On the investigation of population sizing of genetic algorithms using optimal mixing

Genetic algorithms using optimal mixing have shown promising results, while lack of theoretical supports. This paper investigates population sizing from the supply aspect under the optimal mixing scenario. Specifically, more precise analyses on supply, including the expectation and the lower bound, are made. In addition, considering recombining one randomly generated chromosome with the rest of the population to achieve the global optimum, the tight bounds of the size of the population providing proper fragments chosen by restricted oracles are derived. Tight bounds on problems with ring topologies where a subfunction overlaps two other subfunctions are also derived. Finally, experiments are conducted and well match the derivations.

[1]  Dirk Thierens,et al.  Learning bayesian network structures with GOMEA , 2018, GECCO.

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

[3]  Peter A. N. Bosman,et al.  Exploiting Linkage Information and Problem-Specific Knowledge in Evolutionary Distribution Network Expansion Planning , 2018, Evolutionary Computation.

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

[5]  Thomas D. LaToza,et al.  On the supply of building blocks , 2001 .

[6]  Tian-Li Yu,et al.  Theoretical Perspective of Convergence Complexity of Evolutionary Algorithms Adopting Optimal Mixing , 2015, GECCO.

[7]  Abraham De Moivre.  De mensura sortis, seu, de probabilitate eventuum in ludis a casu fortuito pendentibus , 1710, Philosophical Transactions of the Royal Society of London.

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

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

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

[11]  Tian-Li Yu,et al.  Optimization by Pairwise Linkage Detection, Incremental Linkage Set, and Restricted / Back Mixing: DSMGA-II , 2015, GECCO.

[12]  Dirk Thierens,et al.  Linkage neighbors, optimal mixing and forced improvements in genetic algorithms , 2012, GECCO '12.

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

[14]  Dirk Thierens,et al.  Optimal mixing evolutionary algorithms , 2011, GECCO '11.

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

[16]  Peter A. N. Bosman,et al.  Scalable genetic programming by gene-pool optimal mixing and input-space entropy-based building-block learning , 2017, GECCO.