Uppsala Theses in Computing Science Integration of Constraint Programming and Integer Programming for Combinatorial Optimization Integration of Constraint Programming and Integer Programming for Combinatorial Optimization

The last several years have seen an increasing interest in combining the models and methods of optimization with those of constraint programming. Integration of the two was initially impeded by their diierent cultural origins , one having developed largely in the operations research community and the other in the computer science and artiicial intelligence communities. The advantages of merger, however, are rapidly overcoming this barrier. The main objective for an integration of Constraint Programming over-nite domains (CP) and Integer Programming (IP) is to take advantage of both the inference through constraint propagation and the (continuous) re-laxations through Linear Programming (LP), in order to reduce the search needed to nd feasible, good and optimal solutions. The key decisions to be made for integrating CP and IP are (a) the model(s), (b) the inference, (c) the relaxations, and, (d) the search and branching strategies to use. In this thesis it is advocated to model speciically for a hybrid solver, having part of the model operated on by CP inference and part of the model constituting an LP relaxation. We propose mixed (global) constraints spanning both discrete and continuous variables to bridge the gap between CP and LP, providing inference as well as information for search strategies. Inference comes as cutting planes and domains reductions for LP and CP respectively. Branching is done in the CP part, utilizing information from the LP relaxation. Apart from a general framework for integration, speciic constraints and structures studied include several variations of variable subscripts and piece-wise linear functions. Computational experiments show the beneet and potential of a hybrid scheme, illustrated on production planning and con-guration problems.