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See detailApproximate dynamic programming with a fuzzy parameterization
Busoniu, Lucian; Ernst, Damien ULg; De Schutter, Bart et al

in Automatica (2010), 46(5), 804-814

Dynamic programming (DP) is a powerful paradigm for general, nonlinear optimal control. Computing exact DP solutions is in general only possible when the process states and the control actions take values ... [more ▼]

Dynamic programming (DP) is a powerful paradigm for general, nonlinear optimal control. Computing exact DP solutions is in general only possible when the process states and the control actions take values in a small discrete set. In practice, it is necessary to approximate the solutions. Therefore, we propose an algorithm for approximate DP that relies on a fuzzy partition of the state space, and on a discretization of the action space. This fuzzy Q-iteration algorithm works for deterministic processes, under the discounted return criterion. We prove that fuzzy Q-iteration asymptotically converges to a solution that lies within a bound of the optimal solution. A bound on the suboptimality of the solution obtained in a finite number of iterations is also derived. Under continuity assumptions on the dynamics and on the reward function, we show that fuzzy Q-iteration is consistent, i.e., that it asymptotically obtains the optimal solution as the approximation accuracy increases. These properties hold both when the parameters of the approximator are updated in a synchronous fashion, and when they are updated asynchronously. The asynchronous algorithm is proven to converge at least as fast as the synchronous one. The performance of fuzzy Q-iteration is illustrated in a two-link manipulator control problem. [less ▲]

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See detailApproximate Numerical Continuation for Aeroelastic Systems Undergoing Aperiodic Limit Cycle Oscillations
Dimitriadis, Grigorios ULg

in Proceedings of the 2007 International Forum on Aeroelasticity and Structural Dynamics (2007, June)

This paper presents a modified numerical continuation approach for predicting the bifurcation behaviour of aeroelastic systems undergoing aperiodic limit cycles oscillations. Such oscillations can occur ... [more ▼]

This paper presents a modified numerical continuation approach for predicting the bifurcation behaviour of aeroelastic systems undergoing aperiodic limit cycles oscillations. Such oscillations can occur due to a number of nonlinear functions. Here, backlash nonlinearity in the aileron stiffness for a Generic Transport Aircraft is considered. It is shown that classical numerical continuation will fail due to the aperiodic nature of the limit cycles and the inability to perform period scaling and phase fixing. An alternative, approximate numerical continuation method is proposed, based on longer numerical integration sequences and a heuristic method for determining the period of the limit cycle oscillations. The approach is applied successfully to a simulated aeroelastic model of the Generic Transport Aircraft with backlash. [less ▲]

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See detailApproximate Policy Iteration for Closed-Loop Learning of Visual Tasks
Jodogne, Sébastien ULg; Briquet, Cyril ULg; Piater, Justus ULg

in Lecture Notes in Computer Science (2006, September), 4212

Approximate Policy Iteration (API) is a reinforcement learning paradigm that is able to solve high- dimensional, continuous control problems. We propose to exploit API for the closed-loop learning of ... [more ▼]

Approximate Policy Iteration (API) is a reinforcement learning paradigm that is able to solve high- dimensional, continuous control problems. We propose to exploit API for the closed-loop learning of mappings from images to actions. This approach requires a family of function approximators that maps visual percepts to a real-valued function. For this purpose, we use Regression Extra-Trees, a fast, yet accurate and versatile machine learning algorithm. The inputs of the Extra-Trees consist of a set of visual features that digest the informative patterns in the visual signal. We also show how to parallelize the Extra-Tree learning process to further reduce the computational expense, which is often essential in visual tasks. Experimental results on real-world images are given that indicate that the combination of API with Extra-Trees is a promising framework for the interactive learning of visual tasks. [less ▲]

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See detailApproximate reinforcement learning: an overview
Busoniu, Lucian; Babuska, Robert; De Schutter, Bart et al

in Proceedings of the 2011 IEEE International Symposium on Adaptive Dynamic Programming and Reinforcement Learning (ADPRL-11) (2011, April)

Reinforcement learning (RL) allows agents to learn how to optimally interact with complex environments. Fueled by recent advances in approximation-based algorithms, RL has obtained impressive successes in ... [more ▼]

Reinforcement learning (RL) allows agents to learn how to optimally interact with complex environments. Fueled by recent advances in approximation-based algorithms, RL has obtained impressive successes in robotics, artificial intelligence, control, operations research, etc. However, the scarcity of survey papers about approximate RL makes it difficult for newcomers to grasp this intricate field. With the present overview, we take a step toward alleviating this situation. We review methods for approximate RL, starting from their dynamic programming roots and organizing them into three major classes: approximate value iteration, policy iteration, and policy search. Each class is subdivided into representative categories, highlighting among others offline and online algorithms, policy gradient methods, and simulation-based techniques. We also compare the different categories of methods, and outline possible ways to enhance the reviewed algorithms. [less ▲]

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See detailApproximate value iteration in the reinforcement learning context. Application to electrical power system control
Ernst, Damien ULg; Glavic, Mevludin; Geurts, Pierre ULg et al

in International Journal of Emerging Electrical Power Systems (2005), 3(1),

In this paper we explain how to design intelligent agents able to process the information acquired from interaction with a system to learn a good control policy and show how the methodology can be applied ... [more ▼]

In this paper we explain how to design intelligent agents able to process the information acquired from interaction with a system to learn a good control policy and show how the methodology can be applied to control some devices aimed to damp electrical power oscillations. The control problem is formalized as a discrete-time optimal control problem and the information acquired from interaction with the system is a set of samples, where each sample is composed of four elements: a state, the action taken while being in this state, the instantaneous reward observed and the successor state of the system. To process this information we consider reinforcement learning algorithms that determine an approximation of the so-called Q-function by mimicking the behavior of the value iteration algorithm. Simulations are first carried on a benchmark power system modeled with two state variables. Then we present a more complex case study on a four-machine power system where the reinforcement learning algorithm controls a Thyristor Controlled Series Capacitor (TCSC) aimed to damp power system oscillations. [less ▲]

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See detailApproximating Functions on a Mesh with Restricted Voronoï Diagrams
Nivoliers, Vincent ULg; Lévy, Bruno

in Computer Graphics Forum (2013), 32(5), 83-92

We propose a method that computes a piecewise constant approximation of a function defined on a mesh. The approximation is associated with the cells of a restricted Voronoï diagram. Our method optimizes ... [more ▼]

We propose a method that computes a piecewise constant approximation of a function defined on a mesh. The approximation is associated with the cells of a restricted Voronoï diagram. Our method optimizes an objective function measuring the quality of the approximation. This objective function depends on the placement of the samples that define the restricted Voronoï diagram and their associated function values. We study the continuity of the objective function, derive the closed-form expression of its derivatives and use them to design a numerical solution mechanism. The method can be applied to a function that has discontinuities, and the result aligns the boundaries of the Voronoï cells with the discontinuities. Some examples are shown, suggesting potential applications in image vectorization and compact representation of lighting. [less ▲]

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See detailApproximation algorithms for multi-dimensional vector assignment problems
Crama, Yves ULg

Conference (2014, July 09)

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See detailApproximation Algorithms for Multi-Dimensional Vector Assignment Problems
Crama, Yves ULg

Conference (2013, July 04)

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See detailApproximation Algorithms for Multi-Dimensional Vector Assignment Problems
Dokka, Trivikram; Crama, Yves ULg; Spieksma, Frits C.R.

E-print/Working paper (2013)

We consider a special class of axial multi-dimensional assignment problems called multi-dimensional vector assignment (MVA) problems. An instance of the MVA problem is defined by $m$ disjoint sets, each ... [more ▼]

We consider a special class of axial multi-dimensional assignment problems called multi-dimensional vector assignment (MVA) problems. An instance of the MVA problem is defined by $m$ disjoint sets, each of which contains the same number $n$ of $p$-dimensional vectors with nonnegative integral components, and a cost function defined on vectors. The cost of an $m$-tuple of vectors is defined as the cost of their component-wise maximum. The problem is now to partition the $m$ sets of vectors into $n$ $m$-tuples so that no two vectors from the same set are in the same $m$-tuple and so that the total cost of the $m$-tuples is minimized. The main motivation comes from a yield optimization problem in semi-conductor manufacturing. We consider two classes of polynomial-time heuristics for MVA, namely, hub heuristics and sequential heuristics, and we study their approximation ratio. In particular, we show that when the cost function is monotone and subadditive, hub heuristics, as well as sequential heuristics, have finite approximation ratio for every fixed $m$. Moreover, we establish better approximation ratios for certain variants of hub heuristics and sequential heuristics when the cost function is monotone and submodular, or when it is additive. We provide examples to illustrate the tightness of our analysis. Furthermore, we show that the MVA problem is APX-hard even for the case $m=3$ and for binary input vectors. Finally, we show that the problem can be solved in polynomial time in the special case of binary vectors with fixed dimension $p$. [less ▲]

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See detailApproximation algorithms for the design of SDH/SONET networks
Brauner, Nadia; Crama, Yves ULg; Finke, Gerd et al

in RAIRO : Operations Research = Recherche Opérationnelle (2003), 37(4, OCT-DEC), 235-247

In this paper, a graph partitioning problem that arises in the design of SONET/SDH networks is defined and formalized. Approximation algorithms with performance guarantees are presented. To solve this ... [more ▼]

In this paper, a graph partitioning problem that arises in the design of SONET/SDH networks is defined and formalized. Approximation algorithms with performance guarantees are presented. To solve this problem efficiently in practice, fast greedy algorithms and a tabu-search method are proposed and analyzed by means of an experimental study. [less ▲]

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See detailApproximation efficace de mélanges bootstrap d’arbres de Markov pour l’estimation de densité
Schnitzler, François ULg; Ammar, Sourour; Leray, Philippe et al

in Bougrain, Laurent (Ed.) Actes de la 14e Conférence Francophone sur l'Apprentissage Automatique (CAp 2012) (2012, May 23)

Nous considérons des algorithmes pour apprendre des Mélanges bootstrap d'Arbres de Markov pour l'estimation de densité. Pour les problèmes comportant un grand nombre de variables et peu d'observations ... [more ▼]

Nous considérons des algorithmes pour apprendre des Mélanges bootstrap d'Arbres de Markov pour l'estimation de densité. Pour les problèmes comportant un grand nombre de variables et peu d'observations, ces mélanges estiment généralement mieux la densité qu'un seul arbre appris au maximum de vraisemblance, mais sont plus coûteux à apprendre. C'est pourquoi nous étudions ici un algorithme pour apprendre ces modèles de manière approchée, afin d'accélérer l'apprentissage sans sacrifier la précision. Plus spécifiquement, nous récupérons lors du calcul d'un premier arbre de Markov les arcs qui constituent de bons candidats pour la structure, et ne considérons que ceux-ci lors de l'apprentissage des arbres suivants. Nous comparons cet algorithme à l'algorithme original de mélange, à un arbre appris au maximum de vraisemblance, à un arbre régularisé et à une autre méthode approchée. [less ▲]

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See detailApproximation of reliability for multiple-trait animal models with missing data by canonical transformation
Gengler, Nicolas ULg; Misztal, I.

in Journal of Dairy Science (1996), 79(2), 317-328

An algorithm for approximation of reliability for multiple traits by multiple diagonalization was modified to support missing data by weighting transformed contributions of records based on the pattern of ... [more ▼]

An algorithm for approximation of reliability for multiple traits by multiple diagonalization was modified to support missing data by weighting transformed contributions of records based on the pattern of missing data. The accuracy of approximation was assessed with simulated and field data by comparing approximate reliabilities with those from direct inversion. Simulated data had several levels of missing data and covariances between traits; correlations were close to those for linear type traits of dairy cattle. Field data were 1) dairy records for milk, fat, and protein yields with 26% of the observations for fat and protein removed and 2) beef records for birth weight, weaning weight, and mean gain after weaning with 43% of observations missing. These files also contained empty fixed effect classes. The algorithm worked best for simulated data, and, when covariances between traits decreased, proportion of missing traits decreased and the number of empty fixed classes decreased. For dairy data, improvement over single-trait reliability occurred only for traits with missing data; for beef data, little or no improvement occurred. The method is useful with multiple diagonalization if the proportion of missing records or number of empty fixed effect classes or covariances between traits is moderate. [less ▲]

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See detailApproximations and their consequences for dynamic modelling of signal transduction pathways
Millat, Thomas; Bullinger, Eric ULg; Rohwer, Johann et al

in Mathematical Biosciences (2007), 207(1), 40-57

Signal transduction is the process by which the cell converts one kind of signal or stimulus into another. This involves a sequence of biochemical reactions, carried out by proteins. The dynamic response ... [more ▼]

Signal transduction is the process by which the cell converts one kind of signal or stimulus into another. This involves a sequence of biochemical reactions, carried out by proteins. The dynamic response of complex cell signalling networks can be modelled and simulated in the framework of chemical kinetics. The mathematical formulation of chemical kinetics results in a system of coupled differential equations. Simplifications can arise through assumptions and approximations. The paper provides a critical discussion of frequently employed approximations in dynamic modelling of signal transduction pathways. We discuss the requirements for conservation laws, steady state approximations, and the neglect of components. We show how these approximations simplify the mathematical treatment of biochemical networks but we also demonstrate differences between the complete system (c) 2006 Elsevier Inc. All rights reserved. [less ▲]

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See detailApproximations of Lovász extensions and their induced interaction index
Marichal, Jean-Luc; Mathonet, Pierre ULg

in Discrete Applied Mathematics (2008), 156(1), 11-24

The Lovasz extension of a pseudo-Boolean function f : (0, 1)(n) -> R is defined on each simplex of the standard triangulation of [0, 1](n) as the unique affine function (f) over cap : [0, 1](n) -> R that ... [more ▼]

The Lovasz extension of a pseudo-Boolean function f : (0, 1)(n) -> R is defined on each simplex of the standard triangulation of [0, 1](n) as the unique affine function (f) over cap : [0, 1](n) -> R that interpolates f at the n + 1 vertices of the simplex. Its degree is that of the unique multilinear polynomial that expresses f. In this paper we investigate the least squares approximation problem of an arbitrary Lovasz extension (f) over cap by Lovasz extensions of (at most) a specified degree. We derive explicit expressions of these approximations. The corresponding approximation problem for pseudo-Boolean functions was investigated by Hammer and Holzman [Approximations of pseudo-Boolean functions; applications to game theory, Z. Oper. Res. 36(1) (1992) 3-21] and then solved explicitly by Grabisch et al. [Equivalent representations of set functions, Math. Oper. Res. 25(2) (2000) 157-178], giving rise to an alternative definition of Banzhaf interaction index. Similarly we introduce a new interaction index from approximations of (f) over cap and we present some of its properties. It turns out that its corresponding power index identifies with the power index introduced by Grabisch and Labreuche [How to improve acts: an alternative representation of the importance of criteria in MCDM, Internat. J. Uncertain. Fuzziness Knowledge-Based Syst. 9(2) (2001) 145-157]. (c) 2007 Elsevier B.V. All rights reserved. [less ▲]

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See detailAppui à l'Assemblée nationale de la RDC
Kabamba, Bob ULg

Report (2010)

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See detailAppui à l'Assemblée provinciale de Bandundu
Kabamba, Bob ULg

Report (2011)

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See detailAppui à l'Assemblée provinciale de Maniema et Sud-Kivu
Kabamba, Bob ULg

Report (2010)

Detailed reference viewed: 12 (1 ULg)
See detailAppui à la création d’un diplôme d’études approfondies en biologie végétale et environnement à l’Université de Lubumbashi et remédiation multiscalaire des sols contaminés.
Ngongo Luhembwe, M; Bogaert, Jan ULg; Colinet, Gilles ULg et al

in Dahdouh-Guebas, F (Ed.) Proceedings of the Symposium on African Botany in Brussels (2009)

Detailed reference viewed: 16 (6 ULg)