Constraints over Structured Domains - Gervet, Carmen (Foundations of Artificial Intelligence, 2006)
The chapter presents higher level modeling facilities utilizing constraints over structured domains. It addresses the bin-packing problem. The main constrained objects are the different bins, each describing a collection of unordered distinct elements, subject to disjointness constraints among them, weight constraints reflecting on each bin capacity and possible cardinality restrictions on the number of items allowed in each bin. Such objects are structured in the sense that they involve more than one element in a specific setting. It discusses that a wide range of combinatorial search problems find a natural formulation in the language of sets, multisets, strings, functions, graphs or other structured objects. Bin-packing, set partitioning, set covering, combinatorial design problems, circuits and mapping problems are some of them. They are non-deterministic polynomial-time (NP)-complete problems originating from areas as diverse as combinatorial mathematics, operations research or artificial intelligence. These problems deal essentially with the search for discrete structured objects. While a high-level modeling approach seems more natural, many solutions have exploited the effectiveness of finite domains or mixed integer programming solvers.