Comparison between MGDA and PAES for Multi-Objective Optimization

In multi-objective optimization, the knowledge of the Pareto set provides valuable information on the reachable optimal performance. A number of evolutionary strategies (PAES, NSGA-II, etc), have been proposed in the literature and proved to be successful to identify the Pareto set. However, these derivative-free algorithms are very remanding in terms of computational time. Today, in many areas of computational sciences, codes are developed that include the calculation of the gradient, cautiously validated and calibrated. Thus, an alternate method applicable when the gradients are known is introduced here. Using a clever combination of the gradients, a descent direction common to all criteria is identified. As a natural outcome, the Multiple Gradient Descent Algorithm (MGDA) is defined as a generalization of steepest-descent method and compared with PAES by numerical experiments.