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Combining Preference Elicitation with Local Search and Greedy Search for Matroid Optimization

Abstract : We propose two incremental preference elicitation methods for interactive preference-based optimization on weighted matroid structures. More precisely, for linear objective (utility) functions, we propose an interactive greedy algorithm interleaving preference queries with the incremental construction of an independent set to obtain an optimal or nearoptimal base of a matroid. We also propose an interactive local search algorithm based on sequences of possibly improving exchanges for the same problem. For both algorithms, we provide performance guarantees on the quality of the returned solutions and the number of queries. Our algorithms are tested on the uniform, graphical and scheduling matroids to solve three different problems (committee election, spanning tree, and scheduling problems) and evaluated in terms of computation times, number of queries, and empirical error.
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Contributor : Nawal Benabbou Connect in order to contact the contributor
Submitted on : Friday, April 30, 2021 - 9:25:08 AM
Last modification on : Sunday, June 26, 2022 - 3:07:47 AM


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  • HAL Id : hal-03106084, version 2


Nawal Benabbou, Cassandre Leroy, Thibaut Lust, Patrice Perny. Combining Preference Elicitation with Local Search and Greedy Search for Matroid Optimization. 35th AAAI Conference on Artificial Intelligence (AAAI'21), Feb 2021, Virtual, France. ⟨hal-03106084v2⟩



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