Bi-objective branch-and-cut algorithms based on LP-relaxation and bound sets

Gadegaard, Sune Lauth and Nielsen, Lars Relund and Ehrgott, Matthias (2019) Bi-objective branch-and-cut algorithms based on LP-relaxation and bound sets. INFORMS Journal on Computing, 31 (4). pp. 790-804. ISSN 1091-9856

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Abstract

Most real-world optimization problems are multi-objective by nature, with conflicting and incomparable objectives. Solving a multi-objective optimization problem requires a method which can generate all rational compromises between the objectives. This paper proposes two distinct bound set based branch-and-cut algorithms for general bi-objective combinatorial optimization problems, based on implicit and explicit lower bound sets, respectively. The algorithm based on explicit lower bound sets computes, for each branching node, a lower bound set and compares it to an upper bound set. The other fathoms branching nodes by generating a single point on the lower bound set for each local nadir point. We outline several approaches for fathoming branching nodes and we propose an updating scheme for the lower bound sets that prevents us from solving the bi-objective LP-relaxation of each branching node. To strengthen the lower bound sets, we propose a bi-objective cutting plane algorithm that adjusts the weights of the objective functions such that different parts of the feasible set are strengthened by cutting planes. In addition, we suggest an extension of the branching strategy "Pareto branching". We prove the effectiveness of the algorithms through extensive computational results.

Item Type:
Journal Article
Journal or Publication Title:
INFORMS Journal on Computing
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/aacsb/disciplinebasedresearch
Subjects:
ID Code:
127861
Deposited By:
Deposited On:
28 Sep 2018 13:14
Refereed?:
Yes
Published?:
Published
Last Modified:
31 May 2020 05:35