Research Of Pareto Dominance Based Many-Objective Evolutionary Algorithm

Real-world problems commonly involve multiple objectives which are required to be optimized simultaneously, these problems are called multi-objective optimal problems (MOPs). Evolutionary algorithm (EA) has been widely used to solve the multi-objective (mainly 2-to 3-objective) optimal problems due to its good convergence and diversity. However, many practical problems always refer to greater than 3 targets (many-objective optimal problem). The common Pareto dominance based evolutionary algorithm in dealing with this kind of problem encounters several difficulties, such as the ineffectiveness of Pareto dominance, time consuming of the Pareto ranking and the imbalance of convergence and diversity. In addition, some restrictions always are introduced into practical problems. It makes the constrained many-objective optimization problem become a challenge for the researchers. This paper mainly improves the Pareto dominance based evolutionary algorithm to solve unconstrained and constrained many-objective optimization problems. The main works of this paper outline as follows:(1) Firstly, we propose a diversity priority strategy to solve the imbalance of convergence and diversity and high computational complexity of the Pareto dominance based evolutionary algorithm on many-objective optimal problems. Being different from the traditional convergence priority method, this strategy maintains the diversity of population by dividing the target space into homogeneous subspace and selects well-convergence individual in the subspace to preserve the convergence of population. It can effectively distinguish well-convergence and well-diversity individuals in a little high-level population of Pareto ranking.(2) Secondly, for the ineffectiveness of the Pareto dominance on Many-objective optimization problems and the preference of the common clustering method for the individual owing the well-diversity and worse-convergence, we introduce two-level clustering and two-level ranking methods. The two-level clustering method firstly clusters non-dominated individuals, then uses these non-dominated individuals to classify the dominated individuals to recognize the unbalanced individuals on diversity and convergence. Next we rank the non-dominated and dominated individuals in each class through the convergence and diversity performance of individuals to keep the diversity and convergence of population. In the end, our method is proved that it can not only obtain well-convergence and well-diversity solutions, but also possess low time complexity through analyzing the time complexity of our method and solving 13 different features test problems.(3) In the end, we introduce a self-adaptive selecting strategy of constraint dominance based many-objective constraint evolutionary algorithm to deal with the preference of constraint handling mechanism for the feasible solutions and solutions owing low constraint violation. The method self-adaptively selects a constraint handing strategy from three methods by the variation of the proportion of infeasible individuals with the number of iteration. Our method is demonstrated to achieve well-convergence and well-diversity solutions by solving different constraint many-objective optimization problems.