Clustering-based Transfer Learning for Dynamic Multimodal MultiObjective Evolutionary Algorithm

TL;DR

The paper tackles the challenge of dynamic multimodal multiobjective optimization by introducing the DMMF benchmark and the CAE-AN algorithm. CAE-AN couples a clustering-based CAE predictor with an adaptive-niching NSGA-II to simultaneously track multiple evolving POSs and maintain diversity in the decision space. Across 12 DMMF instances, CAE-AN demonstrates superior convergence in objective space and more diverse, well-distributed POS sets in decision space, validated by MIGD and MIGDx metrics and ablation studies. The work also includes a real-world transportation planning case, illustrating practical benefits in dynamic multimodal scenarios.

Abstract

Dynamic multimodal multiobjective optimization presents the dual challenge of simultaneously tracking multiple equivalent pareto optimal sets and maintaining population diversity in time-varying environments. However, existing dynamic multiobjective evolutionary algorithms often neglect solution modality, whereas static multimodal multiobjective evolutionary algorithms lack adaptability to dynamic changes. To address above challenge, this paper makes two primary contributions. First, we introduce a new benchmark suite of dynamic multimodal multiobjective test functions constructed by fusing the properties of both dynamic and multimodal optimization to establish a rigorous evaluation platform. Second, we propose a novel algorithm centered on a Clustering-based Autoencoder prediction dynamic response mechanism, which utilizes an autoencoder model to process matched clusters to generate a highly diverse initial population. Furthermore, to balance the algorithm's convergence and diversity, we integrate an adaptive niching strategy into the static optimizer. Empirical analysis on 12 instances of dynamic multimodal multiobjective test functions reveals that, compared with several state-of-the-art dynamic multiobjective evolutionary algorithms and multimodal multiobjective evolutionary algorithms, our algorithm not only preserves population diversity more effectively in the decision space but also achieves superior convergence in the objective space.

Figures (6)

• Figure 1: Illustration of the dynamic multimodal multiobjective urban traffic problem
• Figure 2: An example of DMMF. (a) Illustration of the dynamic POF in the objective space. (b) Illustration of the dynamic POS in the decision space.
• Figure 3: Visualization of the dynamic multi-modal multi-objective test function types: (a) Type I structure; (b) Type II structure; (c) Type III structure.
• Figure 4: Flowchart of CAE Strategy using DBSCAN Clustering and AE Prediction.
• Figure 5: IGD Results of Different Algorithms on the DMMF1–DMMF12 Test Functions