Solving crew scheduling problems by constraint programming

Guerinik, Nabil; Caneghem, Michel Van

doi:10.1007/3-540-60299-2_29

Cited by 27 publications

(10 citation statements)

References 3 publications

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“…On the other hand, constraint propagation techniques are not competitive when compared with global methods like the simplex (e.g. in Hoffmann and Padberg (1992), Guerinik and Van Caneghem (1995)). While completing this work, it appeared to us that the set domain CSP approach is promising when investigating feasibility issues that are problematic with the simplex method.…”

Section: The Set Partitioning Problemmentioning

confidence: 99%

Interval propagation to reason about sets: Definition and implementation of a practical language

Gervet

1997

Constraints

123

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Local consistency techniques have been introduced in logic programming in order to extend the application domain of logic programming languages. The existing languages based on these techniques consider arithmetic constraints applied to variables ranging over finite integer domains. This makes difficult a natural and concise modelling as well as an efficient solving of a class of A/P-complete combinatorial search problems dealing with sets. To overcome these problems, we propose a solution which consists in extending the notion of integer domains to that of set domains (sets of sets). We specify a set domain by an interval whose lower and upper bounds are known sets, ordered by set inclusion. We define the formal and practical framework of a new constraint logic programming language over set domains, called Conjunto. Conjunto comprises the usual set operation symbols (U, N, \), and the set inclusion relation (___). Set expressions built using the operation symbols are interpreted as relations (s U Sl = s2 .... ). In addition, Conjunto provides us with a set of constraints called graduated constraints (e.g. the set cardinality) which map sets onto arithmetic terms. This allows us to handle optimization problems by applying a cost function to the quantifiable, i.e., arithmetic, terms which are associated to set terms. The constraint solving in Conjunto is based on local consistency techniques using interval reasoning which are extended to handle set constraints. The main contribution of this paper concerns the formal definition of the language and its design and implementation as a practical language.

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Section: The Set Partitioning Problemmentioning

confidence: 99%

Interval propagation to reason about sets: Definition and implementation of a practical language

Gervet

1997

Constraints

123

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“…Constraints (12) and (13) ensure that the total number of single or double rest arcs is at least equal to the total length of the solution, expressed in weeks. Similarly, constraints (14) and (15) ensure that the total number of double rest arcs is at least equal to 0.4 times the total number of single and double rest arcs.…”

Section: Lower Bounding Proceduresmentioning

confidence: 99%

“…The OR group of DEIS, University of Bologna, took part in the FARO competition and won the first prize giving the best solution for all the instances, following a pure OR approach. 7 the crew rostering problem Logic Programming (CLP) techniques, 13 to our knowledge, crew rostering has never been solved either by CLP techniques or by a mixture of CLP and OR techniques. In this paper, we propose the integration of these techniques and compare the results obtained using a pure OR approach described in Caprara et al 7 A pure CLP approach has not been fully investigated, but usually suffers from inefficiency when the dimensions of the problem increase.…”

Section: Introductionmentioning

confidence: 99%

Integrating constraint logic programming and operations research techniques for the Crew Rostering Problem

Caprara

Focacci

Lamma

et al. 1998

Softw: Pract. Exper.

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In this paper, we investigate the possibility of integrating Artificial Intelligence (AI) and OperationsResearch (OR) techniques for solving the Crew Rostering Problem (CRP). CRP calls for the optimal sequencing of a given set of duties into rosters satisfying a set of constraints. The optimality criterion requires the minimization of the number of crews needed to cover the duties. This kind of problem has been traditionally solved by OR techniques. In recent years, a new programming paradigm based on Logic Programming, named Constraint Logic Programming (CLP), has been successfully used for solving hard combinatorial optimization problems. CLP maintains all the advantages of logic programming such as declarativeness, non-determinism and an incremental style of programming, while overcoming its limitations, mainly due to the inefficiency in exploring the search space. CLP achieves good results on hard combinatorial optimization problems which, however, are not comparable with those achieved by OR approaches. Therefore, we integrate both techniques in order to design an effective heuristic algorithm for CRP which fully exploits the advantages of the two methodologies: on the one hand, we maintain the declarativeness of CLP, its ease of representing knowledge and its rapid prototyping; on the other hand, we inherit from OR some efficient procedures based on a mathematical approach to the problem. Finally, we compare the results we achieved by means of the integration with those obtained by a pure OR approach, showing that AI and OR techniques for hard combinatorial optimization problems can be effectively integrated. © 1998 by John Wiley & Sons, Ltd. key words: constraint logic programming; operations research; crew rostering problem; combinatorial optimization problems; artificial intelligence (a) a search space that grows exponentially with the size of the problem; (b) many complex constraints;

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“…In our experiments, usually the time for pricing amounts to about 90% of the total computing time. Many algorithms have been suggested to solve the pricing problem exactly as e.g., resource constrained shortest path algorithms (Desrosiers et al, 1995), k-shortest path algorithms (Gustafsson, 1999), and constraint programming (Guerinik andCaneghem, 1995, Yunes et al, 2000). Furthermore, there are also heuristic approaches (Vance et al, 1997).…”

Section: Introductionmentioning

confidence: 98%

BoxStep methods for crew pairing problems

2006

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Crew pairing problems are often solved using column generation in a branch-andprice framework. The oscillation of dual points is the main reason which leads to instability in the standard implementation of this method. One device to deal with the problem is to use the trust-region idea to stabilize the path of dual points. Therefore, a so-called stabilized column generation with respect to control parameters is suggested to overcome this problem. In this paper we report about possible realizations of this principle and show that the performance of algorithms can be improved significantly. Three stabilizing methods are used to investigate good control parameters which contribute to the improved computation time in solving a set of crew pairing problems involving about 400 flights per week.

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Solving crew scheduling problems by constraint programming

Cited by 27 publications

References 3 publications

Interval propagation to reason about sets: Definition and implementation of a practical language

Interval propagation to reason about sets: Definition and implementation of a practical language

Integrating constraint logic programming and operations research techniques for the Crew Rostering Problem

BoxStep methods for crew pairing problems

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