An Adapting Quantum Field Surrogate for Evolution Strategies

Black-box optimization largely suffers from the absence of analytical objective forms. Thus, no derivatives or other structure information can be harnessed for guiding optimization algorithms. But, even with analytic form, high-dimensionality and multi-modality often hinder the search for a global optimum. Heuristics based on populations or evolution strategies are a proven and effective means to, at least partly, overcome these problems. Evolution strategies have thus been successfully applied to optimization problems with rugged, multi-modal fitness landscapes from numerous applications, to nonlinear problems, and to derivative free optimization. One obstacle in heuristics in general is the occurrence of premature convergence, meaning a solution population converges too early and gets stuck in a local optimum. In this paper, we present an approach that harnesses the adapting quantum potential field determined by the spatial distribution of elitist solutions as guidance for the next generation. The potential field evolves to a smoother surface leveling local optima but keeping the global structure what in turn allows for a faster convergence of the solution set. On the other hand, the likelihood of premature convergence decreases. We demonstrate the applicability and the competitiveness of our approach compared with particle swarm optimization and the well-established evolution strategy CMA-ES.