Fahle, T., U. Junker, S. E. Karisch, N. Kohl, M. Sellmann, and B. Vaaben. Constraint Programming Based Column Generation for Crew Assignment. Journal of Heuristics, 8(1):59--81, 2002.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....tackled with OR techniques [10, 1, 20] genetic algorithms [14] neural networks [4, 12] constraint programming [15] etc. Much work has been done also for the crew assignment problem, where pure OR methods have been applied [2, 16, 5] or hybrid methods that combine OR and constraint programming [8, 3, 17, 21, 7]. In this paper, we discuss the crew assignment problem and we propose a formulation of it as a constraint satisfaction problem that may be solved by a speci c constraint logic programming system, the language Prolog IV, developed by the French company Prologia. 2 The Airline Crew Assignment ....

Fahle T., Junker U., Karisch S., Kohl N., Sellmann M., Vaaben B. Constraint Programming Based Column Generation for Crew Assignment. Journal of Heuristics, 8:59-81, 2002.

....posting constraints both to a linear solver (a revised Simplex algorithm) and to a nite domain constraint solver. All possible bin con gurations (columns) are generated at the start and then a pure integer linear problem is solved in order to nd the right quantities for each type of bin. In [21], the authors solve an airline crew assignment problem where the column generation subproblem is modeled as a Constrained Shortest Path Problem (CSPP) on a directed acyclic graph (DAG) This subproblem is formulated as a constraint satisfaction problem. Nevertheless, although they argue that their ....

U. Junker, S. Karisch, N. Kohl, and B. Vaaben. Constraint programming based column generation for crew assignment. In International Workshop on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems (CP-AI-OR'99), Ferrara, Italy, February 1999.

No context found.

Fahle, T., U. Junker, S. E. Karisch, N. Kohl, M. Sellmann, and B. Vaaben. Constraint Programming Based Column Generation for Crew Assignment. Journal of Heuristics, 8(1):59--81, 2002.

No context found.

T. Fahle and M. Sellmann. Constraint Programming Based Column Generation with Knapsack Subproblems. Proc. of the CP-AI-OR'00, Paderborn Center for Parallel Computing, Technical Report tr-001-2000:33--44, 2000.

No context found.

T. Fahle, U. Junker, S.E. Karisch, N. Kohl, M. Sellmann, B. Vaaben. Constraint programming based column generation for crew assignment. University of Paderborn, Technical Report tr-ri-99-212, 1999, accepted by Journal of Heuristics.

No context found.

T. Fahle, U. Junker, S.E. Karisch, N. Kohl, M. Sellmann, B. Vaaben. Constraint programming based column generation for crew assignment. Journal of Heuristics, 8(1):59-81, 2002.

No context found.

Fahle, T., U. Junker, S. E. Karisch, N. Kohl, M. Sellmann, and B. Vaaben. Constraint Programming Based Column Generation for Crew Assignment. Journal of Heuristics, 8(1):59--81, 2002.

No context found.

T. Fahle and M. Sellmann. Constraint Programming Based Column Generation with Knapsack Subproblems. Proc. of the CP-AI-OR'00, Paderborn Center for Parallel Computing, Technical Report tr-001-2000:33--44, 2000.

No context found.

T. Fahle, U. Junker, S.E. Karisch, N. Kohl, M. Sellmann, B. Vaaben. Constraint programming based column generation for crew assignment. To appear in Journal of Heuristics.

No context found.

T. Fahle, U. Junker, S.E. Karisch, N. Kohl, M. Sellmann, B. Vaaben. Constraint programming based column generation for crew assignment. Journal of Heuristics, 8(1):59-81, 2002.

No context found.

T. Fahle, U. Junker, S.E. Karisch, N. Kohl, M. Sellmann, B. Vaaben. Constraint programming based column generation for crew assignment. Journal of Heuristics, 8(1):59-81, 2002.

No context found.

T. Fahle, U. Junker, S.E. Karisch, N. Kohl, M. Sellmann, B. Vaaben. Constraint programming based column generation for crew assignment. Journal of Heuristics, 8(1):59-81, 2002.

No context found.

T. Fahle, U. Junker, S.E. Karisch, N. Kohl, M. Sellmann and B. Vaaben, Constraint programming based column generation for crew assignment, Journal of Heuristics 8(1) (2002) 59--81.

No context found.

T. Fahle and M. Sellmann. Constraint Programming Based Column Generation with Knapsack Subproblems. Proc. of the CP-AI-OR'00, Paderborn Center for Parallel Computing, Technical Report tr-001-2000:33--44, 2000.

No context found.

T. Fahle and M. Sellmann. Constraint Programming Based Column Generation with Knapsack Subproblems. Annals of Operations Reserach, Vol 114, 2003, to appear.

No context found.

T. Fahle, U. Junker, S.E. Karisch, N. Kohl, M. Sellmann, B. Vaaben. Constraint programming based column generation for crew assignment. Journal of Heuristics 8(1):59--81, 2002.

No context found.

T. Fahle and M. Sellmann. Constraint Programming Based Column Generation with Knapsack Subproblems. Proc. of the CP-AI-OR'00, Paderborn, 2000.

No context found.

T. Fahle, U. Junker, S.E. Karisch, N. Kohl, M. Sellmann, B. Vaaben. Constraint programming based column generation for crew assignment. Journal of Heuristics 8(1):59--81, 2002.

....respect to reduced cost information can be done quickly, but is not very effective. The ARP can be viewed as a combination of two simpler optimization problems: a knapsack problem, and a maximum weighted stable set problem on an interval graph. For the knapsack problem, an efficient VFAs exists [4]. It runs in time #(n log n) and in amortized linear time (log n) search nodes. In the following, we develop a VFA for the maximum weighted stable set substructure (MWSSP) of the ARP. 3 Maximum Weighted Stable Set on Interval Graphs On interval graphs, the problem of finding a maximum weighted ....

....constraints with multipliers # 0, we obtain a knapsack problem: Let i : j : i#C j # j i n and # : 0#j m # j . The problem then is to 13 (p i i )x i Relaxations of this problem again yield an upper bound on the objective, and we can apply the knapsack VFA from [4]. In general, two linear optimization constraint families for which efficient VFAs are known can be combined effectively by computing Lagrangian multipliers for the first, using the second for fixing variables in each Lagrangian subproblem L(#) and then handing back dual information of the ....

T. Fahle and M. Sellmann. Constraint Programming Based Column Generation with Knapsack Subproblems. Proc. of the CP-AI-OR'00, Paderborn Center for Parallel Computing, Technical Report tr-001-2000:33--44, 2000.

....in time O(n e) on DAGs with n nodes and e edges. In [23] we showed that bound consistency for a shortest path on a node weighted co interval graph (given as list of negative pro ts and starting and ending times) can be computed in amortized time (n) Knapsack constraints have been studied in [9]. There, amortized linear time propagation routines based on continuous bounds were developed. The multimedia application we use to introduce CP based Lagrangian Relaxation is investigated in [16] The goal there was to develop heuristics for an extension of the ARP. Lagrangian relaxation was ....

....graphs occur when relaxing the initial setting by ignoring the capacity constraint (a) i.e. when tieing constraints (b) and (c) together. An approach to combine constraints (a) and (b) is obviously ine ective. We presented ways of how variable xing can be done for knapsack problems in [9], and for shortest path problems in [8] Moreover, we developed a specialized algorithm for shortest paths on weighted co interval graphs in [23] To keep the paper self contained, we brie y review the relevant ndings regarding knapsack and shortest path propagation. For a detailed description, ....

[Article contains additional citation context not shown here]

T. Fahle and M. Sellmann. Constraint Programming Based Column Generation with Knapsack Subproblems. Proceedings of the CP-AI-OR'00, Paderborn Center for Parallel Computing, Technical Report tr-001-2000:3344, 2000.

....Research (OR) and Constraint Programming (CP) has been subject to intensive research in the last years. A recent overview on attempts of combining CP and OR can be found e.g. in [19] The work presented in this paper is based on some previous results on shortest path and knapsack constraints: In [8, 15], an e cient shortest path constraint was introduced. It is based on a variant of Djikstra algorithm for directed acyclic graphs (see [1] and achieves bound consistency in time O(n e) on DAGs with n nodes and e edges. In [23] we showed that bound consistency for a shortest path on a ....

....initial setting by ignoring the capacity constraint (a) i.e. when tieing constraints (b) and (c) together. An approach to combine constraints (a) and (b) is obviously ine ective. We presented ways of how variable xing can be done for knapsack problems in [9] and for shortest path problems in [8]. Moreover, we developed a specialized algorithm for shortest paths on weighted co interval graphs in [23] To keep the paper self contained, we brie y review the relevant ndings regarding knapsack and shortest path propagation. For a detailed description, we refer to the original papers. ....

T. Fahle, U. Junker, S.E. Karisch, N. Kohl, M. Sellmann, B. Vaaben. Constraint programming based column generation for crew assignment. University of Paderborn, Technical Report tr-ri-99-212, 1999, accepted by Journal of Heuristics.

....calls. Repeated computations with di erent objectives are e.g. important when solving Lagrangian relaxations or when applying the method in a column generation environment (see e.g. 1] In [8] the Constraint Programming based Column Generation Framework has rst been introduced, and in [6] it has been applied with shortest path subproblems to solve the airline crew scheduling problem. Here, the shortest path routine is being used to estimate the reduced costs of an individual line of work and to perform reduced cost propagation. That means, that all nodes (nodes correspond to jobs) ....

T. Fahle, U. Junker, S.E. Karisch, N. Kohl, M. Sellmann, B. Vaaben. Constraint Programming based Column Generation for Crew Assignment. Technical Report trri -99-212, University of Paderborn, 1999, accepted by Journal of Heuristics.

....column generation approaches was developed, the so called Constraint Based Column Generation [11] It describes a generic way of how to treat arbitrary constraints for the constrained subproblem in the column generation phase. The approach has been successfully used for the Crew Assignment Problem [5], where the subproblem is a Constrained Shortest Path Problem (CSP) Until now, the new paradigm has only been used in combination with CSPs. In the following, we will show how to apply the new framework when Constrained Knapsack Problems (CKPs) occur as subproblems in the column generation ....

T. Fahle, U. Junker, S.E. Karisch, N. Kohl, M. Sellmann, B. Vaaben. Constraint programming based column generation for crew assignment. Technical Report tr-ri-99-212, University of Paderborn, 1999, submitted.

.... and to use dual values for crews and pairings provided from the OR side to produce columns that can lead to better solutions of the continuous relaxation of the master problem. Dual values can either be used as heuristic information through the search (e.g. as Shortest Path Constraint, see [4]) or even as new objective function. The use of computationally produced information, such as dual values for guiding the CP search, is generally of great interest, since direct methods conventionally rely heavily on hand made heuristics tailored to speci c problems, which limits their generic ....

T. Fahle, U. Junker, S.E. Karisch, N. Kohl, M. Sellmann, B. Vaaben. Constraint programming based column generation for crew assignment. Technical Report tr-ri-99-212, University of Paderborn, 1999, submitted.

No context found.

Fahle, T., U. Junker, S. Karisch, N. Kohl, M. Sellmann and B. Vaaben, Constraint programming based column generation for crew assignment, Technical Report TR-RI-99-212, University of Paderborn (1999).

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC