Choquet optimal set in biobjective combinatorial optimization

Thibaut Lust 1 Antoine Rolland
1 DECISION
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : We study in this paper the generation of the Choquet optimal solutions of biobjective combinatorial optimization problems. Choquet optimal solutions are solutions that optimize a Choquet integral. The Choquet integral is used as an aggregation function, presenting different parameters, and allowing to take into account the interactions between the objectives. We develop a new property that characterizes the Choquet optimal solutions. From this property, a general method to easily generate these solutions in the case of two objectives is defined. We apply the method to two classical biobjective optimization combinatorial optimization problems: the biobjective knapsack problem and the biobjective minimum spanning tree problem. We show that Choquet optimal solutions that are not weighted sum optimal solutions represent only a small proportion of the Choquet optimal solutions and are located in a specific area of the objective space, but are much harder to compute than weighted sum optimal solutions.
Document type :
Journal articles
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01170501
Contributor : Lip6 Publications <>
Submitted on : Wednesday, July 1, 2015 - 4:15:04 PM
Last modification on : Wednesday, November 28, 2018 - 1:26:28 AM

Identifiers

Collections

Citation

Thibaut Lust, Antoine Rolland. Choquet optimal set in biobjective combinatorial optimization. Computers and Operations Research, Elsevier, 2013, 40 (10), pp.2260-2269. ⟨10.1016/j.cor.2013.04.003⟩. ⟨hal-01170501⟩

Share

Metrics

Record views

61