Research On Evolutionary Algorithm For Imbalanced Optimization Problem And Its Application In Reducer Design

Multi-objective optimization is a type of research which has been widely concerned at present.Among the various optimization algorithms,the evolutionary algorithm which is derived from the idea of biological evolution has been gradually gaining the attention of scholars because it can effectively deal with complex multi-objective optimization problems that are difficult to be solved by traditional optimization algorithms and its global,robust,self-organizing and widely applicable characteristics.Since most real-word optimization problems have constraints,the convergence-hard and diversity-hard constraints make such problems difficult to be solved effectively.Then the use of evolutionary computation to solve constrained multi-objective optimization problems has a very important application prospect.In this paper,we propose a hybrid constrained multi-objective optimization algorithm for solving constrained multi-objective optimization problems based on the latest research results of evolutionary algorithms and constrained optimization handling techniques.The research mainly includes the following parts.1.In order to solve imbalanced CMOPs with simultaneous convergence-hard and diversity-hard constraints,this paper proposes a hybrid algorithm which combines an improved epsilon constraint-handling method(IEpsilon)with a multi-objective to multi-objective(M2M)decomposition approach,namely M2M-IEpsilon.Since M2M-IEpsilon adopts the M2 M decomposition method,it can decompose a CMOP into a set of simple constrained multi-objective optimization subproblems,which can deal with the imbalanced objective optimization problem,to enhance the diversity of the proposed algorithm.At the same time,M2M-IEpsilon employs the IEpsilon constraint handling method,which can help populations get across large infeasible regions,and improve the convergence performance of the proposed algorithm.2.To effectively evaluate the performance of the M2M-IEpsilon algorithm and compensate for the lack of existing CMOPs that only focused on objectives or constraints,imbalanced CMOPs with simultaneous convergence-hard and diversity-hard constraints,namely ICD-CMOPs,are employed to evaluate the performance of M2M-IEpsilon and six state-of-the-art constrained multi-objective evolutionary algorithms(CMOEAs),including CM2M,CM2M2,NSGA-II-CDP,MOEA/D-CDP,PPS-MOEA/D and MOEA/D-IEpsilon.The experimental results demonstrate that the proposed M2M-IEpsilon significantly outperforms the other six algorithms on ICD-CMOPs,which illustrates the superiority of the proposed algorithm in dealing with imbalanced CMOPs with simultaneous convergence-hard and diversity-hard constraints.3.With the six state-of-the-art CMOEAs,including CM2 M,CM2M2,NSGAII-CDP,MOEA/D-CDP,MOEA/D-IEpsilon,PPS-MOEA/D,the proposed M2M-IEpsilon carried out on speed reducer design optimization problem evaluate the performance of the proposed algorithm in real-world optimization problem.The experimental results show that M2M-IEsilon outperforms the other six algorithms for this real-world optimization problem.