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94
GSAT and Dynamic Backtracking
 Journal of Artificial Intelligence Research
, 1994
"... There has been substantial recent interest in two new families of search techniques. One family consists of nonsystematic methods such as gsat; the other contains systematic approaches that use a polynomial amount of justification information to prune the search space. This paper introduces a new te ..."
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Cited by 362 (14 self)
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There has been substantial recent interest in two new families of search techniques. One family consists of nonsystematic methods such as gsat; the other contains systematic approaches that use a polynomial amount of justification information to prune the search space. This paper introduces a new technique that combines these two approaches. The algorithm allows substantial freedom of movement in the search space but enough information is retained to ensure the systematicity of the resulting analysis. Bounds are given for the size of the justification database and conditions are presented that guarantee that this database will be polynomial in the size of the problem in question. 1 INTRODUCTION The past few years have seen rapid progress in the development of algorithms for solving constraintsatisfaction problems, or csps. Csps arise naturally in subfields of AI from planning to vision, and examples include propositional theorem proving, map coloring and scheduling problems. The probl...
Limited Discrepancy Search
 In Proceedings IJCAI’95
, 1995
"... Many problems of practical interest can be solved using tree search methods because carefully tuned successor ordering heuristics guide the search toward regions of the space that are likely to contain solutions. For some problems, the heuristics often lead directly to a solution— but not always. Li ..."
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Cited by 262 (5 self)
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Many problems of practical interest can be solved using tree search methods because carefully tuned successor ordering heuristics guide the search toward regions of the space that are likely to contain solutions. For some problems, the heuristics often lead directly to a solution— but not always. Limited discrepancy search addresses the problem of what to do when the heuristics fail. Our intuition is that a failing heuristic might well have succeeded if it were not for a small number of "wrong turns " along the way. For a binary tree of height d, there are only d ways the heuristic could make a single wrong turn, and only d(di)/2 ways it could make two. A small number of wrong turns can be overcome by systematically searching all paths that differ from the heuristic path in at most a small number of decision points, or "discrepancies." Limited discrepancy search is a backtracking algorithm that searches the nodes of the tree in increasing order of such discrepancies. We show formally and experimentally that limited discrepancy search can be expected to outperform existing approaches. 1
Bridging the gap between planning and scheduling
 KNOWLEDGE ENGINEERING REVIEW
, 2000
"... Planning research in Artificial Intelligence (AI) has often focused on problems where there are cascading levels of action choice and complex interactions between actions. In contrast, Scheduling research has focused on much larger problems where there is little action choice, but the resulting orde ..."
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Cited by 95 (9 self)
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Planning research in Artificial Intelligence (AI) has often focused on problems where there are cascading levels of action choice and complex interactions between actions. In contrast, Scheduling research has focused on much larger problems where there is little action choice, but the resulting ordering problem is hard. In this paper, we give an overview of AI planning and scheduling techniques, focusing on their similarities, differences, and limitations. We also argue that many difficult practical problems lie somewhere between planning and scheduling, and that neither area has the right set of tools for solving these vexing problems.
A constraintbased method for project scheduling with time windows
 Journal of Heuristics
, 2002
"... This paper presents a heuristic algorithm for solving RCPSP/max, the resource constrained project scheduling problem with generalized precedence relations. The algorithm relies, at its core, on a constraint satisfaction problem solving (CSP) search procedure, which generates a consistent set of acti ..."
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Cited by 67 (26 self)
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This paper presents a heuristic algorithm for solving RCPSP/max, the resource constrained project scheduling problem with generalized precedence relations. The algorithm relies, at its core, on a constraint satisfaction problem solving (CSP) search procedure, which generates a consistent set of activity start times by incrementally removing resource conflicts from an otherwise temporally feasible solution. Key to the effectiveness of the CSP search procedure is its heuristic strategy for conflict selection. A conflict sampling method biased toward selection of minimal conflict sets that involve activities with highercapacity requests is introduced, and coupled with a nondeterministic choice heuristic to guide the base conflict resolution process. This CSP search is then embedded within a larger iterativesampling search framework to broaden search space coverage and promote solution optimization. The efficacy of the overall heuristic algorithm is demonstrated empirically on
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 59 (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.
Nonsystematic Backtracking Search
, 1995
"... Many practical problems in Artificial Intelligence have search trees that are too large to search exhaustively in the amount of time allowed. Systematic techniques such as chronological backtracking can be applied to these problems, but the order in which they examine nodes makes them unlikely to fi ..."
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Cited by 54 (1 self)
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Many practical problems in Artificial Intelligence have search trees that are too large to search exhaustively in the amount of time allowed. Systematic techniques such as chronological backtracking can be applied to these problems, but the order in which they examine nodes makes them unlikely to find a solution in the explored fraction of the space. Nonsystematic techniques have been proposed to alleviate the problem by searching nodes in a random order. A technique known as iterative sampling follows random paths from the root of the tree to the fringe, stopping if a path ends at a goal node. Although the nonsystematic techniques do not suffer from the problem of exploring nodes in a bad order, they do reconsider nodes they have already ruled out, a problem that is serious when the density of solutions in the tree is low. Unfortunately, for many practical problems the order of examing nodes matters and the density of solutions is low. Consequently, neither chronological backtracking...
Variable and value ordering heuristics for the job shop scheduling constraint satisfaction problem
 Artificial Intelligence
, 1996
"... Practical Constraint Satisfaction Problems (CSPs) such as design of integrated circuits or scheduling generally entail large search spaces with hundreds or even thousands of variables, each with hundreds or thousands of possible values. Often, only a very tiny fraction of all these possible assignme ..."
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Cited by 51 (2 self)
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Practical Constraint Satisfaction Problems (CSPs) such as design of integrated circuits or scheduling generally entail large search spaces with hundreds or even thousands of variables, each with hundreds or thousands of possible values. Often, only a very tiny fraction of all these possible assignments participates in a satisfactory solution. This article discusses techniques that aim at reducing the effective size of the search space to be explored in order to find a satisfactory solution by judiciously selecting the order in which variables are instantiated and the sequence in which possible values are tried for each variable. In the CSP literature, these techniques are commonly referred to as variable and value ordering heuristics. Our investigation is conducted in the job shop scheduling domain. We show that, in contrast with problems studied earlier in the CSP literature, generic variable and value heuristics do not perform well in this domain. This is attributed to the difficulty of these heuristics to properly account for the tightness of constraints and/or the connectivity of the constraint graphs induced by job shop scheduling CSPs. A new probabilistic framework is introduced that better captures these key aspects of the job shop scheduling search space. Empirical results show that variable and value ordering heuristics
Intelligent Backtracking On Constraint Satisfaction Problems: Experimental And Theoretical Results
, 1995
"... The Constraint Satisfaction Problem is a type of combinatorial search problem of much interest in Artificial Intelligence and Operations Research. The simplest algorithm for solving such a problem is chronological backtracking, but this method suffers from a malady known as "thrashing," in ..."
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Cited by 49 (0 self)
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The Constraint Satisfaction Problem is a type of combinatorial search problem of much interest in Artificial Intelligence and Operations Research. The simplest algorithm for solving such a problem is chronological backtracking, but this method suffers from a malady known as "thrashing," in which essentially the same subproblems end up being solved repeatedly. Intelligent backtracking algorithms, such as backjumping and dependencydirected backtracking, were designed to address this difficulty, but the exact utility and range of applicability of these techniques have not been fully explored. This dissertation describes an experimental and theoretical investigation into the power of these intelligent backtracking algorithms. We compare the empirical performance of several such algorithms on a range of problem distributions. We show that the more sophisticated algorithms are especially useful on those problems with a small number of constraints that happen to be difficult for chronologica...
Applying Constraint Satisfaction Techniques to Job Shop Scheduling
, 1995
"... In this paper, we investigate the applicability of a constraint satisfaction problem solving (CSP) model, recently developed for deadline scheduling, to more commonly studied problems of schedule optimization. Our hypothesis is twofold: (1) that CSP scheduling techniques provide a basis for develop ..."
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Cited by 41 (9 self)
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In this paper, we investigate the applicability of a constraint satisfaction problem solving (CSP) model, recently developed for deadline scheduling, to more commonly studied problems of schedule optimization. Our hypothesis is twofold: (1) that CSP scheduling techniques provide a basis for developing highperformance approximate solution procedures in optimization contexts, and (2) that the representational assumptions underlying CSP models allow these procedures to naturally accommodate the idiosyncratic constraints that complicate most realworld applications. We focus specifically on the objective criterion of makespan minimization, which has received the most attention within the job shop scheduling literature. We define an extended solution procedure somewhat unconventionally by reformulating the makespan problem as one of solving a series of different but related deadline scheduling problems, and embedding a simple CSP procedure as the subproblem solver. We first present the re...
Slackbased Techniques for Robust Schedules
"... . Many scheduling systems assume a static environment within which a schedule will be executed. The real world is not so stable: machines break down, operations take longer to execute than expected, and orders may be added or canceled. One approach to dealing with such disruptions is to generate rob ..."
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Cited by 41 (5 self)
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. Many scheduling systems assume a static environment within which a schedule will be executed. The real world is not so stable: machines break down, operations take longer to execute than expected, and orders may be added or canceled. One approach to dealing with such disruptions is to generate robust schedules: schedules that are able to absorb some level of unexpected events without rescheduling. In this paper we investigate three techniques for generating robust schedules based on the insertion of temporal slack. Simulationbased results indicate that the two novel techniques outperform the existing temporal protection technique both in terms of producing schedules with low simulated tardiness and in producing schedules that better predict the level of simulated tardiness. Keywords: Robustness, Uncertainty, Scheduling, Heuristics 1