Dueling CSP representations: Local search in the primal versus dual constraint graph.

Constraint Satisfaction Problems (CSPs) can be used to represent and solve many problems in Artificial Intelligence and the real world. When solving Constraint Satisfaction Problems, many of the methods developed and studied have focused only on the solution of binary CSPs while a large portion of real life problems are naturally modeled as non-binary CSPs. In this thesis we have designed an empirical study to investigate the behaviour of several local search methods in primal and dual constraint graph representations when solving non-binary CSPs. Local search methods tend to find a solution quickly since they generally give up the guarantee of completeness for polynomial time performance. Such local search methods include simple hill-climbing, steepest ascent hill-climbing and min-conflicts heuristics hill-climbing. We evaluate the performance of these three algorithms in each representation for a variety of parameter settings and we compare the search time cost means of two groups to support the comparison. Our comparison shows that we can use local search to solve a CSP with tight constraints in its dual representation and gain a better performance than using it in its primal representation. When constraints are getting looser, using local search in primal representation is a better choice. Among the three local search methods used in our empirical study, min-conflicts heuristics hill-climbing always gain the best performance while steepest ascent hill-climbing tends to have the worst performance and simple hill climbing is in the middle or sometimes it is the best. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2004 .H824. Source: Masters Abstracts International, Volume: 43-01, page: 0237. Adviser: Scott Goodwin. Thesis (M.Sc.)--University of Windsor (Canada), 2004

A KNOWLEDGE REPRESENTATION FOR CONSTRAINT SATISFACTION PROBLEMS

In this paper we present a general representation for constraint satisfaction problems (CSP) and a - framework for reasoning about their solution that unlike most constraint-based relaxation algorithms. stresses the need for a "natural" encoding of constraint knowledge and can facilitate making inferences for propagation, backtracking, and explanation. The representation consists of two components: a generate-and-test problem solver which contains information about the problem variables, and a constraint-driven reasoner that manages a set of constraints, specified as arbitrarily complex Boolean expressions and represented in the form of a constraint network. This constraint network: incorporates control information (reflected in the syntax of the constraints) that is used for constraint propagation: contains dependency information that can be used for explanation and for dependency-directed backtracking; and is incremental in the sense that if the problem specification is modified, a new solution can be derived by modifying the existing solution.Information Systems Working Papers Serie

Modelling and solving temporal reasoning as propositional satisfiability

AbstractRepresenting and reasoning about time dependent information is a key research issue in many areas of computer science and artificial intelligence. One of the best known and widely used formalisms for representing interval-based qualitative temporal information is Allen's interval algebra (IA). The fundamental reasoning task in IA is to find a scenario that is consistent with the given information. This problem is in general NP-complete.In this paper, we investigate how an interval-based representation, or IA network, can be encoded into a propositional formula of Boolean variables and/or predicates in decidable theories. Our task is to discover whether satisfying such a formula can be more efficient than finding a consistent scenario for the original problem. There are two basic approaches to modelling an IA network: one represents the relations between intervals as variables and the other represents the end-points of each interval as variables. By combining these two approaches with three different Boolean satisfiability (SAT) encoding schemes, we produced six encoding schemes for converting IA to SAT. In addition, we also showed how IA networks can be formulated into satisfiability modulo theories (SMT) formulae based on the quantifier-free integer difference logic (QF-IDL). These encodings were empirically studied using randomly generated IA problems of sizes ranging from 20 to 100 nodes. A general conclusion we draw from these experimental results is that encoding IA into SAT produces better results than existing approaches. More specifically, we show that the new point-based 1-D support SAT encoding of IA produces consistently better results than the other alternatives considered. In comparison with the six different SAT encodings, the SMT encoding came fourth after the point-based and interval-based 1-D support schemes and the point-based direct scheme. Further, we observe that the phase transition region maps directly from the IA encoding to each SAT or SMT encoding, but, surprisingly, the location of the hard region varies according to the encoding scheme. Our results also show a fixed performance ranking order over the various encoding schemes

Scalable intelligent electronic catalogs

The world today is full of information systems which make huge quantities of information available. This incredible amount of information is clearly overwhelming Internet endusers. As a consequence, intelligent tools to identify worthwhile information are needed, in order to fully assist people in finding the right information. Moreover, most systems are ultimately used, not just to provide information, but also to solve problems. Encouraged by the growing popular success of Internet and the enormous business potential of electronic commerce, e-catalogs have been consolidated as one of the most relevant types of information systems. Nearly all currently available electronic catalogs are offering tools for extracting product information based on key-attribute filtering methods. The most advanced electronic catalogs are implemented as recommender systems using collaborative filtering techniques. This dissertation focuses on strategies for coping with the difficulty of building intelligent catalogs which fully support the user in his purchase decision-making process, while maintaining the scalability of the whole system. The contributions of this thesis lie on a mixed-initiative system which is inspired by observations on traditional commerce activities. Such a conversational model consists basically of a dialog between the customer and the system, where the user criticizes proposed products and the catalog suggests new products accordingly. Constraint satisfaction techniques are analyzed in order to provide a uniform framework for modeling electronic catalogs for configurable products. Within the same framework, user preferences and optimization constraints are also easily modeled. Searching strategies for proposing the adequate products according to criteria are described in detail. Another dimension of this dissertation faces the problem of scalability, i.e., the problem of supporting hundreds, or thousands of users simultaneously using intelligent electronic catalogs. Traditional wisdom would presume that in order to provide full assistance to users in complex tasks, the business logic of the system must be complex, thus preventing scalability. SmartClient is a software architectural model that uses constraint satisfaction problems for representing solution spaces, instead of traditional models which represent solution spaces by collections of single solutions. This main idea is supported by the fact that constraint solvers are extreme in their compactness and simplicity, while providing sophisticated business logic. Different SmartClient architecture configurations are provided for different uses and architectural requirements. In order to illustrate the use of constraint satisfaction techniques for complex electronic catalogs with the SmartClient architecture, a commercial Internet-based application for travel planning, called reality, has been successfully developed. Travel planning is a particularly appropriate domain for validating the results of this research, since travel information is dynamic, travel planning problems are combinatorial, and moreover, complex user preferences and optimization constraints must be taken into consideration

Constraints and AI Planning

The University of Edinburgh and research sponsors are authorised to reproduce and distribute reprints and on-line copies for their purposes notwithstanding any copyright annotation hereon. The views and conclusions contained herein are the authorâ s and shouldnâ t be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of other parties.Tackling real-world problems often requires to take various types of constraints into account. Such constraint types range from simple numerical comparators to complex resources. This article describes how planning techniques can be integrated with general constraint-solving frameworks, like SAT, IP and CP. In many cases, the complete planning problem can be cast in these frameworks

Using Restarts in Constraint Programming over Finite Domains - An Experimental Evaluation

The use of restart techniques in complete Satisfiability (SAT) algorithms has made solving hard real world instances possible. Without restarts such algorithms could not solve those instances, in practice. State of the art algorithms for SAT use restart techniques, conflict clause recording (nogoods), heuristics based on activity variable in conflict clauses, among others. Algorithms for SAT and Constraint problems share many techniques; however, the use of restart techniques in constraint programming with finite domains (CP(FD)) is not widely used as it is in SAT. We believe that the use of restarts in CP(FD) algorithms could also be the key to efficiently solve hard combinatorial problems. In this PhD thesis we study restarts and associated techniques in CP(FD) solvers. In particular, we propose to including in a CP(FD) solver restarts, nogoods and heuristics based in nogoods as this should improve search algorithms, and, consequently, efficiently solve hard combinatorial problems. We thus intend to: a) implement restart techniques (successfully used in SAT) to solve constraint problems with finite domains; b) implement nogoods (learning) and heuristics based on nogoods, already in use in SAT and associated with restarts; and c) evaluate the use of restarts and the interplay with the other implemented techniques. We have conducted the study in the context of domain splitting backtrack search algorithms with restarts. We have defined domain splitting nogoods that are extracted from the last branch of the search algorithm before the restart. And, inspired by SAT solvers, we were able to use information within those nogoods to successfully help the variable selection heuristics. A frequent restart strategy is also necessary, since our approach learns from restarts

Working Notes from the 1992 AAAI Spring Symposium on Practical Approaches to Scheduling and Planning

The symposium presented issues involved in the development of scheduling systems that can deal with resource and time limitations. To qualify, a system must be implemented and tested to some degree on non-trivial problems (ideally, on real-world problems). However, a system need not be fully deployed to qualify. Systems that schedule actions in terms of metric time constraints typically represent and reason about an external numeric clock or calendar and can be contrasted with those systems that represent time purely symbolically. The following topics are discussed: integrating planning and scheduling; integrating symbolic goals and numerical utilities; managing uncertainty; incremental rescheduling; managing limited computation time; anytime scheduling and planning algorithms, systems; dependency analysis and schedule reuse; management of schedule and plan execution; and incorporation of discrete event techniques

Managing Complex Scheduling Problems with Dynamic and Hybrid Constraints.

The task of scheduling can often be a difficult one because of the inherent complexity of real-world problems. In the field of Artificial Intelligence, many representations and algorithms have been developed to automate the scheduling process. Many state of the art scheduling systems deal with this complexity by making assumptions that simplify the algorithms, but in doing so, miss some opportunities to improve performance. Scheduling problems are temporal in nature, and so they often contain constraints that change over time. Many scheduling systems assume that the problems they are solving are all independent, and so they ignore the similarities between subsequent sets of scheduling constraints. Additionally, scheduling problems often contain a mixture of finite-domain and temporal constraints. Many of the systems that can solve problems of this type do so by creating finite-domain variables to represent the constraints, but then ignore the distinction between the different types of variables when searching for a solution. In this dissertation, I identify opportunities to improve performance by exploiting structure where it has previously been overlooked. Following this approach, I develop a set of techniques that apply to a wide variety of situations that can arise in real-world scheduling problems. First, I consider dynamic scheduling problems with constraints that change over time. To address such problems, I introduce a new representation called the Dynamic Disjunctive Temporal Problem, along with several techniques to improve both efficiency and stability when solving one. Second, I consider scheduling problems in which a mixture of finite-domain and temporal variables can interact through hybrid constraints. I introduce the Hybrid Scheduling Problem to represent such problems, and I present a set of techniques that capitalize on the distinction between variable types to improve efficiency across the problem space. Finally, I conclude by proposing several ways that the dynamic and hybrid representations and techniques can be combined. To compare many of the techniques presented throughout this dissertation in the context of structured, real-world problems, I use them to solve scheduling problems based on actual air traffic control constraints recorded from the Dallas/Fort Worth International Airport.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/57625/2/pschwart_1.pd