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## Approximate Uni-directional Benders Decomposition

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Citations: | 1 - 1 self |

### Citations

10589 | Introduction to Algorithms
- Cormen, Leiserson, et al.
- 2001
(Show Context)
Citation Context ...set of variables whose domains are finite and discrete. Any graphsearch algorithm can be used in order to find a plan on the underlying state model. Even so, blind search algorithms such as Dijkstra (=-=Cormen et al. 2001-=-) do not scale up due to the size of the state space, which can be exponential in the number of variables in the factored problem. On the other hand, heuristic search algorithms have proven to perform... |

1164 | Fast planning through planning graph analysis
- Blum, Furst
- 1997
(Show Context)
Citation Context ...hallenge is to devise effective methods to obtain such action sequences, called plans. The last two decades have brought significant advances in classical planning (see, e.g., (Kautz and Selman 1996; =-=Blum and Furst 1995-=-; Bonet and Geffner 2001; Richter and Westphal 2010)), with heuristic search—using search algorithms on the underlying state model guided by heuristic estimators extracted automatically from the probl... |

576 | Pushing the envelope: Planning, propositional logic, and stochastic search
- Kautz, Selman
- 1996
(Show Context)
Citation Context ...ng. The computational challenge is to devise effective methods to obtain such action sequences, called plans. The last two decades have brought significant advances in classical planning (see, e.g., (=-=Kautz and Selman 1996-=-; Blum and Furst 1995; Bonet and Geffner 2001; Richter and Westphal 2010)), with heuristic search—using search algorithms on the underlying state model guided by heuristic estimators extracted automat... |

421 | Planning as heuristic search,
- Bonet, Geffner
- 2001
(Show Context)
Citation Context ... effective methods to obtain such action sequences, called plans. The last two decades have brought significant advances in classical planning (see, e.g., (Kautz and Selman 1996; Blum and Furst 1995; =-=Bonet and Geffner 2001-=-; Richter and Westphal 2010)), with heuristic search—using search algorithms on the underlying state model guided by heuristic estimators extracted automatically from the problem—being the most succes... |

377 |
Partitioning procedures for solving mixed-variables programming problems
- Benders
- 1962
(Show Context)
Citation Context ...P1 into a good, and preferably near-optimal, space in order to arrive at better solutions to P2, we approximate η and the corresponding cuts as follows. We know, from Classical Benders decomposition (=-=Benders 1962-=-), that for linear systems, if we substitute the optimal values of x (wrt P ) into P2, and then solve P2, we obtain the optimal solution to P . Let the optimal P1 values be x̄∗, and the corresponding ... |

141 | The lama planner: Guiding cost-based anytime planning with landmarks. - Richter, Westphal - 2010 |

65 | How good is almost perfect? - Helmert, Roger - 2008 |

52 | Deterministic planning in the fifth international planning competition: PDDL3 and experimental evaluation of the planners.
- Gerevini, Haslum, et al.
- 2009
(Show Context)
Citation Context ...siting as many markets as is necessary to meet demand for a set of products,K. The markets may have limited quantities of each product (capacity C). This is known as the Travelling Purchaser Problem (=-=Gerevini et al. 2009-=-). The optimisation version of this problem is as follows. Definition 1 (TPP). Given a graph G = (N , E); a set of products, k ∈ K; demand for each product in the set, Dk; a set of markets, m ∈ M ⊆ N ... |

38 | Forward-chaining partial-order planning
- Coles, Coles, et al.
- 2010
(Show Context)
Citation Context ... 34 times slower than HeurMIP, on average. Mining Operations Planning We solved the MIPs and feasibility problems using CPLEX (v.12.6). We used temporal planners CPT and POPF (Vidal and Geffner 2006; =-=Coles et al. 2010-=-) to solve the mining operations problems, where actions can be executed concurrently with different durations. POPF solutions are suboptimal, while CPT and A∗(hmax) are optimal planners. We provide e... |

37 | Planning and Scheduling by Logic-Based Benders Decomposition, - Hooker - 2007 |

28 | Planning with problems requiring temporal coordination - Coles, Fox, et al. - 2008 |

22 | A Hybrid Relaxed Planning Graph-LP Heuristic for Numeric Planning Domains", - Coles, Fox, et al. - 2008 |

18 | Capacitated facility location/network design problems, - Melkote, Daskin - 2001 |

11 | A branch-and-cut algorithm for the undirected traveling purchaser problem, - Laporte, Ledesma, et al. - 2003 |

6 | Planning multi-modal transportation problems - Flórez, Torralba, et al. - 2011 |

5 | Combining a temporal planner with an external solver for the power balancing problem in an electricity network - Piacentini, Alimisis, et al. - 2013 |

3 | Solving clustered oversubscription problems for planning e-courses - Fernndez, Borrajo |

3 | Optimal planning with global numerical state constraints. - Ivankovic, Haslum, et al. - 2014 |

2 | P.J.: Planning for mining operations with time and resource constraints - Lipovetzky, Burt, et al. - 2014 |