On branching heuristics for the bi-objective 0/1 unidimensional knapsack problem

This paper focuses on branching strategies that are involved in branch and bound algorithms when solving multi-objective optimization problems. The choice of the branching variable at each node of the search tree constitutes indeed an important component of these algorithms. In this work we focus on multi-objective knapsack problems. In the literature, branching heuristics used for these problems are static, i.e., the order on the variables is determined prior to the execution. This study investigates the benefit of defining more sophisticated branching strategies. We first analyze and compare a representative set of classic branching heuristics and conclude that none can be identified as the best overall heuristic. Using an oracle, we highlight that combining branching heuristics within the same branch and bound algorithm leads to considerably reduced search trees but induces high computational costs. Based on learning adaptive techniques, we propose then dynamic adaptive branching strategies that are able to select the suitable heuristic to apply at each node of the search tree. Experiments are conducted on the bi-objective 0/1 unidimensional knapsack problem.