Automatic Decomposition and Branch-and-Price - A Status Report
نویسنده
چکیده
We provide an overview of our recent efforts to automatize Dantzig-Wolfe reformulation and column generation/branch-and-price for structured, large-scale integer programs. We present the need for and the benefits from a generic implementation which does not need any user input or expert knowledge. A focus is on detecting structures in integer programs which are amenable to a Dantzig-Wolfe reformulation. We give computational results and discuss future research topics. 1 Modeling with Integer Programs Integer programming offers undeniably a powerful and versatile, yet industrially relevant approach to model and solve discrete optimization problems from virtually all areas of scientific and practical applications. To get an impression on modeling, consider a simple combinatorial optimization problem, the bin packing problem. We are given n items of size ai, i = 1, . . . , n, which have to be packed into a minimum number of bins of capacity b each. A standard integer program for this problem is built on binary variables xij ∈ {0, 1} to decide whether item i is packed in bin j or not. It is common that a single variable imposes relatively little structure on the overall solution. The model is as follows.
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تاریخ انتشار 2012