20,411 research outputs found
Traveling Salesman Problem
Práce se zaměřuje na Ăşpravu známĂ˝ch postupĹŻ ACO a GA s ohledem na zvyšovánĂ efektivity nalĂ©zanĂ˝ch Ĺ™ešenĂ. Jsou zde prezentovány dva novĂ© pĹ™Ăstupy pro Ĺ™ešenĂ TSP. PomocĂ jednoho z nich lze takĂ© vytvoĹ™it počáteÄŤnĂ populaci pro GA. Je uveden konkrĂ©tnĂ návrh programu a v pĹ™Ăloze pak i jeho implementace v jazyce Java. Aby se zlepšila efektivita Ĺ™ešenĂ, jsou navrĹľenĂ© a implementovanĂ© lokálnĂ optimalizace. Po uplynutĂ pĹ™edem stanovenĂ©ho strojovĂ©ho ÄŤasu jsou mezi sebou porovnány minimálnĂ vzdálenosti dosaĹľenĂ© zvolenĂ˝mi metodami. Experimenty jsou provedeny na sadách s rĹŻznĂ˝mi poÄŤty mĂst, konkrĂ©tnÄ› od 101 aĹľ po 3891.This thesis is focused on modification of known principles ACO and GA to increase their performance. Thesis includes two new principles to solve TSP. One of them can be used as an initial population generator. The appendix contains the implementation of the application in Java. The description of this application is also part of the thesis. One part is devoted to optimization in order to make methods more efficient and produce shorter paths. In the end of the thesis are described experiments and their results with different number of places from 101 up to 3891.
Traveling Salesman Problem
The idea behind TSP was conceived by Austrian mathematician Karl Menger in mid 1930s who invited the research community to consider a problem from the everyday life from a mathematical point of view. A traveling salesman has to visit exactly once each one of a list of m cities and then return to the home city. He knows the cost of traveling from any city i to any other city j. Thus, which is the tour of least possible cost the salesman can take? In this book the problem of finding algorithmic technique leading to good/optimal solutions for TSP (or for some other strictly related problems) is considered. TSP is a very attractive problem for the research community because it arises as a natural subproblem in many applications concerning the every day life. Indeed, each application, in which an optimal ordering of a number of items has to be chosen in a way that the total cost of a solution is determined by adding up the costs arising from two successively items, can be modelled as a TSP instance. Thus, studying TSP can never be considered as an abstract research with no real importance
Traveling Salesman Problem
This book is a collection of current research in the application of evolutionary algorithms and other optimal algorithms to solving the TSP problem. It brings together researchers with applications in Artificial Immune Systems, Genetic Algorithms, Neural Networks and Differential Evolution Algorithm. Hybrid systems, like Fuzzy Maps, Chaotic Maps and Parallelized TSP are also presented. Most importantly, this book presents both theoretical as well as practical applications of TSP, which will be a vital tool for researchers and graduate entry students in the field of applied Mathematics, Computing Science and Engineering
An empirical investigation into randomly generated Euclidean symmetric traveling salesman problems
The traveling salesman problem is one of the most well-solved hard combinatorial optimization problems. Any new algorithm or heuristic for the traveling salesman problem is empirically evaluated based on its performance on standard test instances, as well as on randomly generated instances. However, properties of randomly generated traveling salesman instances have not been reported in the literature. In this paper, we report the results from an empirical investigation on the properties of randomly generated Euclidean traveling salesman problem. Our experiments focus on the properties of the edge lengths and the distribution of the tour lengths of all tours in instances for symmetric traveling salesman problems.
The Geometric Maximum Traveling Salesman Problem
We consider the traveling salesman problem when the cities are points in R^d
for some fixed d and distances are computed according to geometric distances,
determined by some norm. We show that for any polyhedral norm, the problem of
finding a tour of maximum length can be solved in polynomial time. If
arithmetic operations are assumed to take unit time, our algorithms run in time
O(n^{f-2} log n), where f is the number of facets of the polyhedron determining
the polyhedral norm. Thus for example we have O(n^2 log n) algorithms for the
cases of points in the plane under the Rectilinear and Sup norms. This is in
contrast to the fact that finding a minimum length tour in each case is
NP-hard. Our approach can be extended to the more general case of quasi-norms
with not necessarily symmetric unit ball, where we get a complexity of
O(n^{2f-2} log n).
For the special case of two-dimensional metrics with f=4 (which includes the
Rectilinear and Sup norms), we present a simple algorithm with O(n) running
time. The algorithm does not use any indirect addressing, so its running time
remains valid even in comparison based models in which sorting requires Omega(n
\log n) time. The basic mechanism of the algorithm provides some intuition on
why polyhedral norms allow fast algorithms.
Complementing the results on simplicity for polyhedral norms, we prove that
for the case of Euclidean distances in R^d for d>2, the Maximum TSP is NP-hard.
This sheds new light on the well-studied difficulties of Euclidean distances.Comment: 24 pages, 6 figures; revised to appear in Journal of the ACM.
(clarified some minor points, fixed typos
Intuitionistic Fuzzy Rule-Base Model for the Time Dependent Traveling Salesman Problem
The Traveling Salesman Problem is a well-known combinatorial optimization problem. There are many different extensions and modifications of the original problem, such as The Time Dependent Traveling Salesman Problem, this specific extension of the original Traveling Salesman Problem towards more realistic traffic conditions assessment. In the Time Dependent Traveling Salesman Problem the “distances” (costs) between nodes vary in time, they are considered longer during the rush hour period or in the traffic jam region, e.g. the city centre. In this article we introduce an even more realistic approach, the Intuitionistic Fuzzy Time Dependent Traveling Salesman Problem. It is an extension of the Time Dependent Traveling Salesman Problem with the additional notion of intuitionistic fuzzy sets (which is a generalization of the original fuzzy sets). Our goal is to give a useful extended, alternative model instead of the original abstract problem. By demonstrating that the addition of intuitionistic fuzzy elements to quantify the intangible jam factors creates an inference system that approximates the tour cost in a more practical way. Hence, we are one step closer to offering a more realistic solution for the generalized Traveling Salesman Problem. The results of two simple toy examples showed the general effectiveness of the model
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