Choquet optimal set in biobjective combinatorial optimization

Lust, Thibaut; Rolland, Antoine

doi:10.1016/j.cor.2013.04.003

Cited by 5 publications

(1 citation statement)

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“…In this work, we assume that the DM's preferences can be represented by a parameterized scalarizing function (e.g., a weighted sum), allowing some tradeoff between the objectives, but the corresponding preference parameters (e.g., the weights) are initially not known; hence, we have to consider the set of all parameters compatible with the collected preference information. An interesting approach to deal with preference imprecision has been recently developed [20,22,31] and consists in determining the possibly optimal solutions, that is the solutions that are optimal for at least one instance of the preference parameters. The main drawback of this approach, though, is that the number of possibly optimal solutions may still be very large compared to the number of Paretooptimal solutions; therefore there is a need for elicitation methods aiming to specify the preference model by asking preference queries to the DM.…”

Section: Introductionmentioning

confidence: 99%

An Interactive Polyhedral Approach for Multi-objective Combinatorial Optimization with Incomplete Preference Information

Benabbou

Lust

2019

Lecture Notes in Computer Science

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In this paper, we develop a general interactive polyhedral approach to solve multi-objective combinatorial optimization problems with incomplete preference information. Assuming that preferences can be represented by a parameterized scalarizing function, we iteratively ask preferences queries to the decision maker in order to reduce the imprecision over the preference parameters until being able to determine her preferred solution. To produce informative preference queries at each step, we generate promising solutions using the extreme points of the polyhedron representing the admissible preference parameters and then we ask the decision maker to compare two of these solutions (we propose different selection strategies). These extreme points are also used to provide a stopping criterion guaranteeing that the returned solution is optimal (or near-optimal) according to the decision maker's preferences. We provide numerical results for the multi-objective spanning tree and traveling salesman problems with preferences represented by a weighted sum to demonstrate the practical efficiency of our approach. We compare our results to a recent approach based on minimax regret, where preference queries are generated during the construction of an optimal solution. We show that better results are achieved by our method both in terms of running time and number of questions.

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Section: Introductionmentioning

confidence: 99%

An Interactive Polyhedral Approach for Multi-objective Combinatorial Optimization with Incomplete Preference Information

Benabbou

Lust

2019

Lecture Notes in Computer Science

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2-additive Choquet Optimal Solutions in Multiobjective Optimization Problems

Lust

Rolland

2014

Information Processing and Management of Uncertainty in Knowledge-Based Systems

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International audienceIn this paper, we propose a sufficient condition for a solution to be optimal for a 2-additive Choquet integral in the context of multiobjective combinatorial optimization problems. A 2-additive Choquet optimal solution is a solution that optimizes at least one set of parameters of the 2-additive Choquet integral. We also present a method to generate 2-additive Choquet optimal solutions of multiobjective combinatorial optimization problems. The method is experimented on some Pareto fronts and the results are analyzed

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Choquet Integral Versus Weighted Sum in Multicriteria Decision Contexts

Lust

2015

Algorithmic Decision Theory

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Choquet optimal set in biobjective combinatorial optimization

Cited by 5 publications

References 32 publications

An Interactive Polyhedral Approach for Multi-objective Combinatorial Optimization with Incomplete Preference Information

An Interactive Polyhedral Approach for Multi-objective Combinatorial Optimization with Incomplete Preference Information

2-additive Choquet Optimal Solutions in Multiobjective Optimization Problems

Choquet Integral Versus Weighted Sum in Multicriteria Decision Contexts

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