NK landscapes, problem difficulty, and hybrid evolutionary algorithms

This paper presents an experimental study of NK landscapes with the main focus on the relationship between (1) problem parameters, (2) various measures of problem difficulty of fitness landscapes, and (3) performance of hybrid evolutionary algorithms. As the target class of problems, the study considers two types of NK landscapes: (1) Standard, unrestricted NK landscapes and (2) shuffled NK landscapes with nearest-neighbor interactions. As problem difficulty measures, the paper considers the fitness distance correlation, the correlation coefficient, the distance of local and global optima, and the escape rate. Experimental results are presented, analyzed and discussed. Promising avenues for future work are also outlined.

[1]  Bernd Freisleben,et al.  Greedy and Local Search Heuristics for Unconstrained Binary Quadratic Programming , 2002, J. Heuristics.

[2]  David E. Goldberg,et al.  The Gambler's Ruin Problem, Genetic Algorithms, and the Sizing of Populations , 1999, Evolutionary Computation.

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

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

[5]  Martin Pelikan,et al.  Computational Complexity and Simulation of Rare Events of Ising Spin Glasses , 2004, GECCO.

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

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

[8]  Terry Jones,et al.  Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms , 1995, ICGA.

[9]  Andrew M. Sutton,et al.  A polynomial time computation of the exact correlation structure of k-satisfiability landscapes , 2009, GECCO '09.

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

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

[12]  David E. Goldberg,et al.  A hierarchy machine: Learning to optimize from nature and humans , 2003, Complex..

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

[14]  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).

[15]  E. Weinberger,et al.  Correlated and uncorrelated fitness landscapes and how to tell the difference , 1990, Biological Cybernetics.

[16]  David Maxwell Chickering,et al.  Learning Bayesian networks: The combination of knowledge and statistical data , 1995, Mach. Learn..

[17]  Vassilis Zissimopoulos,et al.  Autocorrelation Coefficient for the Graph Bipartitioning Problem , 1998, Theor. Comput. Sci..

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

[19]  Peter Merz,et al.  Advanced Fitness Landscape Analysis and the Performance of Memetic Algorithms , 2004, Evolutionary Computation.

[20]  Martin V. Butz,et al.  Performance of evolutionary algorithms on NK landscapes with nearest neighbor interactions and tunable overlap , 2009, GECCO '09.

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

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

[23]  P. Stadler.  Landscapes and their correlation functions , 1996 .

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

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

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

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

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

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