A New Look at the Easy-Hard-Easy Pattern of Combinatorial Search Difficulty

The easy-hard-easy pattern in the difficulty of combinatorial search problems as constraints are added has been explained as due to a competition between the decrease in number of solutions and increased pruning. We test the generality of this explanation by examining one of its predictions: if the number of solutions is held fixed by the choice of problems, then increased pruning should lead to a monotonic decrease in search cost. Instead, we find the easy-hard-easy pattern in median search cost even when the number of solutions is held constant, for some search methods. This generalizes previous observations of this pattern and shows that the existing theory does not explain the full range of the peak in search cost. In these cases the pattern appears to be due to changes in the size of the minimal unsolvable subproblems, rather than changing numbers of solutions.Comment: See http://www.jair.org/ for any accompanying file

The min-conflicts heuristic: Experimental and theoretical results

This paper describes a simple heuristic method for solving large-scale constraint satisfaction and scheduling problems. Given an initial assignment for the variables in a problem, the method operates by searching through the space of possible repairs. The search is guided by an ordering heuristic, the min-conflicts heuristic, that attempts to minimize the number of constraint violations after each step. We demonstrate empirically that the method performs orders of magnitude better than traditional backtracking techniques on certain standard problems. For example, the one million queens problem can be solved rapidly using our approach. We also describe practical scheduling applications where the method has been successfully applied. A theoretical analysis is presented to explain why the method works so well on certain types of problems and to predict when it is likely to be most effective

Generalizing backdoors

Abstract. A powerful intuition in the design of search methods is that one wants to proactively select variables that simplify the problem instance as much as possible when these variables are assigned values. The notion of “Backdoor ” variables follows this intuition. In this work we generalize Backdoors in such a way to allow more general classes of sub-solvers, both complete and heuristic. In order to do so, Pseudo-Backdoors and Heuristic-Backdoors are formally introduced and then applied firstly to a simple Multiple Knapsack Problem and secondly to a complex combinatorial optimization problem in the area of stochastic inventory control. Our preliminary computational experience shows the effectiveness of these approaches that are able to produce very low run times and — in the case of Heuristic-Backdoors — high quality solutions by employing very simple heuristic rules such as greedy local search strategies.

Informed selection and use of training examples for knowledge refinement.

Knowledge refinement tools seek to correct faulty rule-based systems by identifying and repairing faults indicated by training examples that provide evidence of faults. This thesis proposes mechanisms that improve the effectiveness and efficiency of refinement tools by the best use and selection of training examples. The refinement task is sufficiently complex that the space of possible refinements demands a heuristic search. Refinement tools typically use hill-climbing search to identify suitable repairs but run the risk of getting caught in local optima. A novel contribution of this thesis is solving the local optima problem by converting the hill-climbing search into a best-first search that can backtrack to previous refinement states. The thesis explores how different backtracking heuristics and training example ordering heuristics affect refinement effectiveness and efficiency. Refinement tools rely on a representative set of training examples to identify faults and influence repair choices. In real environments it is often difficult to obtain a large set of training examples, since each problem-solving task must be labelled with the expert's solution. Another novel aspect introduced in this thesis is informed selection of examples for knowledge refinement, where suitable examples are selected from a set of unlabelled examples, so that only the subset requires to be labelled. Conversely, if a large set of labelled examples is available, it still makes sense to have mechanisms that can select a representative set of examples beneficial for the refinement task, thereby avoiding unnecessary example processing costs. Finally, an experimental evaluation of example utilisation and selection strategies on two artificial domains and one real application are presented. Informed backtracking is able to effectively deal with local optima by moving search to more promising areas, while informed ordering of training examples reduces search effort by ensuring that more pressing faults are dealt with early on in the search. Additionally, example selection methods achieve similar refinement accuracy with significantly fewer examples

High performance constraint satisfaction problem solving: State-recomputation versus state-copying.

Constraint Satisfaction Problems (CSPs) in Artificial Intelligence have been an important focus of research and have been a useful model for various applications such as scheduling, image processing and machine vision. CSPs are mathematical problems that try to search values for variables according to constraints. There are many approaches for searching solutions of non-binary CSPs. Traditionally, most CSP methods rely on a single processor. With the increasing popularization of multiple processors, parallel search methods are becoming alternatives to speed up the search process. Parallel search is a subfield of artificial intelligence in which the constraint satisfaction problem is centralized whereas the search processes are distributed among the different processors. In this thesis we present a forward checking algorithm solving non-binary CSPs by distributing different branches to different processors via message passing interface and execute it on a high performance distributed system called SHARCNET. However, the problem is how to efficiently communicate the state of the search among processors. Two communication models, namely, state-recomputation and state-copying via message passing, are implemented and evaluated. This thesis investigates the behaviour of communication from one process to another. The experimental results demonstrate that the state-recomputation model with tighter constraints obtains a better performance than the state-copying model, but when constraints become looser, the state-copying model is a better choice.Dept. of Computer Science. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .Y364. Source: Masters Abstracts International, Volume: 44-01, page: 0417. Thesis (M.Sc.)--University of Windsor (Canada), 2005

Un algorithme heuristique pour l'attribution des cours

À chaque semestre, la direction du Département d'informatique de l'UQAM doit convenablement affecter les divers groupes-cours disponibles à ses professeurs, en se basant sur leurs préférences et certaines règles adoptées par l'assemblée départementale. Le but de notre travail est développer un algorithme qui trouve une solution de bonne qualité à ce problème, et ce dans un temps raisonnable. Dans ce mémoire, nous appliquons deux approches différentes pour résoudre le problème d'affectation des groupes-cours. La première est basée sur un algorithme branch-and-bound, qui est un algorithme de recherche exhaustif et complet. La deuxième est basée sur un processus heuristique de recherche local amélioré. Plus particulièrement, nous nous concentrons sur l'algorithme de recherche local. Des algorithmes de recherche locale divers sont présentés, entre autres, la recherche locale guidée et le recuit simulé. Ce que nous faisons n'est pas simplement d'appliquer ces algorithmes et les combiner ensemble. Nous essayons aussi de nous inspirer de ces algorithmes pour mettre au point quelques nouvelles idées appropriées pour notre propre problème. Finalement, nous utilisons les résultats expérimentaux obtenus par l'algorithme branch-and-bound comme point de référence en ce qui concerne la qualité de la solution et le temps d'exécution pour évaluer les autres approches. Les résultats que nous avons obtenus de données réelles et des données générées aléatoirement montrent que notre algorithme effectue un bon travail tant en termes de qualité de solution que de temps d'exécution. Les résultats montrent aussi que notre algorithme peut trouver une bonne solution à de grands problèmes en un temps raisonnable.\ud _____________________________________________________________________________