Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Column generation has become a porful tool in solving large scale integer programs. It is ll known that most of the often reported compatibility issues beten pricing subproblem and branching rule disappear when branching decisions are based on imposing constraints on the subproblem's variables. This can be generalized to branching on variables of a so-called compact formulation.  constructively show that such a formulation always exists under mild assumptions. It has a block diagonal structure with identical subproblems, each of which contributes only one column in an integer solution. This construction has an interpretation as reversing a Dantzig-Wolfe decomposition. Our proposal opens the way for the development of branching rules adapted to the subproblem's structure and to the linking constraints.
['Daniel Villeneuve', 'Jacques Desrosiers', 'Marco E. Lübbecke', 'François Soumis']
I am writing a research paper on a idea On Compact Formulations for Integer Programs Solved by Column Generation
[{"from": "human", "value": "I am writing a research paper on a idea On Compact Formulations for Integer Programs Solved by Column Generation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Column generation has become a porful tool in solving large scale integer programs. It is ll known that most of the often reported compatibility issues beten pricing subproblem and branching rule disappear when branching decisions are based on imposing constraints on the subproblem's variables. This can be generalized to branching on variables of a so-called compact formulation.  constructively show that such a formulation always exists under mild assumptions. It has a block diagonal structure with identical subproblems, each of which contributes only one column in an integer solution. This construction has an interpretation as reversing a Dantzig-Wolfe decomposition. Our proposal opens the way for the development of branching rules adapted to the subproblem's structure and to the linking constraints."}]