Application Of SVM Algorithm In Expensive Multi-objective Optimization Problems

Expensive multi-objective optimization refers to a type of optimization problem that requires simultaneous optimization of multiple conflicting goals,and target evaluation requires timeconsuming computer simulations or expensive financial cost physical experiments.Using machine learning to establish a proxy model auxiliary algorithm to evaluate candidate solutions is an effective means to solve such problems,this thesis focuses on the SVM classification method for the proxy target design problem in the proxy model auxiliary evolution algorithm,and performs expensive multi-objective optimization Pareto dominant prediction to achieve the purpose of reducing the computational cost of solving expensive optimization problems.The main research contents of the thesis are as follows:(1)Aiming at the cost of the agent target design and modeling of the agent target of the highprecision adaptability function,the Pareto dominant prediction method based on multi-class SVM is proposed.According to the pareto dominance discriminant definition,any two samples are regarded as the two attributes of pareto dominant discriminant,and an SVM classifier is established to directly predict the pareto dominance relationship between samples,and combined with the multi-model co-decision-making method,the candidate solution for expensive evaluation is quickly found,providing accurate information for decision space exploration and model update.By designing the interaction method with MOEAs,an expensive multi-objective optimization solution method based on multi-class SVMs(MOEAs-SVM/MC)is proposed.Experimental simulation results show that the MOEA-SVM/MC algorithm is still excellent in search ability and convergence speed,which is enough to obtain a more ideal Pareto approximation solution.(2)Aiming at the problem that the sample size increases sharply and the sample dimension increases in the multi-class SVM-Pareto dominant prediction method,which makes it more difficult to manage the model in the evolutionary iterative process,the Pareto dominant prediction method based on the single classification SVM is proposed.The decision space where the known sample distribution is located is regarded as a positive space,and the unknown space is regarded as a negative space,and then a single-class SVM classifier is constructed to prejudge the pareto dominance of the candidate solution and the known sample in combination with the reference point distance method,so as to realize the effective exploration of the unknown decision space in the evolutionary process.The candidate solution selection evaluation method based on the hierarchical method is designed to interact with MOEAs,and the Pareto frontier is quickly found,and an expensive multi-objective optimization solution method based on single-class SVM(MOEAsSVM/OC)is proposed.Experiments have proved that the MOEAs-SVM/OC algorithm can effectively save expensive real evaluation costs while maintaining prediction accuracy.(3)The Pareto dominant method of direct classification prediction is secondary vector prediction,and there is a problem that the number of Pareto non-dominant category samples is small and the distribution is uneven,resulting in the difficulty and cost of model training,and the Pareto dominant discrimination method based on SVM classification prediction is proposed.According to the principle of no precision requirement between the order relationship and the target component value,the SVM classification method is used to establish the order relationship classification model for each expensive target component,the combined classification results are used to determine the dominant relationship between the candidate solution and the known sample,and the non-dominant individual expensive evaluation is selected according to the multi-model common decision-making and distribution retention strategy,so as to explore the decision space and gradually approach the real Pareto optimal surface.Experiments show that the algorithm has obvious advantages.