Section: New Results
Modelling and Control of Complex Systems
Abstract: Several research directions were initially targeted toward Robotics, but are in fact relevant to more general Complex Systems. This includes, beside Robotics, activities in e-Science and Grid Modelling, but also Evolutionary Design and Inverse Problems, that have been part of Tao activities for many years, as well as new studies related to Complex Networks.
Four directions have been explored: the first two ones are related to the knowledge transfer from human experts to the robot controller; the third one, investigating the reality gap, aims at transforming an in-silico optimized controller into an in-situ competent one. The last one is concerned with optimization of locomotion for several robot morphologies using Central Pattern Generators.
In collaboration with Lutins (U. Paris 8 - Cognitive Psychology group, Herobot contract), we have considered the problem of imitation learning with visual validation. Specifically, a robot controller aimed at reproducing the behavior of human subjects with impaired perception (exploring a maze in order to find some object), has been devised using the subsumption architecture. In silico , this controller experimentally displayed a plausible behavior, providing the psychologists with relevant insights and suggesting fruitful exploration heuristics. Experiments in situ are under way (C. Tijus, N. Bredeche, Y. Kodratoff, M. Felkin, C. Hartland, E. Zibetti, V. Besson. Human Heuristics for a Team of Mobile Robots. 5th IEEE International Conference on Research, Innovation and Vision for the Future (RIVF'07).).
Fuzzy controllers and prior knowledge
Among the representations investigated for robot control are neural nets and fuzzy controllers. Carlos Kavka, from San Luis University (Argentina), working under Marc Schoenauer's supervision, extended the standard evolutionary design of fuzzy systems to Voronoi diagram-based representation (see section 6.3.3 ). This representation does not only allow for more flexible decision boundaries (whereas standard approaches consider hyper-rectangles); it also enables the easy embedding of expert rules (e.g. ``Go forward if there is no obstacle ahead'') and their automatic optimization, specialization or generalization, depending on the application problem. This approach demonstrated its efficiency for evolutionary robotics(C. Kavka and M. Schoenauer. Evolution of Voronoi-based Fuzzy Controllers. In Xin Yao et al., eds, PPSN'04, LNCS 3242, Springer Verlag, 2004.) and was extended to recurrent fuzzy systems, endowing the robot with some self-managed memory. A comprehensive description will be found in Carlos Kavka's PhD  , defended in July 2006 at Université Paris-Sud.
Anticipation and the Reality Gap
Earlier work explored the use of an anticipation module in order to enhance the autonomous controller stability(Robea contract, coll. LIMSI. N. Godzik and M. Schoenauer and M. Sebag, Robustness in the long run: Auto-teaching vs Anticipation in Evolutionary Robotics. In X. Yao et al., Eds, Proc. PPSN VIII , pp 932-941, LNCS 3242, Springer Verlag, 2004). This anticipation module was reconsidered to facilitate the transfer in situ of a robotic controller after its in silico optimization. Specifically, the anticipation module trained in silico provided the controller with an additional information, the residue (difference between the predicted and actual state in the next time step). This residue was exploited for the on-line adaptation of the controller; experiments successfully demonstrate the on-line robot recovery under motor perturbations  .
In the context of locomotion, we addressed the problem of locomotion for snake and legged robots. These kinds of locomotion share the fact that they rely on oscillatory signals to generate appropriate locomotion patterns. Central Pattern Generator (CPG), inspired from biology, are Dynamical Systems that can be interconnected and are characterized by limit cycles that can generate a relevant activity pattern for locomotion. Moreover, convergence towards this very limit cycle makes is very useful when it comes to recovering from punctual control errors (sliding, hardware temporary failure, etc.). In this scope, we have studied a well known implementation of a CPG and optimized parameters for several topologies corresponding to several robot morphologies. Our approach provides an efficient way to automatically learn locomotion independently of the morphology - Experiments were conducted using the PuppetMaster simulator (section 5.5 ) with a snake-like robot and a hexapodal robot in realistic physics-based simulation (Enguerran Colson, Master 2 recherche, 2006).
e-Science and Grid Modelling
As Cecile Germain joined the TAO group in 2005, her strong expertise in grid computing opens new and strategic perspectives along several main directions.
A first direction, explored in the Programme Pluri-Formation DEMAIN (Des DonnéEs MAssives Aux InterpretatioNs , starting Dec. 2006, headed by C. Germain), is that of e-Science (http://www.lri.fr/ cecile/DEMAIN/DemainSc.htm ). With LRI, LAL (Laboratoire de l'Accélérateur Linéaire), Lab. Maths, IBBMC (Institut de Biochimie et Biophysique Moléculaire et Cellulaire) and Supelec as main partners, DEMAIN aims at developing pump-priming projects on the Orsay campus, concerned with the principled exploitation of the datasets gathered in LAL and IBBMC, using advanced algorithms in machine learning, data mining and optimization. A typical application concerns the analysis of the Auger experiment in collaboration with A. Cordier (LAL). This junction between the LAL and the Tao group was instrumental in recruiting Balazs Kegl as CNRS CR1, researcher in machine learning at LAL and correspondent of the Tao group. DEMAIN avails the computing facilities gathered by the LAL, namely the EGEE (Enabling Grids for e-Science in Europe) grid. Cecile Germain currently chairs the Short Deadline Jobs (http://egee-intranet.web.cern.ch/egee-intranet/NA1/TCG/wgs/sdj.htm ) working group in the EGEE Network of Excellence.
A second and more daring research direction is that of Grid Modelling. A complex system, the grid can hardly be modeled through a-priori analysis: its topology and state at any time can only be estimated; the grid usage, based on a mutualisation paradigm, reflects the collective behavior of the users and results in an uncontrolled and unforeseeable load on the system. Interestingly, the modelling of the computing system is viewed as the first step (building self-aware systems) in the Autonomic Computing effort, declared as a top priority for the IBM company since 2001 (http://www.research.ibm.com/autonomic/overview/ ). First steps toward the EGEE control have been done in 2005 (C. Germain and D. Monnier-Ragaigne. Grid Result Checking. In Procs. 2nd Computing Frontiers, Ischia, Mai 2005.). A Pascal Challenge related to Grid Modelling has been accepted in Dec. 2006 (coll. TAO, LAL, Technion). Xiangliang Zhang (PhD student under M. Sebag and C. Germain's supervision) recently started the modelling of the EGEE grid.
The Grid Modelling Challenge is also relevant to the KD-Ubiq Coordination Action, started in 2006 (http://www.kdubiq.org/ ). M. Sebag is responsible for the Work Package Benchmarking.
Lastly, Cécile Germain chairs the ACI MD AGIR (http://www.aci-agir.org ) contract (starting sept. 2004), concerned with medical data mining and more precisely medical imaging through grid computing (C. Germain, V. Breton, P. Clarysse, Y. Gaudeau, T. Glatard, E. Jeannot, Y. Legré, C. Loomis, J. Montagnat, J-M Moureaux, A. Osorio, X. Pennec et R. Texier. Grid-enabling medical image analysis, Journal of Clinical Monitoring and Computing, 19(4-5), 339-349, 2005.). A multi-disciplinary project, AGIR gathers researchers in computer science, physics and medicine from CNRS, Université Paris-Sud, INRIA, INSERM and hospitals.
Julien Perez (PhD student under C. Germain and A. Osorio from LIMSI supervision) is concerned with the reconstruction of 3D images through mining the logs of the PTM3D software, developed at LIMSI and ported on the grid(PTM3D has been part of the first EGEE review and of the HealthGrid demonstrations at SC'05). This study ultimately aims at grid-aware mining algorithms.
Earlier work about evolutionary design, applied to Topological Optimum Design of Mechanical Structures(H. Hamda, F. Jouve, E. Lutton, M. Schoenauer and M. Sebag. Compact Unstructured Representations in Evolutionary Topological Optimum Design. Applied Intelligence, 16, pp 139-155, 2002.) or Architecture (EZCT contract(Results of chair designs have been exposed in the Innovative Design Techniques section of the ArchiLab exhibition in Orléans in 2005, and have been acquired by the Beaubourg Modern Art Museum.)) explored several shape representations overcoming the limitations of the standard bitarray representations, including Voronoi diagrams (see also Section 6.3.1 ).
Another representation, that of construction plans, was investigated by A. Devert (PhD under N. Bredèche' and M. Schoenauer's supervision). This representation is close to the so-called ``embryogenic'' representations, in which the evolution optimizes a program that actually builds the phenotype (here, the actual structure). The program, a directed acyclic graph, describes a sequence of possible actions (drop, move in straight line, rotate, ...). Such representation addresses some deep requirements for design, e.g. modularity, re-usability, and not least in the domain of Structural Design, constructibility, as only feasible moves are planned in the program. The scalability of the approach (handling up to a few hundred modules) is higher by an order of magnitude than that of existing approaches  ,  .
On-going work extends the construction plan representation towards embryogenesis. Specifically, the goal is to both optimize the ``basic cell'', and the connectivity of a network made of some hundred basic cells under locality and network diameter constraints (see also section 6.3.5 ).
Another daring design problem concerns the optimization of mesh topologies (Airbus Contract), motivated by the fact that mesh topology design requires both considerable time and expertise from the designers; an extensive corporate knowledge is encapsulated in the mesh topology archive. The Airbus project involves three phases; the first one is about representing available meshes in a tractable way, using propositionalization (the intrinsic description of a mesh is through a few thousands/ hundred thousands of finite elements); the second phase is concerned with characterizing good meshes (using a one-class learning approach, as only good topologies are stored); the third phase uses the above characterization to derive new good meshes. Due to the unexpected leave of Mathieu Pierres, PhD in May 2006, this project has not made any progress in 2006. Damien Tessier will take over the project in 2007.
Inverse Problems (IP) aim at determining unknown causes based on the observation of their effects. In contrast, direct problems are concerned with computing the effects of (exhaustively described) causes. Inverse problems are often mathematically ill-posed in the sense that the existence, uniqueness and stability of solutions cannot be assured.
IPs are present in many areas of science and engineering, such as mechanical engineering, meteorology, heat transfer, electromagnetism, material science, etc. The TAO project has focused on the problems of system identification, modeling physical (mechanical, chemical, biological, etc.) phenomena from available observations and current theories.
Domain Knowledge for Seismic Velocity Identification
A long collaboration with IFP, the seismic inverse problem aims at identifying some underground characteristics from recorded seismic data. Earlier work(F. Mansanné, Analyse d'Algorithmes d'Évolution Artificielle appliqués au domaine pétrolier : Inversion sismique et approximation de fonctions, PhD Université de Pau, 2000) has been using Voronoi diagrams for representing the underground, demonstrating that the available objective function was not sufficient to enforce plausible solutions (e.g., some underground profiles with not so bad fitness were geophysically absurd).
Vijay Pratap Singh (PhD under Marc Schoenauer's supervision) remedied the above limitations through a more knowledgeable representation, evolving an initial state of layered underground as well as the geological conditions across the geological ages. However, though it allowed good results on the geological problem(V.P. Singh, M. Schoenauer and M. Léger, A geologically-sound representation for evolutionary multi-objective subsurface identification, in B. McKay et al., Eds, CEC'05, pp 454-462, IEEE Press, 2005), and also let to a patent in 2005, this representation didn't allow to successfully solve the geophysical problem. The only way to handle the large computational cost of evolutionary methods was to introduce domain knowledge wherever it was possible. But the results were a computational gains of orders of magnitude! These results are extensively described in his PhD, defended in December 2006  .
Representations for isotherm law in chromatography In the framework of the ACI NIM Nouvelles Interfaces des Mathématiques , Marc Schoenauer is part of the Chromalgema project, whose aim is the identification of the isotherm function in analytical chromatography. This is an inverse problem for which the direct problem is solved by standard numerical approaches (e.g. Godunov scheme for Non-Linear Hyperbolic Systems).
When the unknown isotherm function is sought as a rational fraction of the concentrations (e.g. in the family of so-called ``Langmuir'' models), the inverse problem amounts to parametric optimization. A recent improvement was to use the recent ``CMA-ES'' method and its refinements (the restart strategy). On-going work is related to the hybridization of evolutionary and gradient methods: what is the best hybridization method: sequential (and when to switch), fine-grained (and what amount of local optimization to perform inside evolution), or both? Those results, as well as validation on real-world data, will be presented exhaustively in Mohamed Jebalia's PhD dissertation.
The automatic generation of test data can indeed be seen as an inverse problem: what data should be input to the program under test to reach this or that instruction (for structural testing), or to trigger such or such functional error (for functional testing)? TAO is part of the European STREP EvoTest , that started on October 1. 2006, funded under FP6 FET ``complex systems'' call. The coordinator is ITI, University of Valencia, and the main partners are Daimler-Chrysler, Berlin, Franhofer FIRST, Berlin, and Kings College, London.
Optimization and Identification of Complex Networks
This section describes prospective work that has started in TAO in 2006, and hence has not yet resulted in any publication.
Approximate stochastic simulation of chemically reacting system
Two mathematical models exist for describing the time behavior of chemical system: In the deterministic model, the time evolution of the chemical species is modeled as a set of ordinary differential equations; In the stochastic model, the different species are random variables obeying the chemical master equation that takes into account their inherent fluctuations and correlations, that cannot be neglected when dealing with biological systems where the overall number of molecules is usually small. An exact simulation algorithm for the chemical master equation was introduced by Gillespie in 1977 (D.T. Gillespie. Exact stochastic simulation of coupled chemical reactions. J. Phys. Chem. , Vol. 81, pp 2340-2361, 1977.).
Anne Auger, who joined TAO in 2006 as Chargée de Recherche, recently proposed (with co-authors) a new accelerated scheme  where the complexity is reduced in the case of (moderately) stiff systems.
Optimizing the topology of large neural networks
The performance of large networks of small computational units like neural networks or ...the next generation of multi-core micro-processors highly depends on the topology of the network. Fei Jiang, that started a PhD in September, following his engineer internship, works on both the direct problem (what is the influence of the topology of given networks on their performance) and the inverse problem (how to design optimal networks for a given task). This thesis is co-directed by Hugues Berry, CR1 in the Alchemy project, and Marc Schoenauer.
Genetic Regulatory Networks
The GENNETEC European project, funded under FP6 FET ``complex systems'' call, has begun in October 2006, and deals with Genetic Regulatory Networks (GRN): W. Banzhaf's GRN model(W. Banzhaf, Artificial Regulatory Networks and Genetic Programming, in Rick L. Riolo and Bill Worzel, Eds, Genetic Programming Theory and Practice, pp 43-62, Kluwer, 2003), is a generative model where an interaction network between genes emerges from a series of genetic evolutionary variations. The resulting system of ODEs can then be solved to compute the evolution of protein concentrations. The work of Miguel Nicolau, hired on Gennetec project in October 2006, will be to tune the evolutionary variations of the genome, in order to control both the topology of the interaction network and the behavior (transient as well as steady-state) of the system of proteins.
Cellular Evolutionary Design
Recent research direction by A. Devert is also concerned with the evolution or large networks of interacting elements: to cope with the scaling issue of evolving construction plans (section 6.3.3 ), the idea is to evolve local rules for some ``cells'' that will exchange ``chemicals'', and the steady-state of those chemicals will describe the target structure. However, the neighborhood topology of the whole domain can be evolved, too ...