Multi-Objective Mixed Integer Programming: An Objective Space Algorithm
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.
Cite
@article{arxiv.1909.03829,
title = {Multi-Objective Mixed Integer Programming: An Objective Space Algorithm},
author = {William Pettersson and Melih Ozlen},
journal= {arXiv preprint arXiv:1909.03829},
year = {2019}
}
Comments
6 pages, presented at LeGO International Global Optimization Workshop. At time of submission, no competing algorithm was known, but a competing algorithm was published between submission and presentation of this work