TY - JOUR
T1 - Branch-and-bound and objective branching with three or more objectives
AU - Forget, Nicolas
AU - Gadegaard, Sune Lauth
AU - Klamroth, Kathrin
AU - Nielsen, Lars Relund
AU - Przybylski, Anthony
PY - 2022/12
Y1 - 2022/12
N2 - The recent success of bi-objective Branch-and-Bound (B&B) algorithms heavily relies on the efficient computation of upper and lower bound sets. These bound sets are used as a supplement to the classical dominance test to improve the computational time by imposing inequalities derived from (partial) dominance in the objective space. This process is called objective branching since it is mostly applied when generating child nodes. In this paper, we extend the concept of objective branching to multi-objective integer optimization problems with three or more objective functions. Several difficulties arise in this case, as there is no longer a lexicographic order among non-dominated outcome vectors when there are three or more objectives. We discuss the general concept of objective branching in any number of dimensions and suggest a merging operation of local upper bounds to avoid the generation of redundant sub-problems. Finally, results from extensive experimental studies on several classes of multi-objective optimization problems is reported.
AB - The recent success of bi-objective Branch-and-Bound (B&B) algorithms heavily relies on the efficient computation of upper and lower bound sets. These bound sets are used as a supplement to the classical dominance test to improve the computational time by imposing inequalities derived from (partial) dominance in the objective space. This process is called objective branching since it is mostly applied when generating child nodes. In this paper, we extend the concept of objective branching to multi-objective integer optimization problems with three or more objective functions. Several difficulties arise in this case, as there is no longer a lexicographic order among non-dominated outcome vectors when there are three or more objectives. We discuss the general concept of objective branching in any number of dimensions and suggest a merging operation of local upper bounds to avoid the generation of redundant sub-problems. Finally, results from extensive experimental studies on several classes of multi-objective optimization problems is reported.
KW - Bound sets
KW - Branch & bound
KW - Multi-objective combinatorial optimization
KW - Multi-objective integer programming
KW - Objective branching
UR - http://www.scopus.com/inward/record.url?scp=85137797302&partnerID=8YFLogxK
U2 - 10.1016/j.cor.2022.106012
DO - 10.1016/j.cor.2022.106012
M3 - Journal article
AN - SCOPUS:85137797302
SN - 0305-0548
VL - 148
JO - Computers and Operations Research
JF - Computers and Operations Research
M1 - 106012
ER -