Network crossover performance on NK landscapes and deceptive problems

Practitioners often have some information about the problem being solved, which may be represented as a graph of dependencies or correlations between problem variables. Similar information can also be obtained automatically, for example by mining the probabilistic models obtained by EDAs or by using other methods for linkage learning. This information can be used to bias variation operators, be it in EDAs (where it can be used to speed up model building) or in GAs (where the linkages can be explored by modifying crossover). This can allow us to solve problems unsolvable with conventional, problem-independent variation operators, or speed up adaptive operators such as those of EDAs. This paper describes a method to build a network crossover operator that can be used in a GA to easily incorporate problem-specific knowledge. The performance of this operator in the simple genetic algorithm(GA) is then compared to other operators as well as the hierarchical Bayesian Optimization Algorithm (hBOA) on several different problem types, all with both elitism replacement and Restricted Tournament Replacement (RTR). The performance of all the algorithms are then analyzed and the results are discussed.

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

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

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

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

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

[6]  Josef Schwarz,et al.  The Parallel Bayesian Optimization Algorithm , 2000 .

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

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

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

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

[11]  David E. Goldberg,et al.  Sporadic model building for efficiency enhancement of hierarchical BOA , 2006, GECCO '06.

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

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

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

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

[16]  David E. Goldberg,et al.  iBOA: the incremental bayesian optimization algorithm , 2008, GECCO '08.

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

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

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

[20]  Heinz Mühlenbein,et al.  Evolutionary optimization and the estimation of search distributions with applications to graph bipartitioning , 2002, Int. J. Approx. Reason..

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

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

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

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

[25]  Xavier Llorà,et al.  Towards billion-bit optimization via a parallel estimation of distribution algorithm , 2007, GECCO '07.

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

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

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

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

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

[31]  Shumeet Baluja,et al.  Incorporating a priori Knowledge in Probabilistic-Model Based Optimization , 2006, Scalable Optimization via Probabilistic Modeling.

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

[33]  William Rand,et al.  CrossNet: a framework for crossover with network-based chromosomal representations , 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]  H. Mühlenbein,et al.  From Recombination of Genes to the Estimation of Distributions I. Binary Parameters , 1996, PPSN.