We consider a family of problems defined on a common solution space. A problem is characterized by a subset of the solution space whose elements are defined to be feasible for that problem. Each solution is associated...
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We consider a family of problems defined on a common solution space. A problem is characterized by a subset of the solution space whose elements are defined to be feasible for that problem. Each solution is associated with a cost. Solving a problem means finding a feasible solution of minimum cost. It is assumed that an algorithm for solving any single problem is available. We show how to solve all of the problems in the family by selecting and solving a small subset of them.
As known in literature a flow-type approach to the Euclidean Traveling Salesman Problem gives better assignment lower bounds, using cities on the convex hull as sources and sinks, By selecting them carefully this appr...
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A simple transformation of the distance matrix for the Euclidean traveling salesman problem is presented that produces a tighter lower bound on the length of the optimal tour than has previously been attainable using ...
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A simple transformation of the distance matrix for the Euclidean traveling salesman problem is presented that produces a tighter lower bound on the length of the optimal tour than has previously been attainable using the assignment relaxation. The improved lower bound is obtained by exploiting geometric properties of the problem to produce fewer and larger subtours on the first solution of the assignment problem. This research should improve the performance of assignment based exact procedures and may lead to improved heuristics for the traveling salesman problem.
An algorithm for finding the K best cuts in a network is presented. Using a branch technique introduced by Lawler [4] we reduce the problem to K computations of 2nd best cuts. The latter problem can be solved by an O(...
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