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Surrogate-assisted evolutionary algorithms have been widely developed tosolve complex and computationally expensive multi-objective optimizationproblems in recent years. However, when dealing with high-dimensionaloptimization problems, the performance of these surrogate-assistedmulti-objective evolutionary algorithms deteriorate drastically. In this work,a novel Classifier-assisted rank-based learning and Local Model basedmulti-objective Evolutionary Algorithm (CLMEA) is proposed for high-dimensionalexpensive multi-objective optimization problems. The proposed algorithmconsists of three parts: classifier-assisted rank-based learning,hypervolume-based non-dominated search, and local search in the relativelysparse objective space. Specifically, a probabilistic neural network is builtas classifier to divide the offspring into a number of ranks. The offspring indifferent ranks uses rank-based learning strategy to generate more promisingand informative candidates for real function evaluations. Then, radial basisfunction networks are built as surrogates to approximate the objectivefunctions. After searching non-dominated solutions assisted by the surrogatemodel, the candidates with higher hypervolume improvement are selected for realevaluations. Subsequently, in order to maintain the diversity of solutions, themost uncertain sample point from the non-dominated solutions measured by thecrowding distance is selected as the guided parent to further infill in theuncertain region of the front. The experimental results of benchmark problemsand a real-world application on geothermal reservoir heat extractionoptimization demonstrate that the proposed algorithm shows superior performancecompared with the state-of-the-art surrogate-assisted multi-objectiveevolutionary algorithms. The source code for this work is available athttps://github.com/JellyChen7/CLMEA.

Rank-Based Learning and Local Model Based Evolutionary Algorithm for High-Dimensional Expensive Multi-Objective Problems