Given a discretisation of an orebody as a block model, the open pit mining production scheduling problem (OPMPSP) consists of finding the sequence in which the blocks should be removed from the pit, over the lifetime of the mine, such that the net present value (NPV) of the operation is maximised. In practice, due to the large number of blocks and precedence constraints linking them, blocks are...

We study some linear programming relaxations for the Unsplittable Flow problem on trees (UFPtree). Inspired by results obtained by Chekuri, Ene, and Korula for Unsplittable Flow on paths (UFP-path), we present a relaxation with polynomially many constraints that has an integrality gap bound of O(logn ·min{logm, logn}) where n denotes the number of tasks and m denotes the number of edges in the ...

Structured prediction applications often involve complex inference problems that require the use of approximate methods. Approximations based on linear programming (LP) relaxations have proved particularly successful in this setting, with both theoretical and empirical support. Despite the general intractability of inference, it has been observed that in many real-world applications the LP rela...

Pseudo-Boolean problems lie on the border between satisfiability problems, constraint programming, and integer programming. In particular, nonlinear constraints in pseudo-Boolean optimization can be handled by methods arising in these different fields: One can either linearize them and work on a linear programming relaxation or one can treat them directly by propagation. In this paper, we inves...

Split cuts constitute a class of cutting planes that has been successfully employed by the majority of Branch-and-Cut solvers for Mixed Integer Linear Programs. Given a basis of the LP relaxation and a split disjunction, the corresponding split cut can be computed with a closed form expression. In this paper, we use the Lift-and-Project framework [10] to provide the basis, and the Reduce-andSpl...

We experimentally observe two separate time scales governing the entropic recoil in the linear force-extension regime of single double-stranded DNA in slit confinement. We demonstrate the existence of two distinct relaxation regimes at different extensions during relaxation. Contrary to bulk measurements, the true longest relaxation time may only be probed very close to equilibrium. A simple mo...

Recently, Linear Programming (LP)-based relaxations have been shown promising in boosting the performance of exact MAX-SAT solvers. We compare Semidefinite Programming (SDP) based relaxations with LP relaxations for MAX2SAT. We will show how SDP relaxations are surprisingly powerful, providing much tighter bounds than LP relaxations, across different constrainedness regions. SDP relaxations can...

The global constraint sum can be used as a tool to implement summations over sets of variables whose indices are not known in advance. This paper has two major contributions. On the theoretical side, we present the convex hull relaxation for the sum constraint in terms of linear inequalities, whose importance in the context of hybrid models is then justified. On the practical side, we demonstra...

Each of n items (products) is to be processed on two, capacity limited machines in order to satisfy known demands in each of T periods. Only one item can be processed on each machine at any given time and period. Each switch from one item to another requires sequence dependent setup time. The object is to minimize the sum of the costs of production, storage and setup. We define a quadratic mixe...

Dantzig-Wolfe reformulation of a mixed integer program partially convexifies a subset of the constraints, i.e., it implicitly adds all valid inequalities for the associated integer hull. Projecting an optimal basic solution of the reformulation’s LP relaxation to the original space does is in general not yield a basic solution of the original LP relaxation. Cutting planes in the original proble...