An Estimation of Distribution Algorithm Based on Maximum Entropy

Estimation of distribution algorithms (EDA) are similar to genetic algorithms except that they replace crossover and mutation with sampling from an estimated probability distribution. We develop a framework for estimation of distribution algorithms based on the principle of maximum entropy and the conservation of schema frequencies. An algorithm of this type gives better performance than a standard genetic algorithm (GA) on a number of standard test problems involving deception and epistasis (i.e. Trap and NK).

[1]  Stuart A. Kauffman,et al.  ORIGINS OF ORDER , 2019, Origins of Order.

[2]  Pedro Larrañaga,et al.  A Review on Estimation of Distribution Algorithms , 2002, Estimation of Distribution Algorithms.

[3]  Paul A. Viola,et al.  MIMIC: Finding Optima by Estimating Probability Densities , 1996, NIPS.

[4]  Heinz Mühlenbein,et al.  FDA -A Scalable Evolutionary Algorithm for the Optimization of Additively Decomposed Functions , 1999, Evolutionary Computation.

[5]  Alden H. Wright,et al.  Bistability in a Gene Pool GA with Mutation , 2002, FOGA.

[6]  E. Jaynes.  Information Theory and Statistical Mechanics , 1957 .

[7]  John Holland,et al.  Adaptation in Natural and Artificial Sys-tems: An Introductory Analysis with Applications to Biology , 1975 .

[8]  David E. Goldberg,et al.  Linkage Problem, Distribution Estimation, and Bayesian Networks , 2000, Evolutionary Computation.

[9]  Julian F. Miller,et al.  Genetic and Evolutionary Computation — GECCO 2003 , 2003, Lecture Notes in Computer Science.

[10]  A. Feinstein,et al.  Foundations of Information Theory , 1959 .

[11]  Riccardo Poli,et al.  Exact Schema Theory for Genetic Programming and Variable-Length Genetic Algorithms with One-Point Crossover , 2001, Genetic Programming and Evolvable Machines.

[12]  Christopher R. Stephens,et al.  Schemata Evolution and Building Blocks , 1999, Evolutionary Computation.

[13]  H. M. Rwcp.  The equation for the response to selection and its use for prediction , 1997 .

[14]  Christopher R. Stephens,et al.  Schemata as Building Blocks: Does Size Matter? , 2000, FOGA.

[15]  Alden H. Wright,et al.  Efficient Linkage Discovery by Limited Probing , 2003, Evolutionary Computation.

[16]  Kalyanmoy Deb,et al.  Analyzing Deception in Trap Functions , 1992, FOGA.

[17]  Riccardo Poli,et al.  Foundations of Genetic Programming , 1999, Springer Berlin Heidelberg.

[18]  Silviu Guiasu,et al.  The principle of maximum entropy , 1985 .