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

Abstract

International audienceThis 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

Bi-objective Discrete Graphical Model Optimization

“…We present a summary of our comparative results in Table 1. 12 The comparison measure is the number of instances completely solved per class of benchmark. 1.…”

“…for VertexCover, a multi-objective depth-first branch and bound (MO-BB) using multi-objective minibucket elimination (MO-MB M OM BE ) (experiments were made on a Pentium IV at 3GHz with 2GB) [36] ; for SetCover, a Max-SAT based hybrid method between core-guided and SAT-UNSAT search methods (MSHybrid) [24] (experiments made on Intel Xeon E5-2670 at 2.6GHz with 64GB and 1.5-hour CPU-time limit) ; for Knapsack, a two-phase method including dedicated instance preprocessing and where the second phase is a branch and bound with an adaptive branching heuristic (UCB) [11,12] (experiments made on Intel Xeon E5620 at 2.40GHz with 6GB) ; for Warehouse, a multi-objective hybrid branch and bound combined with scalarization and using Bensolve/GLPK for solving the linear relaxations (M2.1.1.2) (experiments made on an Intel i7-8700 at 3.2GHz with 32GB) [5].…”

On the design and anytime performance of indicator-based branch and bound for multi-objective combinatorial optimization

“…Nonetheless, both approaches can have good performance if the subspace division order leads to optimal, or close to optimal, solutions early on. Unfortunately, such orderings may not be available for every problem or it may not always be clear which order is the best since it can depend on the problem instance being solved [4]. A third strategy is the best-first selection (BeFS), which corresponds to finding the most promising node in the queue.…”

“…Preliminary results comparing the O sum , O max [2], and O min [2] orders, showed better anytime behavior for the former. For other possible orders, we refer to [4] where various branching orders and heuristics are analyzed.…”

A generalized decision support framework for large‐scale project portfolio decisions

“…In many real-life PPS settings like the one we consider in this study, spending budgets are rarely fixed; the decision process may involve the revising of portfolio budgets, depending on the revenue performance. Therefore, rather than presenting a single optimal portfolio, it is much more informative to formulate the problem as a bicriteria knapsack problem where the solution process yields an efficient frontier of solutions that represent different optimal trade-offs between the two criteria as discussed in Levine (2005), Clímaco and Pascoal (2016), Naldi et al (2016), Cerqueus et al (2017), Röglin and Rösner (2017), and Correia et al (2018). Generating the efficient frontier for a PPS problem provides decision makers with a set of portfolio options that reflect the optimal trade-off between benefit and spending, and allows them the above-mentioned "interaction" to eventually select the portfolio that achieves the most desirable trade-offs.…”