An adaptive method to solve multilevel multiobjective linear programming problems

TL;DR

This paper presents an innovative adaptive nested linear programming algorithm to efficiently solve multilevel multiobjective linear programming problems by generating all possible compromises and selecting the optimal one.

Contribution

It introduces a novel adaptive nested linear programming approach that improves efficiency over traditional methods for solving ML-MOLPPs.

Findings

The method successfully generates all non-dominated solutions.

It efficiently identifies the best compromise among solutions.

The approach is validated with a numerical example.

Abstract

This paper is a follow-up to a previous work where we defined and generated the set of all possible compromises of multilevel multiobjective linear programming problems (ML-MOLPP). In this paper, we introduce a new algorithm to solve ML-MOLPP in which the adaptive method of linear programming is nested. First, we start by generating the set of all possible compromises (set of all non-dominated solutions). After that, an algorithm based on the adaptive method of linear programming is developed to select the best compromise among all the possible compromises achieved. This method will allow us to transform the initial multilevel problem into an ML-MOLPP with bounded variables. Then, apply the adaptive method which is the most efficient to solve all the multiobjective linear programming problems involved in the resolution process instead of the simplex method (It should be noted that the adaptive method is more efficient than the simplex method). Finally, all the construction stages are carefully checked and illustrated with a numerical example.