Differential evolution (DE) is a simple and powerful evolutionary algorithm for global optimization. DE with constraint handling techniques, named constrained differential evolution (CDE), can be used to solve constrained optimization problems (COPs). In existing CDEs, the parents are randomly selected from the current population to produce trial vectors. However, individuals with fitness and diversity information should have more chances to be selected. This study proposes a new CDE framework that uses nondominated sorting mutation operator based on fitness and diversity information, named MS-CDE. In MS-CDE, firstly, the fitness of each individual in the population is calculated according to the current population situation. Secondly, individuals in the current population are ranked according to their fitness and diversity contribution. Lastly, parents in the mutation operators are selected in proportion to their rankings based on fitness and diversity. Thus, promising individuals with better fitness and diversity are more likely to be selected as parents. The MS-CDE framework can be applied to most CDE variants. In this study, the framework is applied to two popular representative CDE variants, (μ+λ)-CDE and ECHT-DE. Experiment results on 24 benchmark functions from CEC’2006 and 18 benchmark functions from CEC’2010 show that the proposed framework is an effective approach to enhance the performance of CDE algorithms. 
Constrained differential evolution with multiobjective sorting mutation operators for constrained optimization