Min-Cost Multicommodity Network Flows: A Linear Case for the Convergence and Reoptimization of Multiple Single-Commodity Network Flows
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Date
2009-05-11
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Abstract
Network Flow problems are prevalent in Operations Research, Computer Science, Industrial Engineering and Management Science. They constitute a class of problems that are frequently faced by real world applications, including transportation, telecommunications, production planning, etc. While many problems can be modeled as Network Flows, these problems can quickly become unwieldy in size and difficult to solve. One particularly large instance is the Min-Cost Multicommodity Network Flow problem. Due to the time-sensitive nature of the industry, faster algorithms are always desired: recent advances in decomposition methods may provide a remedy. One area of improvement is the cost reoptimization of the min-cost single commodity network flow subproblems that arise from the decomposition. Since similar single commodity network flow problems are solved, information from the previous solution provides a "warm-start" of the current solution. While certain single commodity network flow algorithms may be faster "from scratch," the goal is to reduce the overall time of computation. Reoptimization is the key to this endeavor. Three single commodity network flow algorithms, namely, cost scaling, network simplex and relaxation, will be examined. They are known to reoptimize well. The overall goal is to analyze the effectiveness of this approach within one particular class of network problems.
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Keywords
decomposition, network flows, reoptimization
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Degree
MS
Discipline
Operations Research
