Purpose: This study proposes a new two-stage clustering method to break down the symmetric multiple traveling salesman problem (mTSP) into several single standard traveling salesman problems, each of which can then be solved separately using a heuristic optimization algorithm....

The k-traveling salesman problem, or k-TSP is: given a graph with edge weights and an integer k, find a simple cycle of minimum weight visiting exactly k nodes. To obtain lower bounds for the traveling salesman problem the 2-matching relaxation and the 1-tree relaxation can be used. We...