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We address the solution of Mixed Integer Linear Programming (MILP) models with strong relaxations that are derived from Dantzig-Wolfe decompositions and allow a pseudo-polynomial pricing algorithm. We exploit their network-flow characterization and provide a framework based on column generation, reduced-cost variable-fixing, and a highly asymmetric branching scheme that allows us to take advantage of the potential of the current MILP solvers. We apply our framework to a variety of cutting and packing problems from the literature. The efficiency of the framework is proved by extensive computational experiments, in which a significant number of open instances could be solved to proven optimality for the first time.
The prize-collecting Steiner tree problem PCSTP is a well-known generalization of the classical Steiner tree problem in graphs, with a large number of practical applications. It attracted particular interest during the latest (11th) DIMACS Challenge
We consider optimization problems with polynomial inequality constraints in non-commuting variables. These non-commuting variables are viewed as bounded operators on a Hilbert space whose dimension is not fixed and the associated polynomial inequalit
We study the vertex classification problem on a graph whose vertices are in $k (kgeq 2)$ different communities, edges are only allowed between distinct communities, and the number of vertices in different communities are not necessarily equal. The ob
Signomial programs (SPs) are optimization problems specified in terms of signomials, which are weighted sums of exponentials composed with linear functionals of a decision variable. SPs are non-convex optimization problems in general, and families of
We prove super-polynomial lower bounds on the size of linear programming relaxations for approximati