Generic algorithms as a tool in the study of aperiodic order, with application to the case of X-ray diffraction spectra of GaAs-AlAs multilayer heterostructures

fichier pdf déposé avec l'aimable autorisation de EdP sciences donnée à l'un des auteurs (Françoise Axel)International audienceWe present the first application of genetic algorithms to the analysis of data froma an aperiodically ordered system, high resolution X-ray diffraction spectra from multilayer heterostructures arranged according to a deterministic or random scheme. This method paves the way to the solution of the "inverse problem", that is the retrieval of the generating disorder from the investigation of th espectra of an unknown sample having non crystallographic, non quasi-crystallographic order

Artificial Darwinism: an overview

Genetic algorithms, genetic programming, evolution strategies, and what is now called evolutionary algorithms, are stochastic optimisation techniques inspired by Darwin’s theory. We present here an overview of these techniques, while stressing on the extreme versatility of the artificial evolution concept. Their applicative framework is very large and is not limited to pure optimisation. Artifical evolution implementations are however computationally expensive: an efficient tuning of the components and parameter of these algorithms should be based on a clear comprehension of the evolutionary mechanisms. Moreover, it is noticeable that the killer-applications of the domain are for the most part based on hybridisation with other optimisation techniques. As a consequence, evolutionary algorithms are not to be considered in competition but rather in complement to the “classical ” optimisation techniques.Les algorithmes génétiques, la programmation génétique, les stratégies d’évolution, et ce que l’on appelle maintenant en général les algorithmes évolutionnaires, sont des techniques d’optimisation stochastiques inspirées de la théorie de l’évolution selon Darwin. Nous donnons ici une vision globale de ces techniques, en insistant sur l’extrême flexibilité du concept d’évolution artificielle. Cet outil a un champ très vaste d’applications, qui ne se limite pas à l’optimisation pure. Leur mise en oeuvre se fait cependant au prix d’un coût calculatoire important, d’où la nécessité de bien comprendre ces mécanismes d’évolution pour adapter et régler efficacement les différentes composantes de ces algorithmes. Par ailleurs, on note que les applications-phares de ce domaine sont assez souvent fondées sur une hybridation avec d’autres techniques d’optimisation. Les algorithmes évolutionnaires ne sont donc pas à considérer comme une méthode d’optimisation concurrente des méthodes d’optimisation classiques, mais plutôt comme une approche complémentaire

Theory of Genetic Algorithms II: models for genetic operators over the string-tensor representation of populations and convergence to global optima for arbitrary fitness function under scaling

AbstractWe present a theoretical framework for an asymptotically converging, scaled genetic algorithm which uses an arbitrary-size alphabet and common scaled genetic operators. The alphabet can be interpreted as a set of equidistant real numbers and multiple-spot mutation performs a scalable compromise between pure random search and neighborhood-based change on the alphabet level. We discuss several versions of the crossover operator and their interplay with mutation. In particular, we consider uniform crossover and gene-lottery crossover which does not commute with mutation. The Vose–Liepins version of mutation-crossover is also integrated in our approach. In order to achieve convergence to global optima, the mutation rate and the crossover rate have to be annealed to zero in proper fashion, and unbounded, power-law scaled proportional fitness selection is used with logarithmic growth in the exponent. Our analysis shows that using certain types of crossover operators and large population size allows for particularly slow annealing schedules for the crossover rate. In our discussion, we focus on the following three major aspects based upon contraction properties of the mutation and fitness selection operators: (i) the drive towards uniform populations in a genetic algorithm using standard operations, (ii) weak ergodicity of the inhomogeneous Markov chain describing the probabilistic model for the scaled algorithm, (iii) convergence to globally optimal solutions. In particular, we remove two restrictions imposed in Theorem 8.6 and Remark 8.7 of (Theoret. Comput. Sci. 259 (2001) 1) where a similar type of algorithm is considered as described here: mutation need not commute with crossover and the fitness function (which may come from a coevolutionary single species setting) need not have a single maximum

An adaptive hybrid genetic-annealing approach for solving the map problem on belief networks

Genetic algorithms (GAs) and simulated annealing (SA) are two important search methods that have been used successfully in solving difficult problems such as combinatorial optimization problems. Genetic algorithms are capable of wide exploration of the search space, while simulated annealing is capable of fine tuning a good solution. Combining both techniques may result in achieving the benefits of both and improving the quality of the solutions obtained. Several attempts have been made to hybridize GAs and SA. One such attempt was to augment a standard GA with simulated annealing as a genetic operator. SA in that case acted as a directed or intelligent mutation operator as opposed to the random, undirected mutation operator of GAs. Although using this technique showed some advantages over GA used alone, one problem was to find fixed global annealing parameters that work for all solutions and all stages in the search process. Failing to find optimum annealing parameters affects the quality of the solution obtained and may degrade performance. In this research, we try to overcome this weakness by introducing an adaptive hybrid GA - SA algorithm, in which simulated annealing acts as a special case of mutation. However, the annealing operator used in this technique is adaptive in the sense that the annealing parameters are evolved and optimized according to the requirements of the search process. Adaptation is expected to help guide the search towards optimum solutions with minimum effort of parameter optimization. The algorithm is tested in solving an important NP-hard problem, which is the MAP (Maximum a-Posteriori) assignment problem on BBNs (Bayesian Belief Networks). The algorithm is also augmented with some problem specific information used to design a new GA crossover operator. The results obtained from testing the algorithm on several BBN graphs with large numbers of nodes and different network structures indicate that the adaptive hybrid algorithm provides an improvement of solution quality over that obtained by GA used alone and GA augmented with standard non-adaptive simulated annealing. Its effect, however, is more profound for problems with large numbers of nodes, which are difficult for GA alone to solve

A grammar-based technique for genetic search and optimization

The genetic algorithm (GA) is a robust search technique which has been theoretically and empirically proven to provide efficient search for a variety of problems. Due largely to the semantic and expressive limitations of adopting a bitstring representation, however, the traditional GA has not found wide acceptance in the Artificial Intelligence community. In addition, binary chromosones can unevenly weight genetic search, reduce the effectiveness of recombination operators, make it difficult to solve problems whose solution schemata are of high order and defining length, and hinder new schema discovery in cases where chromosome-wide changes are required.;The research presented in this dissertation describes a grammar-based approach to genetic algorithms. Under this new paradigm, all members of the population are strings produced by a problem-specific grammar. Since any structure which can be expressed in Backus-Naur Form can thus be manipulated by genetic operators, a grammar-based GA strategy provides a consistent methodology for handling any population structure expressible in terms of a context-free grammar.;In order to lend theoretical support to the development of the syntactic GA, the concept of a trace schema--a similarity template for matching the derivation traces of grammar-defined rules--was introduced. An analysis of the manner in which a grammar-based GA operates yielded a Trace Schema Theorem for rule processing, which states that above-average trace schemata containing relatively few non-terminal productions are sampled with increasing frequency by syntactic genetic search. Schemata thus serve as the building blocks in the construction of the complex rule structures manipulated by syntactic GAs.;As part of the research presented in this dissertation, the GEnetic Rule Discovery System (GERDS) implementation of the grammar-based GA was developed. A comparison between the performance of GERDS and the traditional GA showed that the class of problems solvable by a syntactic GA is a superset of the class solvable by its binary counterpart, and that the added expressiveness greatly facilitates the representation of GA problems. to strengthen that conclusion, several experiments encompassing diverse domains were performed with favorable results