Interval Multimodal Particle Swarm Optimization Algorithm Assisted by Heterogeneous Ensemble Surrogate

Many real-world black-box optimization problems can be classified as multimodal optimization problems (MMOPs) with high computational cost, that is, expensive multimodal optimization problems (EMMOPs). When dealing with such problems, decision-makers hope to find multiple high-quality solutions with less computational cost (i.e., the least number of real function evaluations). However, existing surrogate-assisted evolutionary algorithms (SAEAs) seldom consider the multimodal properties of problem, and they can only obtain one optimal solution of the problem at a time. In view of this, this paper studies an interval multimodal particle swarm optimization (PSO) algorithm assisted by heterogeneous ensemble surrogate (IMPSO-HES). Firstly, a model pool composed of multiple basic surrogate models is constructed with the idea of heterogeneous ensemble. Then, according to the matching relationship between the particle to be evaluated and the discovered modalities, some basic surrogate models will be selected from the model pool for integration, and the integrated surrogate model is utilized to predict the fitness value of the particle. Furthermore, in order to save the cost of model management, an incremental surrogate model management strategy is designed. In order to reduce the influence of prediction error of surrogate model on the algorithmś performance, the interval ordering relation is introduced into the evolutionary process for the first time. The proposed algorithm is compared with five SAEAs and seven state-of-the-art multimodal algorithms, experimental results on 20 benchmark functions and the building energy conservation problem show that the proposed algorithm can obtain multiple highly-competitive optimal solutions at a low computational cost. © 2024 Science Press. All rights reserved.