Directional Pareto Front and Its Estimation to Encourage Multi-Objective Decision-Making

This work introduces the following concepts of directional and estimated directional Pareto front to encourage multi-objective decision making, especially when the Pareto front exists in limited regions in the objective space. The general output of multi-objective optimization is a set of non-dominated solutions to approximate the Pareto front. When the Pareto front exists in limited regions, few solutions are obtained and presented to the decision maker. The limited output representing the objective value trade-off is a barrier to multi-objective decision making. The directional Pareto front introduced in this study is a superset of the Pareto front and supplements the objective value trade-off between the Pareto fronts. The estimated directional Pareto front is a response surface that represents the directional Pareto front using a limited number of points, which are objective vectors of the obtained solutions. The experimental results show that the directional Pareto front and the estimated front provide an objective value trade-off even in areas where the Pareto front does not exist and enhances the explanation of the objective space of the target problem.