On Possibly Optimal Tradeoffs in Multicriteria Spanning Tree Problems

Benabbou, Nawal; Perny, Patrice

doi:10.1007/978-3-319-23114-3_20

Cited by 14 publications

(18 citation statements)

References 12 publications

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“…However, this would not be very efficient in practice due to the large size of X (recall that X is the feasible set of a MOCO problem). This observation has led a group of researchers to propose a new approach consisting in combining preference elicitation and search by asking preference queries during the construction of the (near-)optimal solution (e.g., [3]). In this work, we propose to combine incremental elicitation and search in a different way: at each iteration step, we generate a set of promising solutions using the extreme points of Ω Θ (the set of admissible parameters), we ask the DM to compare two of these solutions, we update Ω Θ according to her answer and we stop the process whenever a (near-)optimal solution is detected (i.e.…”

Section: An Interactive Polyhedral Methodsmentioning

confidence: 99%

“…Comparison with the State-of-the-Art Method. In this subsection, we compare our interactive method with the state-of-the-art method proposed in [3]. The latter consists essentially in integrating incremental elicitation into Prim algorithm [23]; therefore, this method will be called IE-Prim hereafter.…”

Section: Ieep -Randommentioning

confidence: 99%

“…We have implemented ourselves IE-Prim, using the same programming language and data structures than IEEP, in order to allow a fair comparison between these methods. Although IE-Prim was only proposed and tested with CSS in [3], we have integrated the two other strategies (i.e., Max-Dist and Random) in IE-Prim. In Table 2, we compare IEEP with Max-Dist and IE-Prim in terms of running times and number of queries 3 .…”

Section: Ieep -Randommentioning

confidence: 99%

“…Although IE-Prim was only proposed and tested with CSS in [3], we have integrated the two other strategies (i.e., Max-Dist and Random) in IE-Prim. In Table 2, we compare IEEP with Max-Dist and IE-Prim in terms of running times and number of queries 3 . We see that IEEP outperforms IE-Prim in all settings, allowing the running time and the number of queries to be divided by three in our biggest instances.…”

Section: Ieep -Randommentioning

confidence: 99%

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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: An Interactive Polyhedral Methodsmentioning

confidence: 99%

Section: Ieep -Randommentioning

confidence: 99%

Section: Ieep -Randommentioning

confidence: 99%

Section: Ieep -Randommentioning

confidence: 99%

See 2 more Smart Citations

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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“…Unfortunately, as soon as the number of criteria is greater than 2, the problem becomes intractable because the number of Pareto-optimal cost vectors associated to spanning trees is, in the worst case, exponential in the number nodes. In the paper "On Possibly Optimal Tradeoffs in Multicriteria Spanning Tree Problems" that has been accepted for publication in ADT 2015 [3], we proposed a multiobjective extension of Prim's algorithm which can compute the exact set of possibly optimal cost vectors associated to spanning trees; this algorithm is a greedy search based on a specific decomposition of the feasible set of parameters. Then, we proposed to interweave incremental elicitation and search to determine a necessary optimal spanning tree.…”

mentioning

confidence: 99%

Possible Optimality and Preference Elicitation for Decision Making

Benabbou

2015

Algorithmic Decision Theory

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Combining Local Search and Elicitation for Multi-Objective Combinatorial Optimization

Benabbou

Leroy

Lust

et al. 2019

Algorithmic Decision Theory

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In this paper, we propose a general approach based on local search and incremental preference elicitation for solving multi-objective combinatorial optimization problems with imprecise preferences. We assume that the decision maker's preferences over solutions can be represented by a parameterized scalarizing function but the parameters are initially not known. In our approach, the parameter imprecision is progressively reduced by iteratively asking preference queries to the decision maker 1) before the local search in order to identify a promising starting solution and 2) during the local search but only when preference information are needed to discriminate between the solutions within a neighborhood. This new approach is general in the sense that it can be applied to any multi-objective combinatorial optimization problem provided that the scalarizing function is linear in its parameters (e.g., a weighted sum, an OWA aggregator, a Choquet integral) and that a (near-)optimal solution can be efficiently determined when preferences are precisely known. For the multi-objective traveling salesman problem, we provide numerical results obtained with different query generation strategies to show the practical efficiency of our approach in terms of number of queries, computation time and gap to optimality.

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On Possibly Optimal Tradeoffs in Multicriteria Spanning Tree Problems

Cited by 14 publications

References 12 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

Possible Optimality and Preference Elicitation for Decision Making

Combining Local Search and Elicitation for Multi-Objective Combinatorial Optimization

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