## Tabu Search, Generalized k-Path Inequalities, and Partial Elementarity for the Vehicle Routing Problem with Time Windows (2006)

### BibTeX

@MISC{Desaulniers06tabusearch,,

author = {Guy Desaulniers and François Lessard and Ahmed Hadjar},

title = {Tabu Search, Generalized k-Path Inequalities, and Partial Elementarity for the Vehicle Routing Problem with Time Windows},

year = {2006}

}

### OpenURL

### Abstract

### Citations

601 | Tabu search
- Glover, Laguna
- 1993
(Show Context)
Citation Context ...ences.s10 G–2006–45 Les Cahiers du GERAD 4.3 Tabu search Another heuristic alternative to rapidly generate negative reduced cost columns is to use tabu search for solving the espprc. Tabu search (see =-=Glover and Laguna, 1997-=-) is a wellknown metaheuristic that has been successful at solving difficult combinatorial optimization problems, namely the vrptw (see Bräysy and Gendreau, 2005b). It starts with an initial solution ... |

231 |
The Decomposition Principle for Linear Programs
- Dantzig, Wolfe
- 1960
(Show Context)
Citation Context ...und at a node of the search tree, we apply column generation for solving the linear relaxation of model (1)–(3) augmented by the appropriate branching decisions and cutting planes. Column generation (=-=Dantzig and Wolfe, 1960-=-; see also Desrosiers and Lübbecke, 2005) is an iterative process that solves alternately a restricted master problem and a subproblem. The restricted master problem is simply the linear relaxation of... |

228 | Algorithms for the Vehicle Routing and Scheduling Problems with Time Window Constraints - Solomon - 1987 |

211 | Branch-and-price: Column generation for solving huge integer programs
- Barnhart, Johnson, et al.
- 1998
(Show Context)
Citation Context ...ables. In practice, model (1)–(3) contains a huge number of variables. Like several authors (see Section 2), we propose to solve it using a branch-and-price-and-cut approach. In such an approach (see =-=Barnhart et al., 1998-=-, Desaulniers et al., 1998), column generation is applied to compute lower bounds, cutting planes are generated to improve the quality of these bounds, and a branch-and-bound procedure is used, when n... |

122 | A New Optimization Algorithm for the Vehicle Routing Problem with Time Windows - Desrochers, Desrosiers, et al. - 1992 |

74 | Vehicle Routing Problem With Time Windows - Bräysy, Gendreau |

46 | 2- path cuts for the vehicle routing problem with time windows - Kohl, Desrosiers, et al. - 1999 |

39 | A General Heuristic for Vehicle Routing Problems - Pisinger, Ropke |

37 |
An exact algorithm for the elementary shortest path problem with resource constraints: application to some vehicle routing problems
- Feillet, Dejax, et al.
(Show Context)
Citation Context ...bset of its variables. It is solved by the simplex algorithm to provide a primal and a dual solution. The subproblem corresponds to an espprc which can typically be solved by dynamic programming (see =-=Feillet et al., 2004-=-, and Irnich and Desaulniers, 2005) to generate negative reduced cost columns (variables) that are added to the restricted master problem before beginning another iteration. The solution process stops... |

36 | A primer in column generation
- Desrosiers, Lu¨bbecke
- 2005
(Show Context)
Citation Context ...we apply column generation for solving the linear relaxation of model (1)–(3) augmented by the appropriate branching decisions and cutting planes. Column generation (Dantzig and Wolfe, 1960; see also =-=Desrosiers and Lübbecke, 2005-=-) is an iterative process that solves alternately a restricted master problem and a subproblem. The restricted master problem is simply the linear relaxation of the augmented model restricted to a sma... |

28 | The Shortest Path Problem with Resource Constraints and K-Cycle Elimination for K>=3 - Irnich, Villeneuve |

24 | Vehicle routing problem with time windows - Kallehauge, Larsen, et al. - 2005 |

23 | VRP with Time Windows - Cordeau, Desaulniers, et al. - 2002 |

19 | An Optimization Algorithm for the Vehicle Routing Problem with Time Windows Based on Lagrangian Relaxation - Kohl, Madsen - 1997 |

14 |
Note on the Complexity of the Shortest Path Models for Column Generation in VRPTW
- Dror
- 1994
(Show Context)
Citation Context ...rptw linear relaxation into a master problem and a subproblem which corresponds to an elementary shortest path problem with resource constraints (espprc). Because the espprc is an NPhard problem (see =-=Dror, 1994-=-), several researchers have replaced it by a relaxation which allows cycles, namely, the shortest path problem with resource constraints (spprc). Such an spprc-based decomposition method produces good... |

13 | A Branch-and-Cut Procedure for the Vehicle Routing Problem with Time Windows - Bard, Kontoravdis, et al. - 2002 |

11 | A parallel cutting-plane algorithm for the vehicle routing problem with time windows - Cook, Rich - 1999 |

11 | Symmetry Helps: Bounded Bi-directional Dynamic Programming for the Elementary Shortest Path Problem with Resource Constraints - Righini, Salani |

10 | Accelerated label setting algorithms for the elementary resource constrained shortest path problem - Boland, Dethridge, et al. |

7 | Reachability cuts for the vehicle routing problem with time windows - Lysgaard |

3 | A Non-Robust Branch-and-Cut-and-Price Algorithm for the Vehicle Routing Problem with Time Windows - Jepsen - 2006 |

3 | Path inequalities for the vehicle routing problem with time windows - Kallehauge, Boland, et al. - 2005 |

2 |
A unified framework for time constrained vehicle routing and crew scheduling problems
- Desaulniers, Desrosiers, et al.
- 1998
(Show Context)
Citation Context ...d and is still playing an important role in the development and improvement of solution methodologies for the class of deterministic time constrained vehicle routing and crew scheduling problems (see =-=Desaulniers et al., 1998-=-). Several research teams (see the literature review below) have been working actively on this problem in the past few years. This effervescence is certainly due to the fact that most of the 56 Solomo... |

2 |
La fabrication d’horaires de travail pour les conducteurs d’autobus par une méthode de génération de colonnes
- Desrochers
- 1986
(Show Context)
Citation Context ...price approaches based on the ESPPRC Feillet et al. (2004) were the first to propose a branch-and-price approach in which the subproblem is modeled as an espprc and solved by dynamic programming (see =-=Desrochers, 1986-=-, and Irnich and Desaulniers, 2005). They define one resource for each customer that indicates whether or not the customer has been visited along a path. To improve the efficiency of the dominance pro... |

2 | Branch-and-price algorithms for vehicle routing problems - Salani, M - 2005 |

1 | Cahiers du GERAD G–2006–45 29 - Les - 2006 |

1 | Pape (2005). Branch-and-price heuristics: A case study on the vehicle routing problem with time windows - Danna, Le |

1 | New refinements for the solution of vehicle routing problems with branch and price - Feillet, Gendreau, et al. - 2005 |

1 | Logistics/SCM Research Group, Aarhus School of Business - Report - 2005 |