Multiobjective optimization using an aggregative gradient-based method

A process of compromise that addresses conflicting objective functions such as performance and cost is often involved in real-world engineering design activities. If such conflicting relationships among objective functions exist in a multiobjective design optimization problem, no single solution can simultaneously minimize all objective functions, and the solutions of the optimization problem are obtained as a set of design alternatives called a Pareto optimal solution set. This paper proposes a new gradient-based multiobjective c that incorporates a population-based aggregative strategy 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 approximate optimization-based 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, including a structural optimization problem, are provided to illustrate the effectiveness and utility of the proposed method.