Browsing by Subject "Cutting planes"

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Open Access
Cutting plane algorithms for 0-1 programming based on cardinality cuts
(Elsevier, 2010) Oguz, O.
We present new valid inequalities for 0-1 programming problems that work in similar ways to well known cover inequalities. Discussion and analysis of these cuts is followed by their revision and use in integer programming as a new generation of cuts that excludes not only portions of polyhedra containing noninteger points, also parts with some integer points that have been explored in search of an optimal solution. Our computational experimentations demonstrate that this new approach has significant potential for solving large scale integer programming problems.
Open Access
Provisioning virtual private networks under traffic uncertainty
(Wiley, 2007) Altın, Ayşegül; Amaldi, E.; Belotti, P.; Pınar, Mustafa Çelebi
We investigate a network design problem under traffic uncertainty that arises when provisioning Virtual Private Networks (VPNs): given a set of terminals that must communicate with one another, and a set of possible traffic matrices, sufficient capacity has to be reserved on the links of the large underlying public network to support all possible traffic matrices while minimizing the total reservation cost. The problem admits several versions depending on the desired topology of the reserved links, and the nature of the traffic data uncertainty. We present compact linear mixed-integer programming formulations for the problem with the classical hose traffic model and for a less conservative robust variant relying on the traffic statistics that are often available. These flow-based formulations allow us to solve optimally medium-to-large instances with commercial MIP solvers. We also propose a combined branch-and-price and cutting-plane algorithm to tackle larger instances. Computational results obtained for several classes of instances are reported and discussed.