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76
A C++ implementation of CLP
, 1994
"... Wehave implemented a C++ library, called ILOG SOLVER, that embodies Constraint Logic Programming #CLP# concepts such as logical variables, incremental constraint satisfaction and backtracking. This library combines Object Oriented Programming #OOP# with CLP. This has two advantages. First of all, ev ..."
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Cited by 141 (2 self)
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Wehave implemented a C++ library, called ILOG SOLVER, that embodies Constraint Logic Programming #CLP# concepts such as logical variables, incremental constraint satisfaction and backtracking. This library combines Object Oriented Programming #OOP# with CLP. This has two advantages. First of all, everything is an object in SOLVER:variables, constraints and search algorithms #goals#. Thus, SOLVER is easily extendable by de#ning new classes. Second, objects can be used for modeling the real problem that has to be solved, which is a great software engineering advantage. In particular, SOLVER provides for the de#nition of class constraints, that are inherited by all the objects of that class.
Algorithms for hybrid MILP/CP models for a class of optimization problems
 INFORMS Journal on Computing
, 2001
"... The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered ..."
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Cited by 98 (12 self)
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The goal of this paper is to develop models and methods that use complementary strengths of Mixed Integer Linear Programming (MILP) and Constraint Programming (CP) techniques to solve problems that are otherwise intractable if solved using either of the two methods. The class of problems considered in this paper have the characteristic that only a subset of the binary variables have nonzero objective function coefficients if modeled as an MILP. This class of problems is formulated as a hybrid MILP/CP model that involves some of the MILP constraints, a reduced set of the CP constraints, and equivalence relations between the MILP and the CP variables. An MILP/CP based decomposition method and an LP/CPbased branchandbound algorithm are proposed to solve these hybrid models. Both these algorithms rely on the same relaxed MILP and feasibility CP problems. An application example is considered in which the leastcost schedule has to be derived for processing a set of orders with release and due dates using a set of dissimilar parallel machines. It is shown that this problem can be modeled as an MILP, a CP, a combined MILPCP OPL model (Van Hentenryck 1999), and a hybrid MILP/CP model. The computational performance of these models for several sets shows that the hybrid MILP/CP model can achieve two to three orders of magnitude reduction in CPU time.
Increasing Constraint Propagation by Redundant Modeling: an Experience Report
 CONSTRAINTS
, 1999
"... This paper describes our experience with a simple modeling and programming approach for increasing the amount of constraint propagation in the constraint solving process. The idea, although similar to redundant constraints, is based on the concept of redundant modeling. We introduce the notions of ..."
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Cited by 74 (8 self)
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This paper describes our experience with a simple modeling and programming approach for increasing the amount of constraint propagation in the constraint solving process. The idea, although similar to redundant constraints, is based on the concept of redundant modeling. We introduce the notions of CSP model and model redundancy, and show how mutually redundant models can be combined and connected using channeling constraints. The combined model contains the mutually redundant models as submodels. Channeling constraints allow the submodels to cooperate during constraint solving by propagating constraints freely amongst the submodels. This extra level of pruning and propagation activities becomes the source of execution speedup. We perform two case studies to evaluate the effectiveness and efficiency of our method. The first case study is based on the simple and wellknown nqueens problem, while the second case study applies our method in the design and construction of a reallife ...
A Theoretical and Experimental Comparison of Constraint Propagation Techniques for Disjunctive Scheduling
, 1995
"... Disjunctive constraints are widely used to ensure that the time intervals over whichtwo activities require the same resource cannot overlap: if a resource is required bytwo activities A and B, the disjunctive constraint states that either A precedes B or B precedes A. The #propagation " ..."
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Cited by 66 (8 self)
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Disjunctive constraints are widely used to ensure that the time intervals over whichtwo activities require the same resource cannot overlap: if a resource is required bytwo activities A and B, the disjunctive constraint states that either A precedes B or B precedes A. The #propagation " of disjunctive constraints consists in determining cases where only one of the two orderings is feasible. It results in updating the timebounds of the two activities. The standard algorithm for propagating disjunctive constraints achieves arcBconsistency.Twotypes of methods that provide more precise timebounds are studied and compared. The #rst type of method consists in determining whether an activity A must, can, or cannot be the #rst or the last to execute among a set of activities that require the same resource. The second consists in comparing the amount of #resource energy" required over a time interval #t 1 t 2 #to the amount of energy that is available over the same interval. The main result of the study is an implementation of the #rst method in Ilog Schedule, a generic tool for constraintbased scheduling which exhibits performance in the same range of e#ciency as speci#c operations research algorithms.
A Computational Study of Constraint Satisfaction for Multiple Capacitated Job Shop Scheduling
 European Journal of Operational Research
, 1996
"... Weintroduce the multiple capacitated job shop scheduling problem as a generalization of the job shop scheduling problem. In this problem machines may process several operations simultaneously.We presentan algorithm based on constraint satisfaction techniques to handle the problem e#ectively. The ..."
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Cited by 45 (3 self)
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Weintroduce the multiple capacitated job shop scheduling problem as a generalization of the job shop scheduling problem. In this problem machines may process several operations simultaneously.We presentan algorithm based on constraint satisfaction techniques to handle the problem e#ectively. The most importantnovel feature of our algorithm is the consistency checking. An empirical performance analysis is performed using a wellknown set of instances of the job shop scheduling problem and a newly constructed set of instances of the multiple capacitated job shop scheduling problem. We show that our algorithm performs well for both sets of instances.
Constraint propagation and decomposition techniques for highly disjunctive and highly cumulative project scheduling problems
 Constraints
"... Abstract. In recent years, constraint satisfaction techniques have been successfully applied to “disjunctive” scheduling problems, i.e., scheduling problems where each resource can execute at most one activity at a time. Less significant and less generally applicable results have been obtained in th ..."
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Cited by 44 (4 self)
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Abstract. In recent years, constraint satisfaction techniques have been successfully applied to “disjunctive” scheduling problems, i.e., scheduling problems where each resource can execute at most one activity at a time. Less significant and less generally applicable results have been obtained in the area of “cumulative” scheduling. Multiple constraint propagation algorithms have been developed for cumulative resources but they tend to be less uniformly effective than their disjunctive counterparts. Different problems in the cumulative scheduling class seem to have different characteristics that make them either easy or hard to solve with a given technique. The aim of this paper is to investigate one particular dimension along which problems differ. Within the cumulative scheduling class, we distinguish between “highly disjunctive ” and “highly cumulative” problems: a problem is highly disjunctive when many pairs of activities cannot execute in parallel, e.g., because many activities require more than half of the capacity of a resource; on the contrary, a problem is highly cumulative if many activities can effectively execute in parallel. New constraint propagation and problem decomposition techniques are introduced with this distinction in mind. This includes an O(n 2) “edgefinding ” algorithm for cumulative resources (where n is the number of activities requiring the same resource) and a problem decomposition scheme which applies well to highly disjunctive project scheduling problems. Experimental results confirm that the impact of these techniques varies from highly disjunctive to
Cumulative Scheduling with Task Intervals
, 1994
"... This paper presents a set of propagation rules to solve cumulative constraints. As in our previous paper on jobshop scheduling [8], our goal is to propose to the CLP community techniques that allow a constraint satisfaction program to obtain performances which are competitive with adhoc approaches. ..."
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Cited by 43 (0 self)
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This paper presents a set of propagation rules to solve cumulative constraints. As in our previous paper on jobshop scheduling [8], our goal is to propose to the CLP community techniques that allow a constraint satisfaction program to obtain performances which are competitive with adhoc approaches. The rules that we propose are a mix of an extension of the concept of task intervals to the cumulative case and the use of a traditional resource histogram. We also explain how to use a branching scheme inherited from operations research to address complex multiresources problems (similar to the use of edgefinding for jobshop scheduling). We show that the complex propagation patterns associated with our rules make a strong arguments for using logic programming. We also identify a phenomenon of phase transition in our examples that illustrates why cumulative scheduling is hard. 1. Introduction Many realworld scheduling problems are really cumulative scheduling problems, where each resou...
An Ontology for Constructing Scheduling Systems
 In Working Notes from 1997 AAAI Spring Symposium on Ontological Engineering
, 1997
"... In this paper, we consider the use of ontologies as a basis for structuring and simplifying the process of constructing domainspecific problemsolving tools. We focus specifically on the task of scheduling. Though there is commonality in scheduling system requirements and design at several levels ac ..."
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Cited by 43 (6 self)
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In this paper, we consider the use of ontologies as a basis for structuring and simplifying the process of constructing domainspecific problemsolving tools. We focus specifically on the task of scheduling. Though there is commonality in scheduling system requirements and design at several levels across application domains, different scheduling environments invariably present different challenges (e.g., different dominating constraints, different objectives, different domain structure, different sources of uncertainty, etc.), and hence we can expect highperformance application systems to require customized solutions. Unfortunately, the time and cost associated with such domainspecific system development at present is typically quite large. Our work toward overcoming this application construction bottleneck has led to the development of OZONE, a toolkit for configuring constraintbased scheduling systems. A central component of OZONE is its scheduling ontology, which defines a reusabl...
Satisfiability Tests and TimeBound Adjustments for Cumulative Scheduling Problems
, 1997
"... This paper presents a set of satisfiability tests and timebound adjustment algorithms that can be applied to cumulative scheduling problems. An instance of the Cumulative Scheduling Problem (CuSP) consists of (1) one resource with a given capacity and (2) a set of activities, each having a relea ..."
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Cited by 40 (2 self)
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This paper presents a set of satisfiability tests and timebound adjustment algorithms that can be applied to cumulative scheduling problems. An instance of the Cumulative Scheduling Problem (CuSP) consists of (1) one resource with a given capacity and (2) a set of activities, each having a release date, a deadline, a processing time and a resource capacity requirement. The problem is to decide whether there exists a start time assignment to all activities such that at no point in time the capacity of the resource is exceeded and all timing constraints are satisfied. The Cumulative Scheduling Problem can be seen as a relaxation of the decision variant of the ResourceConstrained Project Scheduling Problem. We present three necessary conditions for the existence of a feasible schedule. Two of them are obtained by polynomial relaxations of the CuSP. The third one is based on energetic reasoning. We show that the second condition is closely related to the subset bound, a well
TextureBased Heuristics for Scheduling Revisited
, 1997
"... Recent scheduling work has challenged the need for sophisticated heuristics such as those based on texture measurements. This paper examines these claims in the light of advances in scheduling technology. We compare a number of current heuristic commitment techniques against a texturebased heur ..."
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Cited by 39 (10 self)
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Recent scheduling work has challenged the need for sophisticated heuristics such as those based on texture measurements. This paper examines these claims in the light of advances in scheduling technology. We compare a number of current heuristic commitment techniques against a texturebased heuristic. Our results demonstrate that texturebased heuristics can outperform these widelyused heuristic commitment techniques. Introduction Our research goal is to be able to model and quickly solve scheduling problems as they exist in the real world. We are less interested in optimal solutions than in fast approximate solutions: a quickly found solution that takes into account all the constraints in the real problem is of significantly more use than an optimal solution that either takes too long to find or does not accurately represent the problem. We are applying and extending constraintdirected scheduling techniques toward this end. Our search philosophy is to spend significant but ...