Artificial Intelligence
Constraint satisfaction in logic programming
Constraint satisfaction in logic programming
Enhancement schemes for constraint processing: backjumping, learning, and cutset decomposition
Artificial Intelligence
Maximising the net present value for resource-constrained project scheduling
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
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Testing the satisfiability of a Boolean formula over linear constraints is not a simple matter. Existing AI systems handle that kind of problems with a general proof method for their Boolean parts and a separate module for combining linear constraints. On the contrary, traditional operations research methods need the problem to be transformed, and solved with a Mixed Integer Linear Programming algorithm. Both approaches appear to be improvable if no early separation is introduced between the logical and numerical parts. In this case, combinatorial explosion can be dramatically reduced thanks to efficient looking-ahead techniques and learning methods. Indeed, propagating bounds following the initial formula gives precious information. Besides, an especially tight linear relaxation can be driven from the formula, and allows a Simplex algorithm to make a good test for satisfiability. Finally, these two looking-ahead methods can be easily coupled for more efficiency and completed by local enumeration. Moreover, discovering a good failure explanation is relatively easy in the proposed framework. By "learning" these explanations, it is possible to prune important redundant parts of the search tree.