Evolutionary programming (EP) has been applied with success to many numerical and combinatorial optimization problems in recent years. EP has rather slow convergence rates, however, on some function optimization problems. In this paper, a "fast EP" (FEP) is proposed which uses a Cauchy instead of Gaussian mutation as the primary search operator. The relationship between FEP and classical EP (CEP) is similar to that between fast simulated annealing and the classical version. Both analytical and empirical studies have been carried out to evaluate the performance of FEP and CEP for different function optimization problems. This paper shows that FEP is very good at search in a large neighborhood while CEP is better at search in a small local neighborhood. For a suite of 23 benchmark problems, FEP performs much better than CEP for multimodal functions with many local minima while being comparable to CEP in performance for unimodal and multimodal functions with only a few local minima. This paper also shows the relationship between the search step size and the probability of finding a global optimum and thus explains why FEP performs better than CEP on some functions but not on others. In addition, the importance of the neighborhood size and its relationship to the probability of finding a near-optimum is investigated. Based on these analyses, an improved FEP (IFEP) is proposed and tested empirically. This technique mixes different search operators (mutations). The experimental results show that IFEP performs better than or as well as the better of FEP and CEP for most benchmark problems tested.

s: Jan. 1992 -- Dec. 1994 ffl CTI: Current Technology Index Jan./Feb. 1993 -- Jan./Feb. 1994 ffl DAI: Dissertation Abstracts International: Vol. 53 No. 1 -- Vol. 55 No. 4 (1994) ffl EEA: Electrical & Electronics Abstracts: Jan. 1991 -- Dec. 1994 ffl P: Index to Scientific & Technical Proceedings: Jan. 1986 -- Feb. 1995 (except Nov. 1994) ffl EI A: The Engineering Index Annual: 1987 -- 1992 ffl EI M: The Engineering Index Monthly: Jan. 1993 -- Dec. 1994 The following GA researchers have already kindly supplied their complete autobibliographies and/or proofread references to their papers: Dan Adler, Patrick Argos, Jarmo T. Alander, James E. Baker, Wolfgang Banzhaf, Ralf Bruns, I. L. Bukatova, Thomas Back, Yuval Davidor, Dipankar Dasgupta, Marco Dorigo, Bogdan Filipic, Terence C. Fogarty, David B. Fogel, Toshio Fukuda, Hugo de Garis, Robert C. Glen, David E. Goldberg, Martina Gorges-Schleuter, Jeffrey Horn, Aristides T. Hatjimihail, Mark J. Jakiela, Richard S. Judson, Akihiko Konaga...

Evolution strategies are a class of general optimisation algorithms which are applicable to functions that are multimodal, nondifferentiable, or even discontinuous. Although recombination operators have been introduced into evolution strategies, the primary search operator is still mutation. Classical evolution strategies rely on Gaussian mutations. A new mutation operator based on the Cauchy distribution is proposed in this paper. It is shown empirically that the new evolution strategy based on Cauchy mutation outperforms the classical evolution strategy on most of the 23 benchmark problems tested in this paper. The paper also shows empirically that changing the order of mutating the objective variables and mutating the strategy parameters does not alter the previous conclusion significantly, and that Cauchy mutations with different scaling parameters still outperform the Gaussian mutation with self-adaptation. However, the advantage of Cauchy mutations disappears when recombination i...

Almost all analyses of time complexity of evolutionary algorithms (EAs) have been conducted for (1+1) EAs only. Theoretical results on the average computation time of population-based EAs are few. However, the vast majority of applications of EAs use a population size that is greater than one. The use of population has been regarded as one of the key features of EAs. It is important to understand in depth what the real utility of population is in terms of the time complexity of EAs, when EAs are applied to combinatorial optimization problems. This paper compares (1 + 1) EAs and (N + N) EAs theoretically by deriving their first hitting time on the same problems. It is shown that a population can have a drastic impact on an EA’s average computation time, changing an exponential time to a polynomial time (in the input size) in some cases. It is also shown that the first hitting probability can be improved by introducing a population. However, the results presented in this paper do not imply that population-based EAs will always be better than (1 + 1) EAs for all possible problems. I.

Abstract: Computational time complexity analyses of Evolutionary Algorithms (EAs) have been performed since the mid-nineties. The first results were related to very simple algorithms, such as the (1+1)-EA, on toy problems. These efforts produced a deeper understanding of how EAs perform on different kinds of fitness landscapes and general mathematical tools that may be extended to the analysis of more complicated EAs on more realistic problems. In fact, in recent years, it has been possible to analyse the (1+1)-EA on combinatorial optimization problems with practical applications and more realistic population-based EAs on structured toy problems. This paper presents a survey of the results obtained in the last decade along these two research lines. The most common mathematical techniques are introduced, the basic ideas behind them are discussed and their elective applications are highlighted. Solved problems that were still open are enumerated as are those still awaiting for a solution. New questions and problems arisen in the meantime are also considered. Keywords: Evolutionary algorithms, computational complexity, combinatorial optimization, evolutionary computation theory.

Genetic programming is a methodology for program development, consisting of a special form of genetic algorithm capable of handling parse trees representing programs, that has been successfully applied to a variety of problems. In this paper a new approach to the construction of neural networks based on genetic programming is presented. A linear chromosome is combined to a graph representation of the network and new operators are introduced, which allow the evolution of the architecture and the weights simultaneously without the need of local weight optimization. This paper describes the approach, the operators and reports results of the application of the model to several binary classification problems. 1 Introduction The design of neural networks is still largely performed using lengthy process of trial and error definition of the topology, followed by the application of a learning algorithm such as backpropagation [1]. However, the literature describes some approaches which try t...

The lognormal self-adaptation has been used extensively in evolutionary programming (EP) and evolution strategies (ES) to adjust the search step size for each objective variable. However, it was discovered in our previous study [1] that such self-adaptation may rapidly lead to a search step size that is far too small to explore the search space any further, and thus stagnates search. This is called the loss of step size control. It is necessary to use a lower bound of search step size to avoid this problem. Unfortunately, the optimal setting of lower bound is highly problem dependent. This paper first analyzes both theoretically and empirically how the step size control was lost. Then two schemes of dynamic lower bound are proposed. The schemes enable the EP algorithm to adjust the lower bound dynamically during evolution. Experimental results are presented to demonstrate the e ectiveness and efficiency of the dynamic lower bound for a set of benchmark functions.

. Most analytical and experimental results on evolutionary programming (EP) are obtained using low-dimensional problems, e.g., smaller than 50. It is unclear, however, whether the empirical results obtained from the low-dimensional problems still hold for high-dimensional cases. This paper investigates the behaviour of four different EP algorithms for large-scale problems, i.e., problems whose dimension ranges from 100 to 300. The four are classical EP (CEP) [1, 2], fast EP (FEP) [3], improved FEP (IFEP) [4] and a mixed EP (MEP) proposed in this paper. It is discovered that neither CEP nor FEP performs satisfactorily for the large-scale problems investigated here. However, IFEP and MEP are able to perform consistently well for both unimodal and multimodal functions with various dimensionalities. In addition, the time used by IFEP and MEP to find a near optimal solution appears to grow only polynomially (second-order polynomial) as the dimensionality of the problems studied increases. ...

Crossover plays an important role in GA-based search. There have been many empirical comparisons of different crossover operators in the literature. However, analytical results are limited. No theory has explained the behaviours of different crossover operators satisfactorily. This paper analyses crossover from quite a different point of view from the classical schema theorem. It explains the behaviours of different crossover operators through the investigation of crossover's search neighbourhood and search step size. It is shown that given the binary chromosome encoding scheme GAs with a large search step size is better than GAs with a small step size for most problems. Since uniform crossover's search step size is larger than that of either one-point or twopoint crossover, uniform crossover is expected to perform better than the other two. Similarly, two-point crossover is expected to perform better than one-point crossover due to its larger search step size. It is also shown in this...

We review the applications of artificial life (ALife), the creation of synthetic life on computers to study, simulate, and understand living systems. The definition and features of ALife are shown by application studies. ALife application fields treated include robot control, robot manufacturing, practical robots, computer graphics, natural phenomenon modeling, entertainment, games, music, economics, Internet, information processing, industrial design, simulation software, electronics, security, data mining, and telecommunications. In order to show the status of ALife application research, this review primarily features a survey of about 180 ALife application articles rather than a selected representation of a few articles. Evolutionary computation is the most popular method for designing such applications, but recently swarm intelligence, artificial immune network, and agent-based modeling have also produced results. Applications were initially restricted to the robotics