Integrating column generation in a method to compute a discrete representation of the non-dominated set of multi-objective linear programmes

Lin, Kuan-Min and Ehrgott, Matthias and Raith, Andrea (2016) Integrating column generation in a method to compute a discrete representation of the non-dominated set of multi-objective linear programmes. 4OR: A Quarterly Journal of Operations Research. ISSN 1619-4500

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Abstract

In this paper we propose the integration of column generation in the revised normal boundary intersection (RNBI) approach to compute a representative set of non-dominated points for multi-objective linear programmes (MOLPs). The RNBI approach solves single objective linear programmes, the RNBI subproblems, to project a set of evenly distributed reference points to the non-dominated set of an MOLP. We solve each RNBI subproblem using column generation, which moves the current point in objective space of the MOLP towards the non-dominated set. Since RNBI subproblems may be infeasible, we attempt to detect this infeasibility early. First, a reference point bounding method is proposed to eliminate reference points that lead to infeasible RNBI subproblems. Furthermore, different initialisation approaches for column generation are implemented, including Farkas pricing. We investigate the quality of the representation obtained. To demonstrate the efficacy of the proposed approach, we apply it to an MOLP arising in radiotherapy treatment design. In contrast to conventional optimisation approaches, treatment design using column generation provides deliverable treatment plans, avoiding a segmentation step which deteriorates treatment quality. As a result total monitor units is considerably reduced. We also note that reference point bounding dramatically reduces the number of RNBI subproblems that need to be solved.

Item Type:
Journal Article
Journal or Publication Title:
4OR: A Quarterly Journal of Operations Research
Additional Information:
The final publication is available at Springer via http://dx.doi.org/10.1007/S10288-016-0336-9
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/aacsb/disciplinebasedresearch
Subjects:
ID Code:
83758
Deposited By:
Deposited On:
22 Dec 2016 09:34
Refereed?:
Yes
Published?:
Published
Last Modified:
19 Sep 2020 04:23