A gradient-based multiobjective optimization technique using an adaptive weighting method

1. Abstract While various multiobjective optimization methods based on metaheuristic techniques have been proposed, these methods still encounter difficulties when handling many variables, or numerous objectives and constraints. This paper proposes a new aggregative gradient-based multiobjective optimization method for obtaining a Pareto-optimal solution set. In this method, the objective functions and constraints are evaluated at multiple points in the objective function space, and design variables at each point are updated using information aggregatively obtained from all other points. In the proposed method, a multiobjective optimization problem is converted to a single objective optimization problem using a weighting method, with weighting coefficients adaptively determined by solving a linear programming problem. A sequential linear programming technique is used to update the design variables, since it allows effective use of design sensitivities that can be easily obtained in many engineering optimization problems. Several numerical examples illustrate the effectiveness the proposed method. 2.