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- Ashutosh Mahajan, Ted K. Ralphs
- SIAM Journal on Optimization
- 2010

The imposition of general disjunctions of the form " πx ≤ π 0 ∨ πx ≥ π 0 + 1 " , where π, π 0 are integer valued, is a fundamental operation in both the branch-and-bound and cutting-plane algorithms for solving mixed integer linear programs. Such disjunctions can be used for branching at each iteration of the branch-and-bound algorithm or to generate split… (More)

- Ted K. Ralphs, L. Kopman, William R. Pulleyblank, Leslie E. Trotter
- Math. Program.
- 2003

We consider the Vehicle Routing Problem, in which a fixed fleet of delivery vehicles of uniform capacity must service known customer demands for a single commodity from a common depot at minimum transit cost. This difficult combinatorial problem contains both the Bin Packing Problem and the Traveling Salesman Problem (TSP) as special cases and conceptually… (More)

- Ted Ralphs, Menal Guzelsoy
- 2004

SYMPHONY is a customizable, open-source library for solving mixed-integer linear programs (MILP) by branch, cut, and price. With its large assortment of parameter settings, user callback functions, and compile-time options, SYMPHONY can be configured as a generic MILP solver or an engine for solving difficult MILPs by means of a fully customized algorithm.… (More)

- Ted K. Ralphs, Matthew J. Saltzman, Margaret M. Wiecek
- Annals OR
- 2006

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… (More)

- Ted K. Ralphs
- Parallel Computing
- 2003

Combinatorial optimization problems arise commonly in logistics applications. The most successful approaches to date for solving such problems involve modeling them as integer programs and then applying some variant of the branch and bound algorithm. Although branch and bound is conceptually easy to parallelize, achieving scalability can be a challenge. In… (More)

- Ted K. Ralphs, Laszlo Ladányi, Matthew J. Saltzman
- Math. Program.
- 2003

In discrete optimization, most exact solution approaches are based on branch and bound, which is conceptually easy to parallelize in its simplest forms. More sophisticated variants, such as the so-called branch, cut, and price algorithms, are more difficult to parallelize because of the need to share large amounts of knowledge discovered during the search… (More)

- Laszlo Ladányi, Ted K. Ralphs, Leslie E. Trotter
- Computational Combinatorial Optimization
- 2001

Branch, cut, and price (BCP) is an LP-based branch and bound technique for solving large-scale discrete optimization problems (DOPs). In BCP, both cuts and variables can be generated dynamically throughout the search tree. The ability to handle constantly changing sets of cuts and variables allows these algorithms to undertake the solution of very… (More)

- Pietro Belotti, Julio C. Góez, Imre Pólik, Ted K. Ralphs, Tamás Terlaky
- Discrete Applied Mathematics
- 2013

In this paper we investigate families of quadrics that have fixed intersections with two given hyperplanes. The cases when the two hyperplanes are parallel and when they are nonparallel are discussed. We show that these families can be described with only one parameter. In particular we show how the quadrics are transformed as the parameter changes. This… (More)

ALPS is a framework for implementing and parallelizing tree search algorithms. It employs a number of features to improve scalability and is designed specifically to support the implementation of data intensive algorithms, in which large amounts of knowledge are generated and must be maintained and shared during the search. Implementing such algorithms in a… (More)

- Y. Xu, Ted K. Ralphs, Laszlo Ladányi, Matthew J. Saltzman
- INFORMS Journal on Computing
- 2009

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… (More)