Adaptive multi-region prediction strategy for dynamic multi-objective optimization

This paper proposes a novel adaptive multi-region prediction strategy for dynamic multi-objective optimization problems (DMOPs), which aims to efficiently generate diverse populations in response to environmental changes and facilitate the exploration of the new Pareto front. The strategy consists of two main phases: predictive population initialization and elite-guided resampling. In the predictive population initialization phase, the strategy integrates global exploration and local exploitation. Global exploration divides the population into $N$ subregions based on population distribution characteristics. For each subregion, the historical information of its center point is used to predict its new position in the next environment, and then a Gaussian mixture model (GMM) is used to sample new individuals based on the position information of all new center points. Local exploitation employs the K-Medoids method to cluster historical Pareto fronts and selects individuals corresponding to the medoids in the decision space as representative individuals. These representative individuals are then used to predict their new locations, followed by Gaussian sampling to generate individuals. The initial predicted population is formed by combining the individuals from global exploration, local exploitation, and randomly generated individuals. In the elite-guided resampling phase, the initial predicted population is evaluated, and top-ranked elite individuals are selected. These elites guide the generation of the final population through Gaussian sampling and Latin Hypercube Sampling (LHS), enhancing solution quality and diversity. The proposed strategy is validated on 14 benchmark problems using MIGD, MHV, R(IGD), and DMIGD metrics. Results demonstrate its better comprehensive performance under varying environmental change intensities (mild, moderate, and severe) compared to existing approaches. Furthermore, its application to a real-world PID controller tuning problem highlights the strategy’s practical potential, showcasing superior performance.