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 goal of this paper is to develop a Decision Support System (DSS) as a journey planner in complex and large multimodal urban network called Rahyar. Rahyar attempts to identify the most desirable itinerary among all feasible alternatives. The desirability of an itinerary is measured by a disutility function, which is defined as a weighted sum of some criteria. The weight...

When the matrix of distances between cities is symmetric and circulant, the traveling salesman problem (TSP) reduces to the so-called symmetric circulant traveling salesman problem (SCTSP), that has applications in the design of reconfigurable networks, and in minimizing wallpaper waste. The complexity of the SCTSP is open, but conjectured to be NP-hard, and we compare different lower bounds on...

In the quadratic traveling salesman problem a cost is associated with any three nodes traversed in succession. This structure arises, e. g., if the succession of two edges represents energetic conformations, a change of direction or a possible change of transportation means. In the symmetric case, costs do not depend on the direction of traversal. We study the polyhedral structure of a lineariz...

This paper solves the dynamic traveling salesman problem (DTSP) using dynamic Gaussian Process Regression (DGPR) method. The problem of varying correlation tour is alleviated by the nonstationary covariance function interleaved with DGPR to generate a predictive distribution for DTSP tour. This approach is conjoined with Nearest Neighbor (NN) method and the iterated local search to track dynami...

The traveling salesman problem (TSP) belongs to the most basic, most important, and most investigated problems in combinatorial optimization. Although it is an NP-hard problem, many of its special cases can be solved efficiently in polynomial time. We survey these special cases with emphasis on the results that have been obtained during the decade 1985–1995. This survey complements an earlier s...

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. ...