An Adaptive Penalty Function for Handling Constraint in Multi-objective Evolutionary Optimization

This chapter proposes a constraint handling technique for multi-objective evolutionary algorithms based on an adaptive penalty function and a distance measure. These two functions vary dependent upon the objective function value and the sum of constraint violations of an individual. Through this design, the objective space is modified to account for the performance and constraint violation of each individual. The modified objective functions are used in the non-dominance sorting to facilitate the search of optimal solutions not only in the feasible space but also in the infeasible regions. The search in the infeasible space is designed to exploit those individuals with better objective values and lower constraint violations. The number of feasible individuals in the population is used to guide the search process either toward finding more feasible solutions or favor in search for optimal solutions. The proposed method is simple to implement and does not need any parameter tuning. The constraint handling technique is tested on several constrained multi-objective optimization problems and has shown superior results compared to some chosen state-of-the-art designs.