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Sample search results for: a-priori traveling salesman

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1 SIAM J. COMPUT. Vol. 24, No. 3, pp. 665-671, June 1995
 

Summary:  _< 2 ( r + ) 2r _<2 (/-l)r+6cr -2r (1 3 + #12;A PRIORI BOUNDS ON THE EUCLIDEAN TRAVELING SALESMAN 669 a... and then applying (3.8), we obtain #12;A PRIORI BOUNDS ON THE EUCLIDEAN TRAVELING SALESMAN 671 f x dv(n, x) tu(n. ...

  

Source: Steele, J. Michael - Department of Statistics, University of Pennsylvania

 

Collection: Mathematics

 
2 CS 352 (Advanced Algorithms) Spring 2011 Lecture #8: Problem Set #1 Debrief and the Traveling Salesman Problem Scribe: Daniel Schroeder
 

Summary:  of the edges crossing the cut, making the resulting cut a (1/2)-approximation. 2 Traveling Salesman Problem... The problem is defined as follows. Traveling Salesman Problem: Given: a set of n cities, and distances dij 0... ) for the Hamiltonian Cycle problem, define an instance X of ...

  

Source: Liben-Nowell, David - School of Mathematics and Statistics, Carleton University

 

Collection: Computer Technologies and Information Sciences

 
3 The Traveling Salesman Problem The traveling salesman problem, or TSP for short, is this
 

Summary:  The Traveling Salesman Problem The traveling salesman problem, or TSP for short, is this: given... ://www.math.princeton.edu/tsp/index.html #12;Applications of The Traveling Salesman Problem ·Transportation and logistics applications (e... ·and many other ...

  

Source: Gomes, Carla P. - Department of Computer Science, Cornell University

 

Collection: Computer Technologies and Information Sciences

 
4 Mathematical Programming 59 (1993) 413-420 413 North-Holland
 

Summary:  traveling salesman problem Daniel Bienstock Department of Industrial Engineeringand Research, Columbia... received 19 November 1991 We study the version of the prize collecting traveling salesman problem, where... algorithm with constant bound. The algorithm is based on Christofides' algorithm for the ...

  

Source: Goemans, Michel X. - Computer Science and Artificial Intelligence Laboratory & Department of Mathematics, Massachusetts Institute of Technology (MIT)

 

Collection: Computer Technologies and Information Sciences ; Mathematics

 
5 STUDIA UNIV. "BABESBOLYAI", MATHEMATICA, Volume LIII, Number 1, March 2008 A CUTTING PLANE APPROACH TO SOLVE THE RAILWAY
 

Summary:  APPROACH TO SOLVE THE RAILWAY TRAVELING SALESMAN PROBLEM PETRIC A C. POP, CHRISTOS D. ZAROLIAGIS... , AND GEORGIA HADJICHARALAMBOUS Abstract. We consider the Railway Traveling Salesman Problem. We show... that this problem can be reduced to a variant of the generalized traveling ...

  

Source: Zaroliagis, Christos D. - Department of Computer Engineering and Informatics, University of Patras

 

Collection: Computer Technologies and Information Sciences

 
6 A PRIORI OPTIMIZATION DIMITRIS J. BERTSIMAS
 

Summary:  optimally for every instance. We consider four problems: the traveling salesman problem (TSP), the minimum... spanning tree, vehicle routing, and traveling salesman facility location. We discuss the applicability... /graphs: stochastic heuristics, traveling salesman. ...

  

Source: Bertsimas, Dimitris - Laboratory for Information and Decision Systems, Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology (MIT)

 

Collection: Engineering

 
7 Statistical Engineering Division Seminar Friday April 21, 1995 11:00 am
 

Summary:  the Traveling Salesman Problem. Wing H. Wong is currently a Professor of Statistics at the Chinese University... Gaithersburg, MD Markov Chain Monte Carlo and the Salesman Problem Wing H. Wong Chinese University of Hong Kong

  

Source: Magee, Joseph W. - Experimental Properties of Fluids Group, Physical and Chemical Properties Division, National Institute of Standards and Technology

 

Collection: Chemistry

 
8 A Priori Optimization Author(s): Dimitris J. Bertsimas, Patrick Jaillet, Amedeo R. Odoni
 

Summary:  optimally for every instance. We consider four problems: the traveling salesman problem (TSP), the minimum... spanning tree, vehicle routing, and traveling salesman facility location. We discuss the applicability... Iassifications: Networks/graphs: stochastic heuristics, traveling ...

  

Source: Jaillet, Patrick - Department of Civil and Environmental Engineering, Massachusetts Institute of Technology (MIT)

 

Collection: Energy Storage, Conversion and Utilization ; Engineering

 
9 202 Matchings and Independent Sets 5.5 The Travelling Salesman Problem
 

Summary:  202 Matchings and Independent Sets 5.5 The Travelling Salesman Problem The Travelling Salesman... Problem A travelling salesman, starting in his own town, has to visit each of towns where he should go... , no efficient algorithm for solving the ...

  

Source: Xu, Jun-Ming - Department of Mathematics, University of Science and Technology of China

 

Collection: Mathematics

 
10 Physica A 314 (2002) 151155 www.elsevier.com/locate/physa
 

Summary:  Physica A 314 (2002) 151­155 www.elsevier.com/locate/physa The time-dependent traveling salesman... and Computational Physics is the traveling salesman problem, in which a traveling salesperson has to ÿnd... -dependent traveling salesman problem, ...

  

Source: Schneider, Johannes Josef - Institut für Physik, Johannes Gutenberg Universität Mainz

 

Collection: Physics

 
11 Approximation Hardness of the Traveling Salesman Reoptimization Problem
 

Summary:  Approximation Hardness of the Traveling Salesman Reoptimization Problem Richard Kr... with given Hamiltonian path. To deal with such a-priori knowledge in a more general way, the concept... in the reoptimization problem itself. For example, the reoptimization of the traveling salesman ...

  

Source: Kralovic, Rastislav - Fakulta matematiky, fyziky a informatiky, Univerzita Komenského

 

Collection: Computer Technologies and Information Sciences

 
12 Approximation Results for Kinetic Variants of TSP Mikael Hammar and Bengt J. Nilsson
 

Summary:  that the mice are moving. This problem is an instance of the Kinetic Traveling Salesman Problem. The Traveling... ­dimensional Euclidean TSP has been signiøcantly improved [2,12]. #12; 2 In the kinetic traveling salesman problem, we... In the Traveling ...

  

Source: Lunds Universitet, Department of Computer Science, Algorithms Group

 

Collection: Computer Technologies and Information Sciences

 
13 MIC 2007: The Seventh Metaheuristics International Conference 1 Estimation-based Local Search for the Probabilistic Traveling
 

Summary:  for the Probabilistic Traveling Salesman Problem Mauro Birattari Prasanna Balaprakash Thomas St¨utzle Marco Dorigo... competitive. 1 Introduction The probabilistic traveling salesman problem (PTSP) [1] is a paradigmatic example... ., and Odoni A. (1990): "A priori ...

  

Source: Birattari, Mauro - Computer and Decision Engineering Department, Université Libre de Bruxelles

 

Collection: Engineering ; Computer Technologies and Information Sciences

 
14 DNA DNA . DNA
 

Summary:  . . 26 traveling salesman problem (TSP) , 1-base mismatch dangling ends [4... ] . NP . . 2 3 . 4 . 5 . 2. The traveling-salesman problem Traveling-salesman... is a function from V×V Z, k Z, and G ...

  

Source: Zhang, Byoung-Tak - School of Computer Science and Engineering, Seoul National University

 

Collection: Computer Technologies and Information Sciences ; Biology and Medicine

 
15 Solving the Homogeneous Probabilistic Traveling Salesman Problem by the ACO Metaheuristic
 

Summary:  Solving the Homogeneous Probabilistic Traveling Salesman Problem by the ACO Metaheuristic Leonora... ://iridia.ulb.ac.be/mdorigo/ Abstract. The Probabilistic Traveling Salesman Problem (PTSP) is a TSP problem in which each customer has... is defined as the Probabilistic Traveling ...

  

Source: Libre de Bruxelles, Université - Computer and Decision Engineering Department

 

Collection: Computer Technologies and Information Sciences ; Engineering

 
16 Lecture 20: NPCompleteness II Main Topics of this Lecture
 

Summary:  .1008­1012 2. The traveling salesman problem. CLRS pp 1012­1013 3. Some other NPC problems. 1 Recall how... that the reduction exists but do not need to know the details. 3 Traveling Salesman Problem Informally, the Traveling... the tour with the minimum cost. 4 #12; ...

  

Source: Golin, Mordecai J. - Department of Computer Science, Hong Kong University of Science and Technology

 

Collection: Computer Technologies and Information Sciences

 
17 13 May 1983, Volume 220, Number 4598 Optimization by
 

Summary:  on optimization. involving a few hundred cities or less. The traveling salesman belongs to the'.:l,,"`, large... from optimi- zation. Of classic optimization problems, the traveling salesman problem has received... stated. of a combinatorial optimi- zation problem is the traveling ...

  

Source: Hutter, Frank - Department of Computer Science, University of British Columbia

 

Collection: Computer Technologies and Information Sciences

 
18 CS 538: Combinatorial Optimization The course will introduce techniques and tools for combinatorial optimization problem such as maximum weight
 

Summary:  (time permitting) Approximation Algorithms: Set Cover, Traveling Salesman Edited March 2006 (html, css

  

Source: Saniie, Jafar - Department of Electrical and Computer Engineering, Illinois Institute of Technology

 

Collection: Engineering ; Computer Technologies and Information Sciences

 
19 Lecture 20: Approximate algorithms Outline of this Lecture
 

Summary:  for approximation algorithms. ffl Vertex­cover problem. ffl Traveling­salesman problem. 1 #12; Introduction Many... ; Traveling­salesman problem Imagine your are a salesman, and you need to visit n cities. You want to start... is called Traveling­salesman problem (TSP). We can model the cities as a ...

  

Source: Wu, Dekai - Department of Computer Science, Hong Kong University of Science and Technology

 

Collection: Computer Technologies and Information Sciences

 
20 Lecture 20: Approximate algorithms Outline of this Lecture
 

Summary:  for approximation algorithms. Vertex-cover problem. Traveling-salesman problem. 1 #12;Introduction Many... ¢ ¡ ¡ ¢ © ¢ ¢ ¡ 10 #12;Traveling-salesman problem Imagine your are a salesman, and you need to visit ¤ cities. You... are connected. Such problem is called ...

  

Source: Wu, Dekai - Department of Computer Science, Hong Kong University of Science and Technology

 

Collection: Computer Technologies and Information Sciences


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21 A Priori Solution of a Traveling Salesman Problem in Which a Random Subset of the Customers are Visited
 

Summary:  A Priori Solution of a Traveling Salesman Problem in Which a Random Subset of the Customers... minimumlengthintheexpected valuesenseisdefinedasa ProbabilisticTravelingSalesman... , an analysisof these expressionsand deriveseveral interestingpropertiesof theproblem. T he Traveling Salesman

  

Source: Jaillet, Patrick - Department of Civil and Environmental Engineering, Massachusetts Institute of Technology (MIT)

 

Collection: Energy Storage, Conversion and Utilization ; Engineering

 
22 Active Learning with Spatially Sensitive Labeling Alexander Liu
 

Summary:  salesman problem (and its variant, the traveling salesman problem with profits). 2 Active learning... active learning with the traveling salesman problem. A simple but somewhat naive approach... to the traveling salesman problem (TSP) to find the ...

  

Source: Ghosh, Joydeep - Department of Electrical and Computer Engineering, University of Texas at Austin

 

Collection: Computer Technologies and Information Sciences

 
23 ORMS1020 Operations Research Final Exam University of Vaasa 20.12.2010
 

Summary:  is the traveling salesman problem. (b) Formulate the traveling salesman problem as an MILP. (c) Why... is the traveling salesman problem considered "difficult", although it can be solved e.g. as a MILP? #12;Solutions 1... . (a) In the traveling ...

  

Source: Sottinen, Tommi - Department of Mathematics and Statistics, University of Vaasa

 

Collection: Mathematics

 
24 TSP Heuristics: Domination Analysis and Abraham Punnen a;1 , Francois Margot b , Santosh Kabadi c;2
 

Summary:  and 3-Opt heuristics for the traveling salesman problem (TSP) on a complete graph K n produce a solution... Algorithms, Traveling Salesman Problem, Computational Complexity Email addresses: punnen@unbsj.ca (Abraham

  

Source: Kentucky, University of - Department of Mathematics, Mathematics Preprint Series

 

Collection: Mathematics

 
25 MATH 100 Exam 2 March 23, 2009 Part 1 2 3 Total
 

Summary:  Salesman Problem in which he wants to travel to each of ten cities exactly once. (a) (4 pts.) How many... the cost that it takes a traveling salesman to get from one town to another. A B C D E 50 100 80 90 60 75... , how many vertices does it have? 2 #12;Part 2: Longer Computations and Answers 1. Consider a ...

  

Source: Koban, Lori - Department of Mathematics, University of Maine at Farmington

 

Collection: Mathematics

 
26 Assignment Problem based algorithms are impractical for the Generalized TSP
 

Summary:  Abstract In the Generalized Traveling Salesman Problem (GTSP), given a weighted complete digraph D... of the sets X i are empty. In the Generalized Traveling Salesman Problem (GTSP), given a weighted complete... traveling salesman problem: Algorithms, instance ...

  

Source: Gutin, Gregory - Department of Computer Science, Royal Holloway, University of London

 

Collection: Computer Technologies and Information Sciences

 
27 The Railway Traveling Salesman Problem Georgia Hadjicharalambous1
 

Summary:  The Railway Traveling Salesman Problem Georgia Hadjicharalambous1 , Petrica Pop1 , Evangelia Pyrga1... {hadjicha,ppop,pirga,tsaggour,zaro}@ceid.upatras.gr Abstract. We consider the Railway Traveling Salesman... Asymmetric Traveling Salesman Problem, in this paper we ...

  

Source: Zaroliagis, Christos D. - Department of Computer Engineering and Informatics, University of Patras

 

Collection: Computer Technologies and Information Sciences

 
28 Spatially Cost-sensitive Active Learning Alexander Liu
 

Summary:  with methods used for approximating solutions to the Traveling Salesman Problem(TSP) and one of its variants... , the Traveling Salesman Problem with Profits(TSPP). Details on both active learning and the traveling salesman... not depend on a particular solution to ...

  

Source: Ghosh, Joydeep - Department of Electrical and Computer Engineering, University of Texas at Austin

 

Collection: Computer Technologies and Information Sciences

 
29 Spatially Cost-sensitive Active Learning Alexander Liu
 

Summary:  with methods used for approximating solutions to the Traveling Salesman Problem(TSP) and one of its variants... , the Traveling Salesman Problem with Profits(TSPP). Details on both active learning and the traveling salesman... not depend on a particular solution to ...

  

Source: Ghosh, Joydeep - Department of Electrical and Computer Engineering, University of Texas at Austin

 

Collection: Computer Technologies and Information Sciences

 
30 Toward a Generic Comet Implementation of Very Large-Scale Neighborhoods
 

Summary:  efficiently. One example of such VLSN for the Traveling Salesman Problem (TSP) is given in #12;[4], where... ], they focus on the Traveling Salesman Problem (TSP) and it is shown that some VLSN can be specified... and P. Villon, "A new heuristic for the travel- ing ...

  

Source: Deville, Yves - Département d'ingénierie Informatique, Université Catholique de Louvain

 

Collection: Biotechnology ; Computer Technologies and Information Sciences

 
31 A New Operator for Efficient Evolutionary Solutions to the Travelling Salesman GEORGE G. MITCHELL DIARMUID O'DONOGHUE ADRIAN TRENAMAN
 

Summary:  A New Operator for Efficient Evolutionary Solutions to the Travelling Salesman Problem GEORGE G... approaches to the travelling salesman problem (TSP). For raw data we have used standard road mileage charts... Words Evolutionary Algorithms, Optimisation, Travelling ...

  

Source: Coello, Carlos A. Coello - Laboratorio Nacional de Informatica Avanzada (LANIA)

 

Collection: Computer Technologies and Information Sciences

 
32 THEORY OF COMPUTING, Volume 4 (2008), pp. 191--193 http://theoryofcomputing.org
 

Summary:  Relaxation of the Asymmetric Traveling Salesman Path Problem Viswanath Nagarajan Received: January 2, 2008... for the Asymmetric Traveling Salesman Path Problem'' by C. Chekuri and M. P’al, Theory of Com­ puting 3 (2007), 197... --209. We observe that the LP relaxation for the Asymmetric ...

  

Source: Håstad, Johan - Department of Numerical Analysis and Computer Science, Royal Institute of Technology, Sweden (KTH)

 

Collection: Computer Technologies and Information Sciences

 
33 THEORY OF COMPUTING, Volume 4 (2008), pp. 191193 http://theoryofcomputing.org
 

Summary:  Relaxation of the Asymmetric Traveling Salesman Path Problem Viswanath Nagarajan Received: January 2, 2008... for the Asymmetric Traveling Salesman Path Problem" by C. Chekuri and M. P´al, Theory of Com- puting 3 (2007), 197... ­209. We observe that the LP relaxation for the Asymmetric ...

  

Source: Håstad, Johan - Department of Numerical Analysis and Computer Science, Royal Institute of Technology, Sweden (KTH)

 

Collection: Computer Technologies and Information Sciences

 
34 Lecture 20: NPCompleteness II Main Topics of this Lecture
 

Summary:  .1008­1012 2. The traveling salesman problem. CLRS pp 1012­1013 3. Some other NPC problems. 1 #12... Salesman Problem Informally, the Traveling Salesman Problem (TSP) can be described as follows: A salesman... . There is an integer cost c(i, j) to ...

  

Source: Golin, Mordecai J. - Department of Computer Science, Hong Kong University of Science and Technology

 

Collection: Computer Technologies and Information Sciences

 
35 Lecture 20: NP-Completeness II Main Topics of this Lecture
 

Summary:  .1008-1012 2. The traveling salesman problem. CLRS pp 1012-1013 3. Some other N PC problems. 1 #12... that the reduction exists but do not need to know the details. 3 #12;Traveling Salesman Problem Informally... , the Traveling Salesman Problem (TSP) can be described ...

  

Source: Golin, Mordecai J. - Department of Computer Science, Hong Kong University of Science and Technology

 

Collection: Computer Technologies and Information Sciences

 
36 A Comparison of Genetic Sequencing Operators T. Starkweather, S. McDaniel, C. Whitley
 

Summary:  of these opera­ tors, and results are compared for a 30 city ``Blind'' Traveling Salesman Problem and a real... adjacency is important (e.g., the Traveling Salesman) may not be effective for other types of sequencing... '' (a genetic operator specifically designed for the Traveling ...

  

Source: Whitley, Darrell - Department of Computer Science, Colorado State University

 

Collection: Computer Technologies and Information Sciences

 
37 Traveling Salesman Problem with non-Euclidean Distances
 

Summary:  Traveling Salesman Problem with non-Euclidean Distances Yll Haxhimusa, Joseph Catrambone, Zygmunt... Salesman Problem Traveling Salesman Problem TSP Given a set of cities, find the route that visits all... Salesman Problem Traveling ...

  

Source: Haxhimusa, Yll - Institut für Rechnergestützte Automation, Technische Universität Wien

 

Collection: Computer Technologies and Information Sciences

 
38 Online Routing Problems: Value of Advanced Information as
 

Summary:  online versions of the Traveling Salesman Problem (TSP) and Traveling Repair- man Problem (TRP) where... traveling salesman 2 #12;problem where new cities are revealed locally during the traversal of a tour (i... date. 5. The salesman (repairman) ...

  

Source: Jaillet, Patrick - Department of Civil and Environmental Engineering, Massachusetts Institute of Technology (MIT)

 

Collection: Energy Storage, Conversion and Utilization ; Engineering

 
39 CAS776: Computational Complexity Instructor: Michael Soltys <soltys@mcmaster.ca>
 

Summary:  with an informal analysis of three simple algorithms: graph reachability, Maximum Flow, and the Traveling Salesman

  

Source: Soltys, Michael - Department of Computing and Software, McMaster University

 

Collection: Mathematics ; Computer Technologies and Information Sciences

 
40 SYLLABUS FOR MATH 170 Text: For all practical purposes, 8e, COMAP
 

Summary:  (Hamilton circuits, Traveling Salesman Problem, critical-path analysis). · Planning and scheduling

  

Source: Zywina, David - Department of Mathematics, University of Pennsylvania

 

Collection: Mathematics


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41 (3-0-0; --) Graph Theory MATH-401* This course is directed to students in Mathematics or Computer Science. The emphasis
 

Summary:  with four colours so that adjacent regions have different colours), and the Traveling Salesman Problem

  

Source: Offin, Dan - Department of Mathematics and Statistics, Queen's University (Kingston)

 

Collection: Mathematics

 
42 Stochastic Combinatorial Optimization: From the TSP and MST to Dogapillars
 

Summary:  combinatorial optimization are the traveling salesman problem (TSP) where one considers the shortest tour

  

Source: Jin, Jiashun - Department of Statistics, Carnegie Mellon University

 

Collection: Mathematics

 
43 Online MTH 108 Practical Mathematics (Topics in Mathematics)
 

Summary:  - Identification numbers - Euler and Hamiltonian circuits - Traveling Salesman Problem (TSP) - Mortgage payments

  

Source: Rhode Island, University of - Rhode Island Water Resources Center

 

Collection: Environmental Sciences and Ecology ; Geosciences

 
44 BIOLOGY COLLOQUIUM Monday, February 14, 2011
 

Summary:  of analysis in the past. Using the W-curve and Traveling Salesman Problem ("TSP") solutions we have found

  

Source: Saniie, Jafar - Department of Electrical and Computer Engineering, Illinois Institute of Technology

 

Collection: Engineering ; Computer Technologies and Information Sciences

 
45 Paul Ossenbruggen speaking on
 

Summary:  of Optimization using planar graphs Transportation problems: Traveling Salesman (Branch & Bound), Traffic

  

Source: New Hampshire, University of - Department of Electrical and Computer Engineering, Consolidated Advanced Technologies Lab.

 

Collection: Engineering

 
46 Spring 2009 Weighted Graphs
 

Summary:  spanning tree c) Single source shortest paths using Dijkstra's algorithm Part II The Travelling Salesman

  

Source: Fuentes, Olac - Department of Computer Science, University of Texas at El Paso

 

Collection: Computer Technologies and Information Sciences ; Physics

 
47 Course Outline: ffl Introduction and Fibonacci Numbers.
 

Summary:  flows, maximum matching. ffl NP­completeness #12; -- Cook's theorem, Satisfiability, Traveling Salesman

  

Source: Vazirani, Umesh - Department of Electrical Engineering and Computer Sciences, University of California at Berkeley

 

Collection: Computer Technologies and Information Sciences

 
48 Reproduced with permission of the copyright owner. Further reproduction prohibited without permission. Chained Lin-Kernighan for large traveling salesman problems
 

Summary:  permission. Chained Lin-Kernighan for large traveling salesman problems David Applegate; Wiliam Cook; Andre

  

Source: Cook, William - School of Industrial and Systems Engineering, Georgia Institute of Technology

 

Collection: Computer Technologies and Information Sciences

 
49 Optimization of the time-dependent traveling salesman problem with Monte Carlo methods Johannes Bentner,* Gunter Bauer, Gustav M. Obermair, and Ingo Morgenstern
 

Summary:  Optimization of the time-dependent traveling salesman problem with Monte Carlo methods Johannes... considered in operations research and computational physics is the traveling salesman problem, in which... will only give results for SA throughout this paper. B. Application to the ...

  

Source: Schneider, Johannes Josef - Institut für Physik, Johannes Gutenberg Universität Mainz

 

Collection: Physics

 
50 Mathematisches Institut der Universitat Bayreuth Der Geschaftsfuhrende Vorstand
 

Summary:  to the starting position. This problem is known as " Traveling Salesman Problem with Neighborhoods" (a... generalization of the " Traveling Salesman problem"). It can be formulated as a nonconvex MINLP having

  

Source: Schittkowski, Klaus - Mathematisches Institut, Universität Bayreuth

 

Collection: Mathematics ; Computer Technologies and Information Sciences

 
51 Technische Universitat Munchen WS 2008/09 Institut fur Informatik Aufgabenblatt 7
 

Summary:  . Aufgabe 3 Travelling Salesman Gegeben sei eine Matrix Mi,j der Dimension n×n mit Mi,j IN, die die... Entfernungen zwischen n St¨adten kodiert, sowie eine Zahl k IN. Das Travelling Salesman Problem ist definiert

  

Source: Cengarle, María Victoria - Institut für Informatik, Technische Universität München

 

Collection: Computer Technologies and Information Sciences

 
52 Average-Case Approximation Ratio of the 2-Opt Algorithm for the TSP
 

Summary:  that the 2-opt heuristic for the traveling salesman problem achieves an expected approximation ratio... at random. Keywords: traveling salesman problem, 2-opt, average-case analysis, approxima- tion ratio 1... Introduction The traveling salesman problem (TSP) is one ...

  

Source: Manthey, Bodo - Department of Applied Mathematics, Universiteit Twente

 

Collection: Computer Technologies and Information Sciences

 
53 A Heuristic for the Resource-Constrained Traveling Salesman Problem
 

Summary:  A Heuristic for the Resource-Constrained Traveling Salesman Problem Gregory Gutin, Alexei... -Ilan University Ramat Gan, 52900, Israel 1 Introduction The Resource-Constrained Traveling Salesman Problem (RCTSP... some pairs (i, j). RCTSP is a generalization of the well-known Traveling ...

  

Source: Gutin, Gregory - Department of Computer Science, Royal Holloway, University of London

 

Collection: Computer Technologies and Information Sciences

 
54 Algorithms for the Traveling Salesman Problem with Neighborhoods Involving a Dubins Vehicle
 

Summary:  Algorithms for the Traveling Salesman Problem with Neighborhoods Involving a Dubins Vehicle Jason T... Traveling Salesman Problem (ETSP), where the cost to travel from one waypoint to the next is approximated... the optimal sequence of waypoints. This problem is typically referred to as ...

  

Source: Hespanha, João Pedro - Department of Electrical and Computer Engineering, University of California at Santa Barbara

 

Collection: Engineering

 
55 Nature's Algorithms: Natural and Social Metaphors in Algorithm Design
 

Summary:  )!=2 possible tours for any n­city traveling­salesman prob­ lem. Thus, while there are only 2520 possible... is what makes them so challenging. For traveling salesman problems, for example, the size of the problem... . The cost function for a traveling salesman problem is the length of ...

  

Source: Simha, Rahul - Department of Computer Science, George Washington University

 

Collection: Computer Technologies and Information Sciences

 
56 Upper Bounds on ATSP Neighborhood Size Gregory Gutin \Lambda Anders Yeo y
 

Summary:  the Asymmetric Traveling Salesman Problem (ATSP) and use the definition of neighborhood by Deineko and Woeginger... the Asymmetric Traveling Salesman Problem (ATSP): given a weighted complete directed graph, ( $ Kn ; c), where n... , The travelling salesman problem ...

  

Source: Gutin, Gregory - Department of Computer Science, Royal Holloway, University of London

 

Collection: Computer Technologies and Information Sciences

 
57 S-ACO: An Ant-Based Approach to Combinatorial Optimization under Uncertainty
 

Summary:  of fixed- routes type: First, a pre-test is carried out on the probabilistic traveling salesman problem... . Then, more comprehensive tests are performed for a traveling salesman problem with time windows (TSPTW... of the Probabilistic Travelling Salesman Problem ...

  

Source: Gutjahr, Walter - Institut für Statistik und Decision Support, Universität Wien

 

Collection: Mathematics

 
58 WESTON PLAYHOUSE SALESMANwith
 

Summary:  arrive at the theater 30 to 45 minutes before the show. Allow for travel time, parking, and trips... permission to adapt and excerpt portions of their "Death of a Salesman Study Guide for Teachers." Enjoy... of a Salesman GENRE: Theater Death of a Salesman by Arthur Miller was first performed in 1949

  

Source: Lotko, William - Thayer School of Engineering, Dartmouth College

 

Collection: Geosciences ; Engineering

 
59 versionofnormal(ifpremature)ageingthan does dyskeratosis congenita. In people with
 

Summary:  travelling salesman problem is of fundamental interest to mathemati- cians and physicists, and has a number... 'snextstepdependsonhisknowledgeof the location of every client yet to be visited, the solution to the travelling salesman prob... the distances along the trajectory as in the ...

  

Source: Stanley, H. Eugene - Department of Physics, Boston University

 

Collection: Physics ; Computer Technologies and Information Sciences ; Materials Science

 
60 Introduction Acknowledgments
 

Summary:  5 6 T2T1 T3 T4 T5 T7 T8 T9 T6 T10Traveling Salesman Problem Optimization on the basis of spatial... configurations were presented. Each configurations: Exploration trial+ 3 decision trials. ?The traveling salesman... . Traveling Salesman Problem Optimization on the ...

  

Source: Fellous, Jean-Marc - Department of Psychology, University of Arizona

 

Collection: Biology and Medicine


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61 Memetic Algorithms for the Traveling Salesman Problem
 

Summary:  Memetic Algorithms for the Traveling Salesman Problem Peter Merz #3; Department of Computer Science... problems. In this paper, the #12;tness landscapes of several instances of the traveling salesman problem... in a reasonable amount of time. 1. Introduction The traveling ...

  

Source: Merz, Peter - Fachbereich Informatik, Technische Universität Kaiserslautern

 

Collection: Computer Technologies and Information Sciences

 
62 Contexts/Motivation Online optimization
 

Summary:  uncertainty? Probabilistic models stochastic optimization (a priori optimization, stochastic programming... at their release date ri 0; assume r1 r2 · · · rn. The salesman travels at unit speed or is idle. The problem... optimization In-depth Cases TSP Resource Allocation Inventory Management Online ...

  

Source: Jaillet, Patrick - Department of Civil and Environmental Engineering, Massachusetts Institute of Technology (MIT)

 

Collection: Energy Storage, Conversion and Utilization ; Engineering

 
63 A Preprocessing that Combines Heuristic and Surrogate Constraint Analysis to Fix Variables in TSP
 

Summary:  , 20] exploiting of surrogate constraints and constraint pairing is applied to the traveling salesman... that the traveling salesman must visit every city in his territory exactly once and then return to the starting point... documented in 1759, with a different name, by Euler. The term ...

  

Source: Pinto, David Eduardo - Facultad de Ciencias de la Computación, Benemérita Universidad Autónoma de Puebla

 

Collection: Computer Technologies and Information Sciences

 
64 4.5 TRAVELING SALESMAN AND RELATED PROBLEMS 627min 2{25{2003 Gregory Gutin, Royal Holloway, University of London
 

Summary:  4.5 TRAVELING SALESMAN AND RELATED PROBLEMS 627min 2{25{2003 Gregory Gutin, Royal Holloway... , University of London 4.5.1 The Traveling Salesman Problem 4.5.2 Exact Algorithms 4.5.3 Construction... Glossary INTRODUCTION The Traveling Salesman Problem (TSP) is perhaps ...

  

Source: Gutin, Gregory - Department of Computer Science, Royal Holloway, University of London

 

Collection: Computer Technologies and Information Sciences

 
65 Algorithms for the On-Line Quota Traveling Salesman Problem
 

Summary:  Algorithms for the On-Line Quota Traveling Salesman Problem G. Ausiello1 , M. Demange2 , L. Laura1... @lamsade.dauphine.fr Abstract. The Quota Traveling Salesman Problem is a generalization of the well known Traveling Salesman... Problem. The goal of the ...

  

Source: Ecole Polytechnique, Centre de mathématiques

 

Collection: Mathematics

 
66 An Ant Colony Optimization Approach to the Probabilistic Traveling Salesman Problem
 

Summary:  An Ant Colony Optimization Approach to the Probabilistic Traveling Salesman Problem Leonora Bianchi... ://iridia.ulb.ac.be/mdorigo/ Abstract. The Probabilistic Traveling Salesman Problem (PTSP) is a TSP problem where each customer has... of minimum expected length under the skipping strategy is defined as the ...

  

Source: Libre de Bruxelles, Université - Computer and Decision Engineering Department

 

Collection: Computer Technologies and Information Sciences ; Engineering

 
67 Hybrid Metaheuristics for the Vehicle Routing Problem with Stochastic Demands
 

Summary:  for some metaheuristics is the objective function derived from the traveling salesman problem (TSP... may also be seen as a feasible solution for a traveling salesman problem (TSP) on the set of customers... in considering a multiple-vehicle problem by allowing multiple 94 LEONORA BIANCHI ET AL. ...

  

Source: Birattari, Mauro - Computer and Decision Engineering Department, Université Libre de Bruxelles; Libre de Bruxelles, Université - Computer and Decision Engineering Department

 

Collection: Computer Technologies and Information Sciences ; Engineering

 
68 Transformations of Generalized ATSP into ATSP D. Ben-Arieh
 

Summary:  Holloway, University of London, Egham, Surrey TW20 0EX, UK Abstract The Generalized Traveling Salesman... , heuristics. 1 Introduction The Generalized Traveling Salesman Problem (GTSP) is stated as follows. Given... References [1] D. Applegate, R.E. Bixby, V. Chv´atal W., Cook, On the Solution of ...

  

Source: Gutin, Gregory - Department of Computer Science, Royal Holloway, University of London

 

Collection: Computer Technologies and Information Sciences

 
69 Short communication Travelling salesman problem on dilute lattices : visit to a
 

Summary:  255 Short communication Travelling salesman problem on dilute lattices : visit to a fraction... métrique cartésienne (C) . Abstract. 2014 We study the travelling salesman problem on dilute lattices where... .50 The travelling salesman problem (TSP), where, given the ...

  

Source: Ecole Polytechnique, Centre de mathématiques

 

Collection: Mathematics

 
70 SIAM J. DISC. MATH. Vol. 8, No. 4, pp. 678-683, November 1995
 

Summary:  square [0,1]d, an optimal traveling salesman tour of S is a tour of S that is of minimum length. A worst... -case point set for the traveling salesman problem in the unit square is a point set S(n) whose optimal... traveling salesman tour achieves the maximum possible ...

  

Source: Steele, J. Michael - Department of Statistics, University of Pennsylvania

 

Collection: Mathematics

 
71 Well Solved Cases Of Probabilistic Traveling Salesman Problem
 

Summary:  Well Solved Cases Of Probabilistic Traveling Salesman Problem M. Bellalouna, W. Khaznaji, V... The Probabilistic Traveling Salesman Problem is in general NP-Hard, the objective of this paper is to look... that in the small traveling salesman problem, several tours ...

  

Source: Ecole Polytechnique, Centre de mathématiques

 

Collection: Mathematics

 
72 APPROXIMATION RESULTS TOWARD NEAREST NEIGHBOR HEURISTIC JER^OME MONNOT
 

Summary:  sales- man problem. The classical traveling salesman problem can be formulated as follows: given Kn... , a complete graph on n vertices with non-negative integer costs on its edges, the traveling salesman problem... of a new heuristic for the traveling salesman ...

  

Source: Ecole Polytechnique, Centre de mathématiques

 

Collection: Mathematics

 
73 New Genetic Local Search Operators for the Traveling Salesman Problem
 

Summary:  New Genetic Local Search Operators for the Traveling Salesman Problem Bernd Freisleben and Peter... which is used to compute near­optimum solutions to traveling salesman problems (TSP). The ap­ proach... Introduction The traveling salesman problem (TSP) is a ...

  

Source: Merz, Peter - Fachbereich Informatik, Technische Universität Kaiserslautern

 

Collection: Computer Technologies and Information Sciences

 
74 Metaheuristics for the Vehicle Routing Problem with Stochastic Demands
 

Summary:  . Due to the analogies between the VRPSD and the traveling salesman problem (TSP), a natural... of going from a customer i to a customer j in the a-priori tour. An ant which is at customer i chooses... routing problems. Transportation Science, 29(4):342­352, 1995. 3. I. Or. Traveling ...

  

Source: Birattari, Mauro - Computer and Decision Engineering Department, Université Libre de Bruxelles; Libre de Bruxelles, Université - Computer and Decision Engineering Department

 

Collection: Computer Technologies and Information Sciences ; Engineering

 
75 ON THE APPROXIMABILITY OF THE TRAVELING SALESMAN PROBLEM
 

Summary:  ON THE APPROXIMABILITY OF THE TRAVELING SALESMAN PROBLEM CHRISTOS H. PAPADIMITRIOU AND SANTOSH... VEMPALA Abstract. We show that the traveling salesman problem with triangle inequality cannot... , 4, 10, 11, 13, 18], there has been very little progress on the traveling ...

  

Source: Papadimitriou, Christos H. - Department of Electrical Engineering and Computer Sciences, University of California at Berkeley

 

Collection: Computer Technologies and Information Sciences

 
76 MATHEMATICS OF OPERATIONS RESEARCH Vol. 31, No. 2, May 2006, pp. 245252
 

Summary:  for the Asymmetric Traveling Salesman Problem Moses Charikar Department of Computer Science, Princeton University, 35... traveling salesman problem; Held-Karp relaxation; integrality ratio; approximation algorithm; ATSP MSC2000... , 90C10 OR/MS subject classification: Primary: ...

  

Source: Goemans, Michel X. - Computer Science and Artificial Intelligence Laboratory & Department of Mathematics, Massachusetts Institute of Technology (MIT)

 

Collection: Computer Technologies and Information Sciences ; Mathematics

 
77 Nearly Linear Time Approximation Schemes for Euclidean TSP and other Geometric Problems
 

Summary:  scheme finds a (1+ 1 c )­approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time... to understand the Traveling Salesman Problem has motivated research in many areas --- such as linear programming... is that we will allow the salesman to deviate from the ...

  

Source: Arora, Sanjeev - Department of Computer Science, Princeton University

 

Collection: Computer Technologies and Information Sciences

 
78 Algorithms for the Universal and A Priori TSP Frans Schalekamp
 

Summary:  of the traveling salesman problem (TSP): For the universal TSP, we show that one can compute a tour... for the a priori TSP follows as a corollary. Keywords: Traveling Salesman Problem, A Priori Optimization, Universal... decide which subset of clients actually need service). This is known as the universal ...

  

Source: Shmoys, David B. - School of Operations Research and Industrial Engineering, Cornell University

 

Collection: Mathematics ; Computer Technologies and Information Sciences

 
79 ORIGINAL ARTICLE Neurodynamic programming: a case study
 

Summary:  ORIGINAL ARTICLE Neurodynamic programming: a case study of the traveling salesman problem Jia Ma Æ... of solving the large-scale traveling salesman problem (TSP) based on neurodynamic programming. From... Neurodynamic programming Á Temporal difference learning Á Approximate Sarsa Á ...

  

Source: 

 

Collection: Computer Technologies and Information Sciences

 
80 A Genetic Local Search Algorithm for Solving Symmetric and Asymmetric Traveling Salesman
 

Summary:  A Genetic Local Search Algorithm for Solving Symmetric and Asymmetric Traveling Salesman Problems... for finding near­ optimum solutions to the traveling salesman problem (TSP). In this paper, an approach... In the Traveling Salesman Problem (TSP) [18], [27], a ...

  

Source: Merz, Peter - Fachbereich Informatik, Technische Universität Kaiserslautern

 

Collection: Computer Technologies and Information Sciences


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81 Dorigo and Gambardella -Ant colonies for the traveling salesman problem 1 Ant colonies for the traveling salesman problem
 

Summary:  Dorigo and Gambardella - Ant colonies for the traveling salesman problem 1 Ant colonies... for the traveling salesman problem TR/IRIDIA/1996-3 Université Libre de Bruxelles Belgium Marco Dorigo IRIDIA... of solving the traveling salesman problem (TSP). Ants of the ...

  

Source: Gambardella, Luca Maria - Istituto Dalle Molle di Studi sull'Intelligenza Artificiale; Grant, P. W. - Department of Computer Science, University of Wales Swansea

 

Collection: Computer Technologies and Information Sciences

 
82 MATH 100 Exam 2 March 27, 2009 Part 1 2 3 Total
 

Summary:  and Answers 1. Consider a Traveling Salesman Problem in which he wants to travel to each of ten cities exactly... ;2. The weights on the graph below represent the cost that it takes a traveling salesman to get from one town... 's algorithm to find an Eulerian path. Number the edges on the ...

  

Source: Koban, Lori - Department of Mathematics, University of Maine at Farmington

 

Collection: Mathematics

 
83 Seismic Vessel Problem Gregory Gutin
 

Summary:  . We sug- gest a transformation from SVP to the Symmetric Traveling Salesman Problem. We report our... - tions). Keywords: Travelling Salesman, Stacker Crane Problem, Seismic Acquisition. 1 Introduction... for every pair {u, v} P. To see that SCP generalizes the Asymmetric Travelling ...

  

Source: Gutin, Gregory - Department of Computer Science, Royal Holloway, University of London

 

Collection: Computer Technologies and Information Sciences

 
84 Problem 123: Milk Collection Matthew Grum
 

Summary:  This problem is a variation of the travelling salesman problem. A milk refining company is supplied by several... travelled by the tanker. The capacity of the tanker must not be exceeded during it's journey. given n farms

  

Source: St Andrews, University of - School of Mathematics and Statistics, Centre for Interdisciplinary Research in Computational Algebra

 

Collection: Mathematics

 
85 Exponential neighbourhood local search for the traveling salesman problem
 

Summary:  Exponential neighbourhood local search for the traveling salesman problem Gregory Gutin \Lambda... for solving small or quite moderate instances of the traveling salesman problem (TSP), local search remains... (the weights are assigned to the edges). In the traveling ...

  

Source: Gutin, Gregory - Department of Computer Science, Royal Holloway, University of London

 

Collection: Computer Technologies and Information Sciences

 
86 Math 113-Sections 11----16 Review Sheet for Exam 1 Fall 2011 Choose the most appropriate answer among the choices A), B), C), and D).
 

Summary:  . For the traveling salesman problem applied to seven cities, how many distinct tours are possible? A) 360 B) 720 C... for the traveling salesman problem. B) applying Kruskal's algorithm for finding a minimum-cost spanning tree... an Euler circuit on a graph. B) applying the nearest-neighbor algorithm for the ...

  

Source: Xiao, MingQing - Department of Mathematics, Southern Illinois University

 

Collection: Engineering ; Mathematics

 
87 A branch-and-bound algorithm for a travelling salesman problem
 

Summary:  A branch-and-bound algorithm for a travelling salesman problem with colors and two objectives... 'Olmo, Gentili, Raiconi, 2006] Colorful traveling salesman problem (heuristic, GA) [Xiong, Golden, Wasil, 2007... ] Traveling salesman problem with labels (approxitmation ...

  

Source: Ingrand, François - Laboratoire d'Analyse et d'Architecture des Systèmes du CNRS

 

Collection: Engineering ; Computer Technologies and Information Sciences

 
88 TSP tour domination and Hamilton cycle decompositions of regular digraphs
 

Summary:  to the op­ timal value. In particular, we show that for the Asymmetric Traveling Salesman Problem (ATSP... .G. Deineko and G.J. Woeginger, ''The travelling salesman prob­ lem and the PQ­tree'', Proc. IPCO V, LNCS 1084... , 490­504 (1996). [7] J. Carlier and P. Villon, ''A new heuristic for the ...

  

Source: Gutin, Gregory - Department of Computer Science, Royal Holloway, University of London

 

Collection: Computer Technologies and Information Sciences

 
89 Decentralized Algorithms for Vehicle Routing in a Stochastic Time-Varying Environment
 

Summary:  -DTRP); the best previously known control algorithms rely on centralized a-priori task assignment and locational... wish to address. In Section III we provide some background on the Euclidean Traveling Salesman Problem... of the Euclidean traveling salesman problem. Physical Review ...

  

Source: Bullo, Francesco - Department of Mechanical and Environmental Engineering, University of California at Santa Barbara

 

Collection: Engineering

 
90 Approximation Algorithms for the Dubins' Traveling Salesman Problem
 

Summary:  Approximation Algorithms for the Dubins' Traveling Salesman Problem Research supported in part by... for the Dubins' Traveling Salesman Problem Jerome Le Ny Eric Feron Laboratory for Information and Decision... present an approximation algorithm for the traveling ...

  

Source: Le Ny, Jerome - GRASP Laboratory, Department of Electrical and Systems Engineering, University of Pennsylvania

 

Collection: Engineering

 
91 Equidistribution in All Dimensions of Worst-Case Point Sets for the TSP
 

Summary:  points in the unit square [0, 1]d , an optimal traveling salesman tour of S is a tour... of S that is of minimum length. A worst-case point set for the Traveling Salesman Problem in the unit square is a point... set S(n) whose optimal traveling salesman tour achieves ...

  

Source: Steele, J. Michael - Department of Statistics, University of Pennsylvania

 

Collection: Mathematics

 
92 Operations Research Letters 24 (1999) 2935 3-approximation algorithm for the clustered traveling
 

Summary:  traveling salesman tour and path problems Shoshana Anilya , Julien Bramelb;;1 , Alain Hertzc a... September 1998 Abstract We consider the ordered cluster traveling salesman problem (OCTSP). In this problem... algorithm can also be applied to the path version of the OCTSP: the ordered cluster ...

  

Source: Hertz, Alain - Département de Mathématiques et de Génie Industriel, École Polytechnique de Montréal

 

Collection: Mathematics

 
93 The Curvature-Constrained Traveling Salesman Problem For High Point Densities
 

Summary:  The Curvature-Constrained Traveling Salesman Problem For High Point Densities Jerome Le Ny, Emilio... Frazzoli and Eric Feron Abstract-- We consider algorithms for the curvature- constrained traveling salesman... can be very hard to execute on the physical system. In this paper we consider the ...

  

Source: Le Ny, Jerome - GRASP Laboratory, Department of Electrical and Systems Engineering, University of Pennsylvania

 

Collection: Engineering

 
94 Genetic Local Search for the TSP: New Results Peter Merz and Bernd Freisleben
 

Summary:  algorithms for the symmetric and asymmetric traveling salesman problem are revisited and potential im... graph G = (V; E) of n nodes. Thus, the traveling salesman prob­ lem (TSP) [22], [32] consists of finding... possibly more complex TSP instances. References [1] J. L. Bentley, ``Experiments on ...

  

Source: Merz, Peter - Fachbereich Informatik, Technische Universität Kaiserslautern

 

Collection: Computer Technologies and Information Sciences

 
95 MATHEMATICAL PUZZLE @ Fall 2004ResearchHorizons16 @ Professor William
 

Summary:  of the traveling salesman problem (TSP), a complex math puzzle that seeks the most efficient route among... of Industrial and Systems Engineering, Cook is a reigning champ of the traveling salesman problem (TSP... the traveling salesman problem has been a 16-year ...

  

Source: Sherrill, David - School of Chemistry and Biochemistry, Georgia Institute of Technology

 

Collection: Chemistry

 
96 CSC 364H L0101 Problem Set 2 Summer 2000 Due: July 6, at 2:10 (in tutorial)
 

Summary:  (Cormen et al.): (a) 27.2­1 (b) 27.2­3 (c) 27.2­4 (d) 27.2­7 2. Recall that the Traveling Salesman Problem... is a permutation of the set f2; 3; : : : ; ng. Give a decision problem TSPD corresponding to the Traveling Salesman

  

Source: Soltys, Michael - Department of Computing and Software, McMaster University

 

Collection: Mathematics ; Computer Technologies and Information Sciences

 
97 Pitfalls with Adaptive Methods for Combinatorial Optimization
 

Summary:  Pitfalls with Adaptive Methods for Combinatorial Optimization: The Traveling Salesman Problem... ;Traveling Salesman Problem Given are $ cities % 1,2, . . . n & Given is a distance matrix ' ( ) 0 1 We

  

Source: Bein, Wolfgang - School of Computer Science, University of Nevada at Las Vegas

 

Collection: Computer Technologies and Information Sciences

 
98 Pitfalls with Adaptive Methods for Combinatorial Optimization: The Traveling Salesman Problem A Case Study
 

Summary:  Pitfalls with Adaptive Methods for Combinatorial Optimization: The Traveling Salesman Problem... for the symmetric Euclidean Traveling Salesman problem. Specif­ ically, we consider 2­opt, simulated annealing... focus on the the symmetric Euclidean Travel­ ing ...

  

Source: Bein, Wolfgang - School of Computer Science, University of Nevada at Las Vegas

 

Collection: Computer Technologies and Information Sciences

 
99 On the Invariance of Ant System Mauro Birattari1
 

Summary:  ,4,5] for the traveling salesman problem. The theorems we enunciate in the paper are proved first for this specific... solution T of instance I. Definition 2 (Linear transformation of a traveling salesman instance). With ¯I... to the application of ant system to the well-known traveling ...

  

Source: Libre de Bruxelles, Université - Computer and Decision Engineering Department

 

Collection: Computer Technologies and Information Sciences ; Engineering

 
100 AMERICANJOURNAL OF MATHEMATICALAND MANAGEMENT SCIENCES CopyllgMQISM by American SclonurPmr, Inc.
 

Summary:  'sperformancewhen applied to the travelling salesman problem. Key Words and Phrases: Simulated Annealing, travelling... FOR THE TRAVELLING SALESMAN PROBLEM The travelling salesman problem models the salesman who is re- quired ...

  

Source: Waterman, Michael S. - Departments of Biological Sciences & Computer Science, University of Southern California

 

Collection: Computer Technologies and Information Sciences ; Biology and Medicine


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