A General Iterative Procedure of the Non-Numerical Ranking Preferences Method for Multiple Objective Decision Making

Multiple objective evolutionary algorithms (MOEAs), which are biologically-inspired optimization methods, have become popular approaches to solve problems with multiple objective functions. With the use of MOEAs, multiple objective optimization becomes a two-part problem. First, the multiple objective optimization problem needs to be formulated and successfully solved using an MOEA. Then, a non-dominated set -also known as efficient or Pareto frontier-needs to be analyzed to select a solution to the problem. This can represent a challenging task to the decision-maker because this set can contain a large number of solutions. This decision-making stage is usually known as the post-Pareto analysis stage. This paper presents the generalization of a post-Pareto optimality method known as the non-numerical ranking preferences (NNRP) method originally proposed by Taboada et al. (2007). This method can help decision makers reduce the number of design possibilities to small subsets that clearly reflect their objective function preferences. Previous research has only presented the application of the NNRP method using three and four objective functions but had not been generalized to the case of n objective functions. The present paper expands the NNRP method to be able to consider multiple objective optimization problems with n number of objective functions.