Abstract
Optimization problems can be found in many areas of science and technology. Often, not only the global optimum, but also a (larger) number of near-optima are of interest. This gives rise to so-called multimodal optimization problems. In most of the cases, the number and quality of the optima is unknown and assumptions on the objective functions cannot be made. In this paper, we focus on continuous, unconstrained optimization in moderately high dimensional continuous spaces (<=10). We present a scalable algorithm with virtually no parameters, which performs well for general objective functions (non-convex, discontinuous). It is based on two well-established algorithms (CMA-ES, deterministic crowding). Novel elements of the algorithm are the detection of seed points for local searches and collision avoidance, both based on nearest neighbors, and a strategy for semi-sequential optimization to realize scalability. The performance of the proposed algorithm is numerically evaluated on the CEC2013 niching benchmark suite for 1-20 dimensional functions and a 9 dimensional real-world problem from constraint optimization in climate research. The algorithm shows good performance on the CEC2013 benchmarks and falls only short on higher dimensional and strongly inisotropic problems. In case of the climate related problem, the algorithm is able to find a high number (150) of optima, which are of relevance to climate research. The proposed algorithm does not require special configuration for the optimization problems considered in this paper, i.e. it shows good black-box behavior.
Implicitly and densely discrete black-box optimization problems
