Opposition-Based Learning in Compact Differential Evolution

Abstract

This paper proposes the integration of the generalized opposition based learning into compact Differential Evolution frameworks and tests its impact on the algorithmic performance. Opposition-based learning is a technique which has been applied, in several circumstances, to enhance the performance of Differential Evolution. It consists of the generation of additional points by means of a hyper-rectangle. These opposition points are simply generated by making use of a central symmetry within the hyper-rectangle. In the population based Differential Evolution, the inclusion of this search move corrects a limitation of the original algorithm, i.e. the scarcity of search moves, and sometimes leads to benefits in terms of algorithmic performance. The opposition-based learning scheme is further improved in the generalized scheme by integrating some randomness and progressive narrowing of the search. The proposed study shows how the generalized opposition-based learning can be encoded within a compact Differential Evolution framework and displays its effect on a set of diverse problems. Numerical results show that the generalized opposition-based learning is beneficial for compact Differential Evolution employing the binomial crossover while its implementation is not always successful when the exponential crossover is used. In particular, the opposition-based logic appears to be in general promising for non-separable problems whilst it seems detrimental for separable problems.

This research is supported by the Academy of Finland, Akatemiatutkija 130600, Algorithmic Design Issues in Memetic Computing and Tutkijatohtori 140487, Algorithmic Design and Software Implementation: a Novel Optimization Platform. This research is also supported by Tekes - the Finnish Funding Agency for Technology and Innovation, grant 40214/08 (Dynergia).