کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5128281 1378587 2016 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Integer programming as projection
ترجمه فارسی عنوان
برنامه ریزی عدد صحی به عنوان طرح
کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات کنترل و بهینه سازی
چکیده انگلیسی

We generalise polyhedral projection (Fourier-Motzkin elimination) to integer programming (IP) and derive from this an alternative perspective on IP that parallels the classical theory. We first observe that projection of an IP yields an IP augmented with linear congruence relations and finite-domain variables, which we term a generalised IP. The projection algorithm can be converted to a branch-and-bound algorithm for generalised IP in which the search tree has bounded depth (as opposed to conventional branching, in which there is no bound). It also leads to valid inequalities that are analogous to Chvátal-Gomory cuts but are derived from congruences rather than rounding, and whose rank is bounded by the number of variables. Finally, projection provides an alternative approach to IP duality. It yields a value function that consists of nested roundings as in the classical case, but in which ordinary rounding is replaced by rounding to the nearest multiple of an appropriate modulus, and the depth of nesting is again bounded by the number of variables. For large perturbations of the right-hand sides, the value function is shift periodic and can be interpreted economically as yielding “average” shadow prices.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Discrete Optimization - Volume 22, Part B, November 2016, Pages 291-311
نویسندگان
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