Achieving highly scalable evolutionary real-valued optimization by exploiting partial evaluations

It is known that to achieve efficient scalability of an Evolutionary Algorithm (EA), dependencies (also known as linkage) must be properly taken into account during variation. In a Gray-Box Optimization (GBO) setting, exploiting prior knowledge regarding these dependencies can greatly benefit optimization. We specifically consider the setting where partial evaluations are possible, meaning that the partial modification of a solution can be efficiently evaluated. Such problems are potentially very difficult, for example, non-separable, multimodal, and multiobjective. The Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) can effectively exploit partial evaluations, leading to a substantial improvement in performance and scalability. GOMEA was recently shown to be extendable to real-valued optimization through a combination with the real-valued estimation of distribution algorithm AMaLGaM. In this article, we definitively introduce the Real-Valued GOMEA (RV-GOMEA), and introduce a new variant, constructed by combining GOMEA with what is arguably the best-known real-valued EA, the Covariance Matrix Adaptation Evolution Strategies (CMA-ES). Both variants of GOMEA are compared to L-BFGS and the Limited Memory CMA-ES (LM-CMA-ES). We show that both variants of RV-GOMEA achieve excellent performance and scalability in a GBO setting, which can be orders of magnitude better than that of EAs unable to efficiently exploit the GBO setting.