We present a new symmetric traveling salesman problem tour construction heuristic. Two sequential matchings yield a set of cycles over the given point set; these are then stitched to form a tour. Our method outperforms all previous tour construction methods, but is dominated by several tour improvement heuristics. c © 2004 Elsevier B.V. All rights reserved.

An important endeavor in computer science is to understand the expressive power of logical formalisms over discrete structures, such as words. Naturally,"understanding"is not a mathematical notion. This investigation requires therefore a concrete objective to capture this understanding. In the literature, the standard choice for this objective is the membership problem, whose aim is to find a p...

This research investigates the feasibility of applying a guaranteed-accuracy heuristic learning algorithm to address the traveling salesman problem. The research focuses on tour construction. The advantage of tour construction heuristic is its simplicity in concept. However, tour construction heuristic often results in a sub-optimal solution and the tour often needs to be improved after it is b...

For a given set A C_ (-Tr; +Tr] of angles, the problem "Angle-Restricted Tour" (ART) is to decide whether a set P of n points in the Euclidean plane allows a closed directed tour consisting of straight line segments, such that all angles between consecutive line segments are from the set A. We present a variety of algorithmic and combinatorial results on this problem. In particular, we show tha...

This paper presents stop conditions for solving General Assignment Problems (GAP), in particular for Travel Salesman Problem in an Euclidian 2D space the well known condition Jordan’s simple curve and opposite condition for the Knight Tour Problem. The Jordan’s simple curve condition means that a optimal trajectory must be simple curve, i.e., without crossing but for Knight Tour Problem we use ...

The watchman route of a polygon is a closed tour that sees all points of the polygon. Computing the shortest such tour is a well-studied problem. Another reasonable optimization criterion is to require that the tour minimizes the hiding time of the points in the polygon, i.e., the maximum time during which any points is not seen by the agent following the tour at unit speed. We call such tours ...

This work suggests an adaptive tour planning multimedia system designed to meet the tour routing needs of different tourists. Tour planning is an application of vehicle routing problem. Meanwhile, vehicle routing problem is a ‘traveling salesman problem’ (TSP) type problem. TSP is an example of a combinatorial optimization problem and is known as NP-hard. As studied by many researchers exact, h...

The traveling salesman problem is a problem of finding the shortest tour through given points. In 1959, Beardwood, Halton, and Hammersley studied asymptotic length of the shortest tour through points on Euclidean space. In particular they described the optimal tour length with Euclidean dimension for the case that points are distributed with respect to Lebesgue absolutely continuous measure. In...