Consistency techniques for the localization of a satellite

International audienceThis paper recalls that the problem of estimating the state vector of a nonlinear dynamic system can be interpreted as a constraint satisfaction problem over continuous domains with a large number (several thousands) of variables and constraints. Consistency techniques are then shown to be particularly efficient to contract the domains for the variables involved. This is probably due to the large number of redundancies naturally involved in the constraints of the problem. The approach is illustrated on the estimation of the position of a satellite in orbit around the earth

Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings

Constraint programming is a paradigm wherein relations between variables are stated in the form of constraints. Many real life problems come from uncertain and dynamic environments, where the initial constraints and domains may change during its execution. Thus, the solution found for the problem may become invalid. The search forrobustsolutions for constraint satisfaction problems (CSPs) has become an important issue in the ¿eld of constraint programming. In some cases, there exists knowledge about the uncertain and dynamic environment. In other cases, this information is unknown or hard to obtain. In this paper, we consider CSPs with discrete and ordered domains where changes only involve restrictions or expansions of domains or constraints. To this end, we model CSPs as weighted CSPs (WCSPs) by assigning weights to each valid tuple of the problem constraints and domains. The weight of each valid tuple is based on its distance from the borders of the space of valid tuples in the corresponding constraint/domain. This distance is estimated by a new concept introduced in this paper: coverings. Thus, the best solution for the modeled WCSP can be considered as a most robust solution for the original CSP according to these assumptionsThis work has been partially supported by the research projects TIN2010-20976-C02-01 (Min. de Ciencia e Innovacion, Spain) and P19/08 (Min. de Fomento, Spain-FEDER), and the fellowship program FPU.Climent Aunés, LI.; Wallace, RJ.; Salido Gregorio, MA.; Barber Sanchís, F. (2013). Finding robust solutions for constraint satisfaction problems with discrete and ordered domains by coverings. Artificial Intelligence Review. 1-26. https://doi.org/10.1007/s10462-013-9420-0S126Climent L, Salido M, Barber F (2011) Reformulating dynamic linear constraint satisfaction problems as weighted csps for searching robust solutions. 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Robust fault detection using consistency techniques for uncertainty handling

Often practical performance of analytical redundancy for fault detection and diagnosis is decreased by uncertainties prevailing not only in the system model, but also in the measurements. In this paper, the problem of fault detection is stated as a constraint satisfaction problem over continuous domains with a big number of variables and constraints. This problem can be solved using modal interval analysis and consistency techniques. Consistency techniques are then shown to be particularly efficient to check the consistency of the analytical redundancy relations (ARRs), dealing with uncertain measurements and parameters. Through the work presented in this paper, it can be observed that consistency techniques can be used to increase the performance of a robust fault detection tool, which is based on interval arithmetic. The proposed method is illustrated using a nonlinear dynamic model of a hydraulic syste

Biased landscapes for random Constraint Satisfaction Problems

The typical complexity of Constraint Satisfaction Problems (CSPs) can be investigated by means of random ensembles of instances. The latter exhibit many threshold phenomena besides their satisfiability phase transition, in particular a clustering or dynamic phase transition (related to the tree reconstruction problem) at which their typical solutions shatter into disconnected components. In this paper we study the evolution of this phenomenon under a bias that breaks the uniformity among solutions of one CSP instance, concentrating on the bicoloring of k-uniform random hypergraphs. We show that for small k the clustering transition can be delayed in this way to higher density of constraints, and that this strategy has a positive impact on the performances of Simulated Annealing algorithms. We characterize the modest gain that can be expected in the large k limit from the simple implementation of the biasing idea studied here. This paper contains also a contribution of a more methodological nature, made of a review and extension of the methods to determine numerically the discontinuous dynamic transition threshold.Comment: 32 pages, 16 figure

Solving Factored MDPs with Hybrid State and Action Variables

Efficient representations and solutions for large decision problems with continuous and discrete variables are among the most important challenges faced by the designers of automated decision support systems. In this paper, we describe a novel hybrid factored Markov decision process (MDP) model that allows for a compact representation of these problems, and a new hybrid approximate linear programming (HALP) framework that permits their efficient solutions. The central idea of HALP is to approximate the optimal value function by a linear combination of basis functions and optimize its weights by linear programming. We analyze both theoretical and computational aspects of this approach, and demonstrate its scale-up potential on several hybrid optimization problems

A reusable iterative optimization software library to solve combinatorial problems with approximate reasoning

Real world combinatorial optimization problems such as scheduling are typically too complex to solve with exact methods. Additionally, the problems often have to observe vaguely specified constraints of different importance, the available data may be uncertain, and compromises between antagonistic criteria may be necessary. We present a combination of approximate reasoning based constraints and iterative optimization based heuristics that help to model and solve such problems in a framework of C++ software libraries called StarFLIP++. While initially developed to schedule continuous caster units in steel plants, we present in this paper results from reusing the library components in a shift scheduling system for the workforce of an industrial production plant.Comment: 33 pages, 9 figures; for a project overview see http://www.dbai.tuwien.ac.at/proj/StarFLIP

Manufacturing requirements in design: The RTM process in aeronautics

A sub-unit of an aeronautical structure (fuselage, fin, wing, etc.) consists of a set of components fixed rigidly together. One of today’s major industrial challenges is to produce these sub-units out of composite materials in order to increase the level of integration and reduce and cost. This article describes a procedure to assist in the industrialisation of aeronautical components produced from composite materials in a design for manufacturing context. In a multi-expertise approach, the problem of optimising integration is combined with the feasibility of injection for the Resin Transfer Molding process. This approach then takes into account admissible manufacturing deviations, defined from a classification of the structure parts. The limits set for admissible deviations guarantee the mechanical behaviour of the assembled component and the requirements of the assembly as a whole. Finally, an industrialisation solutions space is defined. A constraint satisfaction problem solver is used to carry out this research with a spar from a horizontal plane in an aircraft used to illustrate the procedure

A Landscape Analysis of Constraint Satisfaction Problems

We discuss an analysis of Constraint Satisfaction problems, such as Sphere Packing, K-SAT and Graph Coloring, in terms of an effective energy landscape. Several intriguing geometrical properties of the solution space become in this light familiar in terms of the well-studied ones of rugged (glassy) energy landscapes. A `benchmark' algorithm naturally suggested by this construction finds solutions in polynomial time up to a point beyond the `clustering' and in some cases even the `thermodynamic' transitions. This point has a simple geometric meaning and can be in principle determined with standard Statistical Mechanical methods, thus pushing the analytic bound up to which problems are guaranteed to be easy. We illustrate this for the graph three and four-coloring problem. For Packing problems the present discussion allows to better characterize the `J-point', proposed as a systematic definition of Random Close Packing, and to place it in the context of other theories of glasses.Comment: 17 pages, 69 citations, 12 figure