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210,156
Solving the Railway Traveling Salesman Problem via a Transformation into the Classical Traveling Salesman Problem
"... The Railway Traveling Salesman Problem (RTSP) is a practical extension of the classical traveling salesman problem considering a railway network and train schedules. We are given a salesman who has to visit a number of cities to carry out some business. He starts and ends at a specified home city, a ..."
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The Railway Traveling Salesman Problem (RTSP) is a practical extension of the classical traveling salesman problem considering a railway network and train schedules. We are given a salesman who has to visit a number of cities to carry out some business. He starts and ends at a specified home city
Classical Travelling Salesman Problem (TSP) based Approach to Solve Fuzzy TSP using Yager’s Ranking S.Dhanasekar
"... Travelling salesman problem (TSP) is a classical and most widely studied problem in both operation research and computer science. If in the TSP the cost or time or distance is not certain then it is said to be Fuzzy TSP. We propose a new algorithm to solve the fuzzy TSP and also implemented the same ..."
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Travelling salesman problem (TSP) is a classical and most widely studied problem in both operation research and computer science. If in the TSP the cost or time or distance is not certain then it is said to be Fuzzy TSP. We propose a new algorithm to solve the fuzzy TSP and also implemented
The Ant System: Optimization by a colony of cooperating agents
 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICSPART B
, 1996
"... An analogy with the way ant colonies function has suggested the definition of a new computational paradigm, which we call Ant System. We propose it as a viable new approach to stochastic combinatorial optimization. The main characteristics of this model are positive feedback, distributed computation ..."
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Cited by 1247 (45 self)
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methodology to the classical Traveling Salesman Problem (TSP), and report simulation results. We also discuss parameter selection and the early setups of the model, and compare it with tabu search and simulated annealing using TSP. To demonstrate the robustness of the approach, we show how the Ant System (AS
Ant Colony System: A cooperative learning approach to the traveling salesman problem
 IEEE TRANSACTIONS ON EVOLUTIONARY COMPUTATION
, 1997
"... This paper introduces the ant colony system (ACS), a distributed algorithm that is applied to the traveling salesman problem (TSP). In the ACS, a set of cooperating agents called ants cooperate to find good solutions to TSP’s. Ants cooperate using an indirect form of communication mediated by a pher ..."
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Cited by 1001 (52 self)
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This paper introduces the ant colony system (ACS), a distributed algorithm that is applied to the traveling salesman problem (TSP). In the ACS, a set of cooperating agents called ants cooperate to find good solutions to TSP’s. Ants cooperate using an indirect form of communication mediated by a
Polynomial time approximation schemes for Euclidean Traveling Salesman and other geometric problems
, 1998
"... We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes are in � ..."
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Cited by 390 (2 self)
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We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes
Probabilistic Traveling Salesman Problem: A survey
, 2014
"... The Probabilistic Traveling Salesman Problem (PTSP) is a variation of the classic Traveling Salesman Problem (TSP) in which only a subset of potential nodes needs to be visited on any given instance of the problem. The number of nodes to be visited each time is a random variable. The objective is to ..."
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The Probabilistic Traveling Salesman Problem (PTSP) is a variation of the classic Traveling Salesman Problem (TSP) in which only a subset of potential nodes needs to be visited on any given instance of the problem. The number of nodes to be visited each time is a random variable. The objective
Ant colonies for the travelling salesman problem
, 1997
"... We describe an artificial ant colony capable of solving the travelling salesman problem (TSP). Ants of the artificial colony are able to generate successively shorter feasible tours by using information accumulated in the form of a pheromone trail deposited on the edges of the TSP graph. Computer si ..."
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Cited by 274 (5 self)
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We describe an artificial ant colony capable of solving the travelling salesman problem (TSP). Ants of the artificial colony are able to generate successively shorter feasible tours by using information accumulated in the form of a pheromone trail deposited on the edges of the TSP graph. Computer
The Time Dependent Traveling Salesman Problem: Polyhedra and Algorithm
, 2010
"... The Time Dependent Traveling Salesman Problem (TDTSP) is a generalization of the classical Traveling Salesman Problem (TSP), where arc costs depend on their position in the tour with respect to the source node. While TSP instances with thousands of vertices can be solved routinely, there are very ch ..."
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Cited by 4 (1 self)
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The Time Dependent Traveling Salesman Problem (TDTSP) is a generalization of the classical Traveling Salesman Problem (TSP), where arc costs depend on their position in the tour with respect to the source node. While TSP instances with thousands of vertices can be solved routinely, there are very
Tabu Search  Part I
, 1989
"... This paper presents the fundamental principles underlying tabu search as a strategy for combinatorial optimization problems. Tabu search has achieved impressive practical successes in applications ranging from scheduling and computer channel balancing to cluster analysis and space planning, and more ..."
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Cited by 650 (11 self)
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, and more recently has demonstrated its value in treating classical problems such as the traveling salesman and graph coloring problems. Nevertheless, the approach is still in its infancy, and a good deal remains to be discovered about its most effective forms of implementation and about the range
On the Solution of Traveling Salesman Problems
 DOC. MATH. J. DMV
, 1998
"... Following the theoretical studies of J.B. Robinson and H.W. Kuhn in the late 1940s and the early 1950s, G.B. Dantzig, R. Fulkerson, and S.M. Johnson demonstrated in 1954 that large instances of the TSP could be solved by linear programming. Their approach remains the only known tool for solving TS ..."
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Cited by 223 (7 self)
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Following the theoretical studies of J.B. Robinson and H.W. Kuhn in the late 1940s and the early 1950s, G.B. Dantzig, R. Fulkerson, and S.M. Johnson demonstrated in 1954 that large instances of the TSP could be solved by linear programming. Their approach remains the only known tool for solving TSP instances with more than several hundred cities; over the years, it has evolved further through the work of M. Grötschel , S. Hong , M. Jünger , P. Miliotis , D. Naddef , M. Padberg ... some of its refinements that led to the solution of a 13,509city instance.
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