An evolutionary algorithm based on rank-1 approximation for sparse large-scale multi-objective problems

doi:10.1007/s00500-023-08825-2

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An evolutionary algorithm based on rank-1 approximation for sparse large-scale multi-objective problems

2023-07-03

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DOI：10.1007/s00500-023-08825-2

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Abstract

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Most existing evolutionary algorithms encounter difficulties in dealing with multi-objective problems (MOPs) whose Pareto optimal solutions are sparse, especially when the decision space of the MOP is large. Most existing sparse evolutionary algorithms (EAs) lack the tricks specially for large-scale problems, and the existing tricks need some grouping/variable analysis methods to divide the large-scale variables, which severely affects the effect of optimization. To fill this gap, an evolutionary algorithm based on rank-1 approximation, suitable to reduce the dimensionality of sparse higher-order datasets, is proposed. First, canonical polyadic decomposition is introduced to divide the higher-dimensional set of decision variables into several lower-dimensional sub-sets. These sub-populations are alternatively optimized by a sparse evolution algorithm with special genetic strategies, to search for improved solutions in their respective lower-dimensional decision sub-space. Finally, the whole population is asymptotically optimized by all the sub-populations. The proposed algorithm first introduces the rank-1 approximation into the dimensionality reduction in sparse large-scale variables, combines it with the sparse EA, and proposes efficient alternative optimization strategy to solve the non-convex problem resulted from the multiple sub-problems. It is compared with other state-of-the-art algorithms for large-scale and sparse problems. The experimental results indicate that it outperforms other algorithms in terms of optimization performance and convergence rate.

Keywords:

Evolutionary algorithm

Large-scale multi-objective optimization

Rank-1 approximation

CP decomposition

Sparse Pareto optimal solutions