Multiobjective optimization using an adaptive weighting scheme

A new Pareto front approximation method is proposed for multiobjective optimization problems with bound constraints. The method employs a hybrid optimization approach using two derivative free direct search techniques, and intends to solve blackbox simulation based multiobjective optimization problems where the analytical form of the objectives is not known and/or the evaluation of the objective function(s) is very expensive. A new adaptive weighting scheme is proposed to convert a multiobjective optimization problem to a single objective optimization problem. Another contribution of this paper is the generalization of the star discrepancy based performance measure for problems with more than two objectives. The method is evaluated using five test problems from the literature. Results show that the method achieves an arbitrarily close approximation to the Pareto front with a good collection of well-distributed nondominated points for all five test problems.