Multimodal Optimization by Means of a Topological Species Conservation Algorithm

Any evolutionary technique for multimodal optimization must answer two crucial questions in order to guarantee some success on a given task: How to most unboundedly distinguish between the different attraction basins and how to most accurately safeguard the consequently discovered solutions. This paper thus aims to present a novel technique that integrates the conservation of the best successive local individuals (as in the species conserving genetic algorithm) with a topological subpopulations separation (as in the multinational genetic algorithm) instead of the common but problematic radius-triggered manner. A special treatment for offspring integration, a more rigorous control on the allowed number and uniqueness of the resulting seeds, and a more efficient fitness evaluations budget management further augment a previously suggested naïve combination of the two algorithms. Experiments have been performed on a series of benchmark test functions, including a problem from engineering design. Comparison is primarily conducted to show the significant performance difference to the naïve combination; also the related radius-dependent conserving algorithm is subsequently addressed. Additionally, three more multimodal evolutionary methods, being either conceptually close, competitive as radius-based strategies, or recent state-of-the-art are also taken into account. We detect a clear advantage of three of the six algorithms that, in the case of our method, probably comes from the proper topological separation into subpopulations according to the existing attraction basins, independent of their locations in the function landscape. Additionally, an investigation of the parameter independence of the method as compared to the radius-compelled algorithms is systematically accomplished.