4 research outputs found
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From DNA to protein: Transformations and their possible role in linkage learning
This paper first extends the traditional perspective of linkage using the basic concepts developed in the SEARCH framework and identifies the fundamental objectives of linkage learning. It then explores the computational role of gene-expression (DNA{r_arrow}RNA{r_arrow}Protein transformations) in evolutionary linkage learning, using group representation theory. It offers strong evidence to support the hypothesis that the transformations in gene-expression define a group of symmetry transformations that leaves the fitness invariant; however, they change the eigen functions leading to identifying independent subspaces of the search space (a major objective of linkage learning) using irreducible representations of such transformations
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Gene expression: The missing link in evolutionary computation
This paper points out that the traditional perspective of evolutionary computation may not provide the complete picture of evolutionary search. This paper focuses on gene expression-- transformations of representation (DNA->RNA->Protein) from a the perspective of relation construction. It decomposes the complex process of gene expression into several steps, namely (1) expression control of DNA base pairs, (2) alphabet transformations during transcription and translation, and (3) folding of the proteins from sequence representation to Euclidean space. Each of these steps is investigated on grounds of relation construction and search efficiency. At the end these pieces of the puzzle are put together to develope a possibly crude and cartoon computational description of gene expression
An Efficient Global Optimization Method Based on Multi-Unit Extremum Seeking
RÉSUMÉ
Les problèmes d'optimisation industrielle, telle que la maximisation de la production de produits
chimiques et pétrochimiques, montrent généralement plusieurs points optimaux locaux. Le
développement de méthode pour la sélection du point optimal global a toujours fait l’objet de
nombreuses recherches. Plusieurs techniques dĂ©terministes et stochastiques ont Ă©tĂ© explorĂ©es Ă
cette fin. Les techniques stochastiques ne garantissent pas toujours la convergence vers la
solution globale, mais sont efficaces pour les dimensions supérieures. D'autre part, les méthodes
déterministes se rendent à l'optimum global, mais le défi est d'employer un cloisonnement
efficace de l'espace afin de réduire le nombre d'évaluations fonctionnelles.
Cette thèse propose une approche originale en matière d’optimisation globale, numérique et
déterministe basée sur des techniques d'optimisation locale en temps réel et en particulier, sur
des techniques sans modèle appelé les systèmes de commande extrémale. Pour les problèmes
sans contrainte, les systèmes de commande extrémale représente le problème d'optimisation
comme un contrôle du gradient. La façon dont le gradient est estimé constitue la différence
principale entre les différentes alternatives qui sont proposées dans la littérature scientifique. Pour
les méthodes de perturbation, un signal d'excitation temporelle est utilisé afin de calculer le
gradient. Une alternative existe dans le cadre d'optimisation multi-unité où le gradient est estimé
par la différence finie de la sortie de deux unités identiques, mais dont les données d’entré se
distinguent par un décalage.
Le point de départ de cette recherche a été motivée par les systèmes de commandes extrémales
locales. Ces commandes sont basées sur une perturbation qui peut être utilisée comme un outil
pour l'optimisation globale des polynômes scalaires du quatrième ordre avec un optimum global.
L'objectif de cette thèse est d'étendre ce concept et de développer une technique d'optimisation
globale déterministe pour une classe générale de systèmes multi-variables, statiques, non linéaires
et continus. Dans cette thèse, il est d'abord démontré que si le décalage est réduit à zéro pour une
optimisation multi-unité scalaire, le système converge vers l'optimum global. Le résultat est
également étendu aux problèmes scalaires avec contraintes qui sont caractérisés par des régions
non-convexes. Dans ce cas, une stratégie de commande de “Switching” est utilisée pour faire face
aux contraintes.----------ABSTRACT
Industrial optimization problems, e.g., maximizing production in chemical and petrochemical
facilities, typically exhibit multiple local optimal points and so choosing the global one has
always attracted many researchers. Many deterministic and stochastic techniques have been
explored towards this end. The stochastic techniques do not always guarantee convergence to the
global solution, but fare well computationally for higher dimensions. On the other hand, the
deterministic methods get to the global optimum, while the challenge therein is to employ an
efficient partitioning of the space in order to reduce the number of functional evaluations.
This thesis proposes an original approach to numerical deterministic global optimization based on
real-time local optimization techniques (in particular, model-free techniques termed the
extremum-seeking schemes). For unconstrained problems, extremum-seeking schemes recast the
optimization problem as the control of the gradient. The way the gradient is estimated forms the
main difference between different alternatives that are proposed in the literature. In perturbation
methods, a temporal excitation signal is used in order to compute the gradient. As an alternative,
in the multi-unit optimization framework, the gradient is estimated as the finite difference of the
outputs of two identical units driven with the inputs that differ by an offset.
The starting point of this research was motivated by the perturbation-based extremum seeking
schemes which can be used as a tool for global optimization of scalar fourth order polynomials,
with one local and one global optimum. The objective of this thesis is to extend this concept and
develop a deterministic global optimization technique for a general class of multi-variable, static,
nonlinear and continuous systems. In this thesis, it is first shown that in the scalar multi-unit
optimization framework, if the offset is reduced to zero, the scheme converges to the global
optimum. The result is also extended to scalar constrained problems, with possible non-convex
feasible regions, where a switching control strategy is employed to deal with the constraints.
The next step consists of extending the algorithm to more than one variable. For two-input
systems, univariate global optimization was repeated on the circumference of a circle of reducing
radius. With three variables, the two-variable optimization mentioned above is repeated on the
surface of a sphere of reducing radius. Time-scale separation between the various layer
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SEARCH, blackbox optimization, and sample complexity
The SEARCH (Search Envisioned As Relation and Class Hierarchizing) framework developed elsewhere (Kargupta, 1995; Kargupta and Goldberg, 1995) offered an alternate perspective toward blackbox optimization -- optimization in presence of little domain knowledge. The SEARCH framework investigates the conditions essential for transcending the limits of random enumerative search using a framework developed in terms of relations, classes and partial ordering. This paper presents a summary of some of the main results of that work. A closed form bound on the sample complexity in terms of the cardinality of the relation space, class space, desired quality of the solution and the reliability is presented. This also leads to the identification of the class of order-k delineable problems that can be solved in polynomial sample complexity. These results are applicable to any blackbox search algorithms, including evolutionary optimization techniques