Large scale optimization by differential evolution with landscape modality detection and a diversity archive

In this study, the performance of Differential Evolution with landscape modality detection and a diversity archive (LMDEa) is reported on the set of benchmark functions provided for the CEC2012 Special Session on Large Scale Global Optimization. In Differential Evolution (DE), large population size, which is much larger than the number of decision variables in problem to be solved, is adopted in order to keep the diversity of search. However, it is difficult to adopt such large size to solve large scaled optimization problems because the population size will become too large and the search efficiency will degrade. In this study, we propose to solve large scale optimization problems using small population size and a large archive for diversity. Also, we propose simple control of scaling factor by observing landscape modality of search points in order to keep diversity. The landscape of a problem to be optimized is often unknown and the landscape is changing dynamically while the search process proceeds. In LMDEa, some points on a line connecting the centroid of search points and a search point are sampled. When the objective values of the sampled points are changed decreasingly and then increasingly, it is thought that one valley exists. If there exists only one valley, the landscape is unimodal and small scaling factor is adopted. Otherwise, large scaling factor is adopted. Also, the sampled points realize global search in the region spanned by all search points and realize local search near the best search point. The effect of the proposed method is shown by solving the benchmark functions.