Permutation Problems and Channelling Constraints

When writing a constraint program, we have to decide what to make the decision variable, and how to represent the constraints on these variables. In many cases, there is considerable choice for the decision variables. For example, with permutation problems, we can choose between a primal and a dual representation. In the dual representation, dual variables stand for the primal values, whilst dual values stand for the primal variables. By means of channelling constraints, a combined model can have both primal and dual variables. In this paper, we perform an extensive theoretical and empirical study of these different models. Our results will aid constraint programmers to choose a model for a permutation problem. They also illustrate a general methodology for comparing different constraint models

Redundant Modeling for the QUasigroup Completion Problem

Abstract. The Quasigroup Completion Problem (QCP) is a very challenging benchmark among combinatorial problems, and the focus of much recent interest in the area of constraint programming. [5] reports that QCPs of order 40 could not be solved by pure constraint programming approaches, but could sometimes be solved by hybrid approaches combining constraint programming with mixed integer programming techniques from operations research. In this paper, we show that the pure constraint satisfaction approach can solve many problems of order 45 in the transition phase, which corresponds to the peak of difficulty. Our solution combines a number of known ideas –the use of redundant modeling [3] with primal and dual models of the problem connected by channeling constraints [13] – with some novel aspects, as well as a new and very effective value ordering heuristic.

Symmetry and Search in a Network Design Problem

Abstract. An optimization problem arising in the design of optical fibre networks is discussed. A network contains client nodes, each installed on one or more SONET rings. A constraint programming model of the problem is described and compared with a mixed integer programming formulation. In the CP model the search is decomposed into two stages; first partially solving the problem by deciding how many rings each node should be on, and then making specific assignments of nodes to rings. The model includes implied constraints derived by considering optimal solutions to subproblems. In both the MIP and CP models, it is important to deal with the symmetry of the problem. In the CP model, two sources of symmetry are separated; one is eliminated dynamically during search and the other by assigning ranges rather than explicit values to one set of decision variables. The resulting CP model allows optimal solutions to be found easily for benchmark problems.

Ubiquitous Health in Korea: Progress, Barriers, and Prospects

Abstract. We recently proposed a simple declarative language for specifying a wide range of counting and occurrence constraints. The language uses just two global primitives: the Range constraint, which computes the range of values used by a set of variables, and the Roots constraint, which computes the variables mapping onto particular values. In order for this specification language to be executable, propagation algorithms for the Range and Roots constraints should be developed. In this paper, we focus on the study of the Range constraint. We propose an efficient algorithm for propagating the Range constraint. We also show that decomposing global counting and occurrence constraints using Range is effective and efficient in practice.

A histochemical and biochemical investigation into the relationship between muscle fibre types and adjacent adipose tissue.

Constraint propagation algorithms implement logical inference. For efficiency, it is essential to control whether and in what order basic inference steps are taken. We provide a high-level framework that clearly differentiates between information needed for controlling propagation versus that needed for the logical semantics of complex constraints composed from primitive ones. We argue for the appropriateness of our controlled propagation framework by showing that it captures the underlying principles of manually designed propagation algorithms, such as literal watching for unit clause propagation and the lexicographic ordering constraint. We provide an implementation and benchmark results that demonstrate the practicality and efficiency of our framework

Exploiting functional dependencies in declarative problem specifications

Abstract. In this paper we tackle the issue of the automatic recognition of functional dependencies among guessed predicates in constraint problem specifications. Functional dependencies arise frequently in pure declarative specifications, because of the intermediate results that need to be computed in order to express some of the constraints, or due to precise modelling choices, e.g., to provide multiple viewpoints of the search space in order to increase propagation. In either way, the recognition of dependencies greatly helps solvers, letting them avoid spending search on unfruitful branches, while maintaining the highest degree of declarativeness. By modelling constraint problem specifications as second-order formulae, we provide a characterization of functional dependencies in terms of semantic properties of first-order ones. Additionally, we show how suitable search procedures can be automatically synthesized in order to exploit recognized dependencies. We present opl examples of various problems, from bio-informatics, planning and resource allocation fields, and show how in many cases opl greatly benefits from the addition of such search procedures.