A novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization (DPb-MOPSO) algorithm

Distributed architecture-based Particle Swarm Optimization is very useful for static optimization and not yet explored to solve complex dynamic multi-objective optimization problems. This study proposes a novel Dynamic Pareto bi-level Multi-Objective Particle Swarm Optimization (DPb-MOPSO) algorithm with two optimization levels. In the first level, all solutions are optimized in the same search space and the second level is based on a distributed architecture using the Pareto ranking operator for dynamic multi-swarm subdivision. The proposed approach adopts a dynamic handling strategy using a set of detectors to keep track of change in the objective function that is impacted by the problem’s time-varying parameters at each level. To ensure timely adaptation during the optimization process, a dynamic response strategy is considered for the reevaluation of all non-improved solutions, while the worst particles are replaced with a newly generated one. The convergence anddiversity performance of the DPb-MOPSO algorithm are proven through Friedman Analysis of Variance, and the Lyapunov theorem is used to prove stability analysis over the Inverted Generational Distance (IGD) and Hypervolume Difference (HVD) metrics. Compared to other evolutionary algorithms, the novel DPb-MOPSO is shown to be most robust for solving complex problems over a range of changes in both the Pareto Optimal Set and Pareto Optimal Front.