Chun-kit Au
Ho-fung Leung
ABSTRACT
This paper studies the performance for evolution strategies with the optimal weighed recombination on spherical problems in finite dimensions. We first discuss the different forms of functions that are used to derive the optimal recombination weights and step size, and then derive an inequality that establishes the relationship between these functions. We prove that using the expectation of random variables to derive the optimal recombination weights and step size can be disappointing in terms of the expected performance of evolution strategies. We show that using the realizations of random variables is a better choice. We generalize the results to any convex functions and establish an inequality for the normalized quality gain. We prove that the normalized quality gain of the evolution strategies have a better and robust performance when they use the optimal recombination weights and the optimal step size that are derived from the realizations of random variables rather than using the expectations of random variables.
- Youhei Akimoto, Anne Auger, and Nikolaus Hansen. 2017. Quality gain analysis of the weighted recombination evolution strategy on general convex quadratic functions. In Proceedings of the 14th ACM/SIGEVO Conference on Foundations of Genetic Algorithms. ACM, 111--126. Google Scholar
Digital Library
- Dirk V Arnold. 2005. Optimal weighted recombination. In FOGA. Springer, 215--237. Google ScholarDigital Library
- Dirk V Arnold. 2006. Weighted multirecombination evolution strategies. Theoretical computer science 361, 1 (2006), 18--37. Google ScholarDigital Library
- Hans-Georg Beyer. 2013. The theory of evolution strategies. Springer Science & Business Media.Google Scholar
- Hans-Georg Beyer and Dirk V Arnold. 2003. Qualms regarding the optimality of cumulative path length control in CSA/CMA-evolution strategies. Evolutionary Computation 11, 1 (2003), 19--28. Google ScholarDigital Library
- Mohamed Jebalia and Anne Auger. 2010. Log-linear Convergence of the Scale-invariant (μ/μ w, λ)-ES and Optimal μ for Intermediate Recombination for Large Population Sizes. Parallel Problem Solving from Nature, PPSN XI (2010), 52--62. Google ScholarDigital Library
- I. Rechenberg. 1973. Evolutionsstrategie : Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Number 15 in Problemata. Frommann-Holzboog, Stuttgart-Bad Cannstatt.Google Scholar
Index Terms
- Analysis of evolution strategies with the optimal weighted recombination
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