We discuss how constraint programming can improve the performance of a column generation solution process for the NP-hard Tail Assignment problem in aircraft scheduling. Combining a constraint model of a relaxed Tail ...
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We discuss how constraint programming can improve the performance of a column generation solution process for the NP-hard Tail Assignment problem in aircraft scheduling. Combining a constraint model of a relaxed Tail Assignment problem with column generation, we achieve substantially improved performance. A generalized preprocessing technique based on constraint propagation is presented that can dramatically reduce the size of the flight network. We also present a heuristic preprocessing method based on the costs of connections, and show how constraint propagation can be used to improve fixing heuristics. Proof of concept is provided using real world Tail Assignment instances. (c) 2005 Elsevier Ltd. All rights reserved.
Simplified protein models are used for investigating general properties of proteins and principles of protein folding. Furthermore, they are suited for hierarchical approaches to protein structure prediction, A well k...
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Simplified protein models are used for investigating general properties of proteins and principles of protein folding. Furthermore, they are suited for hierarchical approaches to protein structure prediction, A well known protein model is the HP-model of Lau and Dill [Lau, K. F., & Dill, K. A. (1989)]. A lattice statistical mechanics model of the conformational and sequence spaces of proteins. Macromolecules, 22, 3986-3997) which models the important aspect of hydrophobicity. One can define the HP-model for various lattices, among them two-dimensional and three-dimensional ones, Here, we investigate the three-dimensional case. The main motivation for studying simplified protein models is to be able to predict model structures much more quickly and more accurately than is possible for real proteins. However, up to now there was a dilemma: the algorithmically tractable, simple protein models can not model real protein structures with good quality and introduce strong artifacts. We present a constraint-based method that largely improves this situation. It outperforms all existing approaches for lattice protein folding in HP-models. This approach is the first one that can be applied to two three-dimensional lattices, namely the cubic lattice and the face-centered-cubic (FCC) lattice. Moreover, it is the only exact method for the FCC lattice. The ability to use the FCC lattice is a significant improvement over the cubic lattice. The key to our approach is the ability to compute maximally compact sets of points (used as hydrophobic cores), which we accomplish for the first time for the FCC lattice.
The Travelling Tournament Problem is a sports timetabling problem requiring production of a minimum distance double round-robin tournament for a group of n teams. Even small instances of this problem seem to be very d...
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ISBN:
(纸本)3540406999
The Travelling Tournament Problem is a sports timetabling problem requiring production of a minimum distance double round-robin tournament for a group of n teams. Even small instances of this problem seem to be very difficult to solve. In this paper, we present the first provably optimal solution for an instance of eight teams. The solution methodology is a parallel implementation of a branch-and-price algorithm that uses integer programming to solve the master problem and constraint programming to solve the pricing problem. Additionally, constraint programming is used as a primal heuristic.
This paper presents a multiple time grid continuous time MILP model for the short-term scheduling of single stage, multiproduct batch plants. It can handle both release and due dates and the objective can be either th...
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This paper presents a multiple time grid continuous time MILP model for the short-term scheduling of single stage, multiproduct batch plants. It can handle both release and due dates and the objective can be either the minimization of total cost or total earliness. This formulation is compared to other mixed-integer linear programming approaches that have appeared in the literature, to a constraint programming model, and to a hybrid mixed-integer linear/constraint programming algorithm. The results show that the proposed formulation is significantly more efficient than the MILP and CP models and comparable to the hybrid model. For one large instance, both methods exceeded the time limit but the hybrid method failed to find a feasible solution. The results also show that a discrete-time formulation performs very efficiently even when a large number of time intervals are used. (c) 2006 Elsevier Ltd. All rights reserved.
Finite-domain constraint programming has been used with great success to tackle a wide variety of combinatorial problems in industry and academia. To apply finite-domain constraint programming to a problem, it is mode...
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Finite-domain constraint programming has been used with great success to tackle a wide variety of combinatorial problems in industry and academia. To apply finite-domain constraint programming to a problem, it is modelled by a set of constraints on a set of decision variables. A common modelling pattern is the use of matrices of decision variables. The rows and/or columns of these matrices are often symmetric, leading to redundancy in a systematic search for solutions. An effective method of breaking this symmetry is to constrain the assignments of the affected rows and columns to be ordered lexicographically. This paper develops an incremental propagation algorithm, GACLexLeq, that establishes generalised arc consistency on this constraint in O(n) operations, where n is the length of the vectors. Furthermore, this paper shows that decomposing GACLexLeq into primitive constraints available in current finite-domain constraint toolkits reduces the strength or increases the cost of constraint propagation. Also presented are extensions and modifications to the algorithm to handle strict lexicographic ordering, detection of entailment, and vectors of unequal length. Experimental results on a number of domains demonstrate the value of GACLexLeq. (c) 2006 Elsevier B.V. All rights reserved.
Timetabling problems have been much studied over the last decade. Due to the complexity and the variety of such problems, most work concerns static problems in which activities to schedule and resources are known in a...
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ISBN:
(纸本)3540406999
Timetabling problems have been much studied over the last decade. Due to the complexity and the variety of such problems, most work concerns static problems in which activities to schedule and resources are known in advance, and constraints are fixed. However, every timetabling problem is subject to unexpected events (for example, for university timetabling problems, a missing teacher, or a slide projector breakdown). In such a situation, one has to quickly build a new solution which takes these events into account and which is preferably not too different from the current one. We introduce in this paper constraint-programming-based tools for solving dynamic timetabling problems modelled as Resource-Constrained Project Scheduling Problems. This approach uses explanation-based constraint programming and operational research techniques.
Peg Solitaire is a well known puzzle, which can prove difficult despite its simple rules. Pegs are arranged on a board such that at least one 'hole' remains. By making draughts/checkers-like moves, pegs are gr...
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Peg Solitaire is a well known puzzle, which can prove difficult despite its simple rules. Pegs are arranged on a board such that at least one 'hole' remains. By making draughts/checkers-like moves, pegs are gradually removed until no further moves are possible or some goal configuration is achieved. This paper considers the English variant, consisting of a board in a cross shape with 33 holes. Modelling Peg Solitaire via constraint or integer programming techniques presents a considerable challenge and is examined in detail. The merits of the resulting models are discussed and they are compared empirically. The sequential nature of the puzzle naturally conforms to a planning problem, hence we also present an experimental comparison with several leading AI planning systems. Other variants of the puzzle, such as 'Fool's Solitaire' and 'Long-hop' Solitaire are also considered. (c) 2005 Elsevier Ltd. All rights reserved.
In constraint-based design, components are modeled by variables describing their properties and subject to physical or mechanical constraints. However, some other constraints are difficult to represent, like comfort o...
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In constraint-based design, components are modeled by variables describing their properties and subject to physical or mechanical constraints. However, some other constraints are difficult to represent, like comfort or user satisfaction. Partially defined constraints can be used to model the incomplete knowledge of a concept or a relation. Instead of only computing with the known part of the constraint, we propose to complete its definition by using machine-learning techniques. Because constraints are actively used during solving for pruning domains, building a classifier for instances is not enough: we need a solver able to reduce variable domains. Our technique is composed of two steps: first we learn a classifier for the constraint's projections and then we transform the classifier into a propagator. We show that our technique not only has good learning performances but also yields a very efficient solver for the learned constraint.
Symmetries abound in logically formulated problems where many axioms are universally quantified, as this is the case in equational theories. Two complementary approaches have been used so far to dynamically tackle tho...
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Symmetries abound in logically formulated problems where many axioms are universally quantified, as this is the case in equational theories. Two complementary approaches have been used so far to dynamically tackle those symmetries: prediction and detection. The best-known predictive symmetry elimination method is the least number heuristic (LNH). A more recent predictive method, the extended least number heuristic (XLNH), focuses first on the enumeration of a bijection in the problem and easily exploits in the sequel the remaining isomorphisms. On the other hand, dynamic symmetry detection is costly in the general case (the problem is Graph Iso complete) but allows one to exploit more symmetries, and efficient (polytime) yet incomplete detection algorithms can be used on each node. This paper presents a generalization of XLNH that focuses on the enumeration of a unary function that does not require the function to be bijective, a general notion of symmetry for finite-model search in first-order logic together with an efficient symmetry detection algorithm, and a function-ordering heuristic that exploits the inherent structure of first-order logic theories to improve the search when using function-centric methods. A comprehensive study of the compared efficiency of all methods, in isolation and in combination, demonstrates the acceleration that can be expected in all cases. These ideas are implemented by using the known system SEM as an experimentation framework, to allow for accurate comparisons.
Home health care, i.e. visiting and nursing patients in their homes, is a growing sector in the medical service business. From a staff rostering point of view, the problem is to find a feasible working plan for all nu...
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Home health care, i.e. visiting and nursing patients in their homes, is a growing sector in the medical service business. From a staff rostering point of view, the problem is to find a feasible working plan for all nurses that has to respect a variety of hard and soft constraints, and preferences. Additionally, home health care problems contain a routing component: a nurse must be able to visit her patients in a given roster using a car or public transport. It is desired to design rosters that consider both, the staff rostering and vehicle routing components while minimizing transportation costs and maximizing satisfaction of patients and nurses. In this paper we present the core optimization components of the PARPAP software. In the optimization kernel, a combination of linear programming, constraint programming, and (meta-)heuristics for the home health care problem is used, and we show how to apply these different heuristics efficiently to solve home health care problems. The overall concept is able to adapt to various changes in the constraint structure, thus providing the flexibility needed in a generic tool for real-world settings. (c) 2005 Elsevier Ltd. All rights reserved.
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