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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 374 (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 277 (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
Backtracking Algorithms for Disjunctions of Temporal Constraints
 Artificial Intelligence
, 1998
"... We extend the framework of simple temporal problems studied originally by Dechter, Meiri and Pearl to consider constraints of the form x1 \Gamma y1 r1 : : : xn \Gamma yn rn , where x1 : : : xn ; y1 : : : yn are variables ranging over the real numbers, r1 : : : rn are real constants, and n 1. W ..."
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Cited by 112 (2 self)
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We extend the framework of simple temporal problems studied originally by Dechter, Meiri and Pearl to consider constraints of the form x1 \Gamma y1 r1 : : : xn \Gamma yn rn , where x1 : : : xn ; y1 : : : yn are variables ranging over the real numbers, r1 : : : rn are real constants, and n 1. We have implemented four progressively more efficient algorithms for the consistency checking problem for this class of temporal constraints. We have partially ordered those algorithms according to the number of visited search nodes and the number of performed consistency checks. Finally, we have carried out a series of experimental results on the location of the hard region. The results show that hard problems occur at a critical value of the ratio of disjunctions to variables. This value is between 6 and 7. Introduction Reasoning with temporal constraints has been a hot research topic for the last fifteen years. The importance of this problem has been demonstrated in many areas of artifici...
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 77 (29 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
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 56 (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...
SATbased Procedures for Temporal Reasoning
, 1999
"... In this paper we study the consistency problem for a set of disjunctive temporal constraints [Stergiou and Koubarakis, 1998]. We propose two SATbased procedures, and show thaton sets of binary randomly generated disjunctive constraintsthey perform up to 2 orders of magnitude less consistency ..."
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Cited by 55 (6 self)
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In this paper we study the consistency problem for a set of disjunctive temporal constraints [Stergiou and Koubarakis, 1998]. We propose two SATbased procedures, and show thaton sets of binary randomly generated disjunctive constraintsthey perform up to 2 orders of magnitude less consistency checks than the best procedure presented in [Stergiou and Koubarakis, 1998]. On these tests, our experimental analysis conrms Stergiou and Koubarakis's result about the existence of an easyhardeasy pattern whose peak corresponds to a value in between 6 and 7 of the ratio of clauses to variables.
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 45 (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...
Stochastic Procedures for Generating Feasible Schedules
 In Proceedings 14th National Conference on AI (AAAI97
, 1997
"... In this paper, we investigate the use of stochastic variable and value ordering heuristics for solving job shop scheduling problems with nonrelaxable deadlines and complex metric constraints. Previous research in constraint satisfaction scheduling has developed highly effective, deterministic heuri ..."
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Cited by 29 (14 self)
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In this paper, we investigate the use of stochastic variable and value ordering heuristics for solving job shop scheduling problems with nonrelaxable deadlines and complex metric constraints. Previous research in constraint satisfaction scheduling has developed highly effective, deterministic heuristics for this class of problems based on simple measures of temporal sequencing flexibility. However, they are not infallible, and the possibility of search failure raises the issue of how to most productively enlarge the search. Backtracking is one alternative, but such systematicity generally implies high computational cost. We instead design an iterative sampling procedure, based on the intuition that it is more productive to deviate from heuristic advice in cases where the heuristic is less informed, and likewise better to follow the heuristic in cases where it is more knowledgeable. We specify stochastic counterparts to previously developed search heuristics, which are parameterized to...
A Time and Resource Problem in Planning Architectures
 Proc. ECP96
, 1996
"... Abstract. This paper concerns the problem of resource reasoning in planning. It defines formally a constraint satisfaction problem, the Time and Resource Problem (T RP), in which resource reasoning is seen as integrated with temporal reasoning. Two propagation techniques are introduced that reason ..."
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Cited by 21 (2 self)
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Abstract. This paper concerns the problem of resource reasoning in planning. It defines formally a constraint satisfaction problem, the Time and Resource Problem (T RP), in which resource reasoning is seen as integrated with temporal reasoning. Two propagation techniques are introduced that reason about resource constraints in the T RP framework. The Profile Propagation technique, similar to timetabling techniques, considers resource utilization in single instants of time (the time values) to synthesize necessary quantitative temporal constraints. The Order Propagation technique is more original. It observes single time points (the time variables) and their orderings to synthesize necessary qualitative temporal constraints. 1