A dynamic multi-objective evolutionary algorithm using dual-space prediction and surrogate-based sampling

Abstract The main challenge in handling dynamic multi-objective optimization problems lies in the need for algorithms to accurately track Pareto-optimal solutions in constantly changing environments. Most existing predictionbased dynamic multi-objective evolutionary algorithms (DMOEAs) conduct prediction either in the decision space or the objective space alone, or apply the same prediction model to both spaces. However, such approaches may fail to fully capture the distinct change patterns of each space, especially under nonlinear and complex environmental dynamics, thereby limiting the effectiveness of these algorithms. Furthermore, when sampling methods are used to help the algorithm generate populations in new environments, a large number of sampled individuals can impose a significant computational burden due to the increased number of function evaluations. To address these limitations, this paper proposes a dynamic multi-objective evolutionary algorithm, namely DS-DMOEA, which efficiently adapts to environmental changes through a dual-space prediction strategy and a surrogate-based sampling strategy. The dual-space prediction strategy captures dynamic changes by employing a weight vector-based method in the objective space and a geodesic flow kernel method in the decision space. Simultaneously, the surrogate-based sampling strategy generates a high-quality sampling population by training surrogate models with information from similar historical environments. The predicted and sampled populations are then combined to form an initial population well-suited for the new environment. DS-DMOEA has been tested against nine state-of-the-art DMOEAs on 19 benchmark problems with three types of environmental change patterns. The experimental results validate the effectiveness of the proposed algorithm.