Ted K. Ralphs We present a suite of tools for visualizing the status and progress of branch-and-bound algorithms for mixed integer programming. By integrating these tools with the open-source codes CBC, SYMPHONY, and GLPK, we demonstrate the potential usefulness of visual representations in helping a user predict future progress of the algorithm or analyzing the algorithm’s performance. We … Read more
In this paper, we discuss the challenges that arise in parallelizing algorithms for solving mixed integer linear programs and introduce a software framework that aims to address these challenges. The framework was designed specifically with support for implementation of relaxation-based branch-and-bound algorithms in mind. Achieving efficiency for such algorithms is particularly challenging and involves a … Read more
This paper is a survey of and some minor extensions to the theory of duality for mixed-integer linear programs. The theory of duality for linear programs is well-developed and has been extremely successful in both theory and practice. Much of this broad framework can be extended to MILPs in principle, but this has proven largely … Read more
We present an overview of noncommercial software tools for the solution of mixed-integer linear programs (MILPs). We first review solution methodologies for MILPs and then present an overview of the available software, including detailed descriptions of eight software packages available under open source or other noncommercial licenses. Each package is categorized as a black box … Read more
Both cutting plane methods and traditional decomposition methods are procedures that compute a bound on the optimal value of an integer linear program (ILP) by constructing an approximation to the convex hull of feasible solutions. This approximation is obtained by intersecting the polyhedron associated with the continuous relaxation, which has an explicit representation, with an … Read more
A parametric algorithm for identifying the Pareto set of a biobjective integer program is proposed. The algorithm is based on the weighted Chebyshev (Tchebycheff) scalarization, and its running time is asymptotically optimal. A number of extensions are described, including: a technique for handling weakly dominated outcomes, a Pareto set approximation scheme, and an interactive version … Read more
Decomposition algorithms such as Lagrangian relaxation and Dantzig-Wolfe decomposition are well-known methods that can be used to generate bounds for mixed-integer linear programming problems. Traditionally, these methods have been viewed as distinct from polyhedral methods, in which bounds are obtained by dynamically generating valid inequalities to strengthen the linear programming relaxation. Recently, a number of … Read more