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Conference Papers Year : 2021

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

Abstract

In this article, we propose an indicator-based branch and bound (I-BB) approach for multi-objective combinatorial optimization that uses a best-first search strategy. In particular, assuming maximizing objectives, the next node to be processed is chosen with respect to the quality of its upper bound. This quality is given by a binary quality indicator, such as the binary hypervolume or the ε-indicator, with respect to the archive of solutions maintained by the branch and bound algorithm. Although the I-BB will eventually identify the efficient set, we are particularly interested in analyzing its anytime behavior as a heuristic. Our experimental results, conducted on a multi-objective knapsack problem with 2, 3, 5, and 7 objectives, indicate that the I-BB can often outperform the naive depth-first and breadth-first search strategies, both in terms of runtime and anytime performance. The improvement is especially significant when the branching order for the decision variables is random, which suggests that the I-BB is particularly relevant when more favorable (problem-dependent) branching orders are not available.
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Dates and versions

hal-03331971 , version 1 (02-03-2023)

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Alexandre Jesus, Luís Paquete, Bilel Derbel, Arnaud Liefooghe. On the design and anytime performance of indicator-based branch and bound for multi-objective combinatorial optimization. GECCO 2021 - The Genetic and Evolutionary Computation Conference, Jul 2021, Lille, France. pp.234-242, ⟨10.1145/3449639.3459360⟩. ⟨hal-03331971⟩
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