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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)

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)

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)

Given the steady increase in cores per CPU, it is only a matter of time before supercomputers will have a million or more cores. In this article, we investigate the opportunities and challenges that will arise when trying to utilize this vast computing power to solve a single integer linear optimization problem. We also raise the question of whether best… (More)

We investigate families of quadrics that have fixed intersections with two given hyper-planes. 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 research was… (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)

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 describes the design of the Abstract Library for Parallel Search (ALPS), a framework for implementing scalable, parallel algorithms based on tree search. ALPS is specifically designed to support data-intensive algorithms, in which large amounts of data are required to describe each node in the search tree. Implementing such algorithms in a… (More)

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)

The mixed Chinese postman problem is a version of the well-known Chinese postman problem in which the underlying graph consists of both directed and undirected edges. We give an integer linear programming formulation for this problem and then show that the extreme points of its linear relaxation polyhe-dron are all half-integral.