Rank-Based Solution Methods and their Applications in Determination of Non-Dominated Points Set For A Multi-Objective Integer Programming Model

Abstract

For any single-objective mathematical programming model, rank-based optimal solutions are computationally difficult to find compared to an optimal solution to the same single-objective mathematical programming model. In this paper, several methods have been presented to find these rank-based optimal solutions and based on them a new rank-based solution method (RBSM) is outlined to identify non-dominated points set of a multi-objective integer programming model. Each method is illustrated by a numerical example, and for each approach, we have discussed its limitations, advantages and computational complexity.

Keywords

• exact and approximate methods for ranked-optimal solutions
• ; k-ranked optimal solutions
• multi-objective integer programming model
• non-dominated point set
• rank-based solution method