Experimental Comparison of Six Population-Based Algorithms for Continuous Black Box Optimization Petr Poˇ s´ ık posik@labe.felk.cvut.cz Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic Jiˇ r´ ı Kubal´ ık kubalik@labe.felk.cvut.cz Faculty of Electrical Engineering, Czech Technical University in Prague, Czech Republic Abstract Six population-based methods for real-valued black box optimization are thoroughly compared in this article. One of them, Nelder-Mead simplex search, is rather old, but still a popular technique of direct search. The remaining five (POEMS, G3PCX, Cauchy EDA, BIPOP-CMA-ES, and CMA-ES) are more recent and came from the evolutionary computation community. The recently proposed “comparing continuous optimizers” (COCO) methodology was adopted as the basis for the comparison. The results show that BIPOP-CMA-ES reaches the highest success rates and is often also quite fast. The results of the remaining algorithms are mixed, but Cauchy EDA and POEMS are usually slow. Keywords Benchmarking, real-valued black box optimization, population-based algorithms, esti- mation of distribution algorithm, evolutionary strategy, covariance matrix adaptation. 1 Introduction Population-based optimization algorithms (genetic and evolutionary algorithms, par- ticle swarm optimization, etc.) are often employed to solve optimization problems in the continuous domain. They are derivative-free, thus applicable in the black box sce- nario, and they are said to be less prone to getting stuck in local optima. In this article we have chosen six population-based techniques for a comparison. Despite the fact that they each use different principles in taking advantage of the information hidden in the population, their instances used in this comparison express one common trait: all of them search in the neighborhood of a single point, and can thus be viewed as population-based local optimizers. The population serves in them either as a probe to explore the local neighborhood of the main point, and/or as a source of genetic material from which they construct the neighbors of the main point. The algorithms chosen for the comparison are introduced in the next paragraphs. The iterative prototype optimization with evolved improvement steps, POEMS (Kubal´ ık, 2009a), is a local search (LS) technique hybridized with an evolutionary al- gorithm (EA). Note that it is relatively common to see an LS inside an EA, but POEMS is the opposite—an EA inside an LS. The inner EA is used to evolve a sequence of C  2012 by the Massachusetts Institute of Technology Evolutionary Computation 20(4): 483–508