A Group Theoretic Integer Programming Algorithm System Design And Computational
A Group Theoretic Integer Programming Algorithm System Design And Computational
George Anthony Gorry
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, >^), j = l, ... , n. 15 drawn to every node x except the node ^ = 0- The arc length or cost associated with an arc of type j is c.. Problem (7) in this setting is the problem of finding a shortest route from >^ to 6. In the process of finding this particular shortest route path, the algorithm find the shortest route from x. To all x. , k = 1, ... , D - 1. As we will discuss below, these additional paths are important if a search is required. An optimal solution w to (7) is extracted from the ...shortest route path by letting w. Equal the number of times an arc of type j is used in the optimal path. If w is a feasible correction, it is an optimal correction. Some computational experience with the unconstrained group problem is given in Figure 2. Clearly, w may fail to be feasible because some of the constraints (4d), (4e) or (4g) may be violated. Of these constraints, the 0-1 constraints (4g) on the non-basic variables can be explicitly considered when solving the shortest route group problem.
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