Machine learning strongly relies on the covering test to assess whether a candidate hypothesis covers training examples. The present paper investigates learning relational concepts from examples, termed relational learning or inductive logic programming. In particular, it investigates the chances of success and the computational cost of relational learning, which appears to be severely affected by the presence of a phase transition in the covering test. To this aim, three up-to-date relational learners have been applied to a wide range of artificial, fully relational learning problems. A first experimental observation is that the phase transition behaves as an attractor for relational learning; no matter which region the learning problem belongs to, all three learners produce hypotheses lying within or close to the phase transition region. Second, a failure region appears. All three learners fail to learn any accurate hypothesis in this region. Quite surprisingly, the probability of failure does not systematically increase with the size of the underlying target concept: under some circumstances, longer concepts may be easier to accurately approximate than shorter ones. Some interpretations for these findings are proposed and discussed.

We introduce an algorithm for combinatorial search on quantum computers that is capable of significantly concentrating amplitude into solutions for some NP search problems, on average. This is done by exploiting the same aspects of problem structure as used by classical backtrack methods to avoid unproductive search choices. This quantum algorithm is much more likely to find solutions than the simple direct use of quantum parallelism. Furthermore, empirical evaluation on small problems shows this quantum algorithm displays the same phase transition behavior, and at the same location, as seen in many previously studied classical search methods. Specifically, difficult problem instances are concentrated near the abrupt change from underconstrained to overconstrained problems. August

Tabu search algorithms are among the most effective approaches for solving the job-shop scheduling problem (JSP). Yet, we have little understanding of why these algorithms work so well, and under what conditions. We develop a model of problem difficulty for tabu search in the JSP, borrowing from similar models developed for SAT and other NP - complete problems. We show that the mean distance between random local optima and the nearest optimal solution is highly correlated with the cost of locating optimal solutions to typical, random JSPs. Additionally, this model accounts for the cost of locating suboptimal solutions, and provides an explanation for differences in the relative difficulty of square versus rectangular JSPs. We also identify two important limitations of our model. First, model accuracy is inversely correlated with problem difficulty, and is exceptionally poor for rare, very high-cost problem instances. Second, the model is significantly less accurate for structured, non-random JSPs. Our results are also likely to be useful in future research on difficulty models of local search in SAT, as local search cost in both SAT and the JSP is largely dictated by the same search space features. Similarly, our research represents the first attempt to quantitatively model the cost of tabu search for any NP -complete problem, and may possibly be leveraged in an effort to understand tabu search in problems other than job-shop scheduling.

In order to effectively respond to changing market conditions, business partners must be able to rapidly form supply chains. This thesis approaches the problem of automating supply chain formation—the process of determining the participants in a supply chain, who will exchange what with whom, and the terms of the exchanges—within an economic framework. In this thesis, supply chain formation is formalized as task dependency networks. This model captures subtask decomposition in the presence of resource contention—two important and challenging aspects of supply chain formation. In order to form supply chains in a decentralized fashion, price systems provide an economic framework for guiding the decisions of self-interested agents. In competitive price equilibrium, agents choose optimal allocations with respect to prices, and outcomes are optimal overall. Approximate competitive equilibria yield approximately optimal allocations. Different market protocols are proposed for agents to negotiate the allocation of resources to form supply chains. In the presence of resource contention, these protocols produce better solutions than the greedy protocols common in the artificial intelligence

Many real-world problems involve constraints that cannot be all satisfied. Solving an overconstrained problem then means to find solutions minimizing the number of constraints violated, which is an optimization problem. In this research, we study the behavior of the phase transitions and backbones of constraint optimization problems. We rst investigate the relationship between the phase transitions of Boolean satisfiability, or precisely 3-SAT (a well-studied NP-complete decision problem), and the phase transitions of MAX 3-SAT (an NP-hard optimization problem). To bridge the gap between the easy-hard-easy phase transitions of 3-SAT and the easy-hard transitions of MAX 3-SAT, we analyze bounded 3-SAT, in which solutions of bounded quality, e.g., solutions with at most a constant number of constraints violated, are sufficient.

This report describes and evaluates optimisation techniques for a tableaux based satisfiability testing algorithm used to compute subsumption in Grail, an expressive description logic. Five techniques are studied in detail: normalisation and encoding, indexing, semantic branching, dependency directed backtracking and caching. The effectiveness of these techniques is evaluated by empirical testing using a large knowledge base from the Galen project. The performance of the optimised classifier and subsumption test are also compared with that of the Kris classifier and KSAT satisfiability testing procedure using both the Galen knowledge base and randomly generated test data. 1 Introduction As part of the European Galen project the Medical Informatics Group at Manchester University have built a large concept model representing knowledge about medical terminology. The model is intended to promote sharing and re-use of medical data by acting as a flexible and extensible classification sche...

The paradigm of advisable planning,inwhichauser provides guidance to influence the content of solutions produced by an underlying planning system, holds much promise for improved usability of planning technology. The success of this approach, however, requires that a planner respond appropriately when presented with conflicting advice. This paper introduces two contrasting methods for planning with conflicting advice, suited to different user requirements. Soft enforcement embodies a heuristic approach that prefers planning choices that are consistent with specified advice but will disregard advice that introduces conflicts. Soft enforcement enables rapid generation of solutions but with suboptimal results. Local maxima search navigates through the space of advice subsets, using strict enforcement techniques to identify satisfiable subsets of advice. As more time is allocated, the search will yield increasingly better results. The paper presents specific algorithms f...

Many distributed problems can be captured as distributed constraint satisfaction problems (CSPs) and constraint optimization problems (COPs). In this research, we study an existing distributed search method, called distributed stochastic algorithm (DSA), and its variations for solving distributed CSPs and COPs. We analyze the relationship between the degree of parallel executions of distributed processes and DSAs ’ performance, including solution quality and communication cost. Our experimental results show that DSAs ’ performance exhibits phase-transition patterns. When the degree of parallel executions increases beyond some critical level, DSAs ’ performance degrades abruptly and dramatically, changing from near optimal solutions to solutions even worse than random solutions. Our experimental results also show that DSAs are generally more effective and efficient than distributed breakout algorithm on many network structures, particularly on over-constrained structures, finding better solutions and having lower communication cost.

A previously developed quantum search algorithm for solving 1-SAT problems in a single step is generalized to apply to a range of highly constrained k-SAT problems. We identify a bound on the number of clauses in satisfiability problems for which the generalized algorithm can find a solution in a constant number of steps as the number of variables increases. This performance contrasts with the linear growth in the number of steps required by the best classical algorithms, and the exponential number required by classical and quantum methods that ignore the problem structure. In some cases, the algorithm can also guarantee that insoluble problems in fact have no solutions, unlike previously proposed quantum search algorithms. 1. Introduction Quantum computers (Benioff, 1982; Bernstein & Vazirani, 1993; Deutsch, 1985, 1989; DiVincenzo, 1995; Feynman, 1986; Lloyd, 1993) offer a new approach to combinatorial search problems (Garey & Johnson, 1979) with quantum parallelism, i.e., the abilit...

Recent empirical and theoretical studies have shown that simple parameters characterizing constraint satisfaction problems predict whether they have a solution and the cost to solve them, on average. This paper examines the effectiveness of using these predictions as a heuristic for solving the graph coloring problem. Specifically, by adding some global information on the consequences of various choices, the use of these parameters can reduce the search required to find a solution. Current limitations of this approach, due to the high variance associated with the predictions, are also presented. More generally, observations of universal behaviors analogous to physical phase transitions can be applied to improve search methods. 1