Integration of Constraint Programming and Integer Programming for Combinatorial Optimization

Abstract: 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 different cultural origins, one having developed largely in the operations research community and the other in the computer science and artificial intelligence communities. The advantages of merger, however, are rapidly overcomingthis barrier.The main objective for an integration of Constraint Programming over finite domains (CP) and Integer Programming (IP) is to take advantage of both the inference through constraint propagation and the (continuous) relaxations through Linear Programming (LP), in order to reduce the search needed to find 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 specifically 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 LPand CP respectively. Branching is done in the CP part, utilizing information from the LP relaxation.Apart from a general framework for integration, specific constraints and structures studied include several variations of variable subscripts and piecewise linear functions. Computational experiments show the benefit and potential of a hybrid scheme, illustrated on production planning and configuration problems.