Abstract
Relaxed decision diagrams have recently been used in constraint programming to improve constraint propagation and optimization reasoning. In most applications, however, a decision diagram is compiled with respect to a single combinatorial structure. We propose to expand this representation by incorporating additional constraints in the decision diagram via a Lagrangian relaxation. With this generic approach we can obtain stronger bounds from the same decision diagram, while the associated cost-based filtering allows for further refining the relaxation. Experimental results on the traveling salesman problem with time windows show that the improved Lagrangian bounds can drastically reduce solution times.
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Bergman, D., Cire, A.A. & van Hoeve, WJ. Lagrangian bounds from decision diagrams. Constraints 20, 346–361 (2015). https://doi.org/10.1007/s10601-015-9193-y
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DOI: https://doi.org/10.1007/s10601-015-9193-y