Warm-starting lower bound set computations for branch-and-bound algorithms for multi objective integer linear programs

•Develops a branch-and-bound algorithm for multi-objective integer problems.•Uses the linear relaxation as a lower bound set in the algorithm.•Warm-starts the linear relaxation using information from the father node.•Warm-starting the linear relaxation improves efficiency considerably.•Reports exten...

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Vydáno v:European journal of operational research Ročník 302; číslo 3; s. 909 - 924
Hlavní autoři: Forget, Nicolas, Gadegaard, Sune Lauth, Nielsen, Lars Relund
Médium: Journal Article
Jazyk:angličtina
Vydáno: Elsevier B.V 01.11.2022
Témata:
Branch and bound
Combinatorial optimization
Linear relaxation
Multiple objective programming
Warm-starting
Warm-starting
Linear relaxation
Branch and bound
Combinatorial optimization
Multiple objective programming
ISSN:0377-2217, 1872-6860
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Shrnutí:•Develops a branch-and-bound algorithm for multi-objective integer problems.•Uses the linear relaxation as a lower bound set in the algorithm.•Warm-starts the linear relaxation using information from the father node.•Warm-starting the linear relaxation improves efficiency considerably.•Reports extensive computational results. In this paper we propose a generic branch-and-bound algorithm for solving multi-objective integer linear programming problems. In the recent literature, competitive frameworks has been proposed for bi-objective 0–1 problems, and many of these frameworks rely on the use of the linear relaxation to obtain lower bound sets. When increasing the number of objective functions, however, the polyhedral structure of the linear relaxation becomes more complex, and consequently requires more computational effort to obtain. In this paper we overcome this obstacle by speeding up the computations. To do so, in each branching node we use information available from its father node to warm-start a Bensons-like algorithm. We show that the proposed algorithm significantly reduces the CPU time of the framework on several different problem classes with three, four and five objective functions. Moreover, we point out difficulties that arise when non-binary integer variables are introduced in the models, and test our algorithm on problem that contains non-binary integer variables too.
ISSN:0377-2217
1872-6860
DOI:10.1016/j.ejor.2022.01.047