Two-stage adaptive differential evolution with dynamic dual-populations for multimodal multi-objective optimization with local Pareto solutions

Several distinctive Pareto Sets (PSs) with an identical Pareto Front (PF) and local PSs with acceptable quality are comprised in multimodal multi-objective optimization problems (MMOPs). Recently, many multimodal multi-objective evolutionary algorithms (MMEAs) have been proposed. However, even though most of MMEAs have the ability to discover equivalent global PSs, these methods encounter failures in developing local PSs. The main reasons are that local PSs are dominated by global PSs and are removed from the population during the evolutionary process. To tackle this matter, a two-stage adaptive differential evolution with a dynamic dual-populations strategy, termed TADE_DDS, is developed. In TADE_DDS, a dynamic population strategy is put forward to divide the population into a global population that locates equivalent global PSs and a local population that aims to locate local PSs. Subsequently, the whole procedure is completed by two evolutionary stages associated with a dynamic population strategy, and an adaptive differential evolution algorithm is adopted for both global and local populations. The first-stage evolution aims to find more favorable local PSs and the second-stage evolution concentrates on finding a variety of global PSs. Additionally, a local environmental selection and a global environmental selection are performed for developing the diversity of local PSs and improving the convergence of global PSs and local PSs, respectively. TADE_DDS and several popular MMEAs are implemented on standard test problems. Experimental results demonstrate that TADE_DDS is equipped to locate both global and local PSs, and is superior to its competing algorithms.