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In the bi-objective branch-and-bound literature, a key ingredient isobjective branching, i.e. to create smaller and disjoint sub-problems in theobjective space, obtained from the partial dominance of the lower bound set bythe upper bound set. When considering three or more objective functions,however, applying objective branching becomes more complex, and its benefit hasso far been unclear. In this paper, we investigate several ingredients whichallow to better exploit objective branching in a multi-objective setting. Weextend the idea of probing to multiple objectives, enhance it in several ways,and show that when coupled with objective branching, it results in significantspeed-ups in terms of CPU times. We also investigate cut generation based onthe objective branching constraints. Besides, we generalize the best-bound ideafor node selection to multiple objectives and we show that the proposed rulesoutperform the, in the multi-objective literature, commonly employeddepth-first and breadth-first strategies. We also analyze problem specificbranching rules. We test the proposed ideas on available benchmark instancesfor three problem classes with three and four objectives, namely thecapacitated facility location problem, the uncapacitated facility locationproblem, and the knapsack problem. Our enhanced multi-objectivebranch-and-bound algorithm outperforms the best existing branch-and-bound basedapproach and is the first to obtain competitive and even slightly betterresults than a state-of-the-art objective space search method on a subset ofthe problem classes.

Enhancing Branch-and-Bound for Multi-Objective 0-1 Programming