Surrogate-assisted multi-objective covariance matrix adaptation evolution strategies

초록

Although the Covariance Matrix Adaptation Evolution Strategy (CMA-ES) is one of the most preferred evolutionary algorithms for single-objective black-box optimization, its performance is limited in the multi-objective space due to its reliance solely on Gaussian-based mutation without any crossover for offspring generation. To address this limitation, this work proposes a surrogate-assisted multi-objective CMA-ES algorithm with an ensemble of offspring generation schemes. In the proposed algorithm, trial solutions are generated from an ensemble of the standard CMA-ES operator and a Genetic Algorithm-inspired operator. Consequently, the solutions are evaluated on a Gaussian Process-based surrogate model, and the solution with the best Expected Improvement (EI) is selected as the generated offspring. Experiments on the Walking Fish Group (WFG) test suite and 18 benchmark multi-objective Neural Architecture Search (NAS) problems demonstrate that the proposed approach is statistically superior to existing multi-objective CMA-ES variants and other state-of-the-art non-CMA-ES multi-objective algorithms. Specifically, the proposed algorithm achieves a win rate of 79.63% and 77.8% on the WFG and NAS test suites, respectively, against other CMA-ES variants, and demonstrates a 68.8% win rate against state-of-the-art algorithms on the NAS test suite.

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