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Evolution Strategies: An Alternative Evolutionary Algorithm

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. In this paper, evolution strategies (ESs) --- a class of evolutionary algorithms using normally distributed mutations, recombination, deterministic selection of the ¯ ? 1 best offspring individuals, and the principle of self-adaptation for the collective on-line learning of strategy parameters --- are described by demonstrating their differences to genetic algorithms. By comparison of the algorithms, it is argued that the application of canonical genetic algorithms for continuous parameter optimization problems implies some difficulties caused by the encoding of continuous object variables by binary strings and the constant mutation rate used in genetic algorithms. Because they utilize a problem-adequate representation and a suitable self-adaptive step size control guaranteeing linear convergence for strictly convex problems, evolution strategies are argued to be more adequate for continuous problems. The main advantage of evolution strategies, the self-adaptation of strategy parame...
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... The following table gives references to the contributions by the year of publishing. 1964, [388] 1965, [351,390,435] 1968, [416] 1970, [296,321,371,417,443] 1971, [372,373,398,418] 1973, [225,378,379,391] 1974, [274,402,411,419] 1975, [420,436] 1976, [327,389,403] 1977, [231,254,271,326,329,335,338,421] 1978, [264,279,322,363,392,422] 1979, [226,255,280,281,295,315,330,337,357] 1980, [236,291,323,380,393,423,424,441] 1981, [252,314,349,385,401,410,425,426] 1982, [256,257,292,294,368,384,394,399,407,437,452] 1983, [229,258,306,308,309,348,382,383,387,439] 1984, [241,272,310,311,334,339,395,400,427,438,440,449,455] 1985, [228,273,312,350,409,447,453] 1986, [285,286,307,328,341,369,377,396,408,445,454,458] 1987, [240,265,332,336,446,457] 1988, [237,250,266,267,287,342,358,448] 1989, [238,242,243,269,284,293,300,305,352,364,365,367,397,428,429,456] 1990, [232,244,268,288,289,297,301,302,313,324,325,347,359,360,366,406,415,430,431,459] 1991, [227,233,234,251,259,260,270,278,303,317,318,344,353,354,355,356,381,404,412,432] 1992, [230,235,239,245,246,253,261,262,276,282,290,298,316,319,331,333,340,343,345,362,374,386,405,413,433,444] 1993, [247,248,249,263,275,277,283,299,304,320,346,361,370,375,376,414,434,442,450,451] 1994, [52,53,54,55,461,56,57,58,59,60,462,61,62,63,64,65,66,67,68,69,70,71,463,72,73,74,75,76,77,78,79,80] 1995, [81,82,464,83,84,85,86,87,465,88,89,90,466,91,92,93,467,468,469,94,95,96,97,98,99,460] 1996, [100,101,102,103,104,105,106,107,108,470,109,110,111,112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136] 1997, [137,138,139,140,142,143,144,145,146,147,148,149,150,151,152,153,154,155,156,471,157,158,159,160,161,162,163,164,165,166,167,168,169,170,171,172,173,174,175,176,177,178,179,180,181] 1998, [182,183,184,185,186,187,188,189,190,191,192,193,194,195,196,197,198,199,200,201,202,472] 1999, [203,204,205,206,207,208,209,210,211,212,213,214,215,216,217,218,219,220,221,222,223,224] 2000, [11,12,13,14,15,16,17,18,19,20,21] 2001, [22,23,24,25,26,27,28,29,30,31,32,141] 2002, [33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49] 2003, [50] 2004, [51] ...
... • Australia: [177] • Austria: [35,292,384,360,459,361,163,186,31,49] • Canada: [277,72,22] • China: [217,223,50] • Finland: [460,150] • France: [60,116,161,197,13,40] • Germany: [242,243,244,12,14,41,388,351,390,435,416,296,321,417,443,398,418,391,274,402,411,419,420,436,327,389,403,254,271,326,338,421,264,279,322,363,392,422,226,255,280,281,295,315,337,357,323,393,423,424,441,252,349,385,425,426,256,257,394,407,452,229,258,308,439,241,400,427,438,440,228,409,285,286,307,328,341,369,377,396,408,458,265,332,336,237,250,266,267,287,342,358,238,269,305,352,397,428,429,232,288,289,302,324,325,347,359,406,415,430,431,227,233,234,251,259,260,270,317,344,353,354,355,356,381,404,432,235,245,246,261,262,276,290,316,331,333,340,345,374,405,433,444,247,248,249,263,299,346,370,375,376,414,434,442,450,451,53,54,55,461,56,57,58,59,61,62,64,66,67,68,69,70,463,73,75,77,78,80,81,82,83,84,85,465,88,89,466,91,92,93,468,469,95,96,98,99,101,102,103,106,107,470,110,114,115,119,120,123,124,125,127,130,132,137,138,139,140,142,148,149,153,156,159,164,166,168,170,171,173,175,178,182,183,184,187,188,189,200,201,202,203,207,208,209,211,212,216,221,224,17,24,29,30,32,141,36,38,39,45,47,48] • Greece: [198] • India: [71] • Iran: [157] • Ireland: [219] • Israel: [18] • Italy: [278,362,275,105,131,218,20,26] • Japan: [33,109,112,151,471,190,194,222] • Mexico: [28] • Portugal: [46] • Romania: [158] • Singapore: [44] • South Korea: [86,108,111,118,152,167,196,213] • Spain: [90,135,136,146,185,199,204,205] • Switzerland: [43,300,301,133,134,176,27,51] • Taiwan: [174] • The Czech Republic: [297,298,195,42,113] • The Netherlands: [253,193] • The Slovak Republic: [160,169] • Turkey: [144] • United Kingdom: [457,293,386,63,79,117,129,145,180,472,215,11,19,23] • United States: [314,382,383,272,462,74,464,87,467,94,97,100,104,121,122,126,128,143,147,154,155,162,172,179,181,191,192,206,210,214,220,15,16,21] • Unknown country: [52,165,25] The words of the titles of the articles are shown in the next table arranged in alphabetical order. The most common words have been excluded. ...
... techniques based on imitating some principles of organic evol. [130] • An alternative evol. alg. ...
... Thomas Back has done a lot of analyses about the mutation rate. To determine the mutation rate, he used 1  where ℓ is the length of the chromosome (Back, 1993(Back, , 1995Back and Schutz, 1996). In this paper, this relationship is used to determine the mutation rate. ...
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We have developed a multi-objective multi-product inventory management model for perishable products, focusing on the inventory management of veterinary drugs. This model minimises holding, shortage, and expired costs and also demand forecast error simultaneously. The number of expired and shortage drugs can be calculated for each period using this model. Data from three types of veterinary drugs have been collected from a distribution centre (DC). In this research, multi-layer perceptron (MLP) neural network is used to forecast the demand and genetic algorithm (GA) and imperialist competitive algorithm (ICA) are used to solve and find satisfactory solutions. In this research, artificial neural network (ANN) is combined with the two above-mentioned algorithms to solve the problem. The results show that the proposed model can find high-quality solutions because it reduces inventory costs and forecast errors in the DC. Finally, the results of combining ANN with each of the algorithms were compared and it was concluded that the combination of ANN and ICA produced better solutions.
... Thomas Back has done a lot of analyses about the mutation rate. To determine the mutation rate, he used 1 where ℓ is the length of the chromosome (Back, 1993(Back, , 1995Back and Schutz, 1996). In this paper, this relationship is used to determine the mutation rate. ...
Article
We have developed a multi-objective multi-product inventory management model for perishable products, focusing on the inventory management of veterinary drugs. This model minimises holding, shortage, and expired costs and also demand forecast error simultaneously. The number of expired and shortage drugs can be calculated for each period using this model. Data from three types of veterinary drugs have been collected from a distribution centre (DC). In this research, multi-layer perceptron (MLP) neural network is used to forecast the demand and genetic algorithm (GA) and imperialist competitive algorithm (ICA) are used to solve and find satisfactory solutions. In this research, artificial neural network (ANN) is combined with the two above-mentioned algorithms to solve the problem. The results show that the proposed model can find high-quality solutions because it reduces inventory costs and forecast errors in the DC. Finally, the results of combining ANN with each of the algorithms were compared and it was concluded that the combination of ANN and ICA produced better solutions.
... For the search of an optimal design on an approximation function or even with direct solver runs, a huge number of optimization algorithms can be found in literature. They can be classified in gradientbased algorithms like steepest descent and Newton methods [4], heuristic gradient-free approaches like grid or pattern search, adaptive response surfaces and simplex optimizers and furthermore nature inspired search methods like genetic and evolutionary algorithms [1], particle swarm optimization [3] and simulated annealing. In Table 1 a set of representative methods is given and assessed with respect to its field of applications. ...
Conference Paper
Full-text available
In this paper suitable methods for robust design optimization are presented and discussed. Starting with an initial sensitivity analysis, the important design parameters can be identified and the optimization task can be significantly simplified. Taking into account uncertainties, the optimization task becomes more challenging. Instead of deterministic response values, uncertain model responses need to be analyzed. For a successful implementation this analysis requires the estimation of the probabilities of rare events. With help of a variance-based and reliability-based robustness evaluation, the required safety level can be implied in the optimization process and verified for the final design. Starting with the accompanying paper, we introduced the overview of robust design optimization and illustrated practical application. In this paper we continue with a more detailed view on the methodology.
... This can be explained in several ways. First, ES [13] is a far more complicated algorithrn that takes into account the interactions between variables more explicitly by selfoptimizing the amount of mutation necessary. Itis nonetheless very sensitive to its parameters so that tuning it is a more dicult task. ...
Article
Full-text available
Evolutionary Algorithms (EA) have demonstrated their abiLity to solve optimi zation tasks in a wide range of applications. In thi s paper, after outlining the basics of such algorithms, the possibilities of one of the latest to emerge, the Breeder Genetic Algorithm (BGA) are exempli ed by addressing a c1ass ical numerical opti-mization problem : the Fletcher-Powell pseudo-random function .
... In most cases the research focus has been the so-called genotype/phenotype mapping [15] [16] [17], but rarely has this research considered real-valued mappings. An exception is the work on evolution strategies, where mutation can be based on a N -dimensional Gaussian distribution, which effectively corresponds to performing a linear transformation of the original representation, followed by 1 -dimensional mutations [18]. As illustrated in Fig. 1 most POT methods require an initial set of parameter values. ...
Article
Full-text available
This paper describes a new approach to optimization that uses a novel representation for the parameters to be optimized. By using genetic programming, the method evolves a population of functions. The purpose of such functions is to transform initial random values of the parameters into better ones. The representation is, in principle, independent of the size of the problem being addressed. Promising results are reported, comparing the new method with differential evolution, particle swarm optimization, and genetic algorithms, on a test suite of benchmark problems.
Chapter
Sequence analysis methods predict macromolecule properties and intermolecular interactions. These data can be used to reconstruct molecular networks, which are complex systems that regulate cell functions. Systems biology uses mathematical modeling and computer-based numerical simulations in order to understand emergent properties of these systems. This chapter describes the approaches to define kinetic models to simulate biochemical pathways dynamics. It deals with three main steps: the definition of the system’s structure, the mathematical formulation to reproduce the time evolution and the parameter estimation to find the set of parameter values such that the model behavior fits the experimental data.
Conference Paper
In this paper, the authors propose the use of the Lévy probability distribution as leading mechanism for solutions differentiation in an efficient and bio-inspired optimization algorithm, ant colony optimization in continuous domains, ACOR. In the classical ACOR, new solutions are constructed starting from one solution, selected from an archive, where Gaussian distribution is used for parameter diversification. In the proposed approach, the Lévy probability distributions are properly introduced in the solution construction step, in order to couple the ACOR algorithm with the exploration properties of the Lévy distribution. The proposed approach has been tested on mathematical test functions and on a real world problem of structural engineering, the composite laminates buckling load maximization. In the latter case, as in many other cases in real world problems, the function to be optimized is multi-modal, and thus the exploration ability of the Levy perturbation operator allow the attainment of better results.
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From the Publisher:With the publication of this book, Hans-Paul Schwefel has responded to rapidly growing interest in Evolutionary Computation, a field that originated, in part, with his pioneering work in the early 1970s. Evolution and Optimum Seeking offers a systematic overview of both new and classical approaches to computer-aided optimum system design methods, including the new class of Evolutionary Algorithms and other "Parallel Problem Solving from Nature" (PPSN) methods. It presents numerical optimization methods and algorithms to computer calculations which will be particularly useful for massively parallel computers. It is the only book in the field that offers in-depth comparisons between classical direct optimization methods and the newer methods. Dr. Schwefel's method consists essentially of the adaptation of simple evolutionary rules to a computer procedure in the search for optimal parameters within a simulation model of a technical device. In addition to its historical and practical value, Evolution and Optimum Seeking will stimulate further research into PPSN and interdisciplinary thinking about multi-agent self-organization in natural and artificial environments. These developments have been accelerated by fortunate changes in the computational environment, especially with respect to new architectures. MIMD (Multiple Instructions Multiple Data) machines with many processors working in parallel on one task seem to lend themselves to inherently parallel problem solving concepts like Evolution Strategies. The most comprehensive work of its kind, Evolution and Optimum Seeking offers a state-of-the-art perspective on the field for researchers in computer-aided design, planning, control, systems analysis, computational intelligence, and artificial life. Its range and depth make it a virtual handbook for practitioners: epistemological introduction to the concepts and strategies of optimum seeking; taxonomy of optimization tasks and solution principles (material found n