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Exploiting separability in search: The island model genetic algorithm
... There are two distinct manners of expanding the function to multiple dimensions. One method of expansion is the Whitley n-dimensional weighted wrap[89]. This is less common than the more obvious linear chaining expansion. ...
... Powell's four dimensional function is a non-separable function that uses a four dimensional version of what Whitley terms a "weighted wrap"[89] expansion function.The net effect of such a combination is that there is no "start" dimension from where the problem unravels, but all the dimensions have strong interactions and have to be approached collectively. It is informative to contrast this characteristic with the Whitley Rosenbrock function Rosenbrock I which also shares this property and the common Rosenbrock function Rosenbrock II which does not.7.7.1 Best results : Powell's functionIt is notable that all the reported results for optimisation of the Powell four dimensional problem are using binary encodings. ...
We present an investigation into the design of an evolutionary mechanism for multiagent
protocol constraint optimisation. Starting with a review of common population
based mechanisms we discuss the properties of the mechanisms used by these search
methods. We derive a novel algorithm for optimisation of vectors of real numbers and
empirically validate the efficacy of the design by comparing against well known results
from the literature. We discuss the application of an optimiser to a novel problem
and remark upon the relevance of the no free lunch theorem. We show the relative
performance of the optimiser is strong and publish details of a new best result for the
Keane optimisation problem. We apply the final algorithm to the multi-agent protocol
optimisation problem and show the design process was successful.
... I propose in this chapter two extensions to Fuzzy CoCo, intended to simplify the task of finding an adequate size of the rule base. The first extension, called Island Fuzzy CoCo, is based on the Island model [172,180]. It takes advantage of the exploration performed separately by concurrent instances of Fuzzy CoCo, where each instance is set to search for systems of different sizes. ...
... Island Fuzzy CoCo, the approach proposed herein, is similar to the so-called island model where several (sub)populations, called islands or demes, evolving separately most of the time, occasionally exchange individuals according to a certain migration policy [172,180]. Below, I sketch Island Fuzzy CoCo and describe two preliminary tests performed to explore its behavior. ...
In the simplified models of evolution discussed in Section 1.3, we consider individuals belonging to a single species–i.e.,
sharing the same genetic encoding, and reproducing with each other. We assume this species evolves in isolation, in an almost
unchanging environment. In nature, species live in the niches afforded by other species, modifying themselves and the environment
and being affected by such modifications.
... The island model is a popular way to implement distributed GAs [4,5]. The basic idea is to set up populations of individuals to evolve independently in a set of islands. ...
... When building up the system, our first concern was how the distributed environment affects the convergence of the GA. Previous studies (as for instance in Whitly et al. [5]) show how the island model in fact helps improving the overall convergence of the system (given that the complexity of the problem we are solving is above a specific, problemdependant minimum threshold). The use of asynchronous communications to ensure fault-tolerance does also not affect convergence, and in some cases can even have a positive effect on both convergence and performance. ...
This paper presents a grid service for solving optimization problems based on genetic algorithms. The proposed solu-tion extensively uses peer-to-peer technology and epidemic protocols in order to improve scalability and failure re-silience. This considerably relaxes the model traditionally used by genetic algorithm libraries. However, experimental results show that the convergence of the genetic algorithm is not necessarily impaired by the weaker model.
... Island models, wherein subpopulations are relatively isolated and individuals occasionally migrate, have been a population structure of interest in the study of both natural and artificial evolution [10]. Another motivation is the development and evaluation of methods for structuring the fine-grained parallelization of genetic algorithms [17]. In such a model, each processor in a computer network or multiprocessor manages one individual or several individuals as different processes; processes and processors exchange fitness values and genetic information as needed with their neighbors. ...
... The structure among cliques could be complete or a path, known as the stepping-stone model representing linear ecosystems such as a beach. The island model has been explored as one structure for parallelization of artificial evolutionary algorithms, as well [17]. ...
We investigate the effect that population structure has upon the course of artificial evolution. We represent an arbitrary
population structure by embedding a population of individuals in a graph. Each individual resides at a vertex of the graph
and can only choose a mating partner from among its neighbors in the graph. Each individual mates with the selected partner
and is replaced by the resultant offspring in the next generation. We embed populations in a variety of trees and mesh-structured
graphs and observe differences in rates of change of average fitness and percent polymorphism over successive generations.
Results indicate that populations embedded in sparse random graphs having relatively low diameter yield results similar to
those embedded in complete graphs.
... I propose in this chapter two extensions to Fuzzy CoCo, intended to simplify the task of finding an adequate size of the rule base. The first extension, called Island Fuzzy CoCo, is based on the Island model [172, 180]. It takes advantage of the exploration performed separately by concurrent instances of Fuzzy CoCo, where each instance is set to search for systems of different sizes. ...
... Such systems exhibit fitness values similar or superior to those of the simpler runs corresponding to their effective number of rules. Island Fuzzy CoCo, the approach proposed herein, is similar to the so-called island model where several (sub)populations, called islands or demes, evolving separately most of the time, occasionally exchange individuals according to a certain migration policy [172, 180] . Below, I sketch Island Fuzzy CoCo and describe two preliminary tests performed to explore its behav- ior. ...
This thesis presents Fuzzy CoCo, a novel approach for system design, conducive to explaining human decisions. Based on fuzzy logic and coevolutionary computation, Fuzzy CoCo is a methodology for constructing systems able to accurately predict the outcome of a human decision-making process, while providing an understandable explanation of the underlying reasoning. Fuzzy logic provides a formal framework for constructing systems exhibiting both good numeric performance (precision) and linguistic representation (interpretability). From a numeric point of view, fuzzy systems exhibit nonlinear behavior and can handle imprecise and incomplete information. Linguistically, they represent knowledge in the form of rules, a natural way for explaining decision processes. Fuzzy modeling —meaning the construction of fuzzy systems— is an arduous task, demanding the identification of many parameters. This thesis analyses the fuzzy-modeling problem and different approaches to coping with it, focusing on evolutionary fuzzy modeling —the design of fuzzy inference systems using evolutionary algorithms— which constitutes the methodological base of my approach. In order to promote this analysis the parameters of a fuzzy system are classified into four categories: logic, structural, connective, and operational. The central contribution of this work is the use of an advanced evolutionary technique —cooperative coevolution— for dealing with the simultaneous design of connective and operational parameters. Cooperative coevolutionary fuzzy modeling succeeds in overcoming several limitations exhibited by other standard evolutionary approaches: stagnation, convergence to local optima, and computational costliness. Designing interpretable systems is a prime goal of my approach, which I study thoroughly herein. Based on a set of semantic and syntactic criteria, regarding the definition of linguistic concepts and their causal connections, I propose a number of strategies for producing more interpretable fuzzy systems. These strategies are implemented in Fuzzy CoCo, resulting in a modeling methodology providing high numeric precision, while incurring as little a loss of interpretability as possible. After testing Fuzzy CoCo on a benchmark problem —Fisher's Iris data— I successfully apply the algorithm to model the decision processes involved in two breast-cancer diagnostic problems: the WBCD problem and the Catalonia mammography interpretation problem. For the WBCD problem, Fuzzy CoCo produces systems both of high performance and high interpretability, comparable (if not better) than the best systems demonstrated to date. For the Catalonia problem, an evolved high-performance system was embedded within a web-based tool —called COBRA— for aiding radiologists in mammography interpretation. Several aspects of Fuzzy CoCo are thoroughly analyzed to provide a deeper understanding of the method. These analyses show the consistency of the results. They also help derive a stepwise guide to applying Fuzzy CoCo, and a set of qualitative relationships between some of its parameters that facilitate setting up the algorithm. Finally, this work proposes and explores preliminarily two extensions to the method: Island Fuzzy CoCo and Incremental Fuzzy CoCo, which together with the original CoCo constitute a family of coevolutionary fuzzy modeling techniques. The aim of these extensions is to guide the choice of an adequate number of rules for a given problem. While Island Fuzzy CoCo performs an extended search over different problem sizes, Incremental Fuzzy CoCo bases its search power on a mechanism of incremental evolution. Cette thèse présente Fuzzy CoCo, une nouvelle approche pour la conception de systèmes favorisant l'explication des décisions humaines. Basée sur la logique floue et sur le calcul coévolutionniste, Fuzzy CoCo est une méthodologie visant à construire des systèmes capables de prédire le résultat d'un processus décisionnel humain et de fournir une explication compréhensible du raisonnement sous-jacent. La logique floue fournit un cadre formel pour construire des systèmes qui offrent à la fois une bonne performance numérique (précision), et une représentation linguistique (interprétabilité). D'un point de vue numérique, les systèmes flous sont des systèmes non linéaires capables de traiter une information imprécise et incomplète. Linguistiquement, ils représentent les connaissances sous forme de règles, ce qui est une façon naturelle d'expliquer des processus décisionnels. La modélisation floue —c'est à dire, la conception de systèmes flous— est une tâche difficile, exigeant l'identification de nombreux paramètres. Cette thèse analyse le problème de modélisation floue ainsi que des différentes approches existant pour le résoudre, se focalisant sur la modélisation floue évolutionniste —la conception de systèmes flous en utilisant des algorithmes évolutionnistes— qui constitue la base méthodologique de mon approche. Afin de favoriser cette analyse, les paramètres d'un système flou sont classifiés en quatre catégories: logiques, structuraux, connectifs, et opérationnels. La contribution centrale de ce travail est l'utilisation d'une technique évolutionniste avancée —la coévolution coopérative— pour faire face à la conception simultanée des paramètres connectifs et opérationnels. La modélisation floue par coévolution coopérative réussit à surmonter plusieurs limitations montrées par d'autres approches évolutionnistes: stagnation, convergence aux optimums locaux, et temps élevé de calcul. Concevoir des systèmes interprétables est un des buts principaux de mon approche, que j'étudie complètement. Basé sur un ensemble de critères sémantiques et syntaxiques concernant la définition des concepts linguistiques et leurs liens causals, je propose un certain nombre de stratégies pour produire des systèmes flous plus facilement interprétables. Ces stratégies sont implantées dans Fuzzy CoCo, ayant pour résultat une méthodologie de modélisation fournissant une précision numérique élevée, tout en gardant une interprétabilité aussi élevée que possible. Après avoir essayé Fuzzy CoCo sur un problème benchmark —le problème des iris de Fisher— j'ai appliqué avec succès l'algorithme pour modéliser les processus de décision impliqués dans deux problèmes de diagnostique de cancer du sein: le problème connu comme WBCD et le problème d'interprétation de mammographies de Catalogne. Pour le problème WBCD, Fuzzy CoCo produit des systèmes très performants et hautement interprétables, comparables (sinon superieures) aux meilleurs systèmes rapportés jusqu'à présent. Pour le problème de Catalogne, un très bon système évolué a été inclus dans un outil en ligne —appelé COBRA— aidant des radiologistes à l'interprétation de mammographies. Plusieurs aspects de Fuzzy CoCo sont minutieusement analysés afin de fournir une compréhension aprofondie de la méthode. Ces analyses montrent l'uniformité des résultats obtenus. Sur la base de ces analyses, je propose un guide pour appliquer Fuzzy CoCo, ainsi qu'un ensemble de rapports qualitatifs entre certains de ses paramètres pour faciliter leur choix lors de l'utilisation de l'algorithme. Finalement, ce travail propose et explore, de façon préliminaire, deux extensions à la méthode: Island Fuzzy CoCo et Incremental Fuzzy CoCo. Combinées avec le CoCo original, elles constituent une famille des techniques de modélisation floue coévolutionniste. Le but de ces extensions est de guider le choix du nombre de règles pour un problème donné; tandis que Island Fuzzy CoCo exécute une recherche étendue sur différentes tailles du problème, Incremental Fuzzy CoCo base sa puissance de recherche sur un mécanisme d'évolution incrémentielle.
... Another strategy for achieving data decomposition in GAs is to distribute the search space among individual processes. It has been shown that genetic algorithms which are seeded with sufficiently distinct initial populations tend to follow separate evolutionary paths, though they would converge to the same final solution [40,41]. ...
... In the present paper, some individuals may be obtained from the search carried out by employing the TS algorithm, which is described later. After the initialization phase, the optimization code used here employs GA, DE and PSO in parallel [19], according to the island model [23]. ...
A hybrid evolutionary algorithm is applied to the optimization of space missions with multiple im- pulses and gravity assists. The optimization procedure runs three different optimizers, based on ge- netic algorithms, differential evolution and particle swa rm optimization, in parallel; the algorithms are used synergistically by letting the best individuals, f ound by each algorithm, migrate to the others at prescribed intervals. A mass mutation operator is also employed to diversify the population and avoid premature convergence to suboptimal solutions. A module based on an enhanced continuous tabu search algorithm is introduced in the initialization p rocess to produce a good starting popula- tion for the optimization algorithm. The results show the good performance obtained with the hybrid algorithm and the improvement in terms of efficiency and comp utational cost which is provided, in most cases, by the tabu search initialization process.
... The subpopulations resulting from the distribution of the global population members can be called demes, a very evocative term from the field of population biology. Parallel GA literature also refers to them as islands [48,27]. ...
The algorithmic form of GAs conforms well to SIMD computing environments with relatively minor adjustments to the operators. In this paper we consider in detail a GA implementation on a MasPar machine. The question of the degree to which control parameters affecting intercommunication impact performance is addressed using ANOVA methods. The purpose is to supplant anecdotal experience with statistical evidence. A set of control parameters—topology, migration operator, migra-tion radius, and migration probability—were chosen together with four representative levels of each. Metrics for three response variables—efficiency, diversity, and schema propagation—were developed that allowed insight into the behavior under the various parametric conditions. These were incorporated into three 4 × 4 × 4 × 4 randomized factorial experiment designs. Among other things, it was determined that the interconnection topology is not in itself a significant factor but the extent of connectivity and frequency of communication are. An important outcome of this study is that, while the individual factors are significant, the factors do not interact in unexpected ways.
... This 2-level GA approach is very similar to a redundant gene approach in [10] where multiple genotypic bits would vote to turn on or off a phenotypic bit. In [1], [11], multiple populations were maintained and migration was allowed among different sub-populations. The primary goal was to maintain diversity. ...
This paper presents an evolutionary coding method that maps geno- type to phenotype in a genetic algorithm. Unlike traditional genetic algorithms, the proposed algorithm involves mating and reproduction of cells that have multiple chromosomes instead of single chromosomes. The algorithm also evolves the mapping from genotype to phenotype rather than using a fixed mapping that is associated with one particular encoding method. The genotype- to-phenotype mapping is conjectured to explicitly capture important schema information. Some empirical results are presented to demonstrate the efficacy of the algorithm with some GA-Hard problems.
... On the other hand, the more performant although slower search performed by the most complex runs, often find good systems that effectively use less rules than the maximum allowed and which are, thus, adequate for simpler populations. In order to exploit these " evolutionary by-products " I propose Island Fuzzy CoCo, an extension to fuzzy CoCo inspired on, and similar to, the so-called island model where several (sub)populations, called islands or demes, evolving separately most of the time, occasionally exchange individuals according to a certain migration policy [6] ...
... One way to help prevent the runs getting stuck in local fitness optima would be to maintain the genetic diversity of the population by introducing some kind of incomplete mixing (e.g., by using an island model genetic algorithm [33]). We have performed some initial experiments with incomplete mixing, but not enough at this stage to say how effective this strategy is at solving the problem. ...
Karl Sims' work on evolving body shapes and controllers for three-dimensional, physically simulated creatures generated wide interest on its publication in 1994. The purpose of this article is threefold: (a) to highlight a spate of recent work by a number of researchers in replicating, and in some cases extending, Sims' results using standard PCs (Sims' original work was done on a Connection Machine CM-5 parallel computer). In particular, a re-implementation of Sims' work by the authors will be described and discussed; (b) to illustrate how off-the-shelf physics engines can be used in this sort of work, and also to highlight some deficiencies of these engines and pitfalls when using them; and (c) to indicate how these recent studies stand in respect to Sims' original work.
... On the other hand, the more performant although slower search performed by the most complex runs, often find good systems that effectively use less rules than the maximum allowed and which are, thus, adequate for simpler populations. In order to exploit these "evolutionary by-products" I propose Island Fuzzy CoCo, an extension to fuzzy CoCo inspired on, and similar to, the so-called island model where several (sub)populations, called islands or demes, evolving separately most of the time, occasionally exchange individuals according to a certain migration policy [6]. ...
In Fuzzy CoCo, a cooperative coevolutionary approach to fuzzy modeling, two coevolving species are defined: database (membership functions) and rule base. However, finding an adequate rule-base size for a given problem is a hard task, usually tackled by running several, independent, instances of Fuzzy CoCo set to search for systems of di#erent sizes. I propose in this paper an extension to Fuzzy CoCo that takes advantage of such parallel exploration, through a carefully conceived migration policy, to improve both global search capabilities and evolutionary dynamics with respect to simple Fuzzy CoCo.
This paper investigates how the policy used to select migrants and the individuals they replace affects the selection pressure in parallel evolutionary algorithms (EAs) with multiple populations. The four possible combinations of random and fitness-based emigration and replacement of existing individuals are considered. The investigation follows two approaches. The first is to calculate the takeover time under the four migration policies. This approach makes several simplifying assumptions, but the qualitative conclusions that are derived from the calculations are confirmed by the second approach. The second approach consists on quantifying the increase in the selection intensity. The selection intensity is a domain-independent adimensional quantity that can be used to compare the selection pressure of common selection methods with the pressure caused by migration. The results may help to avoid excessively high (or low) selection pressures that may cause the search to fail, and offer a plausible explanation to the frequent claims of superlinear speedups in parallel EAs.
A chromosome representation framework based on an ancient game, Tracing a Ghost's Illusive Footprints (TGIF), is proposed for solving search problems that involve permutation or general ordering and mapping. The initial concept was tested on a permutation problem and a variant of the concept was applied successfully to solve deceptive problems for Genetic Algorithms (GAs).
A hybrid evolutionary algorithm which synergistically exploits differential evolution, genetic algorithms and particle swarm
optimization, has been developed and applied to spacecraft trajectory optimization. The cooperative procedure runs the three
basic algorithms in parallel, while letting the best individuals migrate to the other populations at prescribed intervals.
Rendezvous problems and round-trip Earth–Mars missions have been considered. The results show that the hybrid algorithm has
better performance compared to the basic algorithms that are employed. In particular, for the rendezvous problem, a 100% efficiency
can be obtained both by differential evolution and the genetic algorithm only when particular strategies and parameter settings
are adopted. On the other hand, the hybrid algorithm always attains the global optimum, even though nonoptimal strategies
and parameter settings are adopted. Also the number of function evaluations, which must be performed to attain the optimum,
is reduced when the hybrid algorithm is used. In the case of Earth–Mars missions, the hybrid algorithm is successfully employed
to determine mission opportunities in a large search space.
This paper investigates how the policy used to select migrants and the individuals they replace affects the selection pressure in parallel evolutionary algorithms (EAs) with multiple populations. The four possible combinations of random and fitness-based emigration and replacement of existing individuals are considered. The investigation follows two approaches. The first is to calculate the takeover time under the four migration policies. This approach makes several simplifying assumptions, but the qualitative conclusions that are derived from the calculations are confirmed by the second approach. The second approach consists on quantifying the increase in the selection intensity. The selection intensity is a domain-independent adimensional quantity that can be used to compare the selection pressure of common selection methods with the pressure caused by migration. The results may help to avoid excessively high (or low) selection pressures that may cause the search to fail, and offer a plausible explanation to the frequent claims of superlinear speedups in parallel EAs.
Genetic algorithms (GAs) are optimization techniques which imitate the way that nature selects the best individuals (the best adaptation to the environment) to create descendants which are more highly adapted. The first step is to generate a random initial population, where each individual is represented by a character chain like a chromosome and with the greatest diversity, so that this population has the widest range of characteristics. Each individual represents a solution for the targeted problem. Then, each individual is evaluated using a fitness function, which indicates the quality of each individual. Finally, the best-adapted individuals are selected to generate a new population, whose average will be nearer to the desired solution. This new population is created making use of three operators: selection, crossover and mutation.One of the major aspects of GA is their ability to be parallelised. Indeed, because natural evolution deals with an entire population and not only with particular individuals, it is a remarkably highly parallel process. Nowadays computer systems incorporate powerful graphic cards that are commonly idle during a normal execution process of most of the optimization algorithms. Modern graphic cards use a pipelined streaming architecture to perform a significant part of the rendering process. Two stages in the pipelined process are programmable in current graphics hardware. The vertex engine is used to perform transformations on the vertex attributes (normal, position, color, texture, ...). On the other hand, the fragment engine is used to transform the fragments that form the different polygons. Both engines are extremely parallel, processing several elements in parallel and making extensive use of SIMD units. In this work we have presented a parallel implementation of a GA using a GPU. We have implemented not only three well know benchmarks problems with excellent Speed-up results, but also a novel implementation of an algorithm for solving defectives problems proposed in the literature.
The class of genetic algorithms (Gas) is a member of the evolutionary algorithms (EAs). In Gas, a solution is considered as a phenotype and the chromosome representation is a genotype. In a canonical GA, the genotypic search space could be tightly coupled with the phenotypic solution space under a specific encoding scheme. Variants of the canonical Gas are developed based on how the problem is represented in both the genotypic space and phenotypic space. This paper focuses on Gas that utilizes both genotypic and phenotypic spaces and investigates some of the effects of the coupling of the two spaces.
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