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.
- Publication:
-
Proceedings LEGO - 14th International Global Optimization Workshop
- Pub Date:
- February 2019
- DOI:
- 10.1063/1.5090006
- arXiv:
- arXiv:1909.03829
- Bibcode:
- 2019AIPC.2070b0039P
- Keywords:
-
- Mathematics - Optimization and Control;
- Computer Science - Data Structures and Algorithms;
- 90-08
- E-Print:
- 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