Multi-Objective Mixed Integer Programming: An Objective Space Algorithm

TL;DR

This paper presents a novel objective space algorithm capable of exactly identifying all supported and non-supported non-dominated solutions in multi-objective mixed-integer linear programming, regardless of the number of objectives.

Contribution

It introduces the first objective space algorithm for exact solution enumeration in multi-objective mixed-integer linear programs with arbitrary objectives.

Findings

Successfully identifies the complete Pareto front.

Efficiently removes non-Pareto solutions from the super-set.

Applicable to problems with any number of objectives.

Abstract

This paper introduces the first objective space algorithm which can exactly find all supported and non-supported non-dominated solutions to a mixed-integer multi-objective linear program with an arbitrary number of objective functions. This algorithm is presented in three phases. First it builds up a super-set which contains the Pareto front. This super-set is then modified to not contain any intersecting polytopes. Once this is achieved, the algorithm efficiently calculates which portions of the super-set are not part of the Pareto front and removes them, leaving exactly the Pareto front.