This paper considers the effect of stochasticity on the quality of convergence of genetic algorithms (GAs). In many problems, the variance of building-block fitness or so-called collateral noise is the major source of variance, and a population-sizing equation is derived to ensure that average signal-to-collateral-noise ratios are favorable to the discrimination of the best building blocks required to solve a problem of bounded deception. The sizing relation is modified to permit the inclusion of other sources of stochasticity, such as the noise of selection, the noise of genetic operators, and the explicit noise or nondeterminism of the objective function. In a test suite of five functions, the sizing relation proves to be a conservative predictor of average correct convergence, as long as all major sources of noise are considered in the sizing calculation. These results suggest how the sizing equation may be viewed as a coarse delineation of a boundary between what a physicist might call two distinct phases of GA behavior. At low population sizes the GA makes many errors of decision, and the quality of convergence is largely left to the vagaries of chance or the serial fixup of flawed results through mutation or other serial injection of diversity. At large population sizes, GAs can reliably discriminate between good and bad building blocks, and parallel processing and recombination of building blocks lead to quick solution of even difficult deceptive problems. Additionally, the paper outlines a number of extensions to this work, including the development of more refined models of the relation between generational average error and ultimate convergence quality, the development of online methods for sizing populations via the estimation of population-s...

Standard methods for inducing both the structure and weight values of recurrent neural networks fit an assumed class of architectures to every task. This simplification is necessary because the interactions between network structure and function are not well understood. Evolutionary computation, which includes genetic algorithms and evolutionary programming, is a population-based search method that has shown promise in such complex tasks. This paper argues that genetic algorithms are inappropriate for network acquisition and describes an evolutionary program, called GNARL, that simultaneously acquires both the structure and weights for recurrent networks. This algorithm's empirical acquisition method allows for the emergence of complex behaviors and topologies that are potentially excluded by the artificial architectural constraints imposed in standard network induction methods. To Appear in: IEEE Transactions on Neural Networks January The Ohio State University January 17, 1996 1 ...

Niching methods extend genetic algorithms to domains that require the location and maintenance of multiple solutions. Such domains include classification and machine learning, multimodal function optimization, multiobjective function optimization, and simulation of complex and adaptive systems. This study presents a comprehensive treatment of niching methods and the related topic of population diversity. Its purpose is to analyze existing niching methods and to design improved niching methods. To achieve this purpose, it first develops a general framework for the modelling of niching methods, and then applies this framework to construct models of individual niching methods, specifically crowding and sharing methods. Using a constructed model of crowding, this study determines why crowding methods over the last two decades have not made effective niching methods. A series of tests and design modifications results in the development of a highly effective form of crowding, called determin...

Within Genetic Algorithms (GAs) the mutation rate is mostly handled as a global, external parameter, which is constant over time or exogeneously changed over time. In this paper a new approach is presented, which transfers a basic idea from Evolution Strategies (ESs) to GAs. Mutation rates are changed into endogeneous items which are adapting during the search process. First experimental results are presented, which indicate that environment-- dependent self--adaptation of appropriate settings for the mutation rate is possible even for GAs. Furthermore, the reduction of the number of external parameters of a GA is seen as a first step towards achieving a problem--dependent self--adaptation of the algorithm. Introduction Natural evolution has proven to be a powerful mechanism for emergence and improvement of the living beings on our planet by performing a randomized search in the space of possible DNA-sequences. Due to this knowledge about the qualities of natural evolution, some resea...

This paper considers the use of genetic algorithms (GAs) for the solution of problems that are both average-sense misleading (deceptive) and massively multimodal. An archetypical multimodal-deceptive problem, here called a bipolar deceptive problem, is defined and two generalized constructions of such problems are reviewed, one using reflected trap functions and one using low-order Walsh coefficients; sufficient conditions for bipolar deception are also reviewed. The Walsh construction is then used to form a 30-bit, order-six bipolar-deceptive function by concatenating five, six-bit bipolar functions. This test function, with over five million local optima and 32 global optima, poses a difficult challenge to simple and niched GAs alike. Nonetheless, simulations show that a simple GA can reliably find one of the 32 global optima if appropriate signal-to-noise-ratio population sizing is adopted. Simulations also demonstrate that a niched GA can reliably and simultaneously find all 32 global solutions if the population is roughly sized for the expected niche distribution and if the function is appropriately scaled to emphasize global solutions at the expense of suboptimal ones. These results immediately recommend the application of niched GAs using appropriate population sizing and scaling. They also suggest a number of avenues for generalizing the notion of deception.

The conventional understanding of genetic algorithms depends upon analysis by schemata and the notion of intrinsic parallelism. For this reason, only k-ary string representations have had any formal basis and non-standard representations and operators have been regarded largely as heuristics, rather than principled algorithms. This paper extends the analysis to general representations through identification of schemata as equivalence classes induced by implicit equivalence relations over the space of chromosomes.

Abstract. What makes a problem easy or hard for a genetic algorithm (GA)? This question has become increas-ingly important as people have tried to apply the GA to ever more diverse types of problems. Much previous work on this question has studied the relationship between GA performance and the structure of a given fitness function when it is expressed as a Walsh polynomial. The work of Bethke, Goldberg, and others has produced certain theoretical results about this relationship. In this article we review these theoretical results, and then dis-cuss a number of seemingly anomalous experimental results reported by Tanese concerning the performance of the GA on a subclass of Walsh polynomials, some members of which were expected to be easy for the GA to optimize. Tanese found that the GA was poor at optimizing all functions in this subclass, that a partitioning of a single large population into a number of smaller independent populations seemed to improve performance, and that hillclimbing outperformed both the original and partitioned forms of the GA on these functions. These results seemed to contradict several commonly held expectations about GAs. We begin by reviewing schema processing in GAs. We then give an informal description of how Walsh analysis and Bethke's Walsh-schema transform relate to GA performance, and we discuss the relevance of this analysis for GA applications in optimization and machine learning. We then describe Tanese's surprising results, examine them experimentally and theoretically, and propose and evaluate some explanations. These explanations lead to a more fundamental question about GAs: what are the features of problems that determine the likelihood of suc-cessful GA performance?

This paper presents several theorems concerning the nature of deception and the central role that deception plays in function optimization using genetic algorithms. A simple proof is offered which shows that the only problems which pose challenging optimization tasks are problems that involve some degree of deception and which result in conflicting k-arm bandit competitions between hyperplanes. The concept of a deceptive attractor is introduced and shown to be more general than the deceptive optimum found in the deceptive functions that have been constructed to date. Also introduced are the concepts of fully deceptive problems as well as less strict consistently deceptive problems. A proof is given showing that deceptive attractors must have a complementary bit pattern to that found in the binary representation of the global optimum if a function is to be either fully deceptive or consistently deceptive. Some empirical results are presented which demonstrate different methods of dealing with deception and poor linkage during genetic search.

Researchers have long sought genetic algorithms (GAs) that can solve difficult search, optimization, and machine learning problems quickly. Despite years of work on simple GAs and their variants it is still unknown how difficult a problem simple GAs can solve, how quickly they can solve it, and with what reliability. More radical design departures than these have been taken, however, and the messy GA (mGA) approach has attempted to solve problems of bounded difficulty quickly and reliably by taking the notion of building-block linkage quite seriously. Early efforts were apparently successful in achieving polynomial convergence on some difficult problems, but the initialization bottleneck that required a large initial population was thought to be the primary obstacle to faster mGA performance. This paper replaces the partially enumerative initialization and selective primordial phase of the original messy GA with probabilistically complete initialization and a primordial phase that per...

. Genetic algorithms play a significant role, as search techniques for handling complex spaces, in many fields such as artificial intelligence, engineering, robotic, etc. Genetic algorithms are based on the underlying genetic process in biological organisms and on the natural evolution principles of populations. These algorithms process a population of chromosomes, which represent search space solutions, with three operations: selection, crossover and mutation. Under its initial formulation, the search space solutions are coded using the binary alphabet. However, the good properties related with these algorithms do not stem from the use of this alphabet; other coding types have been considered for the representation issue, such as real coding, which would seem particularly natural when tackling optimization problems of parameters with variables in continuous domains. In this paper we review the features of real-coded genetic algorithms. Different models of genetic operators and some me...