Daniel Frost’s research while affiliated with University of California, Irvine and other places

The performance of backtracking algorithms for solving finite-domain constraint satisfaction problems can be improved substantially by look-back and look-ahead methods. Look-back techniques extract information by analyzing failing search paths that are terminated by dead-ends. Look-ahead techniques use constraint propagation algorithms to avoid such dead-ends altogether. This paper describes a number of look-back 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 look-ahead methods such as forward checking and dynamic variable ordering, and discusses their combination with backjumping.

A well-studied problem in the electric power industry is that of optimally scheduling preventative maintenance of power generating units within a power plant. We show how these problems can be cast as constraint satisfaction problems and provide an "iterative learning" algorithm which solves the problem in the following manner. In order to find an optimal schedule, the algorithm solves a series of CSPs with successively tighter cost-bound constraints. For the solution of each problem in the series we use constraint learning, which involves recording additional constraints that are uncovered during search. However, instead of solving each problem independently, after a problem is solved successfully with a certain cost-bound, the new constraints recorded by learning are used in subsequent attempts to find a schedule with a lower cost-bound.

The paper evaluates the e ectiveness 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 di cult problem instances. Our results show that learning can speed up backjumping when using either a xed 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. 1.

A well-studied problem in the electric power industry is that of optimally scheduling preventative maintenance of power generating units within a power plant. We show how these problems can be cast as constraint satisfaction problems and provide an "iterative learning" algorithm which solves the problem in the following manner. In order to find an optimal schedule, the algorithm solves a series of CSPs with successively tighter cost-bound constraints. For the solution of each problem in the series we use constraint learning, which involves recording additional constraints that are uncovered during search. However, instead of solving each problem independently, after a problem is solved successfully with a certain cost-bound, the new constraints recorded by learning are used in subsequent attempts to find a schedule with a lower cost-bound. We show empirically that on a class of randomly generated maintenance scheduling problems iterative learning reduces the time to find a good schedu...

We present the results of an empirical study of several constraint satisfaction search algorithms and heuristics. Using a random problem generator that allows us to create instances with given characteristics, we show how the relative performance of various search methods varies with the number of variables, the tightness of the constraints, and the sparseness of the constraint graph. A version of backjumping using a dynamic variable ordering heuristic is shown to be extremely effective on a wide range of problems. We conducted our experiments with problem instances drawn from our experiments with problem instances drawn from the 50% satisfiable range.

The paper focuses on evaluating constraint satisfaction search algorithms on application based random problem instances. The application we use is a well-studied problem in the electric power industry: optimally scheduling preventive maintenance of power generating units within a power plant. We show how these scheduling problems can be cast as constraint satisfaction problems and used to define the structure of randomly generated non-binary CSPs. The random problem instances are then used to evaluate several previously studied algorithms. The paper also demonstrates how constraint satisfaction can be used for optimization tasks. To find an optimal maintenance schedule, a series of CSPs are solved with successively tighter cost-bound constraints. We introduce and experiment with an "iterative learning" algorithm which records additional constraints uncovered during search. The constraints recorded during the solution of one instance with a certain cost-bound are used again on subsequen...

Since for most artificial intelligence problems worstcase analysis does not necessarily reflect actual performance and since informative performance guarantees are not always available, empirical evaluation of algorithms is necessary. To do that we need to address the question of distributions, and benchmarks.

Over the past twenty years a number of backtracking algorithms for constraint satisfaction problems have been developed. This survey describes the basic backtrack search within the search space framework and then presents a number of improvements including look-back methods such as backjumping, constraint recording, backmarking, and look-ahead methods such as forward checking and dynamic variable ordering. 1 Introduction Constraint networks have proven successful in modeling mundane cognitive tasks such as vision, language comprehension, default reasoning, and abduction, as well as specialized reasoning tasks including diagnosis, design, and temporal and spatial reasoning. The constraint paradigm can be considered a generalization of propositional logic, in that variables may be assigned values from a set with any number of elements not just true and false. This flexibility in the number of values can improve the ease and naturalness with which interesting problems are modeled. ...

A well-studied problem in the electric power industry is that of optimally scheduling preventative maintenance of power generating units within a power plant [1, 3]. The general purpose of determining a maintenance schedule is to determine the duration and sequence of outages of power generating units over a given time period, while minimizing operating and maintenance costs over the planning period, subject to various constraints. We show how maintenance scheduling can be cast as a constraint satisfaction problem and used to define the structure of randomly generated non-binary CSPs. These random problem instances are then used to evaluate several previously studied backtracking-based algorithms, including backjumping and dynamic variable ordering augmented with constraint learning and look-ahead value ordering [2]. We also define and report on a new ⩼erative learning’ algorithm which solves maintenance scheduling problems in the following manner. In order to find an optimal schedule, the algorithm solves a series of CSPs with successively tighter cost-bound constraints. For the solution of each problem in the series constraint learning is applied, which involves recording additional constraints that are uncovered during search. However, instead of solving each problem in the series independently, after a problem is solved successfully with a certain cost-bound, the new constraints recorded by learning are used in subsequent attempts to find a schedule with a lower cost-bound. We show empirically that on a class of randomly generated maintenance scheduling problems iterative learning reduces the time required to find a good schedule.

. We analyze the distribution of computational effort required by backtracking algorithms on unsatisfiable CSPs, using analogies with reliability models, where lifetime of a specimen before failure corresponds to the runtime of backtracking on unsatisfiable CSPs. We extend the results of [7] by showing empirically that the lognormal distribution is a good approximation of the backtracking effort on unsolvable CSPs not only at the 50% satisfiable point, but in a relatively wide region. We also show how the law of proportionate effect [9] commonly used to derive the lognormal distribution can be applied to modeling the number of nodes expanded in a search tree. Moreover, for certain intervals of C=N , where N is the number of variables, and C is the number of constraints, the parameters of the corresponding lognormal distribution can be approximated by the linear lognormal model [11] where mean log(deadends) is linear in C=N , and variance of log(deadends) is close to constant. The line...