Applications and performance of the non-numerical ranking preferences method for post-Pareto optimality

Most real-world engineering optimization problems are implicitly or explicitly multi-objective, and approaches to find the best feasible solution to be implemented can be quite challenging for the decision-maker. In this kind of problem, either the analyst determines a single solution or identifies a set of nondominated solutions, often referred to as Pareto-optimal set. Although, several methods for solving multi-objective optimization problems have been developed and studied, little prior work has been done on the evaluation of results obtained in multi-objective optimization. This selection stage is often referred as post-Pareto optimality. This paper presents a method based on preferences rankings provided from the decision-maker. The method is clearly advantageous because there is no need to provide specific weight values; the only requirement is to provide a non-nominal ranking. Several examples are used to show the performance of the algorithm.