Expensive Multi-Objective Optimization Algorithm Based On Conditional Neural Process And Its Practical Application To Engineering Design

In the past few decades,the evolutionary algorithm EA has become one of the most popular methods for solving multi-objective optimization problems,and has achieved great success due to their simplicity and effectiveness.However,since evolutionary algorithms usually require many function evaluations,the reduction of computational burden has become an important and difficult problem when applying EA to expensive MOPs.In addition,in practical engineering applications,there are many black box optimization problems that cannot be described by specific mathematical expressions.Such optimization problems often have expensive evaluation features such as high computational cost and slow operation speed.Surrogate-Assisted Evolutionary Algorithms(SAEAs)is one of the important methods to solve this kind of expensive optimization problems.This method uses the historical data of optimization problems to build a model to assist the optimization process,which can reduce the number of function evaluation,thereby reducing the cost of function evaluation.Aiming at the shortcomings of the exponential increase in computational complexity of the Gaussian process and the existing algorithms do not consider the relevance of the subproblems,this paper proposes two expensive multi-objective optimization algorithms based on the existing SAEAs framework,That is,Par CNPs algorithm and Par MTCNPs algorithm.The main work includes the following aspects:(1)For the first time,an expensive multi-objective optimization algorithm Par CNPs based on conditional neural processes is proposed.The conditional neural process model used in this algorithm combines the advantages of both Gaussian processes and neural networks,which avoids the complexity of covariance matrix calculation in Gaussian processes High degree of disadvantage.Then for the RMMEDA and DTLZ series multi-objective testing problems,the proposed algorithm Par CNPs is compared with the most widely used expensive multi-objective optimization algorithms Par EGO,KRVEA,MOEA/D-EGO and NSGA-II.The experimental results show that the performance index of Par CNPs on most test problems is better than other comparison algorithms.(2)Based on Par CNPs,an expensive multi-objective optimization algorithm Par MTCNPs based on multi-task conditional neural processes is proposed.This algorithm combines multiple adjacent sub-problems into task groups,and Jointly model the problem.In the experiments,the Par MTCNPs algorithm was compared with Par CNPs,Par EGO,KRVEA,MOEA/D-EGO,and NSGA-II.The experimental results show that Par MTCNPs are better than Par CNPs and four other existing algorithms on most test problems.In addition,it proves that the multi-task joint learning model is more competitive than the single-task CNPs and GPs models in dealing with expensive multi-objective optimization problems.(3)In the Par MTCNPs algorithm,a task group partitioning method with minimum Euclidean distance is proposed for weight vector partitioning task group problem.This method divides sub-problems with high similarity into the same task group and then performs joint modeling.(4)The two algorithms Par CNPs and Par MTCNPs proposed in this paper are applied to actual engineering manufacturing problems and compared with the existing mainstream expensive multi-objective optimization algorithms.The experimental results prove the effectiveness of the proposed algorithm in practical application problems.