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A novel reference solution selection strategy based on auxiliary space for large-scale multi-objective optimization
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AI
DOI：10.1016/j.ins.2026.123101.png)
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Abstract
En 中文
Problem-transformation-based methods have been acknowledged as effective approaches for addressing Large-Scale Multi-objective Optimization Problems (LSMOPs), as they enable the conversion of the original high-dimensional search space into a relatively low-dimensional one. Nevertheless, such methods often exhibit an extremely rapid convergence rate, which is concomitantly accompanied by a significant loss of diversity. Within this context, the selection of reference solutions-upon which the problem transformation is constructed-plays a pivotal role in influencing population diversity. To address these limitations, this paper proposes a novel Reference Solution Selection strategy based on Auxiliary Spaces (RSAS) designed to preserve population diversity. Specifically, orthogonal bases are constructed utilizing extreme feasible solutions positioned on the coordinate axes, with each basis spanning a distinct subspace. The ensemble of subspaces generated by multiple such orthogonal bases is defined as auxiliary spaces. These auxiliary spaces, characterized by their relatively uniform distribution throughout the original decision space, facilitate the algorithm in generating a reference solution set with substantially enhanced diversity. Notably, RSAS can be seamlessly integrated into any problem-transformation-based framework that incorporates a reference selection mechanism, thereby improving their overall performance. To demonstrate the efficacy of RSAS, comprehensive experimental investigations are conducted on benchmark suites with dimensions ranging from 500 to 5000. The experimental results conclusively validate the superiority of RSAS in comparison to other state-of-the-art algorithms on most instances.
Keywords:
Multi-objective optimization
Large-scale optimization
Problem transformation
Auxiliary space construction
Evolutionary algorithm
Journal
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6.8
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540
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