The Boolean quadric polytope: some characteristics, facets and relatives
Mathematical Programming: Series A and B
A recursive procedure to generate all cuts for 0-1 mixed integer programs
Mathematical Programming: Series A and B
Chva´tal closures for mixed integer programming problems
Mathematical Programming: Series A and B
A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
A lift-and-project cutting plane algorithm for mixed 0-1 programs
Mathematical Programming: Series A and B
Mixed-integer bilinear programming problems
Mathematical Programming: Series A and B
Discrete Applied Mathematics
A Genetic Algorithm for the Multidimensional Knapsack Problem
Journal of Heuristics
An Explicit Exact SDP Relaxation for Nonlinear 0-1 Programs
Proceedings of the 8th International IPCO Conference on Integer Programming and Combinatorial Optimization
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming
Mathematics of Operations Research
Split closure and intersection cuts
Mathematical Programming: Series A and B
Optimizing over the first Chvátal closure
Mathematical Programming: Series A and B
Valid inequalities for mixed integer linear programs
Mathematical Programming: Series A and B
Projected Chvátal–Gomory cuts for mixed integer linear programs
Mathematical Programming: Series A and B
Exact MAX-2SAT solution via lift-and-project closure
Operations Research Letters
Elementary closures for integer programs
Operations Research Letters
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In this paper we introduce DRL*, a new hierarchy of linear relaxations for 0-1 mixed integer linear programs (MIPs), based on the idea of Reformulation-Linearization, and explore its links with the Lift-and-Project (L&P) hierarchy and the Sherali-Adams (RLT) hierarchy. The relaxations of the new hierarchy are shown to be intermediate in strength between L&P and RLT relaxations, and examples are shown for which it leads to significantly stronger bounds than those obtained from Lift-and-Project relaxations. On the other hand, as opposed to the RLT relaxations, a key advantage of the DRL* relaxations is that they feature a decomposable structure when formulated in extended space, therefore lending themselves to more efficient solution algorithms by properly exploiting decomposition. Links between DRL* and both the L&P and RLT hierarchies are further explored, and those constraints which should be added to the rank d L&P relaxation (resp to the rank d RLT relaxation) to make it coincide with the rank d DRL* relaxation (resp: to the rank d RLT relaxation) are identified. Furthermore, a full characterization of those 0-1 MIPs for which the DRL* and RLT relaxations coincide is obtained. As an application, we show that both the RLT and DRL* relaxations are the same up to rank d for the problem of optimizing a pseudoboolean function of degree d over a polyhedron. We report computational results comparing the strengths of the rank 2 L&P, DRL* and RLT relaxations. Impact on possible improved efficiency in computing some bounds for the quadratic assignment problem and other directions for future research are suggested in the conclusions.