A surrogate-assisted memetic algorithm for permutation-based combinatorial optimization problems

Abstract

Real-world applications often encounter expensive permutation-based combinatorial optimization problems (PCOPs), where solution evaluation processes become time-consuming. Although many surrogate-assisted evolutionary algorithms have been developed for expensive optimization problems, most of them are designed for expensive continuous optimization problems, not for expensive PCOPs, due to the difficulty of constructing surrogate models effective for permutation spaces. This paper presents a surrogate-assisted memetic algorithm for expensive PCOPs, designed with the following two key insights. First, Gradient Boosting Decision Tree (GBDT) regression models are adopted as surrogates tailored to discrete spaces. Because decision trees do not require distance metrics between training samples, they are well-suited to such spaces, and the boosting mechanism helps improve prediction accuracy. Additionally, we employ memetic algorithms for the search strategy to enhance both global and local search capabilities. Experiments show that the proposed method outperforms state-of-the-art algorithms for at least 41 out of all 42 PCOP instances under a limited budget of 1000 function evaluations, with improved robustness through our memetic algorithm. Furthermore, the GBDT model achieves higher prediction accuracy than other popular models, Radial Basis Function Network and Random Forest, outperforming them on more than 35 instances. These results highlight that our approach effectively enhances the synergy between surrogate models and search strategies in permutation spaces.