Constrained Multi-objective Evolutionary Algorithm For Irregular Pareto Front Problem

The optimization problems in the real world often contain one or more constraints,and it is of great practical significance to effectively solve constrained multi-objective optimization.In general,constraints can lead to irregular Pareto fronts.In this paper,the main research contents are summarized as the following two aspects:Firstly,due to the existing multi-objective constraint handling method has some defects under complex constraints,we propose a constrained multi-objective optimization algorithm(C-TPEA)for two-stage feasibility search.Unlike existing algorithms,which pay more attention to feasibility,C-TPEA aims to better balance convergence,diversity and feasibility.In the first phase,C-TPEA explores the entire space without considering the constraints,the working population can travel through some complex infeasible regions and avoid falling into local optimum.In the second phase,the algorithm adds feasibility considerations and the working population gradually converges to the constraint boundary.By using CDG,C-TPEA avoids loss of population diversity in this process.Besides,some solutions do not satisfy the constraint near the constraint boundary,but they contain information that is helpful to the search process.The existing constraint processing methods often ignore it.To make better use of these solutions,C-TPEA maintains a external set and engages them in the search process.Finally,the performance of C-TPEA on CMOPs is verified by experiments.Secondly,an effective allocation of search effort is important in multi and many-objective optimization.In this paper,a multiobjective evolutionary algorithm based on the adaptive constrained decomposition,called ACDG-MOEA,is proposed.ACDG uses an adaptively adjusted grid system for effective allocation of search effort,which enables it to address problems with both regular and irregular Pareto fronts(PFs),e.g.,discontinuous and degenerated ones.More specifically,the grid system is reset periodically based on the distribution of the current nondominated solutions such that the search efforts are applied on more promising regions.Numerical experiments are conducted on various benchmark problems and the results show that ACDG-MOEA is able to achieve satisfactory performance on problems with various PFs.At the same time,ACDG-MOEA was applied to optimize the actual engineering problems of a carbon fiber drawing process,and also showed excellent performance.