Backdoors to Combinatorial Optimization: Feasibility and Optimality
CPAIOR '09 Proceedings of the 6th International Conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Backdoors to typical case complexity
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Operations Research Letters
INFORMS Journal on Computing
Crowdsourcing backdoor identification for combinatorial optimization
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Which is the minimum number of variables that need branching for a given MIP instance? Can this information be effective in producing compact branching trees, hence improving the performance of a state-of-the-art solver? In this paper we present a restart exact MIP solution scheme where a set covering model is used to find a small set of variables (a "backdoor", in the terminology of [8]) to be used as firstchoice variables for branching. In a preliminary "sampling" phase, our method quickly collects a number of relevant low-cost fractional solutions that qualify as obstacles for LP bound improvement. Then a set covering model is solved to detect a small subset of variables (the backdoor) that "cover the fractionality" of the collected fractional solutions. These backdoor variables are put in a priority branching list, and a black-box MIP solver is eventually run--in its default mode--by taking this list into account, thus avoiding any other interference with its highly-optimized internal mechanisms. Computational results on a large set of instances from MIPLIB 2010 are presented, showing that some speedup can be achieved even with respect to a state-of-the-art solver such as IBM ILOG Cplex 12.2.