The Analysis of Evolutionary Algorithms—A Proof That Crossover Really Can Help

AbstractEvolutionary algorithms are randomized search heuristics that were invented in the sixties and have been intensively applied and studied since the eighties. Since then there have been only a few theoretical investigations and no sound theoretical foundation. One of the main sources of difficulty for theoretical analyses is the crossover operator. It can be useful only if the current population of strings has a certain diversity. Here it is proved that an evolutionary algorithm can produce enough diversity such that the use of crossover can speedup the expected optimization time from superpolynomial to a polynomial of small degree.

[1]  David B. Fogel,et al.  Evolutionary Computation: Towards a New Philosophy of Machine Intelligence , 1995 .

[2]  Kenneth de Jong,et al.  Generation gap methods , 2018, Evolutionary Computation 1.

[3]  Yuval Rabani,et al.  A computational view of population genetics , 1995, STOC '95.

[4]  Thomas Jansen,et al.  On the analysis of the (1+1) evolutionary algorithm , 2002, Theor. Comput. Sci..

[5]  S. Ronald.  Duplicate genotypes in a genetic algorithm , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[6]  John H. Holland,et al.  When will a Genetic Algorithm Outperform Hill Climbing , 1993, NIPS.

[7]  Mark Jerrum,et al.  The Markov chain Monte Carlo method: an approach to approximate counting and integration , 1996 .

[8]  Melanie Mitchell,et al.  An introduction to genetic algorithms , 1996 .

[9]  Ingo Wegener,et al.  A Rigorous Complexity Analysis of the (1 + 1) Evolutionary Algorithm for Separable Functions with Boolean Inputs , 1998, Evolutionary Computation.

[10]  Russ Bubley,et al.  Randomized algorithms , 1995, CSUR.

[11]  Günter Rudolph,et al.  How Mutation and Selection Solve Long-Path Problems in Polynomial Expected Time , 1996, Evolutionary Computation.

[12]  Hans-Paul Schwefel,et al.  Evolution and optimum seeking , 1995, Sixth-generation computer technology series.

[13]  Avi Wigderson,et al.  Quadratic Dynamical Systems (Preliminary Version) , 1992, FOCS 1992.

[14]  A. Sinclair,et al.  A computational view of population genetics , 1998 .

[15]  Heinz Mühlenbein,et al.  How Genetic Algorithms Really Work: Mutation and Hillclimbing , 1992, PPSN.

[16]  Dan Boneh,et al.  On genetic algorithms , 1995, COLT '95.

[17]  Thomas Jansen,et al.  On the Analysis of Evolutionary Algorithms - A Proof That Crossover Really Can Help , 1999 .

[18]  Kalyanmoy Deb,et al.  Long Path Problems , 1994, PPSN.

[19]  Thomas Bäck,et al.  Optimal Mutation Rates in Genetic Search , 1993, ICGA.

[20]  Martin Wattenberg,et al.  Stochastic Hillclimbing as a Baseline Mathod for Evaluating Genetic Algorithms , 1995, NIPS.

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

[22]  Dan Boneh,et al.  Where Genetic Algorithms Excel , 2001, Evolutionary Computation.

[23]  Marc Schoenauer,et al.  Rigorous Hitting Times for Binary Mutations , 1999, Evolutionary Computation.

[24]  I. Wegener,et al.  Design and Management of Complex Technical Processes and Systems by means of Computational Intelligence Methods A Natural and Simple Function Which is Hard For All Evolutionary Algorithms , 2007 .

[25]  Melanie Mitchell,et al.  Relative Building-Block Fitness and the Building Block Hypothesis , 1992, FOGA.

[26]  Dorit S. Hochbaum,et al.  Approximation Algorithms for NP-Hard Problems , 1996 .