Performance Measures Based on the Slacks-Based Measure Model for Evaluating Non-dominated Solution Sets in Multi-Objective Optimization

Multi-objective optimization is a relevant area in operations research due to the necessity to make decisions considering multiple conflicting objectives, where a set of non-dominated solutions is sought. As a result, several methods have been proposed for obtaining this set.  Therefore, performance metrics are required to evaluate the quality of the obtained set. In this study, performance metrics based on data envelopment analysis (DEA) models are proposed for assessing different performance criteria. The proposed DEA models correspond to integer versions of the slacks-based measure (SBM) model. Several sets of non-dominated solutions obtained by different solution methods are evaluated to demonstrate the adequacy of the proposed metrics. These sets consider non-dominated solutions with negative or zero values, located in the convex or non-convex regions of the Pareto frontier, and obtained when different directions of the objective functions are assumed simultaneously.