Clustering-based Transfer Learning for Dynamic Multimodal MultiObjective Evolutionary Algorithm
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.
Summary
This paper addresses the challenge of Dynamic Multimodal Multiobjective Optimization (DMMOP), where algorithms must simultaneously track multiple Pareto optimal sets (POSs) and maintain population diversity in time-varying environments. The authors argue that existing Dynamic Multiobjective Evolutionary Algorithms (DMOEAs) often overlook solution modality, while static Multimodal Multiobjective Evolutionary Algorithms (MMOEAs) lack adaptability to dynamic changes. To tackle this, the paper makes two main contributions: (1) a new benchmark suite of DMMOP test functions (DMMFs) designed by fusing dynamic and multimodal properties, and (2) a novel algorithm called Clustering-based Autoencoder and adaptive niching (CAE-AN). CAE-AN uses a Clustering-based Autoencoder prediction dynamic response mechanism to generate a diverse initial population and integrates an adaptive niching strategy into the static optimizer to balance convergence and diversity. The CAE-AN algorithm leverages DBSCAN to cluster historical solutions and then employs an Autoencoder (AE) to predict the new positions of the solution clusters. These predicted solutions are then used to seed the new population for rapid adaptation to environmental changes. Furthermore, the algorithm incorporates an adaptive niching technique to enhance diversity maintenance during the optimization process. The paper demonstrates through empirical analysis on 12 instances of the proposed DMMF test functions that CAE-AN outperforms several state-of-the-art DMOEAs and MMOEAs in preserving population diversity in the decision space and achieving superior convergence in the objective space. This work matters because it provides both a standardized benchmark for evaluating DMMOP algorithms and a novel algorithmic approach that effectively addresses the challenges of dynamism and multimodality in multiobjective optimization.
Key Insights
- •Novel Benchmark Suite (DMMF): The paper introduces a new suite of 12 dynamic multimodal multiobjective test functions (DMMFs), filling a gap in the literature. These functions are designed with varying degrees of dynamism in both the Pareto Optimal Front (POF) and Pareto Optimal Set (POS), offering a more comprehensive evaluation platform.
- •Clustering-based Autoencoder (CAE) for Prediction: The core innovation lies in the CAE strategy, which uses DBSCAN to cluster historical solutions and then trains an Autoencoder (AE) on each cluster to predict its future position. This allows for independent prediction of multiple, potentially diverse, POSs, addressing the limitations of existing prediction-based DMOEAs.
- •Adaptive Niching Strategy: The algorithm integrates an adaptive niching strategy into the NSGA-II static optimizer, dynamically adjusting the niche radius based on the iteration process and individual density within the niche. This enhances diversity maintenance throughout the optimization. The niche radius is adjusted according to the equation R_i(g) = R_0 * (1 - alpha * g/G_max) * (1 + alpha * Var_i).
- •Decomposition Approach: The algorithm effectively decomposes the problem by clustering solutions and applying independent prediction models to each cluster. This "divide and conquer" approach allows for more targeted adaptation to the heterogeneous dynamics within DMMOPs.
- •Computational Efficiency: While the paper doesn't provide specific runtime comparisons, the use of a linear mapping model (equation 7) for each POS instead of a complex nonlinear AE is likely to contribute to the computational efficiency of the algorithm.
- •Limitations: The paper focuses on the algorithm's performance on the proposed DMMF test suite. Further validation on real-world DMMOPs is needed to assess its practical applicability. The performance depends on the DBSCAN parameters epsilon and eta, which might require tuning for different problems.
Practical Implications
- •Real-world Applications: The research has potential applications in areas like urban traffic and road optimization, resource allocation, and dynamic priority scheduling, where problems often exhibit dynamic and multimodal characteristics.
- •Beneficiaries: Researchers and engineers working on dynamic optimization, evolutionary algorithms, and multiobjective optimization can benefit from the proposed DMMF benchmark suite and the CAE-AN algorithm.
- •Practitioner Usage: Practitioners can use the proposed CAE-AN algorithm as a starting point for solving DMMOPs in their respective domains. The DMMF benchmark suite can be used to compare and evaluate different algorithmic approaches.
- •Future Research Directions: The paper opens up several avenues for future research, including: (1) extending the CAE-AN algorithm to handle large-scale DMMOPs, (2) investigating the use of more sophisticated clustering techniques, and (3) exploring the application of CAE-AN to real-world DMMOPs.