A Surrogate-Assisted Differential Evolution with Knowledge Transfer for Expensive Incremental Optimization Problems

In some real-world applications, the optimization problems may involve multiple design stages. At each design stage, the objective is incrementally modified by incorporating more decision variables and optimized. In addition, the fitness evaluations (FEs) are often highly costly. Such optimization problems can be called expensive incremental optimization problems (EIOPs). Despite their importance, EIOPs have not attracted much attention over the past few years. Since the objectives of different design stages are different but related, reusing the search experience from the past design stages is beneficial to the evolutionary search of the current design stage. Therefore, a surrogate-assisted differential evolution with knowledge transfer (SADE-KT) is proposed in this work, which aims to fill the current gap in solving EIOPs. The major merit of the proposed SADE-KT is its ability to seamlessly integrate knowledge transfer and the surrogate-assisted evolutionary search. In SADE-KT, a surrogate based hybrid knowledge transfer strategy is first proposed. This strategy makes it possible to reuse the knowledge captured from the past design stages by leveraging different knowledge transfer techniques. As a result, the convergence for the current design stage can be speeded up. Then, a two-level surrogate-assisted evolutionary search is developed to search for the optimum. Comprehensive empirical studies have demonstrated that the proposed algorithm works efficiently on EIOPs.