Towards Fast Algorithms for the Preference Consistency Problem Based on Hierarchical Models
This work addresses a computational bottleneck in decision-making systems for applications like recommendation engines or AI planning, but it is incremental as it builds on known NP-completeness results.
The paper tackled the NP-complete Preference Consistency Problem for hierarchical models by developing three algorithmic approaches, including a MILP formulation and two recursive algorithms, and found that the recursive algorithms were significantly faster than the MILP, with running time ratios increasing extremely quickly in experiments on synthetic data.
In this paper, we construct and compare algorithmic approaches to solve the Preference Consistency Problem for preference statements based on hierarchical models. Instances of this problem contain a set of preference statements that are direct comparisons (strict and non-strict) between some alternatives, and a set of evaluation functions by which all alternatives can be rated. An instance is consistent based on hierarchical preference models, if there exists an hierarchical model on the evaluation functions that induces an order relation on the alternatives by which all relations given by the preference statements are satisfied. Deciding if an instance is consistent is known to be NP-complete for hierarchical models. We develop three approaches to solve this decision problem. The first involves a Mixed Integer Linear Programming (MILP) formulation, the other two are recursive algorithms that are based on properties of the problem by which the search space can be pruned. Our experiments on synthetic data show that the recursive algorithms are faster than solving the MILP formulation and that the ratio between the running times increases extremely quickly.