J0110203 A gradient-based multiobjective optimization considering diversity of solutions

Objective functions are often conflicting in real-world engineering design problems. When such conflicts exist in a multiobjective optimization problem, non-dominated solutions called a Pareto optimal solution set can be obtained. Obtaining a broadly distributed Pareto optimal solution set can be highly beneficial because this enables trade-off analysis among conflicting relationships and increases flexibility when making engineering design decisions. Therefore, this paper proposes an aggregative gradient-based multiobjective optimization method that ensures the diversity of solutions. The proposed method utilizes an aggregative search strategy in which multiple points are concurrently updated during the optimization process and a multiobjective optimization problem is converted to single objective problem using a weighting method. The design variables at all points are updated based on a local optimization. During the updating process, the proposed method introduces distance constraints among all points to maintain the diversity of non-dominated solutions. A numerical example is provided to confirm the effectiveness of the proposed method.