Evolution of differential models for concrete complex systems through genetic programming

Created by W.Langdon from gp-bibliography.bib Revision:1.3949

@PhdThesis{phd/hal/SantosPeretta15,
  author =       "Igor Santos Peretta",
  title =        "Evolution of differential models for concrete complex
                 systems through genetic programming",
  titletranslation = "Evolution de mod{\`e}les diff{\'e}rentiels de
                 syst{\`e}mes complexes concrets par programmation
                 g{\'e}n{\'e}tique",
  year =         "2015",
  school =       "Laboratoire des sciences de l'ingenieur, de
                 l'informatique et de l'imagerie (ICube), Universite de
                 Strasbourg (UNISTRA)",
  address =      "France",
  month =        sep # "~21",
  keywords =     "genetic algorithms, genetic programming,
                 computer-automated system modelling, differential
                 models, linear ordinary differential equations, linear
                 partial differential equations, fitness evaluation",
  identifier =   "NNT : 2015STRAD031; tel-01332289",
  language =     "en",
  oai =          "oai:HAL:tel-01332289v1",
  bibdate =      "2016-08-08",
  bibsource =    "OAI-PMH server at api.archives-ouvertes.fr",
  bibsource =    "DBLP,
                 http://dblp.uni-trier.de/https://tel.archives-ouvertes.fr/tel-01332289",
  type =         "info:eu-repo/semantics/doctoralThesis; Theses",
  URL =          "https://tel.archives-ouvertes.fr/tel-01332289",
  URL =          "https://tel.archives-ouvertes.fr/tel-01332289/document",
  URL =          "https://tel.archives-ouvertes.fr/tel-01332289/file/Santos-Peretta_Igor_2015_ED269.pdf",
  abstract =     "A system is defined by its entities and their
                 interrelations in an environment which is determined by
                 an arbitrary boundary. Complex systems exhibit emergent
                 behaviour without a central controller. Concrete
                 systems designate the ones observable in reality. A
                 model allows us to understand, to control and to
                 predict behaviour of the system. A differential model
                 from a system could be understood as some sort of
                 underlying physical law depicted by either one or a set
                 of differential equations. This work aims to
                 investigate and implement methods to perform
                 computer-automated system modelling. This thesis could
                 be divided into three main stages: (1) developments of
                 a computer-automated numerical solver for linear
                 differential equations, partial or ordinary, based on
                 the matrix formulation for an own customization of the
                 Ritz-Galerkin method; (2) proposition of a fitness
                 evaluation scheme which benefits from the developed
                 numerical solver to guide evolution of differential
                 models for concrete complex systems; (3) preliminary
                 implementations of a genetic programming application to
                 perform computer-automated system modelling. In the
                 first stage, it is shown how the proposed solver uses
                 Jacobi orthogonal polynomials as a complete basis for
                 the Galerkin method and how the solver deals with
                 auxiliary conditions of several types. Polynomial
                 approximate solutions are achieved for several types of
                 linear partial differential equations, including
                 hyperbolic, parabolic and elliptic problems. In the
                 second stage, the proposed fitness evaluation scheme is
                 developed to exploit some characteristics from the
                 proposed solver and to perform piecewise polynomial
                 approximations in order to evaluate differential
                 individuals from a given evolutionary algorithm
                 population. Finally, a preliminary implementation of a
                 genetic programming application is presented and some
                 issues are discussed to enable a better understanding
                 of computer-automated system modelling. Indications for
                 some promising subjects for future continuation
                 researches are also addressed here, as how to expand
                 this work to some classes of non-linear partial
                 differential equations.",
  abstract =     "Un syst{\`e}me est d{\'e}fini par les entit{\'e}s et
                 leurs interrelations dans un environnement qui est
                 d{\'e}termin{\'e} par une limite arbitraire. Les
                 syst{\`e}mes complexes pr{\'e}sentent un comportement
                 {\'e}mergent sans un contr{\^o}leur central. Les
                 syst{\`e}mes concrets d{\'e}signent ceux qui sont
                 observables dans la r{\'e}alit{\'e}. Un mod{\`e}le nous
                 permet de comprendre, de contr{\^o}ler et de
                 pr{\'e}dire le comportement du syst{\`e}me. Un
                 mod{\`e}le diff{\'e}rentiel {\`a} partir d'un
                 syst{\`e}me pourrait {\^e}tre compris comme une sorte
                 de loi physique sous-jacent repr{\'e}sent{\'e} par l'un
                 ou d'un ensemble d'{\'e}quations diff{\'e}rentielles.
                 Ce travail vise {\`a} {\'e}tudier et mettre en
                 {\oe}uvre des m{\'e}thodes pour effectuer la
                 mod{\'e}lisation des syst{\`e}mes automatis{\'e}e par
                 l'ordinateur. Cette th{\`e}se pourrait {\^e}tre
                 divis{\'e}e en trois {\'e}tapes principales, ainsi: (1)
                 le d{\'e}veloppement d'un solveur num{\'e}rique
                 automatis{\'e} par l'ordinateur pour les {\'e}quations
                 diff{\'e}rentielles lin{\'e}aires, partielles ou
                 ordinaires, sur la base de la formulation de matrice
                 pour une personnalisation propre de la m{\'e}thode
                 Ritz-Galerkin; (2) la proposition d'un sch{\`e}me de
                 score d'adaptation qui b{\'e}n{\'e}ficie du solveur
                 num{\'e}rique d{\'e}velopp{\'e} pour guider
                 l'{\'e}volution des mod{\`e}les diff{\'e}rentiels pour
                 les syst{\`e}mes complexes concrets; (3) une
                 impl{\'e}mentation pr{\'e}liminaire d'une application
                 de programmation g{\'e}n{\'e}tique pour effectuer la
                 mod{\'e}lisation des syst{\`e}mes automatis{\'e}e par
                 l'ordinateur. Dans la premi{\`e}re {\'e}tape, il est
                 montr{\'e} comment le solveur propos{\'e} utilise les
                 polyn{\^o}mes de Jacobi orthogonaux comme base
                 compl{\`e}te pour la m{\'e}thode de Galerkin et comment
                 le solveur traite des conditions auxiliaires de
                 plusieurs types. Solutions {\`a} approximations
                 polynomiales sont ensuite r{\'e}alis{\'e}s pour
                 plusieurs types des {\'e}quations diff{\'e}rentielles
                 partielles lin{\'e}aires, y compris les probl{\`e}mes
                 hyperboliques, paraboliques et elliptiques. Dans la
                 deuxi{\`e}me {\'e}tape, le sch{\`e}me de score
                 d'adaptation propos{\'e} est con{\c c}u pour exploiter
                 certaines caract{\'e}ristiques du solveur propos{\'e}
                 et d'effectuer l'approximation polyn{\^o}miale par
                 morceaux afin d'{\'e}valuer les individus
                 diff{\'e}rentiels {\`a} partir d'une population fournie
                 par l'algorithme {\'e}volutionnaire. Enfin, une mise en
                 {\oe}uvre pr{\'e}liminaire d'une application GP est
                 pr{\'e}sent{\'e}e et certaines questions sont
                 discut{\'e}es afin de permettre une meilleure
                 compr{\'e}hension de la mod{\'e}lisation des
                 syst{\`e}mes automatis{\'e}e par l'ordinateur.
                 Indications pour certains sujets prometteurs pour la
                 continuation de futures recherches sont {\'e}galement
                 abord{\'e}es dans ce travail, y compris la fa{\c c}on
                 d'{\'e}tendre ce travail {\`a} certaines classes
                 d'{\'e}quations diff{\'e}rentielles partielles
                 non-lin{\'e}aires.",
}

Genetic Programming entries for Igor Santos Peretta

Citations