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.
Highlights
Single-objective mathematical programming models and their solution approaches have made a lot of contributions in solving many industrial and real-life optimization problems in operations research and other related areas of study, yet many of these situations are better represented by a multi-objective model, and a need for solution approaches for these multi-objective models is ever increasing
The proposed rank-based solution method (RBSM) to identify the non-dominated point set of a given multi-objective integer programming model uses Kth ranked optimal solutions, K ≥ 2
Several methods have been discussed that can find these K-ranked optimal solutions and later a rank-based solution method has been developed for identifying the non-dominated point set of the given multi-objective integer programming model
Summary
Single-objective mathematical programming models and their solution approaches have made a lot of contributions in solving many industrial and real-life optimization problems in operations research and other related areas of study, yet many of these situations are better represented by a multi-objective model, and a need for solution approaches for these multi-objective models is ever increasing. The proposed rank-based solution method (RBSM) to identify the non-dominated point set of a given multi-objective integer programming model uses Kth ranked optimal solutions, K ≥ 2. Justifying a need for developing methods that can determine K-ranked optimal solutions for a single-objective mathematical programming model. Several methods have been discussed that can find these K-ranked optimal solutions and later a rank-based solution method has been developed for identifying the non-dominated point set of the given multi-objective integer programming model.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: International Journal of Mathematical, Engineering and Management Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
