Abstract
We discuss generalized travelling-salesman problems where nodes are visited either once or not, and a penalty cost is incurred for each unvisited node. The generalization includes the longest-path problem and the shortest-path problem with specified nodes to be visited. A new transformation of generalized into standard travelling-salesman problem is presented. We give computational results for the shortest-path problem with specified nodes. The transformation makes it possible to solve symmetric problems with a relatively large number of specified nodes, which cannot be solved by previously published algorithms based on a linear assignment relaxation. Furthermore, we show how to obtain improved lower bounds for a special Euclidean-type variant.
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