On the simplex, interior-point and objective space approaches to multiobjective linear programming. (October 2021)

• Record Type: Journal Article
• Authors: Nyiam, Paschal B; Salhi, Abdellah
• Is Part Of: Journal of algorithms & computational technology. Volume 15(2021)
• Publication Date: 2021-10
• Subjects: Multiple objective linear programming -- multiobjective simplex algorithm -- affine scaling interior MOLP algorithm -- outer-approximation algorithm -- most preferred nondominated point; Computer algorithms -- Periodicals; Numerical calculations -- Periodicals; Computer algorithms; Numerical calculations; Periodicals; 518.1
• DOI: 10.1177/17483026211008414
• Languages: English
• ISSNs: 1748-3018

Abstract

Most Multiple Objective Linear Programming (MOLP) algorithms working in the decision variable space, are based on the simplex algorithm or interior-point method of Linear Programming. However, objective space based methods are becoming more and more prominent. This paper investigates three algorithms namely the Extended Multiobjective Simplex Algorithm (EMSA), Arbel's Affine Scaling Interior-point (ASIMOLP) algorithm and Benson's objective space Outer Approximation (BOA) algorithm. An extensive review of these algorithms is also included. Numerical results on non-trivial MOLP problems show that EMSA and BOA are at par and superior in terms of the quality of a most preferred nondominated point to ASIMOLP. However, ASIMOLP more than holds its own in terms of computing efficiency.