Cooperative Differential Evolution With an Attention-Based Prediction Strategy for Dynamic Multiobjective Optimization

In dynamic multiobjective optimization, the Pareto front (PF) or Pareto set varies over time as the problem environment changes. In such scenarios, optimization algorithms are required to efficiently find and continuously track a set of Pareto-optimal and diverse solutions. However, existing algorithms often result in the imbalanced approximation of PFs since some objectives are usually harder to optimize than others. In addition, the prediction strategies of the existing algorithms usually entail additional parameters (e.g., reference points, weights, and clustering parameters) to match available Pareto-optimal solutions for prediction in dynamically changing environments. This article presents a cooperative differential evolution algorithm with an attention-based prediction strategy. Multiple populations are adopted to optimize multiple objectives in search of subparts of PFs. Every population adopts a new fusion-based mutation strategy for coevolution. In addition, an expanding procedure is proposed on archived solutions to further expand the objective space covered by the populations to the entire PF. Specifically, once an environment change is detected, the populations are updated by using a new attention-based prediction strategy according to the historical variation of the objective functions. In this way, every population is adapted to the change of its attentive objective in the dynamic environment. Experimental results on a recent test suite of scalable dynamic multiobjective optimization problems are elaborated to demonstrate the superiority of the proposed method to state-of-the-art algorithms.