Abstract. Constraint satisfaction is the core of many AI and real life problems and much research has been done in this field in recent years. Work has been done in the past on comparing the performance of different algorithms and heuristics. Much of such work has focused on finding "the best " algorithm and heuristic combination for all problems. The objective of this paper is to prove that there is no universally best algorithm and heuristic for all problems-- different problems can be solved most efficiently by different algorithm and heuristic combinations. The implication of this is important because it means that instead of trying to find "the best " algorithms and heuristics, future research should try to identify the application domain of each algorithm and heuristic (i.e. when they are most effective). Furthermore our results point to future research which focuses on how to retrieve the most efficient algorithm for a given problem. The results in this paper provide a first step towards achieving such goals. 1.

The statistical mechanics of combinatorial search problems is described using the example of the well-known NP-complete graph coloring problem. We focus on a recently identified phase transition from under- to overconstrained problems, near which are concentrated many hard to solve search problems. Thus, a readily computed measure of problem structure predicts the difficulty of solving the problem, on average. However, this prediction is associated with a large variance and depends on the somewhat arbitrary choice of the problem ensemble. Thus these results are of limited direct use for individual instances. To help address this limitation, additional parameters, describing problem structure as well as heuristic effectiveness, are introduced. This also highlights the distinction between the statistical mechanics of combinatorial search problems, with their exponentially large search spaces, and physical systems, whose interactions are often governed by a simple euclidean metric. Chapter 1

I highlight some inefficiencies of Graphplan’s backward search algorithm, and describe how these can be eliminated by adding explanation-based learning and dependency-directed backtracking capabilities to Graphplan. I will then demonstrate the effectiveness of these augmentations by describing results of empirical studies that show dramatic improvements in run-time ( 100x speedups) as well as solvability-horizons on benchmark problems across seven different domains. 1

For many constraint satisfaction problems, there are well known, fast algorithms and functions that solve parts of the problem. Using these methods directly to solve the subproblems significantly speeds up the solving process. Unfortunately, doing this has usually required the solver to be changed, or the correctness criteria to be re-examined. We describe a general mechanism to use procedures with almost any search engine, such that it is easy to add any procedures without changing the engine. Furthermore, the framework is formally defined, which allows us to prove conditions that are sufficient to guarantee systematicity and completeness for search engines using procedures. 1 Introduction For many constraint satisfaction problems there are simple functional relations (e.g. arithmetic equations) and simple subproblems (e.g. linear equations with unknowns) that can be solved quickly, using simple algorithms. Needless to say, taking advantage of such algorithms can significantly decrea...

We give some dos and don'ts for those analysing algorithms experimentally. We illustrate these with many examples from our own research on the study of algorithms for NP-complete problems such as satisfiability and constraint satisfaction. Where we have not followed these maxims, we have suffered as a result. 1 Introduction The empirical study of algorithms is a relatively immature field with many technical and scientific problems. We support the calls of McGeoch (1986,1996), Hooker (1994), and others for a more scientific approach to the empirical study of algorithms. Our contribution in this paper is colloquial. We admit to a large number of mistakes in conducting our research. While painful, we hope that this will encourage others to avoid these mistakes, and thereby to develop practices which represent good science. Much of our research has been on the experimental analysis of algorithms and phase transitions in NP-complete problems, most commonly in satisfiability or constraint s...

Abstract. Among backtracking based algorithms for constraint satisfaction problems (CSPs), algorithms employing constraint propagation, like forward checking (FC) and MAC, have had the most practical impact. These algorithms use constraint propagation during search to prune inconsistent values from the domains of the uninstantiated variables. In this paper we present a general approach to extending constraint propagating algorithms, especially forward checking. In particular, we provide a simple yet flexible mechanism for pruning domain values, and show that with this in place it becomes easy to utilize new mechanisms for detecting inconsistent values during search. This leads to a powerful and uniform technique for designing new CSP algorithms: one simply need design new methods for detecting inconsistent values and then interface them with the domain pruning mechanism. Furthermore, we also show that algorithms following this design can proved to be correct in a simple and uniform way. To demonstrate the utility of these ideas five “new ” CSP algorithms are presented. 1

The forward checking routine (FC) of Haralick and Elliott attempts to encourage early failures within the search tree of constraint satisfaction problems, leading to a reduction in nodes visited, which tends to result in reduced search effort. In contrast, Gaschnig's backmarking routine (BM) attempts to avoid performing redundant consistency checks. These two algorithms are combined to give us FC-BM, an algorithm that attempts to minimise the number of nodes visited, while avoiding redundant consistency checks. This algorithm is further enhanced such that it incorporates conflict-directed backjumping (CBJ) to give us FC-BM-CBJ. A series of experiments are then carried out on really hard problems in an attempt to position these new algorithms with respect to the known algorithms.

The ideas of intelligent backtracking (IB) and explanation-based learning (EBL) have developed independently in the constraint satisfaction, planning, machine learning and problem solving communities. The variety of approaches developed for IB and EBL in the various communities have hither-to been incomparable. In this paper, I formalize and unify these ideas under the task-independent framework of refinement search, which can model the search strategies used in both planning and constraint satisfaction problems (CSPs). I show that both IB and EBL depend upon the common theory of explanation analysis--which involves explaining search failures, and regressing them to higher levels of the search tree. My comprehensive analysis shows that most of the differences between the CSP and planning approaches to EBL and IB revolve around different solutions to: (a) how the failure explanations are computed; (b) how they are contextualized (contextualization involves deciding whether or not to keep the flaw description and the description of the violated problem constraints); and (c) how the storage of explanations is managed. The differences themselves can be understood in terms of the differences between planning and CSP problems as instantiations of refinement search. This unified understanding is expected to support a greater cross-fertilization of ideas among CSP, planning and EBL communities.

Many real-life problems belong to the class of constraint satisfaction problems (CSP's), which are NP-complete, and some NP-hard, in general. When the problem size grows, it becomes difficult to program solutions and to execute the solution in a timely manner. In this paper, we present a general framework for integrating artificial neural networks and logic programming to provide an efficient and yet easy-to-program environment for solving CSP's. To realize this framework, we propose a novel constraint logic programming language PROCLANN. Operationally, PROCLANN uses the standard goal reduction strategy as frontend to generate constraints and an efficient backend constraint-solver based on artificial neural networks. PROCLANN retains the simple and elegant declarative semantics of constraint logic programming. Its operational semantics is probabilistic in nature. We show that PROCLANN is sound and weakly complete. A novelty of PROCLANN is that while it is a committed-choice l...

Integrating constraint satisfaction techniques with complex object structures is highly desirable. Several libraries are now available to use algorithms off-the shelf and embed them in large object-oriented systems. However, the design of complex object + constraint problems is an open issue that severely limits the applicability of available libraries. We compare two radically different approaches in designing systems integrating objects and finite domain constraints. In the first approach, constraints are defined within classes and constrain attributes of the class, thereby introducing "partially instanciated " objects in the reasoning. In the second approach, constraints are defined outside classes, and constrain fully instanciated objects. We show that, for a particular class of problem, the second solution yields a simpler design while being more efficient. We exemplify our claims by comparing these two approaches on a hard object + constraint problem: four-voice harmonization of tonal melodies, seen as a representative complex configuration problem. 1.