Xiaoyue Li
ABSTRACT
While it is mathematically proven that the (μ + 1) GA optimizes Jumpk efficiently for low crossover probabilities, theory research still struggles with the analysis of crossover-based optimization for high crossover probabilities on this key test function. Research in this area has improved our understanding of crossover in general, in particular regarding the emergence of diversity, the crucial ingredient for successful optimization with genetic algorithms.
In this paper we study the optimizing process after the (μ + 1) GAhas reached the plateau of Jumpk. We are interested in (a) the stationary distribution of the algorithm on the plateau (when ignoring the optimum) and (b) the dynamics of the stationary distribution. We experimentally show that the (μ+1) GA achieves 10% complementary pairs if μ = 10 · k, unless n is very small. Regarding the dynamics, we show samples of how bit positions gain and lose individuals with a 0 at that position.
- Duc-Cuong Dang, Tobias Friedrich, Martin S. Krejca, Timo Kötzing, Per Kristian Lehre, Pietro S. Oliveto, Dirk Sudholt, and Andrew Michael Sutton. 2016. Escaping Local Optima with Diversity Mechanisms and Crossover. In Proc. of GECCO'16. ACM Press, 645--652.Google Scholar
- Duc-Cuong Dang, Tobias Friedrich, Timo Kötzing, Martin S. Krejca, Per Kristian Lehre, Pietro S. Oliveto, Dirk Sudholt, and Andrew M. Sutton. 2018. Escaping Local Optima Using Crossover With Emergent Diversity. IEEE Transactions on Evolutionary Computation 22, 3 (2018), 484--497.Google ScholarCross Ref
- Grasiele R. Duarte and Beatriz S. L. P. de Lima. 2021. An Operation to Promote Diversity in Evolutionary Algorithms in a Dynamic Hybrid Island Model. In Proc. of GECCO'21 Companion. ACM Press, 1779--1787.Google Scholar
- Thomas Gabor, Lenz Belzner, and Claudia Linnhoff-Popien. 2018. Inheritance-Based Diversity Measures for Explicit Convergence Control in Evolutionary Algorithms. In Proc. of GECCO'18. ACM Press, 841--848.Google ScholarDigital Library
- Thomas Jansen and Ingo Wegener. 2002. The Analysis of Evolutionary Algorithms - A Proof That Crossover Really Can Help. Algorithmica 34 (2002), 47--66.Google ScholarDigital Library
- Valentín Osuna-Enciso, Erik Cuevas, and Bernardo Morales Castañeda. 2022. A diversity metric for population-based metaheuristic algorithms. Information Sciences 586 (2022), 192--208.Google ScholarDigital Library
- Adam Prügel-Bennett. 2010. Benefits of a Population: Five Mechanisms That Advantage Population-Based Algorithms. IEEE TEvC 14 (2010), 500--517.Google Scholar
- Giovanni Squillero and Alberto Tonda. 2016. Divergence of character and premature convergence: A survey of methodologies for promoting diversity in evolutionary optimization. Information Sciences 329 (2016), 782--799.Google ScholarDigital Library
- Dirk Sudholt. 2020. The Benefits of Population Diversity in Evolutionary Algorithms: A Survey of Rigorous Runtime Analyses. Springer, 359--404.Google Scholar
Index Terms
- Experimental Analyses of Crossover and Diversity on Jump
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