Constraint satisfaction techniques under uncertain conditions for fault diagnosis in nonlinear dynamic systems

The speed of fault isolation is crucial for the design and reconfiguration of fault tolerant control (FTC). In this paper the fault isolation problem is stated as a constraint satisfaction problem (CSP) and solved using constraint propagation techniques. The proposed method is based on constraint satisfaction techniques and uncertainty space refining of interval parameters. In comparison with other approaches based on adaptive observers, the major advantage of the presented method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements and model errors and without the monotonicity assumption. In order to illustrate the proposed approach, a case study of a nonlinear dynamic system is presented

Region Connection Calculus: Composition Tables and Constraint Satisfaction Problems

Qualitative spatial reasoning (QSR) is an important field of AI that deals with qualitative aspects of spatial entities. Regions and their relationships are described in qualitative terms instead of numerical values. This approach models human based reasoning about such entities closer than other approaches. Any relationships between regions that we encounter in our daily life situations are normally formulated in natural language. For example, one can outline one's room plan to an expert by indicating which rooms should be connected to each other. Mereotopology as an area of QSR combines mereology, topology and algebraic methods. As mereotopology plays an important role in region based theories of space, our focus is on one of the most widely referenced formalisms for QSR, the region connection calculus (RCC). RCC is a first order theory based on a primitive connectedness relation, which is a binary symmetric relation satisfying some additional properties. By using this relation we can define a set of basic binary relations which have the property of being jointly exhaustive and pairwise disjoint (JEPD), which means that between any two spatial entities exactly one of the basic relations hold. Basic reasoning can now be done by using the composition operation on relations whose results are stored in a composition table. Relation algebras (RAs) have become a main entity for spatial reasoning in the area of QSR. These algebras are based on equational reasoning which can be used to derive further relations between regions in a certain situation. Any of those algebras describe the relation between regions up to a certain degree of detail. In this thesis we will use the method of splitting atoms in a RA in order to reproduce known algebras such as RCC15 and RCC25 systematically and to generate new algebras, and hence a more detailed description of regions, beyond RCC25.

Safe Distributed Coordination of Heterogeneous Robots through Dynamic Simple Temporal Networks

Research on autonomous intelligent systems has focused on how robots can robustly carry out missions in uncertain and harsh environments with very little or no human intervention. Robotic execution languages such as RAPs, ESL, and TDL improve robustness by managing functionally redundant procedures for achieving goals. The model-based programming approach extends this by guaranteeing correctness of execution through pre-planning of non-deterministic timed threads of activities. Executing model-based programs effectively on distributed autonomous platforms requires distributing this pre-planning process. This thesis presents a distributed planner for modelbased programs whose planning and execution is distributed among agents with widely varying levels of processor power and memory resources. We make two key contributions. First, we reformulate a model-based program, which describes cooperative activities, into a hierarchical dynamic simple temporal network. This enables efficient distributed coordination of robots and supports deployment on heterogeneous robots. Second, we introduce a distributed temporal planner, called DTP, which solves hierarchical dynamic simple temporal networks with the assistance of the distributed Bellman-Ford shortest path algorithm. The implementation of DTP has been demonstrated successfully on a wide range of randomly generated examples and on a pursuer-evader challenge problem in simulation.

Constraint satisfaction techniques under uncertain conditions for fault diagnosis in nonlinear dynamic systems

The speed of fault isolation is crucial for the design and reconfiguration of fault tolerant control (FTC). In this paper the fault isolation problem is stated as a constraint satisfaction problem (CSP) and solved using constraint propagation techniques. The proposed method is based on constraint satisfaction techniques and uncertainty space refining of interval parameters. In comparison with other approaches based on adaptive observers, the major advantage of the presented method is that the isolation speed is fast even taking into account uncertainty in parameters, measurements and model errors and without the monotonicity assumption. In order to illustrate the proposed approach, a case study of a nonlinear dynamic system is presented

Compositional Model Repositories via Dynamic Constraint Satisfaction with Order-of-Magnitude Preferences

The predominant knowledge-based approach to automated model construction, compositional modelling, employs a set of models of particular functional components. Its inference mechanism takes a scenario describing the constituent interacting components of a system and translates it into a useful mathematical model. This paper presents a novel compositional modelling approach aimed at building model repositories. It furthers the field in two respects. Firstly, it expands the application domain of compositional modelling to systems that can not be easily described in terms of interacting functional components, such as ecological systems. Secondly, it enables the incorporation of user preferences into the model selection process. These features are achieved by casting the compositional modelling problem as an activity-based dynamic preference constraint satisfaction problem, where the dynamic constraints describe the restrictions imposed over the composition of partial models and the preferences correspond to those of the user of the automated modeller. In addition, the preference levels are represented through the use of symbolic values that differ in orders of magnitude.

Constraint-based analysis of gene interactions using restricted boolean networks and time-series data

Abstract Background A popular model for gene regulatory networks is the Boolean network model. In this paper, we propose an algorithm to perform an analysis of gene regulatory interactions using the Boolean network model and time-series data. Actually, the Boolean network is restricted in the sense that only a subset of all possible Boolean functions are considered. We explore some mathematical properties of the restricted Boolean networks in order to avoid the full search approach. The problem is modeled as a Constraint Satisfaction Problem (CSP) and CSP techniques are used to solve it. Results We applied the proposed algorithm in two data sets. First, we used an artificial dataset obtained from a model for the budding yeast cell cycle. The second data set is derived from experiments performed using HeLa cells. The results show that some interactions can be fully or, at least, partially determined under the Boolean model considered. Conclusions The algorithm proposed can be used as a first step for detection of gene/protein interactions. It is able to infer gene relationships from time-series data of gene expression, and this inference process can be aided by a priori knowledge available.

Addressing the facilities layout design problem through constraint logic programming

One of the most difficult problems that face researchers experimenting with complex systems in real world applications is the Facility Layout Design Problem. It relies with the design and location of production lines, machinery and equipment, inventory storage and shipping facilities. In this work it is intended to address this problem through the use of Constraint Logic Programming (CLP) technology. The use of Genetic Algorithms (GA) as optimisation technique in CLP environment is also an issue addressed. The approach aims the implementation of genetic algorithm operators following the CLP paradigm.

Constraint reasoning for differential models

The basic motivation of this work was the integration of biophysical models within the interval constraints framework for decision support. Comparing the major features of biophysical models with the expressive power of the existing interval constraints framework, it was clear that the most important inadequacy was related with the representation of differential equations. System dynamics is often modelled through differential equations but there was no way of expressing a differential equation as a constraint and integrate it within the constraints framework. Consequently, the goal of this work is focussed on the integration of ordinary differential equations within the interval constraints framework, which for this purpose is extended with the new formalism of Constraint Satisfaction Differential Problems. Such framework allows the specification of ordinary differential equations, together with related information, by means of constraints, and provides efficient propagation techniques for pruning the domains of their variables. This enabled the integration of all such information in a single constraint whose variables may subsequently be used in other constraints of the model. The specific method used for pruning its variable domains can then be combined with the pruning methods associated with the other constraints in an overall propagation algorithm for reducing the bounds of all model variables. The application of the constraint propagation algorithm for pruning the variable domains, that is, the enforcement of local-consistency, turned out to be insufficient to support decision in practical problems that include differential equations. The domain pruning achieved is not, in general, sufficient to allow safe decisions and the main reason derives from the non-linearity of the differential equations. Consequently, a complementary goal of this work proposes a new strong consistency criterion, Global Hull-consistency, particularly suited to decision support with differential models, by presenting an adequate trade-of between domain pruning and computational effort. Several alternative algorithms are proposed for enforcing Global Hull-consistency and, due to their complexity, an effort was made to provide implementations able to supply any-time pruning results. Since the consistency criterion is dependent on the existence of canonical solutions, it is proposed a local search approach that can be integrated with constraint propagation in continuous domains and, in particular, with the enforcing algorithms for anticipating the finding of canonical solutions. The last goal of this work is the validation of the approach as an important contribution for the integration of biophysical models within decision support. Consequently, a prototype application that integrated all the proposed extensions to the interval constraints framework is developed and used for solving problems in different biophysical domains.

Constraint reasoning with local search for continuous optimization

Optimization is a very important field for getting the best possible value for the optimization function. Continuous optimization is optimization over real intervals. There are many global and local search techniques. Global search techniques try to get the global optima of the optimization problem. However, local search techniques are used more since they try to find a local minimal solution within an area of the search space. In Continuous Constraint Satisfaction Problems (CCSP)s, constraints are viewed as relations between variables, and the computations are supported by interval analysis. The continuous constraint programming framework provides branch-and-prune algorithms for covering sets of solutions for the constraints with sets of interval boxes which are the Cartesian product of intervals. These algorithms begin with an initial crude cover of the feasible space (the Cartesian product of the initial variable domains) which is recursively refined by interleaving pruning and branching steps until a stopping criterion is satisfied. In this work, we try to find a convenient way to use the advantages in CCSP branchand- prune with local search of global optimization applied locally over each pruned branch of the CCSP. We apply local search techniques of continuous optimization over the pruned boxes outputted by the CCSP techniques. We mainly use steepest descent technique with different characteristics such as penalty calculation and step length. We implement two main different local search algorithms. We use “Procure”, which is a constraint reasoning and global optimization framework, to implement our techniques, then we produce and introduce our results over a set of benchmarks.

Generating highly balanced sudoku problems as hard problems

Sudoku problems are some of the most known and enjoyed pastimes, with a never diminishing popularity, but, for the last few years those problems have gone from an entertainment to an interesting research area, a twofold interesting area, in fact. On the one side Sudoku problems, being a variant of Gerechte Designs and Latin Squares, are being actively used for experimental design, as in [8, 44, 39, 9]. On the other hand, Sudoku problems, as simple as they seem, are really hard structured combinatorial search problems, and thanks to their characteristics and behavior, they can be used as benchmark problems for refining and testing solving algorithms and approaches. Also, thanks to their high inner structure, their study can contribute more than studies of random problems to our goal of solving real-world problems and applications and understanding problem characteristics that make them hard to solve. In this work we use two techniques for solving and modeling Sudoku problems, namely, Constraint Satisfaction Problem (CSP) and Satisfiability Problem (SAT) approaches. To this effect we define the Generalized Sudoku Problem (GSP), where regions can be of rectangular shape, problems can be of any order, and solution existence is not guaranteed. With respect to the worst-case complexity, we prove that GSP with block regions of m rows and n columns with m = n is NP-complete. For studying the empirical hardness of GSP, we define a series of instance generators, that differ in the balancing level they guarantee between the constraints of the problem, by finely controlling how the holes are distributed in the cells of the GSP. Experimentally, we show that the more balanced are the constraints, the higher the complexity of solving the GSP instances, and that GSP is harder than the Quasigroup Completion Problem (QCP), a problem generalized by GSP. Finally, we provide a study of the correlation between backbone variables – variables with the same value in all the solutions of an instance– and hardness of GSP.

Graphical constraints: a graphical user interface for constraint problems

A constraint satisfaction problem is a classical artificial intelligence paradigm characterized by a set of variables (each variable with an associated domain of possible values), and a set of constraints that specify relations among subsets of these variables. Solutions are assignments of values to all variables that satisfy all the constraints. Many real world problems may be modelled by means of constraints. The range of problems that can use this representation is very diverse and embraces areas like resource allocation, scheduling, timetabling or vehicle routing. Constraint programming is a form of declarative programming in the sense that instead of specifying a sequence of steps to execute, it relies on properties of the solutions to be found, which are explicitly defined by constraints. The idea of constraint programming is to solve problems by stating constraints which must be satisfied by the solutions. Constraint programming is based on specialized constraint solvers that take advantage of constraints to search for solutions. The success and popularity of complex problem solving tools can be greatly enhanced by the availability of friendly user interfaces. User interfaces cover two fundamental areas: receiving information from the user and communicating it to the system; and getting information from the system and deliver it to the user. Despite its potential impact, adequate user interfaces are uncommon in constraint programming in general. The main goal of this project is to develop a graphical user interface that allows to, intuitively, represent constraint satisfaction problems. The idea is to visually represent the variables of the problem, their domains and the problem constraints and enable the user to interact with an adequate constraint solver to process the constraints and compute the solutions. Moreover, the graphical interface should be capable of configure the solver’s parameters and present solutions in an appealing interactive way. As a proof of concept, the developed application – GraphicalConstraints – focus on continuous constraint programming, which deals with real valued variables and numerical constraints (equations and inequalities). RealPaver, a state-of-the-art solver in continuous domains, was used in the application. The graphical interface supports all stages of constraint processing, from the design of the constraint network to the presentation of the end feasible space solutions as 2D or 3D boxes.