Do not Choose Representation just Change: An Experimental Study in States based EA

Our aim in this paper is to analyse the phenotypic effects (evolvability) of diverse coding conversion operators in an instance of the states based evolutionary algorithm (SEA). Since the representation of solutions or the selection of the best encoding during the optimization process has been proved to be very important for the efficiency of evolutionary algorithms (EAs), we will discuss a strategy of coupling more than one representation and different procedures of conversion from one coding to another during the search. Elsewhere, some EAs try to use multiple representations (SM-GA, SEA, etc.) in intention to benefit from the characteristics of each of them. In spite of those results, this paper shows that the change of the representation is also a crucial approach to take into consideration while attempting to increase the performances of such EAs. As a demonstrative example, we use a two states SEA (2-SEA) which has two identical search spaces but different coding conversion operators. The results show that the way of changing from one coding to another and not only the choice of the best representation nor the representation itself is very advantageous and must be taken into account in order to well-desing and improve EAs execution

On the Movement of Vertex Fixed Points in the Simple GA

ABSTRACT The Vose dynamical system model of the simple genetic algorithm models the behavior of this algorithm for large population sizes and is the basis of the exact Markov chain model. Populations consisting of multiple copies of one individual correspond to vertices of the simplex. For zero mutation, these are fixed points of the dynamical system and absorbing states of the Markov chain. For proportional selection, the asymptotic stability of vertex fixed points is understood from previous work. We derive the eigenvalues of the differential at vertex fixed points of the dynamical system model for tournament selection. We show that as mutation increases from zero, hyperbolic asymptotically stable fixed points move into the simplex, and hyperbolic asymptotically unstable fixed points move outside of the simplex. We calculate the derivative of local path of the fixed point with respect to the mutation rate for proportional selection. Simulation analysis shows how fixed points bifurcate with larger changes in the mutation rate and changes in the crossover rate

A probabilistic cooperative-competitive hierarchical search model.

by Wong Yin Bun, Terence.Thesis (M.Phil.)--Chinese University of Hong Kong, 1998.Includes bibliographical references (leaves 99-104).Abstract also in Chinese.List of Figures --- p.ixList of Tables --- p.xiChapter I --- Preliminary --- p.1Chapter 1 --- Introduction --- p.2Chapter 1.1 --- Thesis themes --- p.4Chapter 1.1.1 --- Dynamical view of landscape --- p.4Chapter 1.1.2 --- Bottom-up self-feedback algorithm with memory --- p.4Chapter 1.1.3 --- Cooperation and competition --- p.5Chapter 1.1.4 --- Contributions to genetic algorithms --- p.5Chapter 1.2 --- Thesis outline --- p.5Chapter 1.3 --- Contribution at a glance --- p.6Chapter 1.3.1 --- Problem --- p.6Chapter 1.3.2 --- Approach --- p.7Chapter 1.3.3 --- Contributions --- p.7Chapter 2 --- Background --- p.8Chapter 2.1 --- Iterative stochastic searching algorithms --- p.8Chapter 2.1.1 --- The algorithm --- p.8Chapter 2.1.2 --- Stochasticity --- p.10Chapter 2.2 --- Fitness landscapes and its relation to neighborhood --- p.12Chapter 2.2.1 --- Direct searching --- p.12Chapter 2.2.2 --- Exploration and exploitation --- p.12Chapter 2.2.3 --- Fitness landscapes --- p.13Chapter 2.2.4 --- Neighborhood --- p.16Chapter 2.3 --- Species formation methods --- p.17Chapter 2.3.1 --- Crowding methods --- p.17Chapter 2.3.2 --- Deterministic crowding --- p.18Chapter 2.3.3 --- Sharing method --- p.18Chapter 2.3.4 --- Dynamic niching --- p.19Chapter 2.4 --- Summary --- p.21Chapter II --- Probabilistic Binary Hierarchical Search --- p.22Chapter 3 --- The basic algorithm --- p.23Chapter 3.1 --- Introduction --- p.23Chapter 3.2 --- Search space reduction with binary hierarchy --- p.25Chapter 3.3 --- Search space modeling --- p.26Chapter 3.4 --- The information processing cycle --- p.29Chapter 3.4.1 --- Local searching agents --- p.29Chapter 3.4.2 --- Global environment --- p.30Chapter 3.4.3 --- Cooperative refinement and feedback --- p.33Chapter 3.5 --- Enhancement features --- p.34Chapter 3.5.1 --- Fitness scaling --- p.34Chapter 3.5.2 --- Elitism --- p.35Chapter 3.6 --- Illustration of the algorithm behavior --- p.36Chapter 3.6.1 --- Test problem --- p.36Chapter 3.6.2 --- Performance study --- p.38Chapter 3.6.3 --- Benchmark tests --- p.45Chapter 3.7 --- Discussion and analysis --- p.45Chapter 3.7.1 --- Hierarchy of partitions --- p.45Chapter 3.7.2 --- Availability of global information --- p.47Chapter 3.7.3 --- Adaptation --- p.47Chapter 3.8 --- Summary --- p.48Chapter III --- Cooperation and Competition --- p.50Chapter 4 --- High-dimensionality --- p.51Chapter 4.1 --- Introduction --- p.51Chapter 4.1.1 --- The challenge of high-dimensionality --- p.51Chapter 4.1.2 --- Cooperation - A solution to high-dimensionality --- p.52Chapter 4.2 --- Probabilistic Cooperative Binary Hierarchical Search --- p.52Chapter 4.2.1 --- Decoupling --- p.52Chapter 4.2.2 --- Cooperative fitness --- p.53Chapter 4.2.3 --- The cooperative model --- p.54Chapter 4.3 --- Empirical performance study --- p.56Chapter 4.3.1 --- pBHS versus pcBHS --- p.56Chapter 4.3.2 --- Scaling behavior of pcBHS --- p.60Chapter 4.3.3 --- Benchmark test --- p.62Chapter 4.4 --- Summary --- p.63Chapter 5 --- Deception --- p.65Chapter 5.1 --- Introduction --- p.65Chapter 5.1.1 --- The challenge of deceptiveness --- p.65Chapter 5.1.2 --- Competition: A solution to deception --- p.67Chapter 5.2 --- Probabilistic cooperative-competitive binary hierarchical search --- p.67Chapter 5.2.1 --- Overview --- p.68Chapter 5.2.2 --- The cooperative-competitive model --- p.68Chapter 5.3 --- Empirical performance study --- p.70Chapter 5.3.1 --- Goldberg's deceptive function --- p.70Chapter 5.3.2 --- "Shekel family - S5, S7, and S10" --- p.73Chapter 5.4 --- Summary --- p.74Chapter IV --- Finale --- p.78Chapter 6 --- A new genetic operator --- p.79Chapter 6.1 --- Introduction --- p.79Chapter 6.2 --- Variants of the integration --- p.80Chapter 6.2.1 --- Fixed-fraction-of-all --- p.83Chapter 6.2.2 --- Fixed-fraction-of-best --- p.83Chapter 6.2.3 --- Best-from-both --- p.84Chapter 6.3 --- Empricial performance study --- p.84Chapter 6.4 --- Summary --- p.88Chapter 7 --- Conclusion and Future work --- p.89Chapter A --- The pBHS Algorithm --- p.91Chapter A.1 --- Overview --- p.91Chapter A.2 --- Details --- p.91Chapter B --- Test problems --- p.96Bibliography --- p.9

Adaptive evolution in static and dynamic environments

This thesis provides a framework for describing a canonical evolutionary system. Populations of individuals are envisaged as traversing a search space structured by genetic and developmental operators under the influence of selection. Selection acts on individuals' phenotypic expressions, guiding the population over an evaluation landscape, which describes an idealised evaluation surface over the phenotypic space. The corresponding valuation landscape describes evaluations over the genotypic space and may be transformed by within generation adaptive (learning) or maladaptive (fault induction) local search. Populations subjected to particular genetic and selection operators are claimed to evolve towards a region of the valuation landscape with a characteristic local ruggedness, as given by the runtime operator correlation coefficient. This corresponds to the view of evolution discovering an evolutionarily stable population, or quasi-species, held in a state of dynamic equilibrium by the operator set and evaluation function. This is demonstrated by genetic algorithm experiments using the NK landscapes and a novel, evolvable evaluation function, The Tower of Babel. In fluctuating environments of varying temporal ruggedness, different operator sets are correspondingly more or less adapted. Quantitative genetics analyses of populations in sinusoidally fluctuating conditions are shown to describe certain well known electronic filters. This observation suggests the notion of Evolutionary Signal Processing. Genetic algorithm experiments in which a population tracks a sinusoidally fluctuating optimum support this view. Using a self-adaptive mutation rate, it is possible to tune the evolutionary filter to the environmental frequency. For a time varying frequency, the mutation rate reacts accordingly. With local search, the valuation landscape is transformed through temporal smoothing. By coevolving modifier genes for individual learning and the rate at which the benefits may be directly transmitted to the next generation, the relative adaptedness of individual learning and cultural inheritance according to the rate of environmental change is demonstrated

A Computational View on Natural Evolution: On the Rigorous Analysis of the Speed of Adaptation

Inspired by Darwin’s ideas, Turing (1948) proposed an evolutionary search as an automated problem solving approach. Mimicking natural evolution, evolutionary algorithms evolve a set of solutions through the repeated application of the evolutionary operators (mutation, recombination and selection). Evolutionary algorithms belong to the family of black box algorithms which are general purpose optimisation tools. They are typically used when no good specific algorithm is known for the problem at hand and they have been reported to be surprisingly effective (Eiben and Smith, 2015; Sarker et al., 2002). Interestingly, although evolutionary algorithms are heavily inspired by natural evolution, their study has deviated from the study of evolution by the population genetics community. We believe that this is a missed opportunity and that both fields can benefit from an interdisciplinary collaboration. The question of how long it takes for a natural population to evolve complex adaptations has fascinated researchers for decades. We will argue that this is an equivalent research question to the runtime analysis of algorithms. By making use of the methods and techniques used in both fields, we will derive plenty of meaningful results for both communities, proving that this interdisciplinary approach is effective and relevant. We will apply the tools used in the theoretical analysis of evolutionary algorithms to quantify the complexity of adaptive walks on many landscapes, illustrating how the structure of the fitness landscape and the parameter conditions can impose limits to adaptation. Furthermore, as geneticists use diffusion theory to track the change in the allele frequencies of a population, we will develop a brand new model to analyse the dynamics of evolutionary algorithms. Our model, based on stochastic differential equations, will allow to describe not only the expected behaviour, but also to measure how much the process might deviate from that expectation

An Analysis of Particle Swarm Optimizers

Many scientific, engineering and economic problems involve the optimisation of a set of parameters. These problems include examples like minimising the losses in a power grid by finding the optimal configuration of the components, or training a neural network to recognise images of people's faces. Numerous optimisation algorithms have been proposed to solve these problems, with varying degrees of success. The Particle Swarm Optimiser (PSO) is a relatively new technique that has been empirically shown to perform well on many of these optimisation problems. This thesis presents a theoretical model that can be used to describe the long-term behaviour of the algorithm. An enhanced version of the Particle Swarm Optimiser is constructed and shown to have guaranteed convergence on local minima. This algorithm is extended further, resulting in an algorithm with guaranteed convergence on global minima. A model for constructing cooperative PSO algorithms is developed, resulting in the introduction of two new PSO-based algorithms. Empirical results are presented to support the theoretical properties predicted by the various models, using synthetic benchmark functions to investigate specific properties. The various PSO-based algorithms are then applied to the task of training neural networks, corroborating the results obtained on the synthetic benchmark functions.Thesis (PhD)--University of Pretoria, 2007.Computer ScienceUnrestricte

Complexity Theory for Discrete Black-Box Optimization Heuristics

A predominant topic in the theory of evolutionary algorithms and, more generally, theory of randomized black-box optimization techniques is running time analysis. Running time analysis aims at understanding the performance of a given heuristic on a given problem by bounding the number of function evaluations that are needed by the heuristic to identify a solution of a desired quality. As in general algorithms theory, this running time perspective is most useful when it is complemented by a meaningful complexity theory that studies the limits of algorithmic solutions. In the context of discrete black-box optimization, several black-box complexity models have been developed to analyze the best possible performance that a black-box optimization algorithm can achieve on a given problem. The models differ in the classes of algorithms to which these lower bounds apply. This way, black-box complexity contributes to a better understanding of how certain algorithmic choices (such as the amount of memory used by a heuristic, its selective pressure, or properties of the strategies that it uses to create new solution candidates) influences performance. In this chapter we review the different black-box complexity models that have been proposed in the literature, survey the bounds that have been obtained for these models, and discuss how the interplay of running time analysis and black-box complexity can inspire new algorithmic solutions to well-researched problems in evolutionary computation. We also discuss in this chapter several interesting open questions for future work.Comment: This survey article is to appear (in a slightly modified form) in the book "Theory of Randomized Search Heuristics in Discrete Search Spaces", which will be published by Springer in 2018. The book is edited by Benjamin Doerr and Frank Neumann. Missing numbers of pointers to other chapters of this book will be added as soon as possibl