Adaptive Penalty-based Boundary Intersection Methods For Many-objective Optimization Problems

Multi-objective optimization problems exist widely in different fields and are of great importance.So it is of great scientific value and practical significance to solve multi-objective optimization problems.The most common method to solve multi-objective optimization problems is to use multi-objective evolutionary algorithm?MOEA?,among which the multi-objective evolutionary algorithm based on decomposition?MOEA/D?has attracted wide attention since its introduction.MOEA/D uses the idea of divide-and-conquer to decompose a complex multi-objective optimization problem into multiple single-objective optimization problems,and then optimizes these sub-problems simultaneously.Compared with other MOEAs,MOEA/D has obvious advantages in dealing with multi-objective optimization problems.It has a high search capability for continuous optimization problems and combinatorial optimization problems,but its performance depends on the chosen decomposition methods.Among the existing decomposition methods,the penalty-based boundary intersection?PBI?method with an appropriate penalty factor shows its superiority when dealing with many-objective optimization problems.Its drawback is its performance is highly related to the setting of penalty parameters,and the range of this parameter is very wide.However,there is little work on the penalty value or how to set it of PBI method.In this thesis,through the systematic research of the penalty value of PBI method,two effective algorithms were developed and the above problems have been improved.The main contributions of this thesis are as follows:?1?The sensitivity of PBI method penalty parameter has been studied mainly for many-objective optimization problems and a two-period adaptive PBI algorithm called Ada-PBI was proposed.Firstly,the sensitivities of penalty values were analyzed from two different aspects:the best penalty values of different test problems and the best performance penalty values at different iterations of the same problem.We divide penalty range into three sub-areas according to the similar search behaviors of the PBI method with different penalty values.According to different requirements for convergence and diversity in different periods,we analyzed the key elements of self-adaptive selection of parameters,an adaptive algorithm based on the recent performance of the parameters is developed to select the penalty value that best meets the current needs of with the framework of sliding window multi-armed bandit.Tests under many-objective optimization problems and comparion with the other two common algorithms proved the effectiveness of Ada-PBI algorithm.?2?Based on specific improvements to the two shortcomings of the Ada-PBI algorithm,an adaptive penalty based boundary intersection algorithm according to the diversity of population called Ada-PBI-d₂ has been proposed,and the superiority of it has been proved.Firstly,a dozen kinds of statistics that often used as parameter selection basis in MOEAs are studied.After that,the statistic d₂ from solutions to the weighted vectors was chosed by the result of comparision,and the advantages of choosing d₂ for many-objective optimization problems has been analysed.Then we discussed the way of traversing parameters and chose the increasing order to traverse the candidate parameters to update area of the algorithm gradually make sure that the diversity of knowledge sets will not be greatly lost.Finally,experimental results on many-objective optimization problems and the comparison with other algorithms have showed the superiority and stability of the improved algorithm Ada-PBI-d₂.