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33
Edge finding for cumulative scheduling
, 2005
"... Edgefinding algorithms for cumulative scheduling are at the core of commercial constraintbased schedulers. This paper shows that Nuijten’s edge finder for cumulative scheduling, and its derivatives, are incomplete and use an invalid dominance rule. The paper then presents a new edgefinding algorit ..."
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Cited by 19 (0 self)
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Edgefinding algorithms for cumulative scheduling are at the core of commercial constraintbased schedulers. This paper shows that Nuijten’s edge finder for cumulative scheduling, and its derivatives, are incomplete and use an invalid dominance rule. The paper then presents a new edgefinding algorithm for cumulative resources which runs in time O(n 2 k), where n is the number of tasks and k the number of different capacity requirements of the tasks. The new algorithm is organized in two phases and first uses dynamic programming to precompute the innermost maximization in the edgefinder specification. Finally, this paper also proposes the first extended edgefinding algorithm that runs in time O(n 2 k), improving the running time of available algorithms. 1
Interdistance constraint: An extension of the alldifferent constraint for scheduling equal length jobs
 In Proceedings of the 11th International Conference on Principles and Practice of Constraint Programming
, 2005
"... Abstract. We study a global constraint, the “interdistance constraint” that ensures that the distance between any pair of variables is at least equal to a given value. When this value is 1, the interdistance constraint reduces to the alldifferent constraint. We introduce an algorithm to propagate ..."
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Abstract. We study a global constraint, the “interdistance constraint” that ensures that the distance between any pair of variables is at least equal to a given value. When this value is 1, the interdistance constraint reduces to the alldifferent constraint. We introduce an algorithm to propagate this constraint and we show that, when domains of the variables are intervals, our algorithm achieves arcBconsistency. It provides tighter bounds than generic scheduling constraint propagation algorithms (like edgefinding) that could be used to capture this constraint. The worst case complexity of the algorithm is cubic but it behaves well in practice and it drastically reduces the search space. Experiments on special JobShop problems and on an industrial problem are reported.
Optimal Methods for Resource Allocation and Scheduling: a CrossDisciplinary Survey
, 2010
"... Classical scheduling formulations typically assume static resource requirements and focus on deciding when to start the problem activities, so as to optimize some performance metric. In many practical cases, however, the decision maker has the ability to choose the resource assignment as well as th ..."
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Cited by 6 (0 self)
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Classical scheduling formulations typically assume static resource requirements and focus on deciding when to start the problem activities, so as to optimize some performance metric. In many practical cases, however, the decision maker has the ability to choose the resource assignment as well as the starting times: this is a farfromtrivial task, with deep implications on the quality of the final schedule. Joint resource assignment and scheduling problems are incredibly challenging from a computational perspective. They have been subject of active research in Constraint Programming (CP) and in Operations Research (OR) for a few decades, with quite difference techniques. Both the approaches report individual successes, but they overall perform equally well or (from a different perspective) equally poorly. In particular, despite the well known effectiveness of global constraints for scheduling, comparable results for joint filtering of assignment and scheduling variables have not yet been achieved. Recently, hybrid approaches have been applied to this class of problems: most of them work by splitting the overall problem into an assignment and a scheduling subparts; those are solved in an iterative and interactive fashion with a mix of CP and
Computing Explanations for the Unary Resource Constraint
"... Abstract. Integration of explanations into a CSP solver is a technique addressing difficult question “why my problem has no solution”. Moreover, explanations together with advanced search methods like directed backjumping can effectively cut off parts of the search tree and thus speed up the search. ..."
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Abstract. Integration of explanations into a CSP solver is a technique addressing difficult question “why my problem has no solution”. Moreover, explanations together with advanced search methods like directed backjumping can effectively cut off parts of the search tree and thus speed up the search. In order to use explanations, propagation algorithms must provide some sort of reasons (justifications) for their actions. For binary constraints it is mostly easy. In the case of global constraints computation of factual justifications can be tricky and/or computationally expensive. This paper shows how to effectively compute explanations for the unary resource constraint. The explanations are computed in a lazy way. The technique is experimentally demonstrated on jobshop benchmark problems. The following propagation algorithms are considered: edgefinding, notfirst/notlast and detectable precedences. Speed of these filtering algorithms and speed of the explanation computation is the main interest. 1
Constraint Satisfaction Techniques in Planning and Scheduling
 JOURNAL OF INTELLIGENT MANUFACTURING
"... Over the last few years constraint satisfaction, planning, and scheduling have received increased attention, and substantial effort has been invested in exploiting constraint satisfaction techniques when solving real life planning and scheduling problems. Constraint satisfaction is the process of f ..."
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Cited by 5 (1 self)
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Over the last few years constraint satisfaction, planning, and scheduling have received increased attention, and substantial effort has been invested in exploiting constraint satisfaction techniques when solving real life planning and scheduling problems. Constraint satisfaction is the process of finding a solution to a set of constraints. Planning is the process of finding a sequence of actions that transfer the world from some initial state to a desired state. Scheduling is the problem of assigning a set of tasks to a set of resources subject to a set of constraints. In this paper, we introduce the main definitions and techniques of constraint satisfaction, planning and scheduling from the Artificial Intelligence point of view.
Better propagation for nonpreemptive singleresource constraint problems
 In Proceedings of the ERCIM/CoLogNet workshop
, 2004
"... Abstract. Overload checking, forbidden regions, edge finding, and notfirst/notlast detection are wellknown propagation rules to prune the start times of activities which have to be processed without any interruption and overlapping on an exclusively available resource, i.e. machine. These rules ar ..."
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Abstract. Overload checking, forbidden regions, edge finding, and notfirst/notlast detection are wellknown propagation rules to prune the start times of activities which have to be processed without any interruption and overlapping on an exclusively available resource, i.e. machine. These rules are extendable by two other rules which take the number of activities into account which are at most processable after or before another activity. To our knowledge, these rules are based on approximations of the (minimal) earliest completion times and the (maximal) latest start times of sets of activities. In this paper, the precise definitions of these time values as well as an efficient procedure for their calculations are given. Based on the precise time values the rules are reformulated and applied to a wellknown job shop scheduling benchmark. 1
Multivalued Decision Diagrams for Sequencing Problems
"... Sequencing problems are among the most prominent problems studied in operations research, with primary application in, e.g., scheduling and routing. We propose a novel approach to solving generic sequencing problems using multivalued decision diagrams (MDDs). Because an MDD representation may grow e ..."
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Cited by 4 (4 self)
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Sequencing problems are among the most prominent problems studied in operations research, with primary application in, e.g., scheduling and routing. We propose a novel approach to solving generic sequencing problems using multivalued decision diagrams (MDDs). Because an MDD representation may grow exponentially large, we apply MDDs of limited size as a discrete relaxation to the problem. We show that MDDs can be used to represent a wide range of sequencing problems with various side constraints and objective functions, and demonstrate how MDDs can be added to existing constraintbased scheduling systems. Our computational results indicate that the additional inference obtained by our MDDs can speed up a stateofthe art solver by several orders of magnitude, for a range of different problem classes.
Improving the asymmetric TSP by considering graph structure. arXiv preprint arXiv:1206.3437
, 2012
"... Abstract. Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally sho ..."
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Abstract. Recent works on cost based relaxations have improved Constraint Programming (CP) models for the Traveling Salesman Problem (TSP). We provide a short survey over solving asymmetric TSP with CP. Then, we suggest new implied propagators based on general graph properties. We experimentally show that such implied propagators bring robustness to pathological instances and highlight the fact that graph structure can significantly improve search heuristics behavior. Finally, we show that our approach outperforms current state of the art results. 1
Efficient edgefinding on unary resources with optional activities
 In Dietmar Seipel, Michael Hanus et Armin Wolf, éditeurs : Applications of Declarative Programming and Knowledge Management (Proceedings of INAP/WLP 2007), numéro 5437 in LNCS
, 2009
"... Abstract. Unary resources play a central role in modelling scheduling problems. Edgefinding is one of the most popular techniques to deal with unary resources in constraint programming environments. Often it depends on external factors if an activity will be included in the final schedule, making t ..."
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Abstract. Unary resources play a central role in modelling scheduling problems. Edgefinding is one of the most popular techniques to deal with unary resources in constraint programming environments. Often it depends on external factors if an activity will be included in the final schedule, making the activity optional. Currently known edgefinding algorithms cannot take optional activities into account. This paper introduces an edgefinding algorithm that finds restrictions for enabled and optional activities. The performance of this new algorithm is studied for modified jobshop and randomplacement problems.
Viewbased Propagator Derivation
, 908
"... When implementing a propagator for a constraint, one must decide about variants: When implementing min, should one also implement max? Should one implement linear constraints both with unit and nonunit coefficients? Constraint variants are ubiquitous: implementing them requires considerable (if not ..."
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When implementing a propagator for a constraint, one must decide about variants: When implementing min, should one also implement max? Should one implement linear constraints both with unit and nonunit coefficients? Constraint variants are ubiquitous: implementing them requires considerable (if not prohibitive) effort and decreases maintainability, but will deliver better performance than resorting to constraint decomposition. This paper shows how to use views to derive perfect propagator variants. A model for views and derived propagators is introduced. Derived propagators are proved to be indeed perfect in that they inherit essential properties such as correctness and domain and bounds consistency. Techniques for systematically deriving propagators such as transformation, generalization, specialization, and type conversion are developed. The paper introduces an implementation architecture for views that is independent of the underlying constraint programming system. A detailed evaluation of views implemented in Gecode shows that derived propagators are efficient and that views often incur no overhead. Without views, Gecode would either require 180000 rather than 40000 lines of propagator code, or would lack many efficient propagator variants. Compared to 8000 lines of code for views, the reduction in code for propagators yields a 1750 % return on investment. 1