The lift-and-project closure is the relaxation obtained by computing all lift-and-project cuts from the initial formulation of a mixed integer linear program or equivalently by computing all mixed integer Gomory cuts read from all tableau’s corresponding to feasible and infeasible bases. In this paper, we present an algorithm for approximating the value of the lift-and-project … Read more
In this paper we consider a relaxation of the corner polyhedron introduced by Andersen et al., which we denote by RCP. We study the relative strength of the split and triangle cuts of RCP’s. Basu et al. showed examples where the split closure can be arbitrarily worse than the triangle closure under a `worst-cost’ type … Read more
The cutting plane tree (CPT) algorithm provides a finite disjunctive programming procedure to obtain the solution of general mixed-integer linear programs (MILP) with bounded integer variables. In this paper, we present our computational experience with variants of the CPT algorithm. Because the CPT algorithm is based on discovering multi-term disjunctions, this paper is the first … Read more
This article extends a previous work focused on a mixed integer programming (MIP) based heuristic approach, aimed at solving non-standard three-dimensional problems with additional conditions. The paper that follows considers a mixed integer non-linear (MINLP) reformulation of the previous model, to improve the former heuristic, based on linear relaxation. The approach described herewith is addressed, … Read more
Geometric random walks have been proposed and analyzed for solving optimization problems. In this paper we report our computational experience with generating feasible integer solutions of mixed-integer linear programs using geometric random walks, and a random ray approach. A feasibility pump is used to heuristically round the generated points. Computational results on MIPLIB2003 and COR@L … Read more
We address a 1-dimensional cutting stock problem where, in addition to trim-loss minimization, we require that the set of cutting patterns forming the solution can be sequenced so that the number of stacks of parts maintained open throughout the process never exceeds a given $s$. For this problem, we propose a new integer linear programming … Read more
Mixed-Integer optimization represents a powerful tool for modeling many optimization problems arising from real-world applications. The Feasibility pump is a heuristic for finding feasible solutions to mixed integer linear problems. In this work, we propose a new feasibility pump approach using concave non-differentiable penalty functions for measuring solution integrality. We present computational results on binary … Read more
We show that every facet-defining inequality of the convex hull of a mixed-integer polyhedral set with two integer variables is a crooked cross cut (which we defined recently in another paper). We then extend this observation to show that crooked cross cuts give the convex hull of mixed-integer sets with more integer variables provided that … Read more
We provide a probabilistic comparison of split and type 1 triangle cuts for mixed-integer programs with two rows and two integer variables. Under a simple probabilistic model of the problem parameters, we show that a simple split cut, i.e. a Gomory cut, is more likely to be better than a type 1 triangle cut in … Read more
The Quadratic Assignment Problem (QAP) can be solved by linearization, where one formulates the QAP as a mixed integer linear programming (MILP) problem. On the one hand, most of these linearization are tight, but hardly exploited within a reasonable computing time because of their size. On the other hand, Kaufman and Broeckx formulation [1] is … Read more