Evolution in Time and Space -the Parallel Genetic Algorithm

The parallel genetic algorithm (PGA) uses two major modiications compared to the genetic algorithm. Firstly, selection for mating is distributed. Individuals live i n a 2-D w orld. Selection of a mate is done by each i n d i-vidual independently in its neighborhood. Secondly, e a c h individual may improve its tness during its lifetime by e.g. local hill-climbing. The PGA is totally asynchronous, running with maximal eeciency on MIMD parallel computers. The search strategy of the PGA is based on a small number of active and intelligent individuals, whereas a GA uses a large population of passive individuals. We will investigate the PGA with deceptive problems and the traveling salesman problem. We outline why and when the PGA is succesful. Abstractly, a PGA is a parallel search with information exchange between the individuals. If we represent the optimization problem as a tness landscape in a certain connguration space, we see, that a PGA tries to jump from two local minima to a third, still better local minima, by using the crossover operator. This jump is (probabilistically) successful, if the tness landscape has a certain correlation. We s h o w t h e correlation for the traveling salesman problem by a connguration space analysis. The PGA explores implicitly the above correlation.

[1]  R. Punnett,et al.  The Genetical Theory of Natural Selection , 1930, Nature.

[2]  R. A. Fisher,et al.  The Genetical Theory of Natural Selection , 1931 .

[3]  Shen Lin.  Computer solutions of the traveling salesman problem , 1965 .

[4]  Ingo Rechenberg,et al.  Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution , 1973 .

[5]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[6]  J. Felsenstein.  A Pain in the Torus: Some Difficulties with Models of Isolation by Distance , 1975, The American Naturalist.

[7]  J. Felsenstein.  The theoretical population genetics of variable selection and migration. , 1976, Annual review of genetics.

[8]  F. Glover.  HEURISTICS FOR INTEGER PROGRAMMING USING SURROGATE CONSTRAINTS , 1977 .

[9]  E. Hansen.  Numerical Optimization of Computer Models (Hans-Paul Schwefel) , 1983 .

[10]  S. Kirkpatrick,et al.  Configuration space analysis of travelling salesman problems , 1985 .

[11]  Heinz Mühlenbein,et al.  New solutions to the mapping problem of parallel systems: The evolution approach , 1987, Parallel Comput..

[12]  Dana S. Richards,et al.  Punctuated Equilibria: A Parallel Genetic Algorithm , 1987, ICGA.

[13]  D. Ackley.  A connectionist machine for genetic hillclimbing , 1987 .

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

[15]  J. David Schaffer,et al.  Proceedings of the third international conference on Genetic algorithms , 1989 .

[16]  Carsten Peterson,et al.  A New Method for Mapping Optimization Problems Onto Neural Networks , 1989, Int. J. Neural Syst..

[17]  J. Holland.  Searching nonlinear functions for high values , 1989 .

[18]  Martina Gorges-Schleuter,et al.  ASPARAGOS An Asynchronous Parallel Genetic Optimization Strategy , 1989, ICGA.

[19]  John J. Grefenstette,et al.  How Genetic Algorithms Work: A Critical Look at Implicit Parallelism , 1989, ICGA.

[20]  Bernard Manderick,et al.  Fine-Grained Parallel Genetic Algorithms , 1989, ICGA.

[21]  Reiko Tanese,et al.  Distributed Genetic Algorithms , 1989, ICGA.

[22]  Kalyanmoy Deb,et al.  Messy Genetic Algorithms: Motivation, Analysis, and First Results , 1989, Complex Syst..

[23]  L. Darrell Whitley,et al.  GENITOR II: a distributed genetic algorithm , 1990, J. Exp. Theor. Artif. Intell..

[24]  Kalyanmoy Deb,et al.  Messy Genetic Algorithms Revisited: Studies in Mixed Size and Scale , 1990, Complex Syst..

[25]  Heinz Mühlenbein,et al.  The parallel genetic algorithm as function optimizer , 1991, Parallel Comput..

[26]  Martin Grötschel,et al.  Solution of large-scale symmetric travelling salesman problems , 1991, Math. Program..

[27]  Martina Gorges-Schleuter,et al.  Genetic algorithms and population structures: a massively parallel algorithm , 1991 .

[28]  El-Ghazali Talbi,et al.  A parallel genetic algorithm for the graph partitioning problem , 1991, ICS '91.

[29]  Stephen I. Gallant.  Simulated Annealing and Boltzmann Machines , 1993 .