Browsing by Author "Cook, William"

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    A Parallel Cutting-Plane Algorithm for the Vehicle Routing Problem with Time Windows
    (1999-05) Cook, William; Rich, Jennifer L.
    In the vehicle routing problem with time windows a number of identical vehicles must be routed to and from a depot to cover a given set of customers, each of whom has a specified time interval indicating when they are available for service. Each customer also has a known demand, and a vehicle may only serve the customers on a route if the total demand does not exceed the capacity of the vehicle. The most effective solution method proposed to date for this problem is due to Kohl, Desrosiers, Madsen, Solomon, and Soumis. Their algorithm uses a cutting-plane approach followed by a branch-and-bound search with column generation, where the columns of the LP relaxation represent routes of individual vehicles. We describe a new implementation of their method, using Karger's randomized minimum-cut algorithm to generate cutting planes. The standard benchmark in this area is a set of 87 problem instances generated in 1984 by M. Solomon; making use of parallel processing in both the cutting-plane generation and the branch-and-bound search, we solve 80 of these examples, including 10 that were previously unsolved in the literature. Our parallel implementation utilizes the Tread Marks distributed shared memory system.
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    Finding Tours in the TSP
    (1999-05) Applegate, David; Bixby, Robert; Chvatal, Vasek; Cook, William
    The traveling salesman problem, or TSP for short, is easy to state: given a finite number of "cities" along with the cost of travel between each pair of them, find the cheapest way of visiting all the cities and returning to your starting point. The travel costs are symmetric in the sense that traveling from city X to city Y costs just as much as traveling from Y to X; the "way of visiting all the cities" is simply the order in which the cities are visited. In this report we consider the relaxed version of the TSP where we ask only for a tour of low cost. This is a preliminary version of a chapter of planned monograph on the TSP.