Sequential Randomized Algorithms for Convex Optimization in the Presence of Uncertainty

In this paper, we propose new sequential randomized algorithms for convex optimization problems in the presence of uncertainty. A rigorous analysis of the theoretical properties of the solutions obtained by these algorithms, for full constraint satisfaction and partial constraint satisfaction, respectively, is given. The proposed methods allow to enlarge the applicability of the existing randomized methods to real-world applications involving a large number of design variables. Since the proposed approach does not provide a priori bounds on the sample complexity, extensive numerical simulations, dealing with an application to hard-disk drive servo design, are provided. These simulations testify the goodness of the proposed solution.Comment: 18 pages, Submitted for publication to IEEE Transactions on Automatic Contro

On the Efficiency of Backtracking Algorithms for Binary Constraint Satisfaction Problems

International audienceThe question of tractable classes of constraint satisfaction problems (CSPs) has been studied for a long time, and is now a very active research domain. However, studies of tractable classes are typically very theoretical. They usually introduce classes of instances together with polynomial time algorithms for recognizing and solving them, and the algorithms can be used only for the new class. In this paper, we address the issue of tractable classes of CSPs from a different perspective. We investigate the complexity of classical, generic algorithms for solving CSPs (such as Forward Checking). We introduce a new parameter for measuring their complexity and derive new complexity bounds. By relating the complexity of CSP algorithms to graph-theoretic parameters, our analysis allows us to point at new tractable classes, which can be solved directly by the usual CSP algorithms in polynomial time, and without the need to recognize the classes in advance

Limits of Preprocessing

We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability, Nonmonotonic and Bayesian Reasoning. We show that, subject to a complexity theoretic assumption, none of the considered problems can be reduced by polynomial-time preprocessing to a problem kernel whose size is polynomial in a structural problem parameter of the input, such as induced width or backdoor size. Our results provide a firm theoretical boundary for the performance of polynomial-time preprocessing algorithms for the considered problems.Comment: This is a slightly longer version of a paper that appeared in the proceedings of AAAI 201

Guarantees and Limits of Preprocessing in Constraint Satisfaction and Reasoning

We present a first theoretical analysis of the power of polynomial-time preprocessing for important combinatorial problems from various areas in AI. We consider problems from Constraint Satisfaction, Global Constraints, Satisfiability, Nonmonotonic and Bayesian Reasoning under structural restrictions. All these problems involve two tasks: (i) identifying the structure in the input as required by the restriction, and (ii) using the identified structure to solve the reasoning task efficiently. We show that for most of the considered problems, task (i) admits a polynomial-time preprocessing to a problem kernel whose size is polynomial in a structural problem parameter of the input, in contrast to task (ii) which does not admit such a reduction to a problem kernel of polynomial size, subject to a complexity theoretic assumption. As a notable exception we show that the consistency problem for the AtMost-NValue constraint admits a polynomial kernel consisting of a quadratic number of variables and domain values. Our results provide a firm worst-case guarantees and theoretical boundaries for the performance of polynomial-time preprocessing algorithms for the considered problems.Comment: arXiv admin note: substantial text overlap with arXiv:1104.2541, arXiv:1104.556

Constraint satisfaction adaptive neural network and heuristics combined approaches for generalized job-shop scheduling

Copyright @ 2000 IEEEThis paper presents a constraint satisfaction adaptive neural network, together with several heuristics, to solve the generalized job-shop scheduling problem, one of NP-complete constraint satisfaction problems. The proposed neural network can be easily constructed and can adaptively adjust its weights of connections and biases of units based on the sequence and resource constraints of the job-shop scheduling problem during its processing. Several heuristics that can be combined with the neural network are also presented. In the combined approaches, the neural network is used to obtain feasible solutions, the heuristic algorithms are used to improve the performance of the neural network and the quality of the obtained solutions. Simulations have shown that the proposed neural network and its combined approaches are efficient with respect to the quality of solutions and the solving speed.This work was supported by the Chinese National Natural Science Foundation under Grant 69684005 and the Chinese National High-Tech Program under Grant 863-511-9609-003, the EPSRC under Grant GR/L81468

Experimental evaluation of preprocessing algorithms for constraint satisfaction problems

This paper presents an experimental evaluation of two orthogonal schemes for preprocessing constraint satisfaction problems (CSPs). The first of these schemes involves a class of local consistency techniques that includes directional arc consistency, directional path consistency, and adaptive consistency. The other scheme concerns the prearrangement of variables in a linear order to facilitate an efficient search. In the first series of experiments, we evaluated the effect of each of the local consistency techniques on backtracking and its common enhancement, backjumping. Surprizingly, although adaptive consistency has the best worst-case complexity bounds, we have found that it exhibits the worst performance, unless the constraint graph was very sparse. Directional arc consistency (followed by either backjumping or backtracking) and backjumping (without any pre-processing) outperformed all other techniques; moreover, the former dominated the latter in computationally intensive situations. The second series of experiments suggests that maximum cardinality and minimum width arc the best pre-ordering (i.e., static ordering) strategies, while dynamic search rearrangement is superior to all the preorderings studied

Many Hard Examples in Exact Phase Transitions with Application to Generating Hard Satisfiable Instances

This paper first analyzes the resolution complexity of two random CSP models (i.e. Model RB/RD) for which we can establish the existence of phase transitions and identify the threshold points exactly. By encoding CSPs into CNF formulas, it is proved that almost all instances of Model RB/RD have no tree-like resolution proofs of less than exponential size. Thus, we not only introduce new families of CNF formulas hard for resolution, which is a central task of Proof-Complexity theory, but also propose models with both many hard instances and exact phase transitions. Then, the implications of such models are addressed. It is shown both theoretically and experimentally that an application of Model RB/RD might be in the generation of hard satisfiable instances, which is not only of practical importance but also related to some open problems in cryptography such as generating one-way functions. Subsequently, a further theoretical support for the generation method is shown by establishing exponential lower bounds on the complexity of solving random satisfiable and forced satisfiable instances of RB/RD near the threshold. Finally, conclusions are presented, as well as a detailed comparison of Model RB/RD with the Hamiltonian cycle problem and random 3-SAT, which, respectively, exhibit three different kinds of phase transition behavior in NP-complete problems.Comment: 19 pages, corrected mistakes in Theorems 5 and