model we call the node histogram sampling algorithm (NHBSA). The NHBSA models node frequencies at each absolute position in strings of a population. Sampling methods are similar to that of EHBSA. Performance of NHBSA is compared with that of EHBSA using two types of permutation problems: the FSSP and the quadratic assignment problem (QAP). The results showed that the NHBSA works better than the EHBSA on these problems.

[1]  Shigeyoshi Tsutsui,et al.  Probabilistic Model-Building Genetic Algorithms in Permutation Representation Domain Using Edge Histogram , 2002, PPSN.

[2]  David E. Goldberg,et al.  A Survey of Optimization by Building and Using Probabilistic Models , 2002, Comput. Optim. Appl..

[3]  Thomas Stützle,et al.  MAX-MIN Ant System , 2000, Future Gener. Comput. Syst..

[4]  Thomas Stützle,et al.  An Ant Approach to the Flow Shop Problem , 1998 .

[5]  Marco Dorigo,et al.  Ant system: optimization by a colony of cooperating agents , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[6]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[7]  Éric D. Taillard,et al.  Robust taboo search for the quadratic assignment problem , 1991, Parallel Comput..

[8]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[9]  J. A. Lozano,et al.  Estimation of Distribution Algorithms , 2002, Genetic Algorithms and Evolutionary Computation.

[10]  M Dorigo,et al.  Ant colonies for the quadratic assignment problem , 1999, J. Oper. Res. Soc..

[11]  Pedro Larrañaga,et al.  Solving the Traveling Salesman Problem with EDAs , 2002, Estimation of Distribution Algorithms.

[12]  Dirk Thierens,et al.  Permutation Optimization by Iterated Estimation of Random Keys Marginal Product Factorizations , 2002, PPSN.

[13]  David Connolly An improved annealing scheme for the QAP , 1990 .

[14]  Charles Fleurent,et al.  Genetic Hybrids for the Quadratic Assignment Problem , 1993, Quadratic Assignment and Related Problems.

[15]  L. Darrell Whitley,et al.  A Comparison of Genetic Sequencing Operators , 1991, ICGA.

[16]  David E. Goldberg,et al.  The Design of Innovation: Lessons from and for Competent Genetic Algorithms , 2002 .

[17]  É. Taillard COMPARISON OF ITERATIVE SEARCHES FOR THE QUADRATIC ASSIGNMENT PROBLEM. , 1995 .

[18]  S. Tsutsui,et al.  Solving capacitated vehicle routing problems using edge histogram based sampling algorithms , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

[19]  Mitsunori Miki,et al.  Using Edge Histogram Models to solve Flow shop Scheduling Problems with Probabilistic Model-Building Genetic Algorithms , 2002, SEAL.

[20]  David E. Goldberg,et al.  Bayesian Optimization Algorithm: From Single Level to Hierarchy , 2002 .

[21]  D. J. Smith,et al.  A Study of Permutation Crossover Operators on the Traveling Salesman Problem , 1987, ICGA.

[22]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.

[23]  Shigenobu Kobayashi,et al.  Edge Assembly Crossover: A High-Power Genetic Algorithm for the Travelling Salesman Problem , 1997, ICGA.

[24]  É. Taillard Some efficient heuristic methods for the flow shop sequencing problem , 1990 .