Heuristics to avoid redundant solutions on population-based multimodal continuous optimization

In population-based meta-heuristics, the generation and maintenance of diversity seem to be crucial to deal with multimodal continuous optimization. However, usually this crucial aspect is not an inherent feature of generally adopted meta-heuristics. In this paper, we propose to associate diversity maintenance with the detection and elimination of redundant candidate solutions in the search space, more specifically candidate solutions located at the same attraction basin of a local optimum. Two low computational cost heuristics are proposed to detect redundancy, in a pairwise comparison of candidate solutions and by extracting local features of the fitness landscape at runtime. Those heuristics are not tied to a specific class of algorithms, and are thus able to be incorporated into a broad range of population-based meta-heuristics, and even into multiple executions of non-population-based algorithms. In a set of experimental results, the two heuristics were implemented as an attached module of an already existing multipopulation meta heuristics, and the results indicate that they operate properly, no matter the number and conformation of the attraction basins in multimodal optimization problems.