A cellular genetic algorithm with self-adjusting acceptance threshold

We present a genetic algorithm (GA) whose population possesses a spatial structure. The GA is formulated as a probabilistic cellular automaton: The individuals are distributed over a connected graph and the genetic operators are applied locally in some neighborhood of each individual. By adding a self-organizing acceptance threshold schedule to the proportionate reproduction operator we can prove that the algorithm converges to the global optimum. First results for a multiple knapsack problem indicate a significant improvement in convergence behavior. The algorithm can be mapped easily onto parallel computers.

[1]  Thomas Bäck,et al.  An Overview of Evolutionary Algorithms for Parameter Optimization , 1993, Evolutionary Computation.

[2]  Heinz Mühlenbein,et al.  Evolution algorithms in combinatorial optimization , 1988, Parallel Comput..

[3]  Thomas Bäck,et al.  The zero/one multiple knapsack problem and genetic algorithms , 1994, SAC '94.

[4]  J. Davenport Editor , 1960 .

[5]  Stephen Wolfram,et al.  Theory and Applications of Cellular Automata , 1986 .

[6]  R. L. Dobrushin,et al.  Stochastic cellular systems : ergodicity, memory, morphogenesis , 1990 .

[7]  David E. Goldberg,et al.  A Genetic Algorithm for Parallel Simulated Annealing , 1992, PPSN.

[8]  Marco Tomassini,et al.  The Parallel Genetic Cellular Automata: Application to Global Function Optimization , 1993 .

[9]  Gnter Rudolph,et al.  Parallel Approaches to Stochastic Global Optimization , 1992 .

[10]  Günter Rudolph,et al.  Massively Parallel Simulated Annealing and Its Relation to Evolutionary Algorithms , 1993, Evolutionary Computation.

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

[12]  Michel Loève,et al.  Probability Theory I , 1977 .

[13]  Marius Iosifescu,et al.  Finite Markov Processes and Their Applications , 1981 .

[14]  Bernard Manderick,et al.  A Massively Parallel Genetic Algorithm: Implementation and First Analysis , 1991, ICGA.

[15]  Eric Goles,et al.  Neural and automata networks , 1990 .

[16]  Michael E. Palmer,et al.  Improved Evolutionary Optimization of Difficult Landscapes: Control of Premature Convergence through Scheduled Sharing , 1991, Complex Syst..

[17]  L. Darrell Whitley,et al.  Cellular Genetic Algorithms , 1993, ICGA.

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