Constrained Optimization with Qualitative Preferences

TL;DR

This paper introduces three novel methods to efficiently solve constrained CP-nets by eliminating the need for expensive dominance testing, including a total order model, an extension of LP-trees, and a divide-and-conquer algorithm.

Contribution

It proposes three innovative approaches to address the computational challenge of dominance testing in constrained CP-nets, enhancing efficiency and practicality.

Findings

Constrained CPR-net yields a single optimal outcome without dominance testing.

Search-LP finds the most preferable feasible outcome efficiently.

The divide and conquer algorithm compares outcomes effectively while preserving CP-net semantics.

Abstract

The Conditional Preference Network (CP-net) graphically represents user's qualitative and conditional preference statements under the ceteris paribus interpretation. The constrained CP-net is an extension of the CP-net, to a set of constraints. The existing algorithms for solving the constrained CP-net require the expensive dominance testing operation. We propose three approaches to tackle this challenge. In our first solution, we alter the constrained CP-net by eliciting additional relative importance statements between variables, in order to have a total order over the outcomes. We call this new model, the constrained Relative Importance Network (constrained CPR-net). Consequently, We show that the Constrained CPR-net has one single optimal outcome (assuming the constrained CPR-net is consistent) that we can obtain without dominance testing. In our second solution, we extend the Lexicographic Preference Tree (LP-tree) to a set of constraints. Then, we propose a recursive backtrack search algorithm, that we call Search-LP, to find the most preferable outcome. We prove that the first feasible outcome returned by Search-LP (without dominance testing) is also preferable to any other feasible outcome. Finally, in our third solution, we preserve the semantics of the CP-net and propose a divide and conquer algorithm that compares outcomes according to dominance testing.