Constrained Optimization with Preferentially Ordered Outcomes
Sultan Ahmed, Malek Mouhoub · 2018
The Conditional Preference Network (CP-net) graphically represents user's qualitative and conditional preference statements under the ceteris paribus (all else being equal) interpretation. Given that the CP-net induces a partial order over the outcomes, the optimization for a constrained CP-net can have a set of Pareto optimal solutions. The existing algorithms for solving the constrained CP-net require dominance testing between the outcomes, which is a very expensive operation. In this paper, we propose an extension of the CP-net model by eliciting additional relative importance statements between variables in order to have a total order over the outcomes. As a result, the constrained optimization using the proposed model involves a single optimal solution, assuming the underlying CSP is consistent. In this regard, we provide an efficient algorithm to find this optimal solution without the need for dominance testing.