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A manifold embedding-based evolutionary algorithm for many-objective optimization with irregular Pareto front shapes
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AI
DOI：10.1016/j.ins.2025.122793.png)
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Abstract
En 中文
Many-objective evolutionary algorithms (MaOEAs) have shown great potential for many-objective optimization problems (MaOPs). However, most existing MaOEAs struggle with problems characterized by irregular Pareto fronts (PFs), primarily due to limitations in diversity preservation. To address this challenge, this paper proposes a manifold embedding-based evolutionary algorithm tailored for MaOPs with irregular PFs. The proposed algorithm introduces a customized environmental selection mechanism using an angle-based manifold embedding approach to enhance diversity maintenance. First, hierarchical clustering is applied in a lower-dimensional embedded space to support the environmental selection process, promoting better diversity preservation. Next, a diversity quality indicator, defined in the latent manifold space, is developed to more accurately capture distances between solutions based on the intrinsic structure of the PF. Furthermore, a parameter-free comprehensive quality indicator, integrating both diversity and convergence, is introduced to guide selection within each cluster. To further improve performance, an external archive is employed to retain high-quality solutions throughout the evolutionary process. Comparative studies on 20 widely used test problems with complex and irregular PFs demonstrate that the proposed algorithm consistently outperforms state-of-the-art methods.
Keywords:
Evolutionary algorithm
Many-objective optimization
Irregular Pareto front
Diversity maintenance
Manifold embedding