Thesis (M.S.)--Rochester Institute of Technology, 2006. / Typescript. Includes bibliographical references (leaves [70]-72).

Thesis (Ph. D.)--University of Missouri-Columbia, 2006. / The entire dissertation/thesis text is included in the research.pdf file; the official abstract appears in the short.pdf file (which also appears in the research.pdf); a non-technical general description, or public abstract, appears in the public.pdf file. Title from title screen of research.pdf file (viewed on August 10, 2007) Vita. Includes bibliographical references.

University, Diss., 2001--Saarbrücken.

The traveling salesperson (or, salesman) problem (TSP) is a well known and important combinatorial optimization problem. The goal is to find the shortest tour that visits each city in a given list exactly once and then returns to the starting city. Despite this simple problem statement, solving the TSP is difficult since it belongs to the class of NP-complete problems. The importance of the TSP arises besides from its theoretical appeal from the variety of its applications. Typical applications in operations research include vehicle routing, computer wiring, cutting wallpaper and job sequencing. The main application in statistics is combinatorial data analysis, e.g., reordering rows and columns of data matrices or identifying clusters. In this paper, we introduce the R package TSP which provides a basic infrastructure for handling and solving the traveling salesperson problem. The package features S3 classes for specifying a TSP and its (possibly optimal) solution as well as several heuristics to find good solutions. In addition, it provides an interface to Concorde, one of the best exact TSP solvers currently available. (authors' abstract)

Smith, T.H.C., Prof.

Unmanned aerial vehicles (UAVs) are becoming increasingly popular for surveillance in civil and military applications. Vehicles built for this purpose vary in their sensing capabilities, speed and maneuverability. It is therefore natural to assume that a team of UAVs given the mission of visiting a set of targets would include vehicles with differing capabilities. This paper addresses the problem of assigning each vehicle a sequence of targets to visit such that the mission is completed with the least "cost" possible given that the team of vehicles is heterogeneous. In order to simplify the problem the capabilities of each vehicle are modeled as cost to travel from one target to another. In other words, if a vehicle is particularly suited to visit a certain target, the cost for that vehicle to visit that target is low compared to the other vehicles in the team. After applying this simplification, the problem can be posed as an instance of the combinatorial problem called the Heterogeneous Travelling Salesman Problem (HTSP). This paper presents a transformation of a Heterogenous, Multiple Depot, Multiple Traveling Salesman Problem (HMDMTSP) into a single, Asymmetric, Traveling Salesman Problem (ATSP). As a result, algorithms available for the single salesman problem can be used to solve the HMDMTSP. To show the effectiveness of the transformation, the well known Lin-Kernighan-Helsgaun heuristic was applied to the transformed ATSP. Computational results show that good quality solutions can be obtained for the HMDMTSP relatively fast. Additional complications to the sequencing problem come in the form of precedence constraints which prescribe a partial order in which nodes must be visited. In this context the sequencing problem was studied seperately using the Linear Program (LP) relaxation of a Mixed Integer Linear Program (MILP) formulation of the combinatorial problem known as the "Precedence Constrained Asymmetric Travelling Salesman Problem" (PCATSP).

The Metric Travelling Salesman Problem, henceforth metric TSP, is a fundamental problem in combinatorial optimization which consists of finding a minimum cost Hamiltonian cycle (also called a TSP tour) in a weighted complete graph in which the costs are metric. Metric TSP is known to belong to a class of problems called NP-hard even in the special case of graph-TSP, where the metric costs are based on a given graph. Thus, it is highly unlikely that efficient methods exist for solving large instances of these problems exactly. In this thesis, we develop a new heuristic for metric TSP based on extending ideas successfully used by Mömke and Svensson for the special case of graph-TSP to the more general case of metric TSP. We demonstrate the efficiency and usefulness of our heuristic through empirical testing. Additionally, we turn our attention to graph-TSP. For this special case of metric TSP, there has been much recent progress with regards to improvements on the cost of the solutions. We find the exact value of the ratio between the cost of the optimal TSP tour and the cost of the optimal subtour linear programming relaxation for small instances of graph-TSP, which was previously unknown. We also provide a simplified algorithm for special graph-TSP instances based on the subtour linear programming relaxation.

Σ’ αυτή τη διπλωματική εργασία, παρουσιάζουμε προσεγγιστικούς αλγόριθμους για το Πρόβλημα του Πλανόδιου Πωλητή, μερικές πρακτικές εφαρμογές και κάποιες σχετικές παραλλαγές του κύριου προβλήματος. Ένας πλανόδιος πωλητής θέλει να επισκεφθεί κάθε πόλη ενός συνόλου πόλεων ακριβώς μια φορά ξεκινώντας και επιστρέφοντας στην αρχική πόλη. Το κύριο πρόβλημά του είναι να βρει τη συντομότερη διαδρομή. Παρουσιάζουμε μια αυτόνομη εισαγωγή σε αλγοριθμικές και υπολογιστικές απόψεις του προβλήματος μαζί με τις θεωρητικές απαραίτητες προϋποθέσεις τους από την σκοπιά της Επιχειρησιακής Έρευνας. Η διπλωματική αποσκοπεί να παρουσιάσει τις διαδικασίες επίλυσης του Προβλήματος του Πλανόδιου Πωλητή ανάλογα με το μέγεθος και τη δομή του. Θεωρητικά αποτελέσματα παρουσιάζονται σε μορφή που να καθιστούν σαφή τη σημασία τους στο σχεδιασμό των προσεγγιστικών αλγόριθμων για αποδεδειγμένα καλές ή/και βέλτιστες λύσεις του Προβλήματος. / In this thesis, at short, we present the Travelling Salesman Problem with approximations algorithms, some practical applications and related problems of the main problem. A travelling salesman wants to visit each of a set of towns exactly once starting from and returning to his home town. One of his problems is to find the shortest such trip. We present a self-contained introduction into algorithmic and computational aspects of the TSP along with their theoretical prerequisites as seen from the point of view of an operations researcher who wants to solve practical instances. This thesis is intended to be a guideline of the reader confronted with the question of how to attack a TSP instance depending on its size, its structural properties. Theoretical results are presented in a form which make clear their importance in the design of algorithms for approximate but provably good, and optimal solutions of the TSP.

The target of this thesis is to explain the Travelling Salesman Problem and also create a special program, which will be able to make calculations using the heuristics GENIUS. The Travelling Salesman Problem will be described from two different points of view. The first one is the historical description of the idea of the Travelling Salesman Problem and later will be the problem will be described with some of the very wide number of the calculation methods. For the explanation of the methods, in the thesis there has been chosen some of the algorithms which belong to that methods. The heuristics and also the exact algorithms will be explained. The focus of this thesis is on the heuristics called GENIUS and also in the creation of the program which can calculate it. The program works first with the GENI algorithm and after that it works with US post-optimization algorithm. The program will be described from the point of view of the user and the manual will be written as well. The program will be tested on two different examples and will be compared with the exact algorithm.

by Liang Fa Ming. / Publication date from spine. / Thesis (M.Phil.)--Chinese University of Hong Kong, 1995. / Includes bibliographical references (leaves 49-53). / ABSTRACT --- p.1 / Chapter CHAPTER 1 : --- Introduction --- p.2 / Chapter 1.1 ： --- The TSP Problem --- p.2 / Chapter 1.2: --- Application --- p.3 / Chapter CHAPTER 2 : --- Review of Exact and Approximate Algorithms for TSP --- p.4 / Chapter 2.1 : --- Exact Algorithm --- p.4 / Chapter 2.2 : --- Heuristic Algorithms --- p.8 / Chapter CHAPTER 3 : --- Markov Chain Monte Carlo Methods --- p.16 / Chapter 3.1: --- Markov Chain Monte Carlo --- p.16 / Chapter 3.2 : --- Conditioning and Gibbs Sampler --- p.17 / Chapter 3.3: --- The Metropolis-Hasting Algorithm --- p.18 / Chapter 3.4: --- Auxiliary Variable Methods --- p.21 / Chapter CHAPTER 4: --- Weighted Markov Chain Monte Carlo Method --- p.24 / Chapter CHAPTER 5 : --- Traveling Salesman Problem --- p.31 / Chapter 5.1: --- Buildup Order --- p.33 / Chapter 5.2: --- Path Construction through a Group of Points --- p.34 / Chapter 5.3: --- Solving TSP Using the Weighted Markov Chain Method --- p.38 / Chapter 5.4: --- Temperature Scheme --- p.40 / Chapter 5.5 : --- How to Adjust the Constant Prior-Ratio --- p.41 / Chapter 5.6: --- Validation of Our Algorithm by a Simple Example --- p.41 / Chapter 5.7 : --- Adding/Deleting Blockwise --- p.42 / Chapter 5.8: --- The sequential Optimal Method and Post Optimization --- p.43 / Chapter 5. 9 : --- Composite Algorithm --- p.44 / Chapter 5.10: --- Numerical Comparisons and Tests --- p.45 / Chapter CHAPTER 6 : --- Conclusion --- p.48 / REFERENCES --- p.49 / APPENDIX A --- p.54 / APPENDIX B --- p.58 / APPENDIX C --- p.61