Approximating the Pareto set of multiobjective linear programs via Robust Optimization

TL;DR

This paper introduces a novel approach using Adjustable Robust Optimization and Polynomial Optimization to approximate the Pareto set of multiobjective linear programs with a single polynomial, enhancing visualization capabilities.

Contribution

It proposes a unified polynomial approximation method for the Pareto set, differing from existing piecewise linear techniques, and improves visualization of multiobjective optimization results.

Findings

Provides a polynomial approximation of the Pareto set

Offers a more visualizable representation of Pareto fronts

Uses a single optimization problem for approximation

Abstract

We consider problems with multiple linear objectives and linear constraints and use Adjustable Robust Optimization and Polynomial Optimization as tools to approximate the Pareto set with polynomials of arbitrarily large degree. The main difference with existing techniques is that we optimize a single (extended) optimization problem that provides a polynomial approximation whereas existing methods iteratively construct a piecewise linear approximation. One of the advantages of the proposed method is that it is more useful for visualizing the Pareto set.