| Multi-objective optimization problems generally exist in various fields of the real world,but traditional mathematical methods cannot solve multi-objective optimization problems well.In the past decades,evolutionary algorithms have been widely used to solve multi-objective optimization problems,because they have the characteristics of solving problems without prior information and can obtain multiple non-dominated solutions in one run.Nowadays,the evolutionary computing community has conducted extensive research on a variety of multiobjective optimization problems and has proposed many effective evolutionary algorithms.However,for large-scale sparse multi-objective optimization problems that are widely used in practical engineering applications,existing evolutionary algorithms are difficult to solve effectively.Therefore,this thesis explores and studies the evolutionary algorithm for solving large-scale sparse multi-objective optimization problems from the aspects of performance and efficiency.The main research works of this thesis are as follows:(1)To effectively solve the large-scale sparse multi-objective optimization problem,for the sparse characteristics of only a few non-zero variables in its Pareto optimal solution,the idea of pattern mining is used to treat the Pareto optimal solution as a transaction,and a combination pattern of non-zero variables is mined from it,which reduces the search space.Specifically,this thesis proposes a large-scale sparse multi-objective evolutionary algorithm based on pattern mining(PM-MOEA).PM-MOEA uses a multi-objective pattern mining algorithm to mine the largest and smallest candidate sets of non-zero variables in the Pareto optimal solution and uses them to guide the generation of progeny populations.The experimental results on 8 benchmark problems and 4 practical application problems show that the proposed algorithm is superior to existing evolutionary algorithms in solving large-scale sparse multi-objective optimization problems.(2)For large-scale sparse multi-objective optimization problems,the efficiency and performance of the algorithm are equally important;and most existing evolutionary algorithms are inefficient,in terms of the number of function evaluations.As the scale of large-scale sparse multi-objective optimization problems grows gradually,it is necessary to develop efficient solutions to large-scale sparse multi-objective optimization problems.Therefore,this thesis proposes a large-scale sparse multi-objective evolutionary algorithm based on Pareto optimal subspace learning(MOEA/PSL).MOEA/PSL uses two unsupervised neural networks,Restricted Boltzmann Machine(RBM)and Denoising Autoencoder(DAE)to learn the Pareto optimal subspace during the evolution process,which will greatly reduce the search space.Afterward,a cross mutation operation is performed in the learned Pareto optimal subspace,and then the previously obtained children are mapped back to the original search space through two unsupervised neural networks.The results on 8 benchmark problems and 8 practical application problems show that the proposed algorithm can effectively solve large-scale sparse multiobjective optimization problems with more than 10,000 decision variables using only a small number of function evaluation times. |
