Performance of Network Crossover on NK Landscapes and Spin Glasses

This paper describes a network crossover operator based on knowledge gathered from either prior problem-specific knowledge or linkage learning methods such as estimation of distribution algorithms (EDAs). This operator can be used in a genetic algorithm (GA) to incorporate linkage in recombination. The performance of GA with network crossover is compared to that of GA with uniform crossover and the hierarchical Bayesian optimization algorithm (hBOA) on 2D Ising spin glasses, NK landscapes, and SK spin glasses. The results are analyzed and discussed.

[1]  Martin Pelikan,et al.  Scalable Optimization via Probabilistic Modeling: From Algorithms to Applications (Studies in Computational Intelligence) , 2006 .

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

[3]  David E. Goldberg,et al.  Using Previous Models to Bias Structural Learning in the Hierarchical BOA , 2012, Evolutionary Computation.

[4]  M. Mézard,et al.  Spin Glass Theory and Beyond , 1987 .

[5]  J. A. Lozano,et al.  Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation , 2001 .

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

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

[8]  Zvi Drezner,et al.  Using hybrid metaheuristics for the one‐way and two‐way network design problem , 2002 .

[9]  Helmut G. Katzgraber,et al.  Spin glasses and algorithm benchmarks: A one-dimensional view , 2007, 0711.1532.

[10]  Erick Cantú-Paz,et al.  Efficient and Accurate Parallel Genetic Algorithms , 2000, Genetic Algorithms and Evolutionary Computation.

[11]  David E. Goldberg,et al.  A Survey of Optimization by Building and Using Probabilistic Models , 2002, Comput. Optim. Appl..

[12]  Martin Pelikan,et al.  Intelligent bias of network structures in the hierarchical BOA , 2009, GECCO.

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

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

[15]  S. Kobe,et al.  A recursive branch-and-bound algorithm for the exact ground state of Ising spin-glass models , 1984 .

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

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

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

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

[20]  S. Kirkpatrick,et al.  Infinite-ranged models of spin-glasses , 1978 .

[21]  Martin Pelikan,et al.  Finding ground states of Sherrington-Kirkpatrick spin glasses with hierarchical boa and genetic algorithms , 2008, GECCO '08.

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

[23]  William Rand,et al.  CrossNet: a framework for crossover with network-based chromosomal representations , 2008, GECCO '08.

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

[25]  F. Barahona On the computational complexity of Ising spin glass models , 1982 .

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

[27]  J. A. Lozano,et al.  Towards a New Evolutionary Computation: Advances on Estimation of Distribution Algorithms (Studies in Fuzziness and Soft Computing) , 2006 .

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

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

[31]  David E. Goldberg,et al.  Dependency Structure Matrix, Genetic Algorithms, and Effective Recombination , 2009, Evolutionary Computation.

[32]  Zvi Drezner,et al.  A New Genetic Algorithm for the Quadratic Assignment Problem , 2003, INFORMS J. Comput..