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

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 near-optimal 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.