Djamila Sam-Haroud

Consistency techniques for continuous constraints

We consider constraint satisfaction problems with variables in continuous, numerical domains. Contrary to most existing techniques, which focus on computing one single optimal solution, we address the problem of computing a compact representation of the space of all solutions admitted by the constraints. In particular, we show how globally consistent (also called decomposable) labelings of a constraint satisfaction problem can be computed.Our approach is based on approximating regions of feasible solutions by 2k-trees, a representation commonly used in computer vision and image processing. We give simple and stable algorithms for computing labelings with arbitrary degrees of consistency. The algorithms can process constraints and solution spaces of arbitrary complexity, but with a fixed maximal resolution.Previous work has shown that when constraints are convex and binary, path-consistency is sufficient to ensure global consistency. We show that for continuous domains, this result can be generalized to ternary and in fact arbitrary n-ary constraints using the concept of (3,2)-relational consistency. This leads to polynomial-time algorithms for computing globally consistent labelings for a large class of constraint satisfaction problems with continuous variables.

Global Optimization and Constraint Satisfaction

Constraint Satisfaction.- Efficient Pruning Technique Based on Linear Relaxations.- Inter-block Backtracking: Exploiting the Structure in Continuous CSPs.- Accelerating Consistency Techniques and Pronys Method for Reliable Parameter Estimation of Exponential Sums.- Global Optimization.- Convex Programming Methods for Global Optimization.- A Method for Global Optimization of Large Systems of Quadratic Constraints.- A Comparison of Methods for the Computation of Affine Lower Bound Functions for Polynomials.- Using a Cooperative Solving Approach to Global Optimization Problems.- Global Optimization of Convex Multiplicative Programs by Duality Theory.- Applications.- High-Fidelity Models in Global Optimization.- Incremental Construction of the Robots Environmental Map Using Interval Analysis.- Nonlinear Predictive Control Using Constraints Satisfaction.- Gas Turbine Model-Based Robust Fault Detection Using a Forward - Backward Test.- Benchmarking on Approaches to Interval Observation Applied to Robust Fault Detection.

Consistency Maintenance for ABT

One of the most powerful techniques for solving centralized constraint satisfaction problems (CSPs) consists of maintaining local consistency during backtrack search (e.g. [11]). Yet, no work has been reported on such a combination in asynchronous settings. The difficulty in this case is that, in the usual algorithms, the instantiation and consistency enforcement steps must alternate sequentially. When brought to a distributed setting, a similar approach forces the search algorithm to be synchronous in order to benefit from consistency maintenance. Asynchronism [24,14] is highly desirable since it increases flexibility and parallelism, and makes the solving process robust against timing variations. One of the most well-known asynchronous search algorithms is Asynchronous Backtracking (ABT). This paper shows how an algorithm for maintaining consistency during distributed asynchronous search can be designed upon ABT. The proposed algorithm is complete and has polynomial-space complexity. Since the consistency propagation is optional, this algorithms generalizes forward checking as well as chronological backtracking. An additional advance over existing centralized algorithms is that it can exploit available backtracking-nogoods for increasing the strength of the maintained consistency. The experimental evaluation shows that it can bring substantial gains in computational power compared with existing asynchronous algorithms.

ABT with Asynchronous Reordering

Existing Distributed Constraint Satisfaction (DisCSP) frameworks can model problems where a)variables and/or b)constraints are distributed among agents. Asynchronous Backtracking (ABT) is the first asynchronous complete algorithm for solving DisCSPs of type a. The order on variables is well-known as an important issue for constraint satisfaction. Previous polynomial space asynchronous algorithms require for completeness a static order on their variables. We show how agents can asynchronously and concurrently propose reordering in ABT while maintaining the completeness of the algorithm with polynomial space complexity.

Constraint techniques for collaborative design

The paper presents SpaceSolver, a constraint satisfaction toolbox, providing access to constraint satisfaction techniques on continuous variables through an intuitive, Web based user interface. Moreover, we describe possible applications of such a platform to collaborative design and conclude that Internet based use of constraint satisfaction techniques has the potential of increasing productivity in several fields in engineering.

Using directed acyclic graphs to coordinate propagation and search for numerical constraint satisfaction problems

The paper of H. Schichl & A. Neumaier has given the fundamentals of interval analysis on DAGs for global optimization and constraint propagation. We show in This work how constraint propagation on DAGs can be made efficient and practical by: (i) working on partial DAG representations; and (ii) enabling the flexible choice of the interval inclusion functions during propagation. We then propose a new simple algorithm, which coordinates constraint propagation and exhaustive search for solving numerical constraint satisfaction problems. The experiments carried out on different problems show that the new approach outperforms previously available propagation techniques by an order of magnitude or more in speed, while being roughly the same quality w.r.t. enclosure properties.

Dynamic distributed backjumping

We consider Distributed Constraint Satisfaction Problems (DisCSP) when control of variables and constraints is distributed among a set of agents. This paper presents a distributed version of the centralized BackJumping algorithm, called the Dynamic Distributed BackJumping – DDBJ algorithm. The advantage is twofold: DDBJ inherits the strength of synchronous algorithms that enables it to easily combine with a powerful dynamic ordering of variables and values, and still it maintains some level of autonomy for the agents. Experimental results show that DDBJ outperforms the DiDB and AFC algorithms by a factor of one to two orders of magnitude on hard instances of randomly generated DisCSPs.

Numerical Constraint Satisfaction Problems with Non-isolated Solutions

In recent years, interval constraint-based solvers have shown their ability to efficiently solve complex instances of non-linear numerical CSPs. However, most of the working systems are designed to deliver point-wise solutions with an arbitrary accuracy. This works generally well for systems with isolated solutions but less well when there is a continuum of feasible points (e.g. under-constrained problems, problems with inequalities). In many practical applications, such large sets of solutions express equally relevant alternatives which need to be identified as completely as possible. In this paper, we address the issue of constructing concise inner and outer approximations of the complete solution set for non-linear CSPs. We propose a technique which combines the extreme vertex representation of orthogonal polyhedra 1,2,3, as defined in computational geometry, with adapted splitting strategies 4 to construct the approximations as unions of interval boxes. This allows for compacting the explicit representation of the complete solution set and improves efficiency.

Approximation Techniques for Non-linear Problems with Continuum of Solutions

Most of the working solvers for numerical constraint satisfaction problems (NCSPs) are designed to delivering point-wise solutions with an arbitrary accuracy. When there is a continuum of feasible points this might lead to prohibitively verbose representations of the output. In many practical applications, such large sets of solutions express equally relevant alternatives which need to be identified as completely as possible. The goal of this paper is to show that by using appropriate approximation techniques, explicit representations of the solution sets, preserving both accuracy and completeness, can still be proposed for NCSPs with continuum of solutions. We present a technique for constructing concise inner and outer approximations as unions of interval boxes. The proposed technique combines a new splitting strategy with the extreme vertex representation of orthogonal polyhedra [1,2,3], as defined in computational geometry. This allows for compacting the representation of the approximations and improves efficiency.

Enhancing numerical constraint propagation using multiple inclusion representations

Building tight and conservative enclosures of the solution set is of crucial importance in the design of efficient complete solvers for numerical constraint satisfaction problems (NCSPs). This paper proposes a novel generic algorithm enabling the cooperative use, during constraint propagation, of multiple enclosure techniques. The new algorithm brings into the constraint propagation framework the strength of techniques coming from different areas such as interval arithmetic, affine arithmetic, and mathematical programming. It is based on the directed acyclic graph (DAG) representation of NCSPs whose flexibility and expressiveness facilitates the design of fine-grained combination strategies for general factorable systems. The paper presents several possible combination strategies for creating practical instances of the generic algorithm. The experiments reported on a particular instance using interval constraint propagation, interval arithmetic, affine arithmetic, and linear programming illustrate the flexibility and efficiency of the approach.