Performance of evolutionary algorithms on NK landscapes with nearest neighbor interactions and tunable overlap

This paper presents a class of NK landscapes with nearest-neighbor interactions and tunable overlap. The considered class of NK landscapes is solvable in polynomial time using dynamic programming; this allows us to generate a large number of random problem instances with known optima. Several genetic and evolutionary algorithms are then applied to the generated problem instances. The results are analyzed and related to scalability theory for genetic algorithms and estimation of distribution algorithms.

[1]  Shumeet Baluja,et al.  A Method for Integrating Genetic Search Based Function Optimization and Competitive Learning , 1994 .

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

[3]  Stuart A. Kauffman,et al.  The origins of order , 1993 .

[4]  David Maxwell Chickering,et al.  Learning Bayesian Networks: The Combination of Knowledge and Statistical Data , 1994, Machine Learning.

[5]  Kiyoshi Tanaka,et al.  Genetic Algorithms on NK-Landscapes: Effects of Selection, Drift, Mutation, and Recombination , 2003, EvoWorkshops.

[6]  Franz Rothlauf,et al.  Representations for genetic and evolutionary algorithms , 2002, Studies in Fuzziness and Soft Computing.

[7]  David E. Goldberg,et al.  Learning Linkage , 1996, FOGA.

[8]  H. Mühlenbein Convergence of Estimation of Distribution Algorithms for Finite Samples , 2007 .

[9]  D. Goldberg,et al.  Domino convergence, drift, and the temporal-salience structure of problems , 1998, 1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360).

[10]  D. Goldberg,et al.  Escaping hierarchical traps with competent genetic algorithms , 2001 .

[11]  Peter C. Cheeseman,et al.  Where the Really Hard Problems Are , 1991, IJCAI.

[12]  David H. Ackley,et al.  An empirical study of bit vector function optimization , 1987 .

[13]  Kalyanmoy Deb,et al.  Genetic Algorithms, Noise, and the Sizing of Populations , 1992, Complex Syst..

[14]  Dirk Thierens,et al.  Convergence Models of Genetic Algorithm Selection Schemes , 1994, PPSN.

[15]  David E. Goldberg,et al.  Empirical analysis of ideal recombination on random decomposable problems , 2007, GECCO '07.

[16]  Georges R. Harik,et al.  Finding Multimodal Solutions Using Restricted Tournament Selection , 1995, ICGA.

[17]  Alden H. Wright,et al.  The computational complexity of N-K fitness functions , 2000, IEEE Trans. Evol. Comput..

[18]  David E. Goldberg,et al.  Population sizing for entropy-based model building in discrete estimation of distribution algorithms , 2007, GECCO '07.

[19]  David E. Goldberg,et al.  Hierarchical BOA Solves Ising Spin Glasses and MAXSAT , 2003, GECCO.

[20]  Jeffrey Horn,et al.  Handbook of evolutionary computation , 1997 .

[21]  Franz Rothlauf,et al.  Evaluation-Relaxation Schemes for Genetic and Evolutionary Algorithms , 2004 .

[22]  Martin Pelikan,et al.  Hierarchical Bayesian optimization algorithm: toward a new generation of evolutionary algorithms , 2010, SICE 2003 Annual Conference (IEEE Cat. No.03TH8734).

[23]  E. Cantu-Paz,et al.  The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations , 1997, Evolutionary Computation.

[24]  David E. Goldberg,et al.  Scalability of the Bayesian optimization algorithm , 2002, Int. J. Approx. Reason..

[25]  Robert Elliott Smith,et al.  Why is parity hard for estimation of distribution algorithms? , 2007, GECCO '07.

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

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

[28]  Kyomin Jung,et al.  Phase transition in a random NK landscape model , 2008, Artif. Intell..

[29]  Dirk Thierens,et al.  Scalability Problems of Simple Genetic Algorithms , 1999, Evolutionary Computation.

[30]  Martin V. Butz,et al.  Performance of Evolutionary Algorithms on Random Decomposable Problems , 2006, PPSN.

[31]  David E. Goldberg,et al.  Genetic Algorithms and the Variance of Fitness , 1991, Complex Syst..

[32]  J. Wesley Barnes,et al.  The theory of elementary landscapes , 2003, Appl. Math. Lett..

[33]  Martin Pelikan Analysis of estimation of distribution algorithms and genetic algorithms on NK landscapes , 2008, GECCO '08.

[34]  Yong Gao,et al.  An Analysis of Phase Transition in NK Landscapes , 2002, J. Artif. Intell. Res..

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

[36]  Tian-Li Yu,et al.  Optimization of a Constrained Feed Network for an Antenna Array Using Simple and Competent Genetic Algorithm Techniques , 2004 .

[37]  Dirk Thierens,et al.  Mixing in Genetic Algorithms , 1993, ICGA.

[38]  David Maxwell Chickering,et al.  A Bayesian Approach to Learning Bayesian Networks with Local Structure , 1997, UAI.

[39]  Nir Friedman,et al.  Learning Bayesian Networks with Local Structure , 1996, UAI.

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