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Evolution Strategies: An Alternative Evolutionary Algorithm

  • March 1999
Authors:
Thomas Bäck at Leiden University
Thomas Bäck
Informatik Centrum Dortmund
Informatik Centrum Dortmund
Informatik Centrum Dortmund
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Abstract and Figures

. 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. ...
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... 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 classifi ed in gradientbased algorithms like steepest descent and Newton methods (Kelley 1999), heuristic gradient-free approaches like grid or pattern search, adaptive response surfaces and simplex optimizer, and also natureinspired search methods like genetic and evolutionary algorithms (Bäck 1996), particle swarm optimization (Engelbrecht 2005) and simulated annealing. ...
Robust Design Optimization (RDO) – Key technology for resource-efficient product development and performance enhancement
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  • Mar 2019
CAE-based optimization looks back on a long tradition in engineering. The goal of optimization is often the reduction of material consumption while pushing the design performance to the boundaries of allowable stresses, deformations or other critical design responses. At the same time, safety margins should be reduced, products should remain cost effective and over-engineering should be avoided. Of course a product should perform effectively in the real world, with the variety of manufacturing, assembly and environmental conditions which may be expected to occur not only optimal under one possible set of parameter realizations. It also has to function with sufficient reliability under scattering environmental conditions. In the virtual world, the impact of such variations can be investigated through, for example, stochastic analyses leading to CAE-based robustness evaluation. If CAE- based optimization and robustness evaluation are combined, the area of Robust Design Optimization (RDO) is entered, which may also be called “Design for Six Sigma” (DFSS) or just “Robust Design” (RD). The main idea behind such tethodologies is the consideration of uncertainties within the design process. These uncertainties may have different sources: for example, variations in loading conditions, tolerances of the geometrical dimensions and material properties caused by production or deterioration. In the design optimization procedure, some of these uncertainties may have a significant impact on design performance and must therefore be considered.
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... For top-down feature selection, we manually selected feature sets based on stimuli and type of measure ( Figure 1B). For bottom-up feature selection, we used a genetic algorithm (Back, 1996;Jóhannesson et al., 2002;Snaedal et al., 2012); online supplemental materials) based on the optimization of the area under the curve (AUC) of a 10-fold crossvalidated Support Vector Machine classifier with linear kernel. AUC is an effective and combined measure of sensitivity and specificity, which allows to test the inherent ability of the predictor, providing a useful metric to evaluate diffusivity of the predictive features within the examined population (Kumar & Indrayan, 2011). ...
Understanding the Nature of Face Processing in Early Autism: A Prospective Study
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  • Aug 2022
Dimensional approaches to psychopathology interrogate the core neurocognitive domains interacting at the individual level to shape diagnostic symptoms. Embedding this approach in prospective longitudinal studies could transform our understanding of the mechanisms underlying neurodevelopmental disorders. Such designs require us to move beyond traditional group comparisons and determine which domain-specific alterations apply at the level of the individual, and whether they vary across distinct phenotypic subgroups. As a proof of principle, this study examines how the domain of face processing contributes to the emergence of autism spectrum disorder (ASD). We used an event-related potentials (ERPs) task in a cohort of 8-month-old infants with (n = 148) and without (n = 68) an older sibling with ASD, and combined traditional case-control comparisons with machine-learning techniques for prediction of social traits and ASD diagnosis at 36 months, and Bayesian hierarchical clustering for stratification into subgroups. A broad profile of alterations in the time-course of neural processing of faces in infancy was predictive of later ASD, with a strong convergence in ERP features predicting social traits and diagnosis. We identified two main subgroups in ASD, defined by distinct patterns of neural responses to faces, which differed on later sensory sensitivity. Taken together, our findings suggest that individual differences between infants contribute to the diffuse pattern of alterations predictive of ASD in the first year of life. Moving from group-level comparisons to pattern recognition and stratification can help to understand and reduce heterogeneity in clinical cohorts, and improve our understanding of the mechanisms that lead to later neurodevelopmental outcomes.
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... 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. ...
Perishable inventory management using GA-ANN and ICA-ANN
Article
Full-text available
  • Jan 2020
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.
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... 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. ...
Perishable Inventory Management Using GA-ANN and ICA-ANN
Article
  • Jan 2020
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.
View
... 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. ...
Efficient Methods for Industrial Robust Design Optimization
Conference Paper
Full-text available
  • Mar 2015
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.
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... 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. ...
An application example of the Breeder Genetic Algorithm to function optimization
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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 .
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Modeling Biochemical Pathways
Chapter
  • Oct 2010
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.
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Evolution and Optimum Seeking: The Sixth Generation
Article
Full-text available
  • Jan 1995
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
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