In this paper we study an exact separation algorithm for mixed knapsack sets with the aim of evaluating its effectiveness in a cutting plane algorithm for Mixed-Integer Programming. First proposed by Boyd in the 90’s, exact knapsack separation has recently found a renewed interest. In this paper we present a “lightweight” exact separation procedure for … Read more
We describe a rudimentary branch-and-cut algorithm for solving integer bilevel linear programs that extends existing techniques for standard integer linear programs to this very challenging computational setting. The algorithm improves on the branch-and-bound algorithm of Moore and Bard in that it uses cutting plane techniques to produce improved bounds, does not require specialized branching strategies, … Read more
This paper introduces disjunctive decomposition for two-stage mixed 0-1 stochastic integer programs (SIPs) with random recourse. Disjunctive decomposition allows for cutting planes based on disjunctive programming to be generated for each scenario subproblem under a temporal decomposition setting of the SIP problem. A new class of valid inequalities for mixed 0-1 SIP with random recourse … Read more
This paper is concerned with the single-row facility layout problem (SRFLP). A globally optimal solution to the SRFLP is a linear placement of rectangular facilities with varying lengths that achieves the minimum total cost associated with the (known or projected) inter- actions between them. We demonstrate that the combination of a semidefinite programming relaxation with … Read more
Mixed-integer rounding (MIR) is a simple, yet powerful procedure for generating valid inequalities for mixed-integer programs. When used as cutting planes, MIR inequalities are very effective for problems with unbounded integer variables. For problems with bounded integer variables, however, cutting planes based on lifting techniques appear to be more effective. This is not surprising as … Read more
In this paper we present a cutting plane algorithm for the Set Covering problem. Cutting planes are generated by a “general” (i.e. not based on the “template paradigm”) separation algorithm based on the following idea: i) identify a suitably small subproblem defined by a subset of the constraints of the formulation; ii) run an exact … Read more
In this paper, we propose lifting techniques for generating strong cuts for nonlinear programs that are globally-valid. The theory is geometric and provides intuition into lifting-based cut generation procedures. As a special case, we find short proofs of earlier results on lifting techniques for mixed-integer programs. Using convex extensions, we obtain conditions that allow sequence-independent … Read more
We study a planning problem arising in SDH/WDM multi-layer telecommunication network design. The goal is to find a minimum cost installation of link and node hardware of both network layers such that traffic demands can be realized via grooming and a survivable routing. We present a mixed-integer programming formulation that takes many practical side constraints … Read more
We introduce a new measure of complexity of integer hulls of rational polyhedra called the small Chvatal rank (SCR). The SCR of an integer matrix A is the number of rounds of a Hilbert basis procedure needed to generate all normals of a sufficient set of inequalities to cut out the integer hulls of all … Read more
The Generalized Assignment Problem is a well-known NP-hard combinatorial optimization problem which consists of minimizing the assignment costs a set of jobs to a set of machines satisfying capacity constraints. Most of the existing algorithms are based on Branch-and-Price, with lower bounds computed by Dantzig-Wolfe reformulation and column generation. In this paper we propose a … Read more