Abstract
Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in many engineering and computer science applications. Especially the Earth Mover's Distance is used in a plethora of applications ranging from content-based image retrieval, shape matching, fingerprint recognition, object tracking and phishing web page detection to computing color differences in linguistics and biology. Our starting point is the well-known revised simplex algorithm, which iteratively improves a feasible solution to optimality. The Shortlist Method that we propose substantially reduces the number of candidates inspected for improving the solution, while at the same time balancing the number of pivots required. Tests on simulated benchmarks demonstrate a considerable reduction in computation time for the new method as compared to the usual revised simplex algorithm implemented with state-of-the-art initialization and pivot strategies. As a consequence, the Shortlist Method facilitates the computation of large scale transportation problems in viable time. In addition we describe a novel method for finding an initial feasible solution which we coin Modified Russell's Method.
Highlights
Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in various guises in many real world and theoretical situations
They occur as subproblems in larger problems, e.g. the warehouse location problem or the traveling salesperson problem and in a variety of engineering and computer science applications, such as content based image retrieval [1], automatic scene analysis [2] or for the discrimination between real and artificial fingerprints [3]
The problem was first described by Monge in 1781 [4] in somewhat different form and has been analyzed by many researches including Kantorovich, Hitchcock, Koopmans and especially Dantzig [5,6], the father of the simplex algorithm
Summary
Finding solutions to the classical transportation problem is of great importance, since this optimization problem arises in various guises in many real world and theoretical situations. The problem was first described by Monge in 1781 [4] in somewhat different form and has been analyzed by many researches including Kantorovich, Hitchcock, Koopmans and especially Dantzig [5,6], the father of the simplex algorithm. The solution of this problem is the fundamental ingredient for computing the Earth Mover’s Distance [1] in computer science and the Wasserstein distance, known as Mallows or Kantorovich distance in statistics and physics, see Chapter 6 in [7].
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