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## The Generalized Covering Salesman Problem

Citations: | 3 - 0 self |

### Citations

406 |
effective heuristic algorithm for the traveling salesman problem.
- Lin, Kernighan
- 1973
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Citation Context ...ossibilities for an initial 7solution: (i) the TSP tour obtained using the Lin-Kernighan procedure over the n nodes in the instance, and (ii) the TSP tour obtained using the Lin-Kernighan procedure (=-=Lin and Kernighan, 1973-=-) over the nodes obtained by solving the associated SCP problem to optimality (this solution may not be feasible for the binary GCSP). We found that these two alternatives did not dominate the random ... |

405 | Performance of Various Computers Using Standard Linear Equations Software in a Fortran Environment. - Dongarra - 1988 |

350 |
TSPLIB A traveling salesman problem library
- Reinelt
- 1991
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Citation Context ...ery rapidly. 4.1. Test Problems Since there are no test problems in the literature for the CSP (nor for the variants of the GCSP we introduce), we created datasets based on the TSP library instances (=-=Reinelt, 1991-=-). Our analysis involves two datasets: one consisting of small to medium instances with up to 200 nodes, and the other consisting of large instances with up to 1000 nodes. The first dataset is constru... |

188 | An effective implementation of the Lin–Kernighan traveling salesman heuristic - Helsgaun - 2000 |

81 |
New insertion and postoptimization procedures for the travelling salesman problem
- Gendreau, Hertz, et al.
- 1992
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Citation Context ... of nodes that must be on the tour consists of the entire node set, the CTP reduces to the TSP. Gendreau et al. (1997) proposed a heuristic that combines GENIUS, a high quality heuristic for the TSP (=-=Gendreau et al., 1992-=-), with PRIMAL1, a high quality heuristic for the SCP (Balas and Ho, 1980). Vogt et al. (2007) considered the Single Vehicle Routing Allocation Problem (SVRAP) that further generalizes the CTP. Here, ... |

78 | Approximation algorithms for the geometric covering salesman problem, Discrete Applied Mathematics 55 - Arkin, Hassin - 1994 |

72 | Traveling salesman problems with profits. Transportation Sci - Feillet, Dejax, et al. - 2003 |

55 |
Solution of a Large Scale Traveling Salesman Problem
- G, Dantzig, et al.
- 1954
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Citation Context ... a graph G � ( N, E) , the goal is to find the minimum length tour of the nodes in N, such that the salesman, starting from a node, visits each node exactly once and returns to the starting node (see =-=Dantzig et al., 1954-=-). In recent years, many new variants such as the TSP with profits (Feillet et al., 2005), the Clustered TSP (Chisman, 1975), the Generalized TSP (Fischetti et al., 1997), the Prize Collecting TSP (Fi... |

54 |
The selective travelling salesman problem
- Laporte, Martello
- 1990
(Show Context)
Citation Context ...e TSP with profits (Feillet et al., 2005), the Clustered TSP (Chisman, 1975), the Generalized TSP (Fischetti et al., 1997), the Prize Collecting TSP (Fischetti and Toth, 1988), and the Selective TSP (=-=Laporte and Martello, 1990-=-) have been introduced and studied. The recent monograph by Gutin and Punnen (2002) has a nice discussion of different variations of the TSP and solution procedures. Current (1981) defined and introdu... |

46 | A random-key genetic algorithm for the generalized traveling salesman problem
- Snyder, Daskin
- 2006
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Citation Context ...lti-Start Heuristic by Cacchiani et al. 2011, 2. mrOX: a Genetic Algorithm by Silberholz and Golden 2007, 3. RACS: a Reinforcing Ant Colony System by Pintea et al. 2007, 4. GA: a Genetic Algorithm by =-=Snyder and Daskin 2006-=-, 3 5. GI : a composite algorithm by Renaud and Boctor 1998, 6. NN: a Nearest Neighbor approach by Noon 1988, 7. FST-Lagr and FST-root: Two heuristics by Fischetti et al. 1997. 19In order to perform ... |

20 | Multiobjective design of transportation networks: taxonomy and annotation - Current, Min - 1986 |

20 | The covering salesman problem - Current, Schilling - 1989 |

19 | An efficient composite heuristic for the symmetric generalized traveling salesman problem
- Renaud, Boctor
- 1998
(Show Context)
Citation Context ...netic Algorithm by Silberholz and Golden 2007, 3. RACS: a Reinforcing Ant Colony System by Pintea et al. 2007, 4. GA: a Genetic Algorithm by Snyder and Daskin 2006, 3 5. GI : a composite algorithm by =-=Renaud and Boctor 1998-=-, 6. NN: a Nearest Neighbor approach by Noon 1988, 7. FST-Lagr and FST-root: Two heuristics by Fischetti et al. 1997. 19In order to perform a fair comparison on the running times of the different heu... |

16 |
The clustered traveling salesman problem
- Chisman
- 1975
(Show Context)
Citation Context ..., visits each node exactly once and returns to the starting node (see Dantzig et al., 1954). In recent years, many new variants such as the TSP with profits (Feillet et al., 2005), the Clustered TSP (=-=Chisman, 1975-=-), the Generalized TSP (Fischetti et al., 1997), the Prize Collecting TSP (Fischetti and Toth, 1988), and the Selective TSP (Laporte and Martello, 1990) have been introduced and studied. The recent mo... |

15 |
The generalized traveling salesman problem: a new genetic algorithm approach
- Silberholz, Golden
- 2007
(Show Context)
Citation Context ...uns of LS2 were performed. We compared LS2 to eight other heuristics in the literature that are listed below. 1. MSA: A Multi-Start Heuristic by Cacchiani et al. 2011, 2. mrOX: a Genetic Algorithm by =-=Silberholz and Golden 2007-=-, 3. RACS: a Reinforcing Ant Colony System by Pintea et al. 2007, 4. GA: a Genetic Algorithm by Snyder and Daskin 2006, 3 5. GI : a composite algorithm by Renaud and Boctor 1998, 6. NN: a Nearest Neig... |

14 |
An Additive Approach for the Optimal Solution of the PrizeCollecting Travelling Salesman Problem
- Fischetti, Toth
- 1988
(Show Context)
Citation Context ...54). In recent years, many new variants such as the TSP with profits (Feillet et al., 2005), the Clustered TSP (Chisman, 1975), the Generalized TSP (Fischetti et al., 1997), the Prize Collecting TSP (=-=Fischetti and Toth, 1988-=-), and the Selective TSP (Laporte and Martello, 1990) have been introduced and studied. The recent monograph by Gutin and Punnen (2002) has a nice discussion of different variations of the TSP and sol... |

13 | The Covering Tour Problem - Gendreau, Laporte, et al. - 1997 |

12 |
The Generalized Traveling Salesman Problem
- Noon
- 1988
(Show Context)
Citation Context ...forcing Ant Colony System by Pintea et al. 2007, 4. GA: a Genetic Algorithm by Snyder and Daskin 2006, 3 5. GI : a composite algorithm by Renaud and Boctor 1998, 6. NN: a Nearest Neighbor approach by =-=Noon 1988-=-, 7. FST-Lagr and FST-root: Two heuristics by Fischetti et al. 1997. 19In order to perform a fair comparison on the running times of the different heuristics, we scaled the running times for the diff... |

12 | The generalized traveling salesman problem solved with ant algorithms
- Pintea, Pop, et al.
(Show Context)
Citation Context ...the literature that are listed below. 1. MSA: A Multi-Start Heuristic by Cacchiani et al. 2011, 2. mrOX: a Genetic Algorithm by Silberholz and Golden 2007, 3. RACS: a Reinforcing Ant Colony System by =-=Pintea et al. 2007-=-, 4. GA: a Genetic Algorithm by Snyder and Daskin 2006, 3 5. GI : a composite algorithm by Renaud and Boctor 1998, 6. NN: a Nearest Neighbor approach by Noon 1988, 7. FST-Lagr and FST-root: Two heuris... |

11 |
Set Covering Algorithms Using Cutting Planes
- BALAS, HO
- 1979
(Show Context)
Citation Context ...reduces to the TSP. Gendreau et al. (1997) proposed a heuristic that combines GENIUS, a high quality heuristic for the TSP (Gendreau et al., 1992), with PRIMAL1, a high quality heuristic for the SCP (=-=Balas and Ho, 1980-=-). Vogt et al. (2007) considered the Single Vehicle Routing Allocation Problem (SVRAP) that further generalizes the CTP. Here, in addition to tour (routing) costs, nodes covered by the tour (that are ... |

5 |
A multistart heuristic for the equality generalized traveling salesman problem
- Cacchiani, Muritiba, et al.
- 2010
(Show Context)
Citation Context ...300, K=10, T=10, and max_iter = 50 and 10 independent runs of LS2 were performed. We compared LS2 to eight other heuristics in the literature that are listed below. 1. MSA: A Multi-Start Heuristic by =-=Cacchiani et al. 2011-=-, 2. mrOX: a Genetic Algorithm by Silberholz and Golden 2007, 3. RACS: a Reinforcing Ant Colony System by Pintea et al. 2007, 4. GA: a Genetic Algorithm by Snyder and Daskin 2006, 3 5. GI : a composit... |

3 |
P: A branch and cut algorithm for the symmetric generalized traveling salesman problem. Oper Res 1997, 45(30):378–395
- Fischetti, JJ, et al.
(Show Context)
Citation Context ...eturns to the starting node (see Dantzig et al., 1954). In recent years, many new variants such as the TSP with profits (Feillet et al., 2005), the Clustered TSP (Chisman, 1975), the Generalized TSP (=-=Fischetti et al., 1997-=-), the Prize Collecting TSP (Fischetti and Toth, 1988), and the Selective TSP (Laporte and Martello, 1990) have been introduced and studied. The recent monograph by Gutin and Punnen (2002) has a nice ... |

2 | The Traveling Salesman Problem and Its Variations - P - 2002 |

2 | Heuristics for solving three routing problems: Close-enough traveling salesman problem, close-enough vehicle routing problem, sequence-dependent team orienteering problem - Mennell |

2 | A Tabu Search algorithm for the Single Vehicle Routing Allocation Problem - JE - 2007 |