A semidefinite programming approach for solving Multiobjective Linear Programming

TL;DR

This paper introduces a novel interior point method that transforms multiobjective linear programming into a sequence of semidefinite programs, enabling efficient computation of all Pareto-optimal solutions.

Contribution

It presents the first interior point algorithm that finds all Pareto-optimal solutions in MOLP by transforming the problem into SDP sequences.

Findings

Transforms MOLP into SDP sequences for solution

Uses interior point methods to solve SDPs

Provides a pseudo-polynomial approach for Pareto solutions

Abstract

Several algorithms are available in the literature for finding the entire set of Pareto-optimal solutions in MultiObjective Linear Programming (MOLP). However, it has not been proposed so far an interior point algorithm that finds all Pareto-optimal solutions of MOLP. We present an explicit construction, based on a transformation of any MOLP into a finite sequence of SemiDefinite Programs (SDP), the solutions of which give the entire set of Pareto-optimal extreme points solutions of MOLP. These SDP problems are solved by interior point methods; thus our approach provides a pseudo-polynomial interior point methodology to find the set of Pareto-optimal solutions of MOLP.