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- Ted Ralphs, Francisco Barahona, +8 authors Andreas Waechter
- 2002

- 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
- 2004

- 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)

- S. T. DeNegre, T. K Ralphs
- 2008

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,… (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)

- 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)

- 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)

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)

- 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)