This paper presents a state-of-the-art survey of major algorithms suggested to solve Multiple Objective Linear Programming (MOLP). We have comprehensively reviewed MOLP papers that have appeared since 1964. The algorithms are considered in two broad categories: Non-Interactive algorithms and interactive ones. Interactivity in our view is an essential feature of usable tools. It enhances applicability and robustness of methods on one hand, but hinders them on the other by the mere fact that intervention is required. Note that the Non-Interactive algorithms include the Simplex, Interior Point, Objective Space based algorithms and relevant Nature-inspired population-based stochastic algorithms which are becoming more and more prominent. Note also that in the objective space methods, the simplex algorithm or the dual simplex algorithm are being invoked during the search process. This suggest that they should be put in the simplex based class. However, for more clarity and given that there is a strong trend to refer to them as objective space methods, we prefer to put them on their own since their underlying philosophy is different from that of the simplex based methods. While the Interactive ones only consist of the Simplex and Interior Point algorithms. An illustration of representative algorithms of each category and a tabulated summary of all algorithms are included.
| Published in | Mathematics and Computer Science (Volume 11, Issue 5) |
| DOI | 10.11648/j.mcs.20261105.11 |
| Page(s) | 78-105 |
| Creative Commons |
This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited. |
| Copyright |
Copyright © The Author(s), 2026. Published by Science Publishing Group |
Multiple Objective Linear Programming, Simplex Based Methods, Interior Point Based Methods, Space Based Methods, Heuristics, Meta-heuristics
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APA Style
Nyiam, P. B., Salhi, A. (2026). Multi-objective Linear Programming: A Survey. Mathematics and Computer Science, 11(5), 78-105. https://doi.org/10.11648/j.mcs.20261105.11
ACS Style
Nyiam, P. B.; Salhi, A. Multi-objective Linear Programming: A Survey. Math. Comput. Sci. 2026, 11(5), 78-105. doi: 10.11648/j.mcs.20261105.11
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Download@article{10.11648/j.mcs.20261105.11,
author = {Paschal Bisong Nyiam and Abdellah Salhi},
title = {Multi-objective Linear Programming: A Survey},
journal = {Mathematics and Computer Science},
volume = {11},
number = {5},
pages = {78-105},
doi = {10.11648/j.mcs.20261105.11},
url = {https://doi.org/10.11648/j.mcs.20261105.11},
eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.mcs.20261105.11},
abstract = {This paper presents a state-of-the-art survey of major algorithms suggested to solve Multiple Objective Linear Programming (MOLP). We have comprehensively reviewed MOLP papers that have appeared since 1964. The algorithms are considered in two broad categories: Non-Interactive algorithms and interactive ones. Interactivity in our view is an essential feature of usable tools. It enhances applicability and robustness of methods on one hand, but hinders them on the other by the mere fact that intervention is required. Note that the Non-Interactive algorithms include the Simplex, Interior Point, Objective Space based algorithms and relevant Nature-inspired population-based stochastic algorithms which are becoming more and more prominent. Note also that in the objective space methods, the simplex algorithm or the dual simplex algorithm are being invoked during the search process. This suggest that they should be put in the simplex based class. However, for more clarity and given that there is a strong trend to refer to them as objective space methods, we prefer to put them on their own since their underlying philosophy is different from that of the simplex based methods. While the Interactive ones only consist of the Simplex and Interior Point algorithms. An illustration of representative algorithms of each category and a tabulated summary of all algorithms are included.},
year = {2026}
}
TY - JOUR T1 - Multi-objective Linear Programming: A Survey AU - Paschal Bisong Nyiam AU - Abdellah Salhi Y1 - 2026/09/21 PY - 2026 N1 - https://doi.org/10.11648/j.mcs.20261105.11 DO - 10.11648/j.mcs.20261105.11 T2 - Mathematics and Computer Science JF - Mathematics and Computer Science JO - Mathematics and Computer Science SP - 78 EP - 105 PB - Science Publishing Group SN - 2575-6028 UR - https://doi.org/10.11648/j.mcs.20261105.11 AB - This paper presents a state-of-the-art survey of major algorithms suggested to solve Multiple Objective Linear Programming (MOLP). We have comprehensively reviewed MOLP papers that have appeared since 1964. The algorithms are considered in two broad categories: Non-Interactive algorithms and interactive ones. Interactivity in our view is an essential feature of usable tools. It enhances applicability and robustness of methods on one hand, but hinders them on the other by the mere fact that intervention is required. Note that the Non-Interactive algorithms include the Simplex, Interior Point, Objective Space based algorithms and relevant Nature-inspired population-based stochastic algorithms which are becoming more and more prominent. Note also that in the objective space methods, the simplex algorithm or the dual simplex algorithm are being invoked during the search process. This suggest that they should be put in the simplex based class. However, for more clarity and given that there is a strong trend to refer to them as objective space methods, we prefer to put them on their own since their underlying philosophy is different from that of the simplex based methods. While the Interactive ones only consist of the Simplex and Interior Point algorithms. An illustration of representative algorithms of each category and a tabulated summary of all algorithms are included. VL - 11 IS - 5 ER -
Department of Statistics, University of Calabar, Calabar, Nigeria
School of Mathematics, Statistics & Actuarial Science, University of Essex, Colchester, UK
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