Solving Hierarchical Constraints over Finite Domains

Many real world problems have requirements and constraints which con ict with each other and are not well de ned. One framework for dealing with such over-constrained/fuzzy problems is provided by constraint hierarchies, where constraints are divided into ranks, and where a comparator selects preferred solutions over others. In this paper, we present a framework for formulating hierarchical constraint problems over nite domains (HCPs). We show, how the recent framework of over-constrained integer programs (OIPs) can be extended to handle non-linear constraints and to exploit constraint hierarchies. The motivation for this work arose from solving large airport gate allocation problems. We show how gate allocation problems can be formulated as HCPs using typical gate allocation constraints. Using gate allocation benchmarks with varying problem characteristics, we compare local search on the given HCPs with local search and integer programming on linear reformulations of the HCPs.