BMPGA: a bi-objective multi-population genetic algorithm for multi-modal function optimization

This paper introduces two innovations into the world of multi-modal function optimization: a new multi-population genetic algorithm (GA), with two complementary fitness terms (called BMPGA); and a new similarity function that is used to decide whether two points belong to the same cluster or not, called recursive middling (RM). An empirical comparative study is carried out to provide evidence that RM is a better measure of similarity than Ursem's hill-valley (or HV) function. Another comparative study compares the performance of BMGA with our own single-fitness-term multi-population GA (SMPGA), and with Ursem's multinational GA (MGA). The results show the clear superiority of RM and BMPGA over HV and MGA, respectively. The results also point to the potential of introducing a new aspect to the field of multi-modal optimization, where various complementary (as opposed to competitive) objectives are used to maintain diversity, so the GA can find all the optima of a given fitness surface