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...

For a given graph with vertex set that is partitioned into clusters, the generalized traveling salesman problem (GTSP) of finding cost-minimal cycle contains exactly one every cluster. We introduce three new GTSP neighborhoods allow simultaneous permutation sequence clusters and selection vertices from each The some known literature are combined an effective iterated local search (ILS) for GTSP...

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. ...

Traveling Salesman Problem (TSP) is a generic name that includes diverse practical models. Motivated by applications, a new model of TSP is examined — a synthesis of classical TSP and classical Transportation Problem. Algorithms based on Integer Programming cutting-plane methods and Branch and Bound Techniques are obvious. Mathematics Subject Classification 2000: 91A05, 91A06, 91A10, 91A44, 90C...

In the Attractive Traveling Salesman Problem the vertex set is partitioned into facility vertices and customer vertices. A maximum profit tour must be constructed on a subset of the facility vertices. Profit is computed through an attraction function: every visited facility vertex attracts a portion of the profit from the customer vertices based on the distance between the facility and customer...