Daniel Frost

Backjump-based backtracking for constraint satisfaction problems

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.

Optimizing with Constraints: A Case Study in Scheduling Maintenance of Electric Power Units

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].

Maintenance scheduling problems as benchmarks for constraint algorithms

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 subsequent instances having tighter cost-bounds. Our results show that on a class of randomly generated maintenance scheduling problems, iterative learning reduces the time required to find a good schedule.

Ucigame, a java library for games

Ucigame (pronounced OO-see-GAH-me) is a Java package that supports the programming of 2D sprite-based computer games. Designed for novice programmers, it enables students in an introductory class to write computer games that have animated sprites, music and sound effects, and event-driven keyboard and mouse handling. Ucigame has also been used successfully in a senior-level class for experienced programmers.

Fourth grade computer science

We describe a module, or sequence of lessons, that has been successfully used to teach basic elements of computer science to fourth grade students. The module was designed to reflect a firm grounding in computer science, to be age-appropriate, to be easily installed in schools, and to support a range of teachers. Over 300 students in grades three through six have taken this module or a related module. The programming language used is a modern variant of Logo called VVLogo, which students access through a Java applet on a web page.

Looking at full looking ahead

Haralick and Elliotts full looking ahead algorithm [4] was presented in the same article as forward checking, but is not as commonly used. We give experimental results which indicate that on some types of constraint satisfaction problems, full looking ahead outperforms forward checking. We also present three new looking ahead algorithms, all variations on full looking ahead, which were designed with the goal of achieving performance equal to the better of forward checking and full looking ahead on a variety of constraint satisfaction problems. One of these new algorithms, called smart looking ahead, comes close to achieving our goal.

Statistical analysis of backtracking on inconsistent CSPs

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 linear lognormal model allows us to extrapolate the results from a relativelyeasy overconstrained region to the hard critically constrained region and, in particular, to use more efficient strategies for testing backtracking algorithms. This work was partially supported by NSF grant IRI-9157636, Air Force Office of Scientific Research grant AFOSR 900136, Rockwell Micro grant 22147, and UC Micro grant 96-012.