Multi-objective Linear Programming: A Survey
TL;DR
A state-of-the-art survey of major algorithms suggested to solve Multiple Objective Linear Programming (MOLP) and a tabulated summary of all algorithms are included.
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.