Dual-State-Driven Evolutionary Optimization for Expensive Optimization Problems with Continuous and Categorical Variables

The surrogate-assisted evolutionary algorithm (SAEA) is one of the most efficient approaches for addressing expensive continuous or combinatorial optimization problems. However, it encounters significant challenges in expensive mixed-variable optimization problems (EMVOPs). To overcome this limitation, a dual-state-driven evolutionary optimization (called DSDEO), integrating a surrogate-assisted mixed-variable evolutionary optimization stage (MVEOS) and a surrogate-assisted continuous-variable evolutionary optimization stage (CVEOS), is proposed in this paper. Specifically, MVEOS employs global and local search to enhance the exploration and exploitation of the mixed-variable space. Global and local searches are alternately executed if one search fails to yield a better solution. CVEOS utilizes a continuous-improvement strategy to refine the continuous variables of the best solution obtained so far. Experimental results demonstrate the advantages of DSDEO compared to some state-of-the-art SAEAs on many benchmark problems.