Ted K. Ralphs

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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)
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)
This paper reports on the fifth version of the Mixed Integer Programming Library. The miplib 2010 is the first miplib release that has been assembled by a large group from academia and from industry, all of whom work in integer programming. There was mutual consent that the concept of the library had to be expanded in order to fulfill the needs of the(More)
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)
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)
The imposition of general disjunctions of the form “πx ≤ π0 ∨ πx ≥ π0 + 1”, where π, π0 are integer valued, is a fundamental operation in both the branch-and-bound and cuttingplane 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)
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)
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(More)