We consider the problem of finding a cutset in a directed graph G = (V, E), i.e., a set of vertices that cuts all cycles in G. Finding a cutset of minimum cardinality is NP-hard. There exist several approximate and ex...
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We consider the problem of finding a cutset in a directed graph G = (V, E), i.e., a set of vertices that cuts all cycles in G. Finding a cutset of minimum cardinality is NP-hard. There exist several approximate and exact algorithms, most of them using graph reduction techniques. In this paper, we propose a constraint programming approach to cutset problems and design a global constraint for computing cutsets. This cutset constraint is a global constraint over boolean variables associated to the vertices of a given graph and states that the subgraph restricted to the vertices having their boolean variable set to true is acyclic. We propose a filtering algorithm based on graph contraction operations and inference of simple boolean constraints, that has a linear time complexity in O (vertical bar E vertical bar +/- vertical bar V vertical bar). We discuss search heuristics based on graph properties provided by the cutset constraint, and show the efficiency of the cutset constraint on benchmarks of the literature for pure minimum cutset problems, and on an application to log-based reconciliation problems where the global cutset constraint is mixed with other boolean constraints. (c) 2005 Published by Elsevier Ltd.
In this article, we present a wood procurement problem that arises in Eastern Canada. We solve a multi-period wood supply planning problem, while taking into account bucking decisions. Furthermore, we present a new fo...
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In this article, we present a wood procurement problem that arises in Eastern Canada. We solve a multi-period wood supply planning problem, while taking into account bucking decisions. Furthermore, we present a new form of flexibility which allows the harvesting capacity to change from one time period to another. We study the impact of such flexibility upon the harvesting cost. We assess the performance of the problem by comparing it with a variant where the harvesting capacity is fixed during sites' harvesting. To address this problem, we develop a hybrid approach based on both constraint and mathematical programming. In the first phase, we propose a constraint programming model dealing with forest sites harvesting and bucking problems. The result of this model is used as part of an initial solution for the whole problem formulated as a mixed integer model. We test the two versions of the problem on a set of different demand instances and we compare their results.
In this study we consider the mapping of the main characteristics, i.e., the structural properties, of a classical job shop problem onto well-known combinatorial techniques, i.e., positional sets, disjunctive graphs, ...
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In this study we consider the mapping of the main characteristics, i.e., the structural properties, of a classical job shop problem onto well-known combinatorial techniques, i.e., positional sets, disjunctive graphs, and linear orderings. We procedurally formulate three different models in terms of mixed integer programming (MIP) and constraint programming (CP) paradigms. We utilize the properties of positional sets and disjunctive graphs to construct tight MIP formulations in an efficient manner. In addition, the properties are retrieved by the polyhedral structures of the linear ordering and they are defined on a disjunctive graph to facilitate the formulation of the CP model and to reduce the number of dominant variables. The proposed models are solved and their computational performance levels are compared with well-known benchmarks in the job shop research area using IBM ILog Cplex software. We provide a more explicit analogy of the applicability of the proposed models based on parameters such as time efficiency, thereby producing strong bounds, as well as the expressive power of the modeling process. We also discuss the results to determine the best formulation, which is computationally efficient and structurally parsimonious with respect to different criteria. (C) 2014 Elsevier Inc. All rights reserved.
We introduce five constraint models for the 3-dimensional stable matching problem with cyclic preferences and study their relative performances under diverse configurations. While several constraint models have been p...
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We introduce five constraint models for the 3-dimensional stable matching problem with cyclic preferences and study their relative performances under diverse configurations. While several constraint models have been proposed for variants of the two-dimensional stable matching problem, we are the first to present constraint models for a higher number of dimensions. We show for all five models how to capture two different stability notions, namely weak and strong stability. Additionally, we translate some well-known fairness notions (i.e. sex-equal, minimum regret, egalitarian) into 3-dimensional matchings, and present how to capture them in each model. Our tests cover dozens of problem sizes and four different instance generation methods. We explore two levels of commitment in our models: one where we have an individual variable for each agent (individual commitment), and another one where the determination of a variable involves pairing the three agents at once (group commitment). Our experiments show that the suitability of the commitment depends on the type of stability we are dealing with, and that the choice of the search heuristic can help improve performance. Our experiments not only brought light to the role that learning and restarts can play in solving this kind of problems, but also allowed us to discover that in some cases combining strong and weak stability leads to reduced runtimes for the latter.
Wind farms are frequently located in proximity to human dwellings, natural habitats, and infrastructure making land use constraints and noise matters of increasing concern for all stakeholders. In this study, we perfo...
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Wind farms are frequently located in proximity to human dwellings, natural habitats, and infrastructure making land use constraints and noise matters of increasing concern for all stakeholders. In this study, we perform a constrained multi-objective wind farm layout optimization considering energy and noise as objective functions, and considering land use constraints arising from landowner participation, environmental setbacks and proximity to existing infrastructure. A multi-objective, continuous variable Genetic Algorithm (NSGA-II) is combined with a novel constraint handling approach to solve the optimization problem. This constraint handling approach uses a combination of penalty functions and constraint programming to balance local and global exploration to find feasible solutions. The proposed approach is used to solve the wind farm layout optimization problem with different numbers of turbines and under different levels of land availability (constraint severity). Our results show increasing land availability and/or number of turbines, increases energy generation, noise production, and computational cost. Results also illustrate the potential of the proposed constraint handling approach to outperform existing methods in the context of evolutionary optimization, yielding better solutions at a lower computational cost. (C) 2018 Elsevier Ltd. All rights reserved.
In recent years, pattern mining has evolved from a slow-moving, repetitive three-step process to a much more agile and iterative/user-centric mining model. A crucial element of this framework is the capability to rapi...
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In recent years, pattern mining has evolved from a slow-moving, repetitive three-step process to a much more agile and iterative/user-centric mining model. A crucial element of this framework is the capability to rapidly provide a set of diverse patterns to the user. This paper proposes a pattern mining approach based on constraint programming that incorporates a non-redundancy/diversity constraint into closed pattern enumeration. The level of diversity is controlled through a threshold on the maximum pairwise Jaccard similarity of pattern occurrences. We show that the Jaccard measure does not have nice (anti-)monotonicity properties w.r.t. the general-to-specific enumeration. To address this limitation, we propose anti-monotonic lower and upper-bound relaxations of the Jaccard similarity with nice pruning-enabling properties, and connect the final results to the original Jaccard Index. To evaluate the effectiveness of our relaxations, we conduct a comprehensive comparison against several existing pattern mining techniques designed to control redundancy. Experimental results illustrate that our approach provides an effective solution for mining diverse itemsets, showing competitive performance in both runtime and flexibility.
Due to various factors of flexibility introduced into manufacturing systems, researchers have gradually shifted their focus to the integrated process planning and scheduling (IPPS) problem to improve productivity. The...
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Due to various factors of flexibility introduced into manufacturing systems, researchers have gradually shifted their focus to the integrated process planning and scheduling (IPPS) problem to improve productivity. The previous literature rarely associates IPPS with constraint programming, even though constraint programming has achieved success in the scheduling field. Furthermore, existing approaches are usually customized to certain types of IPPS problems and cannot handle the general problem. In this paper, with a view to obtaining the optimal AND/OR graph automatically, a depth first search generating algorithm is designed to convert the type-1 IPPS problem into our approach's standard input format. Moreover, we propose an approach based on enhanced constraint programming to cope with the general problem, employing advanced schemes to enhance the constraint propagation and improve the search efficiency. Our approach is implemented on ORTOOLS, and its superiority is verified by testing on 15 benchmarks with 50 instances. Experimental results indicate that 41 instances are solved optimally, among which the optimality of the solutions for 20 instances is newly confirmed, and the solutions of six instances are improved. Our approach is the first method to reach the overall optimum in the most influential benchmark with 24 instances.
Constrained Clustering allows to make the clustering task more accurate by integrating user constraints, which can be instance-level or cluster-level constraints. Few works consider the integration of different kinds ...
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Constrained Clustering allows to make the clustering task more accurate by integrating user constraints, which can be instance-level or cluster-level constraints. Few works consider the integration of different kinds of constraints, they are usually based on declarative frameworks and they are often exact methods, which either enumerate all the solutions satisfying the user constraints, or find a global optimum when an optimization criterion is specified. In a previous work, we have proposed a model for Constrained Clustering based on a constraint programming framework. It is declarative, allowing a user to integrate user constraints and to choose an optimization criterion among several ones. In this article we present a new and substantially improved model for Constrained Clustering, still based on a constraint programming framework. It differs from our earlier model in the way partitions are represented by means of variables and constraints. It is also more flexible since the number of clusters does not need to be set beforehand;only a lower and an upper bound on the number of clusters have to be provided. In order to make the model-based approach more efficient, we propose new global optimization constraints with dedicated filtering algorithms. We show that such a framework can easily be embedded in a more general process and we illustrate this on the problem of finding the optimal Pareto front of a bi-criterion constrained clustering task. We compare our approach with existing exact approaches, based either on a branch-and-bound approach or on graph coloring on twelve datasets. Experiments show that the model outperforms exact approaches in most cases. (C) 2015 Elsevier B.V. All rights reserved.
Scheduling of megaprojects is very challenging because of typical characteristics, such as expected long project durations, many activities with multiple modes, scarce resources, and investment decisions. Furthermore,...
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Scheduling of megaprojects is very challenging because of typical characteristics, such as expected long project durations, many activities with multiple modes, scarce resources, and investment decisions. Furthermore, each megaproject has additional specific characteristics to be considered. Since the number of nuclear dismantling projects is expected to increase considerably worldwide in the coming decades, we use this type of megaproject as an application case in this paper. Therefore, we consider the specific characteristics of constrained renewable and non-renewable resources, multiple modes, precedence relations with and without no-wait condition, and a cost minimisation objective. To reliably plan at minimum costs considering all relevant characteristics, scheduling methods can be applied. But the extensive literature review conducted did not reveal a scheduling method considering the special characteristics of nuclear dismantling projects. Consequently, we introduce a novel scheduling problem referred to as the nuclear dismantling project scheduling problem. Furthermore, we developed and implemented an effective metaheuristic to obtain feasible schedules for projects with about 300 activities. We tested our approach with real-life data of three different nuclear dismantling projects in Germany. On average, it took less than a second to find an initial feasible solution for our samples. This solution could be further improved using metaheuristic procedures and exact optimisation techniques such as mixed-integer programming and constraint programming. The computational study shows that utilising exact optimisation techniques is beneficial compared to standard metaheuristics. The main result is the development of an initial solution finding procedure and an adaptive large neighbourhood search with iterative destroy and recreate operations that is competitive with state-of-the-art methods of related problems. The described problem and findings can be transferred
This paper is an introduction to Newton, a constrain-programming language over nonlinear real constraints. Newton originates from an effort to reconcile the declarative nature of constraint logic programming (CLP) lan...
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This paper is an introduction to Newton, a constrain-programming language over nonlinear real constraints. Newton originates from an effort to reconcile the declarative nature of constraint logic programming (CLP) languages over intervals with advanced interval techniques developed in numerical analysis, such as the interval Newton method. Its key conceptual idea is to introduce the notion of box-consistency, which approximates are-consistency, a notion well-known in artificial intelligence. Box-consistency achieves an effective pruning at a reasonable computation cost and generalizes some traditional interval operators. Newton has been applied to numerous applications in science and engineering, including nonlinear equation-solving, unconstrained optimization, and constrained optimization. It is competitive with continuation methods on their equation-solving benchmarks and outperforms the interval-based methods we are aware of on optimization problems. (C) 1998 Elsevier Science B.V.
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