Evolutionary algorithms for multi-objective optimization problems with interval parameters

Multi-objective optimization problems with interval parameters are a kind of complicated optimization problems that are popular in real-world applications and hard to be effectively solved. We present an evolutionary optimization algorithm to solve the problems above in this paper. First, dominance relation among optimal solutions is defined suitable for interval objectives to reflect the quality of an optimal solution; then, crowding distance of an optimal solution is defined suitable for interval objectives to reflect the distribution of optimal solutions; finally, the method of selecting optimal solutions is given based on the rank and the crowding distance. We apply the proposed algorithm in four benchmark optimization problems, and compare it with IP-MOEA, a typical and effective method of solving the problems above. The experimental results show that our algorithm obtains optimal solutions with high quality, small uncertainty as well as uniform distribution. Our achievement provides a novel and feasible way to solve multi-objective optimization problems with uncertainties.