The traveling salesman problem (TSP) is the problem of finding the shortest tour through all the nodes that a salesman has to visit. The TSP is probably the most famous and extensively studied problem in the field of combinatorial optimization. Because this problem is an NP-hard problem, practical large-scale instances cannot be solved by exact algorithms within acceptable computational times. ...

The traveling salesman problem (TSP) is the problem of finding the shortest tour through all the nodes that a salesman has to visit. The TSP is probably the most famous and extensively studied problem in the field of combinatorial optimization. Because this problem is an NP-hard problem, practical large-scale instances cannot be solved by exact algorithms within acceptable computational times. ...

The bottleneck traveling salesman problem (BTSP) is a variation of the well-known traveling salesman problem in which the objective is to minimize the maximum lap (arc length) in a tour of the salesman. In this paper, a lexisearch algorithm using adjacency representation for a tour has been developed for obtaining exact optimal solution to the problem. Then a comparative study has been carried ...

We first prove that the minimum and maximum traveling salesman problems, their metric versions as well as some versions defined on parameterized triangle inequalities (called sharpened and relaxed metric traveling salesman) are all equi-approximable under an approximation measure, called differential-approximation ratio, that measures how the value of an approximate solution is placed in the in...

the traveling salesman problem (tsp) is the problem of finding the shortest tour through all the nodes that a salesman has to visit. the tsp is probably the most famous and extensively studied problem in the field of combinatorial optimization. because this problem is an np-hard problem, practical large-scale instances cannot be solved by exact algorithms within acceptable computational times. ...

The multiple traveling salesman problem (MTSP) involves scheduling m > 1 salesmen to visit a set of n > m nodes so that each node is visited exactly once. The objective is to minimize the total distance traveled by all the salesmen. The MTSP is an example of combinatorial optimization problems, and has a multiplicity of applications, mostly in the areas of routing and scheduling. In this paper,...