Data-Driven Robust Multimodal Multiobjective Particle Swarm Optimization

For the data-driven multimodal multiobjective optimization problems (MMOPs), the inevitable uncertainties will lead to distortion of multiple peak landscapes, thus causing slow convergence in complex landscapes. To solve this problem, a robust multimodal multiobjective particle swarm optimization (RMMPSO) is designed to alleviate slow convergence. There are three novelties in RMMPSO. First, a perturbation observer is proposed to detect perturbation in the fixed point of variance to evaluate the influences of disturbed recording position on convergence. Second, an adaptive adjustment mechanism, based on the perturbation observer, is designed to obtain reasonable search ranges and suppress the abnormal changes in convergence, so as to improve convergence performance. Third, a Lipschitz-based exploitation strategy is designed to search for reliable solutions, which reduces the optimal offset caused by uncertainties. Finally, the effectiveness of RMMPSO is demonstrated in terms of multiobjective multimodal benchmark problems with uncertain components and wastewater treatment simulation platform. The results of experiments demonstrate the superiority of RMMPSO in solving data-driven MMOPs compared to state-of-the-art multimodal multiobjective algorithms.