A surrogate-assisted particle swarm optimization using ensemble learning for expensive problems with small sample datasets

Abstract

Solving the real-world optimization problems often needs a large number of expensive function evaluations (FEs) by using evolutionary algorithms (EAs). To alleviate this difficulty, surrogate-assisted EAs (SAEAs) have attracted more and more attention from academia and industry. However, the existing SAEAs need a large amount of sample points to construct surrogate model within the expected times of FEs, otherwise it cannot achieve satisfactory prediction accuracy. Few SAEAs can reduce the times of expensive FEs while a high-quality surrogate model is constructed using a small number of sample points. In this paper, a novel SAEAs inspired from ensemble learning is proposed. In the proposed algorithm, the small sample date set is divided into multiple subsets, and the surrogate model is trained on each subset. Two new model management strategies based on ensemble learning are applied to global search and local search respectively. Two search methods are cleverly combined to form a high precision surrogate ensemble. In order to verify the performance of the proposed method, we performed comprehensive tests on eight benchmark functions from 10 to 50 dimensions, and compared their result with the five state-of-the-art SAEAs. Experimental results demonstrate that the proposed method shows superior performance in a majority of benchmarks when only a limited computational budget is available. In addition, we apply the proposed algorithm to three real-time optimization problems. The results of each problem are compared with the solutions to verify the effectiveness of the algorithm in solving engineering application problems.