Assigning satisfaction values to constraints: an algorithm to solve dynamic meta-constraints (original) (raw)

Constraint satisfaction---a survey

1998

Constraint satisfaction has been used as a term to cover a wide range of methods to solve problems stated in the form of a set of constraints. As the general constraint satisfaction problem (CSP) is NP-complete, initially the research focused on developing new and more efficient solution methods, resulting in an arsenal of algorithms. Recently, much attention has been paid on how to finetune the use of this arsenal, and to be able to judge which methods are promising for a given problem or problem-type. In the last few years different generalisations of the classical CSP have got much attention too, allowing to model a wider range of everyday problems. In this survey we introduce the classical CSP and the basic solution techniques as well as the ongoing research on the applicability of these methods and on extensions of the classical framework. After giving some introductory examples we define the most essential technical notions in order to explain different solution methods. First, we discuss constraint propagation algorithms, which transform the initially given CSP step by step to an equivalent, but smaller problem. Then we will introduce a family of constructive search algorithms, followed by methods exploiting the structure of the problem. Finally, we discuss the local and stochastic methods, also applicable to solve non-standard problems. The discussion of solution methods will be closed by addressing the issue of choosing a good algorithm for a given problem. Many practical applications have essential characteristics which do not "fit into" the classical formalism of CSP. The extension of the problem definition and appropriate solution methods will be dealt with in the final chapter.

New trends in constraint satisfaction, planning, and scheduling: a survey

The Knowledge Engineering Review, 2010

During recent years the development of new techniques for constraint satisfaction, planning, and scheduling has received increased attention, and substantial effort has been invested in trying to exploit such techniques to find solutions to real life problems. In this paper, we present a survey on constraint satisfaction, planning and scheduling from the Artificial Intelligence point of view. In particular, we present the main definitions and techniques, and we discuss possible ways of integrating such techniques. We also analyze the role of constraint satisfaction in planning and scheduling, and we hint at some open research issues related to planning, scheduling and constraint satisfaction. 2 ROMAN BARTÁK, MIGUEL A. SALIDO, FRANCESCA ROSSI very useful to prune the search space. We then present three families of search techniques: Look-Back, Look-Ahead, and local search. Finally, we discuss some variable and value ordering heuristics, that can improve the efficiency of the previous techniques.

Modeling Planning Problems Using Constraint Satisfaction

Planning problems deal with finding a sequence of actions that transfer the initial state of the world into a desired state. Frequently such problems are solved by dedicated algorithms but there exist planners based on translating the planning problem into a different formalism such as constraint satisfaction or Boolean satisfiability and using a general solver for this formalism. This paper describes the approach to modeling planning as constraint satisfaction and shows how to enhance the existing constraint models of planning problems by using techniques such as symmetry breaking (dominance rules), singleton consistency, nogood learning, and lifting.

Modelling and Reformulating Constraint Satisfaction Problems

Constraint Programming (CP) is a powerful technology to solve combinatorial problems which are ubiquitous in academia and industry. The last ten years or so have witnessed significant research devoted to modelling and solving problems with constraints. CP is now a mature field and has been successfully used for tackling a wide range of real-life complex applications. However, such a technology is currently accessible to only a small number of experts.

A Generalized Framework for Constraint Planning1

Citeseer

Constraint hierarchies have been proposed to solve over-constrained systems of constraints by specifying constraints with hierarchical preferences. They are widely used in HCLP, CIP and graphical user interfaces. A declarative expression of preferred constraints ...

Solution Techniques for Constraint Satisfaction Problems: Foundations

Artificial Intelligence Review, 2001

Conventional techniques for the constraint satisfaction problem (CSP) have had considerable success in their applications. However, there are many areas in which the performance of the basic approaches may be improved. These include heuristic ordering of certain tasks performed by the CSP solver, hybrids which combine compatible solution techniques and graph based methods which exploit the structure of the constraint graph representation of a CSP. Also, conventional constraint satisfaction techniques only address problems with hard constraints (i.e. each of which are completely satisfied or completely violated, and all of which must be satisfied by a valid solution). Many real applications require a more flexible approach which relaxes somewhat these rigid requirements. To address these issues various approaches have been developed. This paper attempts a systematic review of them.

Complex constraints management

Submitted for publication in ECAI

The purpose of this paper is to show a new approximation to manage complex constraints in the framework of CSP problems. Concretely we propose the use of a labelled-CSP to specify complex temporal constraints, as a particular case of constraints. This framework allows us to specify and solve the constraint set associated to several types of CSP problems in an integrated manner. The complex constraints that we can manage are represented by a set of non-disjunctive and disjunctive constraints. We can also associate a cost with the constraints, that can affect to the obtained solution. So, the advantages of this framework are its expressiveness, that allows to specify very complex constraints which are present in real problems, and the fact that all constraints are processed in the same way. 3

An Incremental Approach to Solving Dynamic Constraint Satisfaction Problems

Lecture Notes in Computer Science, 2012

Constraint satisfaction problems (CSPs) underpin many science and engineering applications. Recently introduced intelligent constraint handling evolutionary algorithm (ICHEA) in [14] has demonstrated strong potential in solving them through evolutionary algorithms (EAs). ICHEA outperforms many other evolutionary algorithms to solve CSPs with respect to success rate (SR) and efficiency. This paper is an enhancement of ICHEA to improve its efficiency and SR further by an enhancement of the algorithm to deal with local optima obstacles. The enhancement also includes a capability to handle dynamically introduced constraints without restarting the whole algorithm that uses the knowledge from already solved constraints using an incremental approach. Experiments on benchmark CSPs adapted as dynamic CSPs has shown very promising results.

Algorithms for Constraint-Satisfaction Problems: A Survey

Ai Magazine, 1992

A large number of problems in AI and other areas of computer science can be viewed as special cases of the constraint-satisfaction problem. Some examples are machine vision, belief maintenance, scheduling, temporal reasoning, graph problems, floor plan design, the planning of genetic experiments, and the satisfiability problem. A number of different approaches have been developed for solving these problems. Some of them use constraint propagation to simplify the original problem. Others use backtracking to directly search for possible solutions. Some are a combination of these two techniques. This article overviews many of these approaches in a tutorial fashion. Articles

Exploiting the constrainedness in constraint satisfaction problems

Artificial Intelligence: Methodology, Systems, and …, 2004

Nowadays, many real problem in Artificial Intelligence can be modeled as constraint satisfaction problems (CSPs). A general rule in constraint satisfaction is to tackle the hardest part of a search problem first. In this paper, we introduce a parameter (τ ) that measures the constrainedness of a search problem. This parameter represents the probability of the problem being feasible. A value of τ = 0 corresponds to an over-constrained problem and no states are expected to be solutions. A value of τ = 1 corresponds to an under-constrained problem which every state is a solution. This parameter can also be used in a heuristic to guide search. To achieve this parameter, a sample in finite population is carried out to compute the tightnesses of each constraint. We take advantage of this tightnesses to classify the constraints from the tightest constraint to the loosest constraint. This heuristic may accelerate the search due to inconsistencies can be found earlier and the number of constraint checks can significantly be reduced.