Alban Grastien

AC-Feasibility on Tree Networks is NP-Hard

Recent years have witnessed significant interest in convex relaxations of the power flows, with several papers showing that the second-order cone relaxation is tight for tree networks under various conditions on loads or voltages. This paper shows that ac-feasibility, i.e., to find whether some generator dispatch can satisfy a given demand, is NP-hard for tree networks.

Monitoring Web service networks in a model-based approach

The goal of Web service effort is to achieve universal interoperability between applications by using Web standards: this emergent technology is a promising way to integrate business applications. A business process can then be seen as a set of Web services that could belong to different companies and interact with each other by sending messages. In that context, neither a global model nor a global mechanism is available to monitor and trace faults when the business process fails. In this paper, we address this issue and propose to use model-based reasoning approaches on discrete-event systems (DES). This paper presents an automatic method to model Web service behaviors and their interactions as a set of synchronized discrete-event systems. This modeling is the first step before tracing the evolution of the business process and diagnosing business process faults.

Alarm processing with model-based diagnosis of event discrete systems

Reliable and informative alarm processing is important for improving the situational awareness of operators of electricity networks and other complex systems. Earlier approaches to alarm processing have been predominantly syntactic, based on text-level filtering of alarm sequences or shallow models of the monitored system. We argue that a deep understanding of the current state of the system being monitored is a prerequisite for more advanced forms of alarm processing. We use a model-based approach to infer the (unobservable) events behind alarms and to determine causal connections between events and alarms. Based on this information, we propose implementations of several forms of alarm processing functionalities. We demonstrate and evaluate the resulting framework with data from an Australian transmission network operator.

Optimal any-angle pathfinding in practice

Any-angle pathfinding is a fundamental problem in robotics and computer games. The goal is to find a shortest path between a pair of points on a grid map such that the path is not artificially constrained to the points of the grid. Prior research has focused on approximate online solutions. A number of exact methods exist but they all require super-linear space and pre-processing time. In this study, we describe Anya: a new and optimal any-angle pathfinding algorithm. Where other works find approximate any-angle paths by searching over individual points from the grid, Anya finds optimal paths by searching over sets of states represented as intervals. Each interval is identified on-the-fly. From each interval Anya selects a single representative point that it uses to compute an admissible cost estimate for the entire set. Anya always returns an optimal path if one exists. Moreover it does so without any offine pre-processing or the introduction of additional memory overheads. In a range of empirical comparisons we show that Anya is competitive with several recent (sub-optimal) online and pre-processing based techniques and is up to an order of magnitude faster than the most common benchmark algorithm, a grid-based implementation of A.

Diagnosis of Discrete Event Systems Using Satisfiability Algorithms: A Theoretical and Empirical Study

We propose a novel algorithm for the diagnosis of systems modelled as discrete event systems. Instead of computing all paths of the model that are consistent with the observations, we use a two-level approach: at the first level diagnostic questions are generated in the form does there exist a path from a given subset that is consistent with the observations?, whilst at the second level a satisfiability (SAT) solver is used to answer the questions. Our experiments show that this approach, implemented in SAT, can solve problems that we could not solve with other techniques.

Verifying the precision of diagnostic algorithms

Diagnosis of discrete event systems requires to decide whether the system model allows for certain types of executions to take place. Because this problem is hard, incomplete yet faster algorithms may be needed. This however can lead to a loss of precision. This paper presents a method to decide whether precision is maintained by such incomplete algorithms. To this end we define the Simulation, which is a modification of the model that simulates how the algorithm works. We then use the twin plant method to decide whether diagnosability is maintained despite the imprecision of the diagnostic algorithm. We illustrate the benefits of this approach on two diagnostic algorithms, namely Independent-Windows Algorithms and Chronicle-based Diagnosis.

Critical observations in a diagnostic problem

We claim that presenting a human operator in charge of repairing a faulty system with a small subset of observations relevant to the failure improves awareness and confidence of the operator. Consequently, we introduce the problem of finding a set of relevant observations (called the critical observations) that can be used to derive the same diagnosis as the full problem. We show how this problem can be solved and illustrate its benefits on a real diagnostic problem.

Diagnostic de systèmes à événements discrets à base de cohérence par SAT

We present a new, two-level-based, technique for the diagnosis of discrete-event systems. The first level transforms the diagnosis problem in a sequence of diagnosis questions. The second level answers the diagnosis questions. We propose to implement this second level with a SAT solver. This two-level algorithm allows to explain the observations and to generate a diagnosis of the system. Our experiments show that the SAT-based approach can solve problems that we could not solve with other techniques.

The Maximum Transmission Switching Flow Problem

The Maximum Transmission Switching Flow (MTSF) is the problem of maximizing the power flow of a power grid by switching off lines. This static transmission design problem is known to be NP-hard even on strongly restricted graph classes. In this paper, we study the combinatorial structure of the MTSF problem and its relationship to familiar problems. We tackle the problem by exploiting the structure of the power grid leading to the first algorithms for MTSF having provable performance guarantees. We decrease the theoretical gap not only by developing algorithms with guarantees, but also by proving that the decision problem of MTSF is NP-hard even when the network contains only one generator and one load. In this context, we introduce the Dominating Theta Path, which is an exact algorithm on certain graph structures and can be used as a switching metric in general. Our simulations show that the algorithms provide very good results (in many cases near-optimal) on the NESTA benchmark cases that provide realistic thermal line limits.

Diagnosability of Discrete Faults with Uncertain Observations

This chapter focuses on the discrete event-based transitions of a Hybrid System (HS), that is, it does not deal with the faults inside states, instead it takes into account the faults between states. Hence, the considered model is actually a Discrete-Event System (DES), say the DES underlying the HS, according to which a (type of) fault is one of the discrete events, usually an unobservable one, and a system can be affected by several types of faults. Diagnosability is the property that a DES exhibits if every fault can be detected and isolated within a finite number of (observable) events that have taken place after its occurrence. In the literature, diagnosability of DESs relies on the availability of a certain observation, which equals the sequence of observable events that have taken place in the DES. But can diagnosability be achieved even if the observation is uncertain? This chapter provides an answer to this question when the observation is temporally and/or logically uncertain, that is, when the order of the observed events and/or their (discrete) values are partially unknown. The original notion of compound observable event enables a smooth extension of both the definition of DES diagnosability in the literature and the twin plant method to check such a property. The intuition is to deal with a compound observable event the same way as with a single event. In case a DES is diagnosable even if its observation is uncertain, the diagnosis task can be performed (without any loss in the ability to identify every fault) although the available measuring equipment cannot get a certain observation.