Research On Surrogate-assisted Particle Swarm Optimization Algorithm For Expensive Multimodal Problems

Many real-world black-box optimization problems can be classified as multimodal optimization problems with high computational cost,that is,expensive multimodal optimization problems(EMMOPs).When dealing with such problems,decision-makers hope to find multiple high-quality optimal solutions or alternatives with as less computational cost as possible.However,existing surrogate-assisted evolutionary algorithms(SAEAs)for solving expensive optimization problems seldom consider the multimodal properties of the problem,so they can only obtain one optimal solution of the problem at a time.Aiming at challenging issues such as the matching problem of the size of surrogate models and the number of modalities,the balancing problem of the accuracy of surrogate models and the individual evaluation cost,and the selecting problem of surrogate models,when dealing with unconstrained,constrained and high-dimensional EMMOPs,this thesis studies a variety of surrogate-assisted particle swarm optimization(PSO)algorithms.A dual-surrogate assisted cooperative PSO algorithm is proposed to address the challenge of difficulty in matching the size of surrogate models with the number of modalities.A dual-population cooperative PSO mechanism is developed to simultaneously explore/exploit multiple modalities.Following that,a modal-guided dual-layer cooperative surrogate model,which contains one upper global surrogate model and a group of lower local surrogate models,is constructed with the purpose of reducing the individual evaluation cost.At the same time,a hybrid strategy based on clustering and peak-valley is proposed to help the algorithm continuously discover new modalities with less computational cost.The proposed algorithm is compared with five state-of-the-art SAEAs and seven classical multimodal evolutionary algorithms,and experimental results on benchmark functions show that the proposed algorithm can simultaneously obtain multiple highly competitive optimal solutions at a low computational cost.Aiming at the balancing problem of the accuracy of surrogate models and the individual evaluation cost,a heterogeneous ensemble surrogate-assisted interval multimodal PSO algorithm is proposed.A model pool composed of multiple basic surrogate models is constructed with the idea of heterogeneous ensemble.According to the matching relationship between the particle to be evaluated and the discovered modalities,the 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 particles.Furthermore,to save the cost of model management,an incremental surrogate model management strategy is designed.In order to reduce the influence of model prediction error on algorithm’s performance,the interval ordering relation is introduced into the evolutionary process of population for the first time.Compared with five state-of-the-art SAEAs and seven classical multimodal evolutionary algorithms,experimental results on benchmark functions show the effectiveness of the proposed algorithm.A multi-surrogate assisted multitasking niche PSO algorithm is proposed to address the selecting problem of surrogate models.Several different types of surrogate models fitting the same expensive optimization problem are combined into a multitasking optimization problem,and a multitasking niche PSO algorithm is designed to solve it.A surrogate model management strategy with technical factor and clustering technique is proposed to effectively balance the real function evaluation times and the accuracy of surrogate model.An adaptive surrogate-based trust region local search strategy is designed to enhance the exploitation capability of potential modalities.Compared with five state-of-the-art SAEAs and seven classical multimodal evolutionary algorithms on benchmark functions,experimental results show that the proposed algorithm can obtain multiple highly competitive optimal solutions.Aiming at the cooperative management problem between objective and constraint surrogate models,an objective-constraint mutual-guided surrogate-assisted PSO algorithm is proposed.A two-layer cooperative surrogate model framework based on heterogeneous database is designed to effectively adjust the prediction accuracies of objective and constraint surrogates on different search regions.In order to minimize the number of unnecessary real evaluations,an objective-constraint mutual-guided partial evaluation strategy is developed to generate high-quality infilling samples.A position feature-guided hybrid update mechanism is proposed to find more optimal solutions by searching excellent infeasible and feasible regions simultaneously.A feasible ratio-driven local search strategy is proposed to improve the algorithm’s exploitation.Compared with four state-of-the-art SAEAs and one constraint multimodal evolutionary algorithms on benchmark functions and engineering instances,experimental results show that the proposed algorithm can simultaneously obtain multiple highly-competitive feasible optimal solutions with less computational cost.A multitasking PSO algorithm assisted by surrogate model and autoencoder is proposed to address the problem of ―curse of dimensionality‖ faced by SAEAs when dealing with high-dimensional EMMOPs.On the basis of reducing the dimension of search space by using the autoencoder,the high-dimensional multimodal optimization problem is transformed into several low-dimensional unimodal optimization problems,and a multitasking evolutionary framework embedded with autoencoder is established.The local surrogate model of each modality is rapidly generated by using mirror learning,and a multi-level surrogate model management mechanism combining mirror learning is proposed.In addition,a dual-strategy local exploitation strategy assisted by the surrogate model is proposed to improve the exploitation capability of the swarm for each optimization task.The proposed algorithm is compared with six state-of-the-art SAEAs,and experimental results demonstrate its effectiveness.Furthermore,some of the above achievements are applied to the building energy conservation design problem and the aerodynamic optimization design problem of aeroengine.The mathematical models of the two kinds of problems are established,and their operational optimization frameworks also are given.Experimental results on the two real problmes show that the proposed algorithms can obtain multiple optimal solutions including the global optimal solution with less computational cost.The above research results make up the research vacancy of EMMOPs and improve the performance of evolutionary algorithms,which have important theoretical significance and practical value.The thesis has 54 figures,83 tables,and 182 references.