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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Bi-objective branch-and-cut algorithms based on LP-relaxation and bound sets
AU - Gadegaard, Sune Lauth
AU - Nielsen, Lars Relund
AU - Ehrgott, Matthias
PY - 2019/11/1
Y1 - 2019/11/1
N2 - 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 branchingnode, 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 thatdifferent 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.
AB - 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 branchingnode, 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 thatdifferent 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.
KW - bi-objective branch-and-cut, bi-objective optimization, combinatorial optimization, branch-and-cut
U2 - 10.1287/ijoc.2018.0846
DO - 10.1287/ijoc.2018.0846
M3 - Journal article
VL - 31
SP - 790
EP - 804
JO - INFORMS Journal on Computing
JF - INFORMS Journal on Computing
SN - 1091-9856
IS - 4
ER -