Results 1  10
of
25
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 ..."
Abstract

Cited by 106 (2 self)
 Add to MetaCart
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...
Bridging the gap between planning and scheduling
 Knowledge Engineering Review
"... 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 ..."
Abstract

Cited by 94 (9 self)
 Add to MetaCart
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. 1 The Ambitious Spacecraft Imagine a hypothetical spacecraft enroute to a distant planet. Between propulsion cycles, there are time windows when the craft can be turned for communication and scientific observations. At any given time, the spacecraft has a large set of possible scientific observations that it can perform, each having some value or priority. For each observation, the spacecraft will need to be turned towards the target and the required measurement or exposure taken. Unfortunately, turning to a target is a slow operation that may take up to 30 minutes, depending on the magnitude of the turn. As a result, the choice of experiments and the order in which they are performed has a significant impact on the duration of turns and, therefore, on how much can be accomplished. All this is further complicated by several things:
DeadEnd Driven Learning
, 1994
"... The paper evaluates the effectiveness of learning for speeding up the solution of constraint satisfaction problems. It extends previous work (Dechter 1990) by introducing a new and powerful variant of learning and by presenting an extensive empirical study on much larger and more difficult problem i ..."
Abstract

Cited by 75 (5 self)
 Add to MetaCart
The paper evaluates the effectiveness of learning for speeding up the solution of constraint satisfaction problems. It extends previous work (Dechter 1990) by introducing a new and powerful variant of learning and by presenting an extensive empirical study on much larger and more difficult problem instances. Our results show that learning can speed up backjumping when using either a fixed or dynamic variable ordering. However, the improvement with a dynamic variable ordering is not as great, and for some classes of problems learning is helpful only when a limit is placed on the size of new constraints learned.
An Empirical Study of Dynamic Variable Ordering Heuristics for the Constraint Satisfaction Problem
 In Proceedings of CP96
, 1996
"... . The constraint satisfaction community has developed a number of heuristics for variable ordering during backtracking search. For example, in conjunction with algorithms which check forwards, the FailFirst (FF) and Brelaz (Bz) heuristics are cheap to evaluate and are generally considered to be ver ..."
Abstract

Cited by 70 (15 self)
 Add to MetaCart
. The constraint satisfaction community has developed a number of heuristics for variable ordering during backtracking search. For example, in conjunction with algorithms which check forwards, the FailFirst (FF) and Brelaz (Bz) heuristics are cheap to evaluate and are generally considered to be very effective. Recent work to understand phase transitions in NPcomplete problem classes enables us to compare such heuristics over a large range of different kinds of problems. Furthermore, we are now able to start to understand the reasons for the success, and therefore also the failure, of heuristics, and to introduce new heuristics which achieve the successes and avoid the failures. In this paper, we present a comparison of the Bz and FF heuristics in forward checking algorithms applied to randomlygenerated binary CSP's. We also introduce new and very general heuristics and present an extensive study of these. These new heuristics are usually as good as or better than Bz and FF, and we id...
Trying Harder to Fail First
 In: Thirteenth European Conference on Artificial Intelligence (ECAI 98
, 1997
"... Variable ordering heuristics can have a profound effect on the performance of backtracking search algorithms for constraint satisfaction problems. The smallestremainingdomain heuristic is a commonlyused dynamic variable ordering heuristic, used in conjunction with algorithms such as forward checki ..."
Abstract

Cited by 50 (1 self)
 Add to MetaCart
Variable ordering heuristics can have a profound effect on the performance of backtracking search algorithms for constraint satisfaction problems. The smallestremainingdomain heuristic is a commonlyused dynamic variable ordering heuristic, used in conjunction with algorithms such as forward checking which look ahead at the effects of each variable instantiation on those variables not yet instantiated. This heuristic has been explained as an implementation of the failfirst principle, stated by Haralick and Elliott [7], i.e. that the next variable selected should be the one which is most likely to result in an immediate failure. We calculate the probability that a variable will fail when using the forward checking algorithm to solve a class of binary CSPs. We derive a series of heuristics, starting with smallestremainingdomain, based on increasingly accurate estimates of this probability, and predict that if the failfirst principle is sound, the more accurate the estimate the better...
MAC and Combined Heuristics: Two Reasons to Forsake FC (and CBJ?) on Hard Problems
 In Proceedings of the Second International Conference on Principles and Practice of Constraint Programming
, 1996
"... . In the last twenty years, many algorithms and heuristics were developed to find solutions in constraint networks. Their number increased to such an extent that it quickly became necessary to compare their performances in order to propose a small number of "good" methods. These comparisons often le ..."
Abstract

Cited by 40 (3 self)
 Add to MetaCart
. In the last twenty years, many algorithms and heuristics were developed to find solutions in constraint networks. Their number increased to such an extent that it quickly became necessary to compare their performances in order to propose a small number of "good" methods. These comparisons often led us to consider FC or FCCBJ associated with a "minimum domain" variable ordering heuristic as the best techniques to solve a wide variety of constraint networks. In this paper, we first try to convince once and for all the CSP community that MAC is not only more efficient than FC to solve large practical problems, but it is also really more efficient than FC on hard and large random problems. Afterwards, we introduce an original and efficient way to combine variable ordering heuristics. Finally, we conjecture that when a good variable ordering heuristic is used, CBJ becomes an expensive gadget which almost always slows down the search, even if it saves a few constraint checks. 1 Introducti...
Backjumpbased Backtracking for Constraint Satisfaction Problems
 Artificial Intelligence
, 2002
"... The performance of backtracking algorithms for solving finitedomain constraint satisfaction problems can be improved substantially by lookback and lookahead methods. Lookback techniques extract information by analyzing failing search paths that are terminated by deadends. Lookahead techniques ..."
Abstract

Cited by 37 (2 self)
 Add to MetaCart
The performance of backtracking algorithms for solving finitedomain constraint satisfaction problems can be improved substantially by lookback and lookahead methods. Lookback techniques extract information by analyzing failing search paths that are terminated by deadends. Lookahead techniques use constraint propagation algorithms to avoid such deadends altogether. This survey describes a number of lookback variants including backjumping and constraint recording which recognize and avoid some unnecessary explorations of the search space. The last portion of the paper gives an overview of lookahead methods such as forward checking and dynamic variable ordering, and discusses their combination with backjumping.
Exact Phase Transitions in Random Constraint Satisfaction Problems
 Journal of Artificial Intelligence Research
, 2000
"... In this paper we propose a new type of random CSP model, called Model RB, which is a revision to the standard Model B. It is proved that phase transitions from a region where almost all problems are satis able to a region where almost all problems are unsatis able do exist for Model RB as the number ..."
Abstract

Cited by 31 (9 self)
 Add to MetaCart
In this paper we propose a new type of random CSP model, called Model RB, which is a revision to the standard Model B. It is proved that phase transitions from a region where almost all problems are satis able to a region where almost all problems are unsatis able do exist for Model RB as the number of variables approaches in nity. Moreover, the critical values at which the phase transitions occur are also known exactly. By relating the hardness of Model RB to Model B, it is shown that there exist a lot of hard instances in Model RB.
Summarizing CSP hardness with continuous probability distributions
 In Proceedings of the 14th National Conference on AI
, 1997
"... We present empirical evidence that the distribution of effort required to solve CSPs randomly generated at the 50% satisfiable point, when using a backtracking algorithm, can be approximated by two standard families of continuous probability distribution functions. Solvable problems can be modelled ..."
Abstract

Cited by 30 (2 self)
 Add to MetaCart
We present empirical evidence that the distribution of effort required to solve CSPs randomly generated at the 50% satisfiable point, when using a backtracking algorithm, can be approximated by two standard families of continuous probability distribution functions. Solvable problems can be modelled by the Weibull distribution, and unsolvable problems by the lognormal distribution. These distributions fit equally well over a variety of backtracking based algorithms. 1. Introduction Several key developments in the 1990's have contributed to the advancement of empirical research on CSP algorithms, to the extent that the field may even be called an experimental science. Striking increases in computer power and decreases in cost, coupled with the general adoption of C as the programming language of choice, have made it possible for the developer of a new algorithm or heuristic to test it on large numbers of random instances. Another important advance was the recognition of the "50% satisfi...
Backtracking algorithms for constraint satisfaction problems
, 1999
"... Over the past twenty veyears many backtracking algorithms have been developed for constraint satisfaction problems. This survey describes the basic backtrack search within the search space framework and then presents a number of improvements developed in the past two decades, including lookback met ..."
Abstract

Cited by 28 (6 self)
 Add to MetaCart
Over the past twenty veyears many backtracking algorithms have been developed for constraint satisfaction problems. This survey describes the basic backtrack search within the search space framework and then presents a number of improvements developed in the past two decades, including lookback methods such asbackjumping, constraint recording, backmarking, and lookahead methods such as forward checking and dynamic variable ordering. 1