A simple strategy for maintaining diversity and reducing crowding in differential evolution

Differential evolution (DE) is a widely-effective population-based continuous optimiser that requires convergence to automatically scale its moves. However, once its population has begun to converge its ability to conduct global search is diminished, as the difference vectors used to generate new solutions are derived from the current population members´ positions. In multi-modal search spaces DE may converge too rapidly, i.e., before adequately exploring the search space to identify the best region(s) in which to conduct its finer-grained search. Traditional crowding or niching techniques can be computationally costly or fail to compare new solutions with the most appropriate existing population member. This paper proposes a simple intervention strategy that compares each new solution with the population member it is most likely to be near, and prevents those moves that are below a threshold that decreases over the algorithm´s run, allowing the algorithm to ultimately converge. Comparisons with a standard DE algorithm on a number of multi-modal problems indicate that the proposed technique can achieve real and sizable improvements.