Efforts aimed at combining operations research and constraint programming have become increasingly prominent and successful in the last few years. It is now widely recognized that integration, e.g., inference in the form of constraint propagation and relaxation in the form of linear programming, can yield substantial results. In this paper, we argue the benefits of constraint programming's global constraints as a basis for such an integration and discuss the advantages along with some examples. We illustrate the integration on the global cardinality structure, on piecewise linear functions, on variable subscripts, on the cycle structure and on resource constraints. Each example is completed with a case study.

The complementing strengths of Constraint (Logic) Programming (CLP) and Mixed Integer Programming (IP) have recently received significant attention. Although various optimization and constraint programming packages at a first glance seem to support mixed models, the modeling and solution techniques encapsulated are still rudimentary. Apart from exchanging bounds for variables and objective, little is known of what constitutes a good hybrid model and how a hybrid solver can utilize the complementary strengths of inference and relaxations. This paper adds to the field by identifying constraints as the essential link between CLP and IP and introduces an algorithm for bidirectional inference through these constraints. Together with new search strategies for hybrid solvers and cut-generating mixed global constraints, solution speed is improved over both traditional IP codes and newer mixed solvers.

In hybrid solvers for combinatorial optimisation, combining Constraint (Logic) Programming (CLP) and Mixed Integer Programming (MIP), it is important to have tight connections between the two domains. We extend and generalise previous work on automatic linearisations and propagation of symbolic CLP constraints that cross the boundary between CLP and MIP. We also present how reduced costs from the linear programming relaxation can be used for domain reduction on the CLP side. Computational results comparing our hybrid approach with pure CLP and MIP on a configuration problem show significant speed-ups.

We present Branch-and-Check, a hybrid framework integrating Mixed Integer Programming and Constraint Logic Programming, which encapsulates the traditional Benders Decomposition and Branch-and-Bound as special cases. In particular we describe its relation to Benders and the use of nogoods and linear relaxations. We give two examples of how problems can be modelled and solved using Branch-and-Check and present computational results demonstrating more than order-of-magnitude speedup compared to previous approaches. We also mention important future research issues such as hierarchical, dynamic and adjustable linear relaxations.

this paper we argue the benets of global constraintsas a basis for such an integration. We demonstrate the advantages of modellingwith global constraints, explain their operational benets and illustrate thiswith a series of case studies.(Integer Programming, Constraint Programming, Global Constraints, Integration,Hybrid Methods)1 IntroductionSince its origins, Constraint Programming (CP) has integrated algorithms fromdierent areas [25] such as Mathematical Programming, Networks...

Optimization and constraint satisfaction methods are complementary to a large extent, and there has been much recent interest in combining them. Yet no generally accepted principle or scheme for their merger has evolved. We propose a scheme based on two fundamental dualities: the duality of search and inference, and the duality of strengthening and relaxation. Optimization as well as constraint satisfaction methods can be seen as exploiting these dualities in their respective ways. Our proposal is that rather than employ either type of method exclusively, one can focus on how these dualities can be exploited in a given problem class. The resulting algorithm is likely to contain elements from both optimization and constraint satisfaction, and perhaps new methods that belong to neither.

We present a Modeler-Optimizer Interface (MOI) for general closed form Non-Linear Programs(NLP), which can be used to to transfer NLPs in a clear and simple manner between optimizationcomponents in a distributed environment. We demonstrate how this interface allows rst orderderivative information to be easily calculated on the optimizer's side, using automatic dierentiation,hence removing the bottleneck of communicating derivative information between the modelerand the optimizer....

Efforts aimed at combining Operations Research and Constraint Programming have become increasingly prominent and successful in the last few years. It is now widely recognized that integrating inference in the form of constraint propagation and relaxation in the form of linear programming can yield substantial results. In this paper we argue the benefits of global constraints as a basis for such an integration. We demonstrate the advantages of modeling with global constraints, explain their operational benefits and illustrate this with a series of case studies.

We present a le format for Non-Linear Programs (NLP), the extended MPS format (xMPS).This format directly extends the standard MPS le format for Linear and Mixed Integer Programsto include NLPs and permits a standardized way of transferring benchmark problems. The formatspares the modeler the tedious task of calculating derivative information with minimal extra workrequired by the optimizer and thus increases eciency.1 IntroductionThe main criteria for a le format for Non-Linear...

Linear programming and constraint propagation are complementary techniques with the potential for integration to benefit the solution of combinatorial optimization problems. Attempts to combine them have mainly focused on incorporating either technique into the framework of the other -- traditional models have been left intact. We argue that a rethinking of our modeling traditions is necessary to achieve the greatest benefit of such an integration. We propose a declarative modeling framework in which the structure of the constraints indicates how LP and CP can interact to solve the problem.