Evolutionary computation has started to receive significant attention during the last decade, although the origins can be traced back to the late 1950s. This article surveys the history as well as the current state of this rapidly growing field. We describe the purpose, the general structure and the working principles of different approaches, including genetic algorithms (GA) (with links to genetic programming (GP) and classifier systems (CS)), evolution strategies (ES), and evolutionary programming (EP), by analysis and comparison of their most important constituents (i.e., representations, variation operators, reproduction and selection mechanism). Finally, we give a brief overview on the manifold of application domains, although this necessarily must remain incomplete.

This paper analyzes the Self-Adaptation (SA) algorithm widely used to adapt strategy parameters of the Evolution Strategy (ES) in order to obtain maximal ES-performance. The investigations are concentrated on the adaptation of one general mutation strength oe (called oeSA) in (1; ) ESs. The hypersphere serves as the fitness model. Starting from an introduction into the basic concept of self-adaptation, a framework for the analysis of oeSA is developed on two levels: a microscopic level concerning the description of the stochastic changes from one generation to the next, and a macroscopic level describing the evolutionary dynamics of the oeSA over the time (generations). The oe-SA requires the fixing of a new strategy parameter, the so-called learning parameter. The influence of this parameter on the ES performance is investigated and rules for its tuning are presented and discussed. The results of the theoretical analysis are compared with ES experiments and it will be shown that apply...

Self-adaptation is an essential feature of natural evolution. However, in the context of function optimization, self-adaptation features of evolutionary search algorithms have been explored only with evolution strategy (ES) and evolutionary programming (EP). In this paper, we demonstrate the selfadaptive feature of real-parameter genetic algorithms (GAs) using simulated binary crossover (SBX) operator and without any mutation operator. The connection between the working of self-adaptive ESs and real-parameter GAs with SBX operator is also discussed. Thereafter, the self-adaptive behavior of real-parameter GAs is demonstrated on a number of test problems commonly-used in the ES literature. The remarkable similarity in the working principle of real-parameter GAs and self-adaptive ESs shown in this study suggests the need of emphasizing further studies on self-adaptive GAs.

. The breeder genetic algorithm BGA depends on a set of control parameters and genetic operators. In this paper it is shown that strategy adaptation by competing subpopulations makes the BGA more robust and more efficient. Each subpopulation uses a different strategy which competes with other subpopulations. Numerical results are presented for a number of test functions. Keywords: breeder genetic algorithm, strategy adaptation, competition, multiresolution search 1 Introduction Many evolutionary algorithms depend on a set of control parameters. Often the optimal setting of the parameter depends on the particular application. Moreover the optimal control parameters may be different at the start of the run and at the end where the individuals are very similar to each other. Basically two approaches have been pursuit to solve the above problem. In the first approach some externally specified schedule is used. The schedule may depend for instance on the time, measured in number of genera...

Evolution strategies are general, nature-inspired heuristics for search and optimization. Supported both by empirical evidence and by recent theoretical findings, there is a common belief that evolution strategies are robust and reliable, and frequently they are the method of choice if neither derivatives of the objective function are at hand nor differentiability and numerical accuracy can be assumed. However, despite their widespread use, there is little exchange between members of the “classical ” optimization community and people working in the field of evolutionary computation. It is our belief that both sides would benefit from such an exchange. In this paper, we present a brief outline of evolution strategies and discuss some of their properties in the presence of noise. We then empirically demonstrate that for a simple but nonetheless nontrivial noisy objective function, an evolution strategy outperforms other optimization algorithms designed to be able to cope with noise. The environment in which the algorithms are tested is deliberately chosen to afford a transparency of the results that reveals the strengths and shortcomings of the strategies, making it possible to draw conclusions with regard to the design of better optimization algorithms for noisy environments. 1

Due to the flexibility in adapting to different fitness landscapes, self-adaptive evolutionary algorithms (SA-EAs) have been gaining popularity in the recent past. In this paper, we postulate the properties that SA-EA operators should have for successful applications in real-valued search spaces. Specifically, population mean and variance of a number of SA-EA operators, such as various real-parameter crossover operators and self-adaptive evolution strategies, are calculated for this purpose. Simulation results are shown to verify the theoretical calculations. The postulations and population variance calculations explain why self-adaptive GAs and ESs have shown similar performance in the past and also suggest appropriate strategy parameter values which must be chosen while applying and comparing different SA-EAs.

In evolutionary algorithms, the fitness of a population increases with time by mutating and recombining individuals and by a biased selection of more fit individuals. The right selection pressure is critical in ensuring sufficient optimization progress on the one hand and in preserving genetic diversity to be able to escape from local optima on the other. We propose a new selection scheme, which is uniform in the fitness values. It generates selection pressure towards sparsely populated fitness regions, not necessarily towards higher fitness, as is the case for all other selection schemes. We show that the new selection scheme can be much more effective than standard selection schemes. 1

Genetic algorithms have been applied fairly successful to a number of optimization problems. Nevertheless, a common theory why and when they work is still missing. In this paper a theory is outlined which is based on the science of plant and animal breeding. A central part of the theory is the response to selection equation and the concept of heritability. A fundamental theorem states that the heritability is equal to the regression coe cient of parent to o spring. The theory is applied to analyze selection, mutation and recombination. The results are used in the Breeder Genetic Algorithm whose performance is shown to be superior to other genetic algorithms.

How well an optimization algorithm satisfies short-term and long-term goals, can be verified using appropriate test functions, respective convergence measures, theoretical analysis, and simulations. This paper analyses the convergence behavior of the evolution strategy (ES) at the parabolic ridge function using the standard (1 + ; λ)-ES. Some further results are given for the case of more general ridge functions. The results obtained are counter-intuitive and different from if not contrary to those obtained from the sphere model theory. Furthermore, using static analysis, we show that the progress rate and the quality gain possess entirely different characteristics.

We present a state-of-the-art survey of parallel meta-heuristic developments and results, discuss general design and implementation principles that apply to most meta-heuristic classes, instantiate these principles for the three meta-heuristic classes currently most extensively used - genetic methods, simulated annealing, and tabu search, and identify a number of trends and promising research directions.