Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present an exact mixed-integer programming MIP solution scheme where a set-covering model is used to find a small set of first-choice branching variables. In a preliminary “sampling” phase, our method quickly collects a number of relevant low-cost fractional solutions that qualify as obstacles for the linear programming LP relaxation bound improvement. Then a set covering model is solved to detect a small subset of variables a “backdoor,” in the artificial intelligence jargon 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 the literature 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.
['Matteo Fischetti', 'Michele Monaci']
I am writing a research paper on a idea Backdoor Branching
[{"from": "human", "value": "I am writing a research paper on a idea Backdoor Branching"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  present an exact mixed-integer programming MIP solution scheme where a set-covering model is used to find a small set of first-choice branching variables. In a preliminary \u201csampling\u201d phase, our method quickly collects a number of relevant low-cost fractional solutions that qualify as obstacles for the linear programming LP relaxation bound improvement. Then a set covering model is solved to detect a small subset of variables a \u201cbackdoor,\u201d in the artificial intelligence jargon that \u201ccover the fractionality\u201d 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 the literature 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."}]