Research And Application Of Multi-objective Optimization Problem Based On Decomposition

When the traditional multi-objective optimization algorithm solves the multi-objective problem,it is easy to fall into local convergence and the distribution of solution set is poor.In this paper,the multi-objective evolutionary algorithm based on decomposition(MOEA/D)is improved in different cases,so as to improve the algorithm capability and the performance of the solution set.The main research contents are as follows:In order to improve the ability of MOEA/D for dealing with the problem of continuous Pareto Front,an improved MOEA/D based on adaptive mutation operator and neighborhood size is proposed.It aims at the problem of the degradation of population quality and algorithm performance caused by the preset control parameters of MOEA/D.Firstly,the algorithm calculates the fitness value of all individuals and then adjusts the mutation operator adaptively according to the degree of fitness value concentration.It can improve its searching ability.Secondly,the information of the population fitness value and the evolution stage are used to adjust the neighborhood value.Finally,the dominated number of newly generated individuals in the neighborhood is counted.According to whether it exceeds the set threshold,the algorithm considers whether to use Pareto dominance relation as one of the criteria to judge the performance of individuals.In order to improve the ability of MOEA/D for dealing with the problem of discontinuous Pareto Front,an improved MOEA/D based on adaptive weight vector and matching strategy is proposed.It aims at the problem of degradation of population diversity caused by the preset weight vectors and random matching strategy of MOEA/D.Firstly,the algorithm finds the invalid sub-problems in the discontinuous region,and then updates these sub-problems.It can reduce the possibility that the invalid sub-problems mislead evolutionary process.Secondly,the matching mechanism is established according to the value of penalty-based boundary intersection and the Euclidean distance between the sub-problems and individuals.This mechanism can enhance the relationship between individuals and sub-problems.Finally,individuals who perform well in the neighborhood replacement operation are saved in the external archive.It can improve the diversity of population.In order to improve the ability of MOEA/D for dealing with the problem of complicated Pareto Set,an improved MOEA/D based on double differential evolution process and neighbor model in double space is proposed.It aims at the problems of large randomness of genetic operation,failure of replacement operation and mismatch between individuals and neighbor solutions in MOEA/D.Firstly,the algorithm divides the neighbors by the distance between individuals in the decision space,and establishes the neighborhood by the corresponding sub-problems in the objective space.This strategy will be updated regularly to improve the quality of neighbors.Secondly,the locally linear embedding(LLE)is used to distance calculation in the high-dimensional decision space.Finally,by changing the step of differential evolution and using the information of the first differential evolution in a single genetic operation to construct the operation of the second differential evolution,the problem of the replacement operation fails in the complex Pareto Set is solved.At the same time,it effectively reduces the randomness of genetic operation.The above three evolutionary algorithms are applied to two practical engineering problems: flow-shop scheduling problem(FSP)and flexible job-shop scheduling problem(FJSP).The first and second improved algorithms are used to solve the FSP.In practice,Pareto front shape cannot be known in advance,so a judgment mechanism is introduced.By judging the number of invalid sub-problems in the evolution process,this mechanism can switch the needed algorithm in time for the next evolution stage.In the FJSP,the workpiece processing method is not a pipeline processing.So its Pareto solution set is more complex than that of the FSP.Therefore,the third improved algorithm combined with the two-level integer encoding method is used to solve this problem.The effectiveness of the algorithm is verified by the experimental results.