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Shengxiang Yang, Yew-Soon Ong, Yaochu Jin (Eds.) Evolutionary Computation in Dynamic and Uncertain Environments

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Page 1: Shengxiang Yang, Yew-Soon Ong, Yaochu Jin (Eds ...syang/ECiDUE07FrontMatter.pdfthe most recent advances, present sophisticated real-world applications, and explore future research

Shengxiang Yang, Yew-Soon Ong, Yaochu Jin (Eds.)

Evolutionary Computation in Dynamic and Uncertain Environments

Page 2: Shengxiang Yang, Yew-Soon Ong, Yaochu Jin (Eds ...syang/ECiDUE07FrontMatter.pdfthe most recent advances, present sophisticated real-world applications, and explore future research

Studies in Computational Intelligence, Volume 51

Editor-in-chiefProf. Janusz KacprzykSystems Research InstitutePolish Academy of Sciencesul. Newelska 601-447 WarsawPolandE-mail: [email protected]

Further volumes of this seriescan be found on our homepage:springer.com

Vol. 31. Ajith Abraham, Crina Grosan, Vitorino Ramos(Eds.)Stigmergic Optimization, 2006ISBN 978-3-540-34689-0

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Vol. 33. Martin Pelikan, Kumara Sastry, ErickCantu-Paz (Eds.)Scalable Optimization via ProbabilisticModeling, 2006ISBN 978-3-540-34953-2

Vol. 34. Ajith Abraham, Crina Grosan, VitorinoRamos (Eds.)Swarm Intelligence in Data Mining, 2006ISBN 978-3-540-34955-6

Vol. 35. Ke Chen, Lipo Wang (Eds.)Trends in Neural Computation, 2007ISBN 978-3-540-36121-3

Vol. 36. Ildar Batyrshin, Janusz Kacprzyk, LeonidSheremetor, Lotfi A. Zadeh (Eds.)Preception-based Data Mining and Decision Makingin Economics and Finance, 2006ISBN 978-3-540-36244-9

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Vol. 40. Gregory Levitin (Ed.)Computational Intelligence in Reliability Engineering,2007ISBN 978-3-540-37371-1

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Vol. 43. Fabrice Guillet, Howard J. Hamilton (Eds.)Quality Measures in Data Mining, 2007ISBN 978-3-540-44911-9

Vol. 44. Nadia Nedjah, Luiza de MacedoMourelle, Mario Neto Borges,Nival Nunes de Almeida (Eds.)Intelligent Educational Machines, 2007ISBN 978-3-540-44920-1

Vol. 45. Vladimir G. Ivancevic, Tijana T. IvancevicNeuro-Fuzzy Associative Machinery for ComprehensiveBrain and Cognition Modeling, 2007ISBN 978-3-540-47463-0

Vol. 46. Valentina Zharkova, Lakhmi C. JainArtificial Intelligence in Recognition and Classificationof Astrophysical and Medical Images, 2007ISBN 978-3-540-47511-8

Vol. 47. S. Sumathi, S. EsakkirajanFundamentals of Relational Database ManagementSystems, 2007ISBN 978-3-540-48397-7

Vol. 48. H. Yoshida (Ed.)Advanced Computational Intelligence Paradigmsin Healthcare, 2007ISBN 978-3-540-47523-1

Vol. 49. Keshav P. Dahal, Kay Chen Tan, Peter I. Cowling(Eds.)Evolutionary Scheduling, 2007ISBN 978-3-540-48582-7

Vol. 50. Nadia Nedjah, Leandro dos Santos Coelho,Luiza de Macedo Mourelle (Eds.)Mobile Robots: The Evolutionary Approach, 2007ISBN 978-3-540-49719-6

Vol. 51. Shengxiang Yang, Yew-Soon Ong, Yaochu Jin(Eds.)Evolutionary Computation in Dynamic and UncertainEnvironments, 2007ISBN 978-3-540-49772-1

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Shengxiang YangYew-Soon OngYaochu Jin(Eds.)

Evolutionary Computationin Dynamic and UncertainEnvironments

With 272 Figures and 89 Tables

123

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Dr. Shengxiang YangDepartment of Computer Science

University of Leicester

University Road

Leicester, LE1 7RH

UK

E-mail: [email protected]

Dr. Yaochu JinHonda Research Institute Europe

Carl-Legien-Str. 30

63073 Offenbach

Germany

E-mail: [email protected]

Dr. Yew-Soon OngSchool of Computer Engineering

Nanyang Technology

University Block N4

Nanyang Avenue

Singapore, 639798

E-mail: [email protected]

Library of Congress Control Number: 2006939142

ISSN print edition: 1860-949XISSN electronic edition: 1860-9503ISBN-10 3-540-49772-2 Springer Berlin Heidelberg New YorkISBN-13 978-3-540-49772-1 Springer Berlin Heidelberg New York

This work is subject to copyright. All rights are reserved, whether the whole or part of the materialis concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broad-casting, reproduction on microfilm or in any other way, and storage in data banks. Duplication ofthis publication or parts thereof is permitted only under the provisions of the German Copyright Lawof September 9, 1965, in its current version, and permission for use must always be obtained fromSpringer-Verlag. Violations are liable to prosecution under the German Copyright Law.

Springer is a part of Springer Science+Business Mediaspringer.comc© Springer-Verlag Berlin Heidelberg 2007

The use of general descriptive names, registered names, trademarks, etc. in this publication does notimply, even in the absence of a specific statement, that such names are exempt from the relevantprotective laws and regulations and therefore free for general use.

Cover design: deblik, BerlinTypesetting by the editors using a Springer LATEX macro packagePrinted on acid-free paper SPIN: 11431411 89/SPi 5 4 3 2 1 0

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To our families

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Preface

Evolutionary computation is a class of problem optimization methodologywith the inspiration from the natural evolution of species. In nature, the pop-ulation of a species evolves by means of selection and variation. These twoprinciples of natural evolution form the fundamental of evolutionary algo-rithms (EAs). During the past several decades, EAs have been extensivelystudied by the computer science and artificial intelligence communities. As aclass of stochastic optimization techniques, EAs can often outperform classicaloptimization techniques for difficult real world problems.

Due to the ease of use and robustness, EAs have been applied to a widevariety of optimization problems. Most of these optimization problems tack-led are stationary and deterministic. However, many real-world optimizationproblems are subjected to dynamic and uncertain environments that are oftenimpossible to avoid in practice. For example, the fitness function is uncertainor noisy as a result of simulation errors, measurement errors or approximationerrors. In addition, the design variables or environmental conditions may alsoperturb or change over time. For these dynamic and uncertain optimizationproblems, the objective of the EA is no longer to simply locate the globaloptimum solution, but to continuously track the optimum in dynamic envi-ronments, or to find a robust solution that operates optimally in the presenceof uncertainties. This poses serious challenges to classical optimization tech-niques and conventional EAs as well. However, conventional EAs with properenhancements are still good tools of choice for optimization problems in dy-namic and uncertain environments. This is because EAs are inspired by prin-ciples of natural evolution, which takes place in the ever-changing dynamicand uncertain environments in nature.

Handling dynamic and uncertain optimization problems has been a topicsince the early days of evolutionary computation and has received increasingresearch interests over recent years due to its challenge and its importance inpractice. Several events, e.g., journal special issues, workshops and conferencespecial sessions, have taken place in recent years in the field of evolutionarycomputation in dynamic and uncertain environments. A variety of methods

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VIII Preface

have been reported across a broad range of application backgrounds in recentyears. This motivated the project of this book. This book aims to timely reflectthe most recent advances, present sophisticated real-world applications, andexplore future research directions in the field.

We have a total of 26 chapters in this book, which cover a broad rangeof topics relevant to evolutionary computation in dynamic and uncertain en-vironments. Further, the chapters in this book are presented as the followingfour categories:

• Part I: Optimum Tracking in Dynamic Environments• Part II: Approximation of Fitness Functions• Part III: Handling Noisy Fitness Functions• Part IV: Search for Robust Solutions

Part I: Optimum Tracking in Dynamic Environments

Most problems studied by the evolutionary computation community are sta-tionary optimization problems where no change occurs over time. For station-ary optimization problems, the goal is to design EAs that can quickly andprecisely locate the optimal solution(s) to the problem at hand. However, fordynamic optimization problems (DOPs) where change occurs over time, themain task is not to find one optimal solution but to track the moving optimumas soon and narrow as possible. This poses a serious challenge to conventionalEAs due to the convergence problem. For stationary optimization problems,convergence at a proper pace other than premature convergence is exactlywhat is expected for EAs to locate the optimal solution. However, conver-gence becomes a big problem for DOPs because once converged, it is difficultfor conventional EAs to adapt to the changing environment. DOPs usuallyrequire EAs to maintain certain level of diversity in the population. In orderto deal with this problem, several approaches have been developed in recentyears to enhance the performance of EAs in dynamic environments. Part Iof the book encapsulates nine chapters that reflect the state-of-the-art re-search on EAs for problem optimization in dynamic environments and theirapplication to real world dynamic problems.

The first six chapters of Part I present advanced EA approaches for gen-eral DOPs. In Chapter 1, Yang investigates the application of two kinds ofexplicit memory schemes, direct memory and associative memory, for geneticalgorithms (GAs) and univariate marginal distribution algorithms (UMDAs)for DOPs. Based on a series of systematically constructed dynamic test envi-ronments, experiments are carried out to compare the direct and associativememory schemes for GAs and UMDAs. Blackwell in Chapter 2 studies theuse of charged swarms in the particle swarm optimization (PSO) algorithmfor DOPs. A self-adapting multi-swarm approach with an exclusion operatorthat provides effective repulsion between swarms is advocated in this chapter.

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Preface IX

A simple rule for swarm birth and death is proposed so that the multi-swarmmay adjust its size dynamically and in relation to the number of peaks in thedynamic environments. Chapter 3 by Schonemann experimentally investigatesevolution strategies (ESs) for dynamic numerical optimization problems. Theresults demonstrates that self-adaptive ESs are powerful methods for dynamicenvironments. To avoid the handicaps of existing performance measures, anew measurement, called average best function value (ABFV), is developedto compare EAs for DOPs. This chapter also discusses the choice for differ-ent strategy parameters, e.g., the optimal number of mutation step sizes, forESs for practical application. An orthogonal dynamic hill-climbing algorithm(ODHC) is presented by Zeng et al. in Chapter 4 for continuous DOPs. InODHC, the local peak climber is not a solution, but a “niche” (a small hyper-rectangle). An orthogonal design method is employed on the niche in order toseek a potential peak more quickly. An archive is also used to store the latestfound higher peaks, so the ODHC algorithm can learn from the past search.Chapter 5 by Tinos and Yang presents a self-organizing random immigrantsscheme for GAs to address DOPs. In this scheme, the worst individual andits neighbours are replaced by random immigrants, which are placed in a sub-population to protect them from being replaced by fitter individuals in themain population. In this way, when the fitness of the individuals are close,one single replacement of an individual can affect a large number of individ-uals of the population in a chain reaction. This simple approach can take thesystem to a self-organization behaviour, which is useful for GAs in dynamicenvironments. Bosman in Chapter 6 investigates the use of learning and an-ticipation for EAs for online DOPs. The time–linkage property, i.e., decisionstaken now may influence the score in the future, has been identified as animportant source of problem–difficulty. A means to address time–linkage is topredict the future (i.e. anticipation) by learning from the past. This is for-malized into an algorithmic framework. Experimental results show that in thepresence of time–linkage EAs based on this algorithmic framework outperformconventional EAs.

The last three chapters of Part I present work on the application of EAsfor real world dynamic problems. In Chapter 7, Dam et al. investigates XCS,a genetics-based learning classifier system, for online dynamic data miningproblems with different degrees of concept changes. In order to reduce therecovery time of XCS after concept changes, three strategies are proposed toforce the system to learn quickly after severe changes. The effect of noise onthe recovery time after a concept change is also experimentally investigated.Chapter 8 by Michalewicz et al. discusses the prediction and optimizationissues in dynamic environments and suggests a system architecture, calledAdaptive Business Intelligence, to handle a kind of real world problems wherethe evaluation functions are based on the prediction of the future values ofsome variables. Three diverse case studies in dynamic environments: pollu-tion control, ship navigation, and car distribution, are presented. All theseproblems require some level of prediction and optimization for recommending

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X Preface

the best course of action. Quintao et al. in Chapter 9 present the applica-tion of EAs to the area coverage and node connectivity problems in wirelesssensor networks (WSNs), a kind of ad-hoc networks with distributed commu-nication, sensing, and processing capacities. EAs are provided to support thenetwork manager with the concern of controlling the energy consumption inthe network and the quality of service.

Part II: Approximation of Fitness Functions

A continuing trend in science and engineering is the use of increasingly ac-curate simulation codes in the design and analysis process so as to produceever more reliable and high quality products. Such technologies now play acentral role in aiding scientists validate crucial designs and to study the effectsof altering key design parameters on product performance. Nonetheless, theuse of accurate simulation methods can be very timing consuming, leadingto possibly unrealistic design cycle. Further, it poses a serious impediment tothe practical application of existing optimization methods for automaticallyestablishing the critical design parameters present in real world problems inscience and engineering. Particularly, EAs typically require many thousandsof function calls to the simulation codes in order to locate a near optimal solu-tion. One promising way to significantly reduce the computational cost of EAsby employing computationally cheap approximation models or surrogates inplace of the original computationally expensive fitness functions during evo-lutionary optimization. The five chapters showcased in Part II of the bookreflect the recent state-of-the-art research on single and multi-objective evo-lutionary frameworks for tackling problems with computationally expensiveoptimization functions in the context of real world applications.

To reduce the number of expensive fitness function evaluations in evolu-tionary optimization, Graning et al. in Chapter 10 present a study on severalindividual-based and generation-based adaptive strategies for neural networkmetamodel management. In their preliminary study, it was reported that someof adaptation mechanisms proposed do not perform well as expected. Theindividual-based meta-model management was found to be most promisingamong all and subsequently applied to real world 3D blade design optimiza-tion problem. Song in Chapter 11 considers the use of approximation modelsbased on Gaussian Processes for structural shape optimization. Applicationexamples of the proposed surrogate-assisted evolutionary approaches are givenin areas of firtree shape optimization using finite element method and enginenacelle optimization using computational fluid dynamics.

The next three chapters contributed by Reyes-Sierra and Coello in Chap-ter 12, Deb and Nain in Chpater 13, and Mack et al. in Chapter 14 presentthree independent studies on using approximation models in the context ofmulti-objective optimization. In particular, Reyes-Sierra and Coello presentan empirical study on using fitness inheritance over approximation models

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Preface XI

in the context of PSO and multi-objective optimization for enhancing evolu-tionary search. Deb and Nain, on the other hand, present a successive fitnesslandscape modelling for reducing the exact function evaluation calls while re-taining the basic search capability of NSGA-II. Using a case study in spacepropulsion, Mack et al. show that besides obtaining substantial improvementsin the efficiency of the evolutionary search, surrogate-based optimization isalso useful for novel or exploratory design tasks by offering a global view ofthe characteristics of the design space, thus enabling one to define previouslyunknown feasible design space boundaries and to reveal important physics inthe design.

Part III: Handling Noisy Fitness Functions

It rarely happens that the fitness of real-world problems can be calculated bya deterministic analytical function. In most cases, the quality of a candidatesolution has either to be measured by sensors or estimated using a numericalmethod. The sensory measurements are usually contaminated with noise in theenvironment, and the estimations are often subject to randomness. ThoughEAs are more robust against noise compared to derivative-dependent opti-mization methods, special attention needs to be paid in many cases. This partof the book presents four interesting chapters describing various approachesto handling noise in fitness evaluations.

Chapter 15 by Neri and Makinen describes a hierarchical EA for optimaldesign of an electrical grounding grid and an elastic structure. In this hierar-chical algorithm, the fitness of a population depends on the results from an-other population, which is therefore noisy. To achieve reliable results, countermeasures including population sizing, sampling sizing and survivor selectionare taken. Evolution of multi-rover systems in noisy environments has beendiscussed in Chapter 16 by Tumer and Agogino. Since it is unpractical toevaluate the fitness of rovers in collective, the authors presented differentmethods for designing the fitness function for individual rovers without de-grading the performance. Noise introduced by sensors are also considered. Amemetic algorithm combining a trust-region based local search with evolu-tionary global search is presented in Chapter 17 where a trust-region methodis combined with an evolutionary search. It is shown that on the one hand,evolutionary algorithms are inherently more robust against noise due to theirderivative-free characteristics, the quadratic model used for fitness estimationalso contributes to reducing the influence of noise. Chapter 18 by Tezuka etal deals with a financial optimization problem where the fitness values arebased on a Monte Carlo method. The explicit sampling method is adopted forreducing the influence of noise. To reduce the computational costs, a selectionefficiency index is proposed and the sampling size is adapted in such a waythat the selection efficiency is maximized.

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XII Preface

Part IV: Search for Robust Solutions

Solving optimization problems using EAs has always been perceived as findingthe optimal solution over the entire search space. However, the global optimamay not always be the most desirable solution in many real world engineeringdesign problems. In practice, if the global optimal solution is very sensitiveto uncertainties, for example, small changes in design variables or operatingconditions, then it may not be appropriate to use this highly sensitive solution.Part III showcases eight chapters primarily on new methodologies of EAs forrobust search.

Lim et al. in Chapter 19 report a study on several single and multi-objective inverse robust evolutionary optimization schemes that make littleassumption on the uncertainty structure. The inverse approach searches forsolutions that guarantee a certain degree of maximum uncertainty and, atthe same time, satisfy the desired nominal performance of the final designsolution. A multi-objective algorithm is also proposed in Chapter 20 by Gohand Tan for robust optimization. Their method incorporates the features ofmicro-GA (as a local search) to locate a worst case scenario of the candi-date solution, a memory-based feature of tabu restriction to guide the evo-lutionary process and periodic re-evaluation of archived solutions to reduceuncertainty of evolved solutions. In the context of real world robust designapplications, Hu et al. in Chapter 21 describe a robust design approach thatexploits the open-ended topological synthesis capability of genetic program-ming and bond graph modelling (GPBG) for evolving robust lowpass andhighpass analog filters with respect to parameter perturbations. Handa etal. on the other hand, describes a novel route planning memetic optimizationsystem for a fleet of salting trucks that remains robust under different roadtemperatures and different temperature distributions in a road network inChapter 22. Fan et al. in Chapter 23 report a method for robust layout syn-thesis of micro-electromechanical resonators subjected to inherent geometricuncertainties such as the fabrication error on the sidewall of the structure.An alternative technique that hybridizes EAs and Interval Arithmetic is alsodescribed in Chapter 24 by Rocco et al. Barrico and Antunes in Chapter 25present the concept of degree of robustness in a multi-objective evolutionaryapproach. The information on the degree of robustness of solutions can thenbe used to support the decision maker in the selection of a robust compromisesolution. Finally, Ling et al. report a study on the effect of the sampling num-ber of Monte-Carlo simulation method used in a standard crowding geneticalgorithm for robust optimal design of varied-line-spacing holographic gratingin recording optics in Chapter 26.

Generally speaking, this book fulfils the original aims quite well. The fourparts represent a great variety of work in the area of evolutionary computationin dynamic and uncertain environments. We hope that the publication of thisbook will further promote this emerging research field.

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Preface XIII

Finally, we would like to thank Dr. Janusz Kacprzyk for inviting us to editthis book in the Springer book series “Studies in Computational Intelligence”.We acknowledge the authors for their fine contributions and cooperation dur-ing the book preparation. We are grateful to Thomas Ditzinger and HeatherKing of Springer for their kind support for this book.

Shengxiang YangYew-Soon Ong

Yaochu JinNovember 2006

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Contents

Part I Optimum Tracking in Dynamic Environments

1 Explicit Memory Schemes for Evolutionary Algorithms inDynamic EnvironmentsShengxiang Yang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3

2 Particle Swarm Optimization in Dynamic EnvironmentsTim Blackwell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29

3 Evolution Strategies in Dynamic EnvironmentsLutz Schonemann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

4 Orthogonal Dynamic Hill Climbing Algorithm: ODHCSanyou Zeng, Hui Shi, Lishan Kang, Lixin Ding . . . . . . . . . . . . . . . . . . . . . 79

5 Genetic Algorithms with Self-Organizing Behaviour inDynamic EnvironmentsRenato Tinos, Shengxiang Yang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105

6 Learning and Anticipation in Online Dynamic OptimizationPeter A.N. Bosman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

7 Evolutionary Online Data Mining: An Investigation in aDynamic EnvironmentHai H. Dam, Chris Lokan, Hussein A. Abbass . . . . . . . . . . . . . . . . . . . . . . . 153

8 Adaptive Business Intelligence: Three Case StudiesZbigniew Michalewicz, Martin Schmidt, Matthew Michalewicz,Constantin Chiriac . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

9 Evolutionary Algorithms for Combinatorial Problems inthe Uncertain Environment of the Wireless Sensor Networks

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XVI Contents

Frederico Paiva Quintao, Fabıola Guerra Nakamura, Geraldo RobsonMateus . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

Part II Approximation of Fitness Functions

10 Individual-based Management of Meta-models forEvolutionary Optimization with Application to Three-Dimensional Blade OptimizationLars Graning, Yaochu Jin, Bernhard Sendhoff . . . . . . . . . . . . . . . . . . . . . . . 225

11 Evolutionary Shape Optimization Using GaussianProcessesWenbin Song . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

12 A Study of Techniques to Improve the Efficiency of aMulti-Objective Particle Swarm OptimizerMargarita Reyes-Sierra, Carlos A. Coello Coello . . . . . . . . . . . . . . . . . . . . . 269

13 An Evolutionary Multi-objective Adaptive Meta-modelingProcedure Using Artificial Neural NetworksKalyanmoy Deb, Pawan K. S. Nain . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

14 Surrogate Model-Based Optimization Framework: A CaseStudy in Aerospace DesignYolanda Mack, Tushar Goel, Wei Shyy, Raphael Haftka . . . . . . . . . . . . . . . 323

Part III Handling Noisy Fitness Functions

15 Hierarchical Evolutionary Algorithms and NoiseCompensation via AdaptationFerrante Neri, Raino A. E. Makinen . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 347

16 Evolving Multi Rover Systems in Dynamic and NoisyEnvironmentsKagan Tumer, Adrian Agogino . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373

17 A Memetic Algorithm Using a Trust-Region Derivative-Free Optimization with Quadratic Modelling for Optimizationof Expensive and Noisy Black-box FunctionsYoel Tenne, Steven William Armfield . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391

18 Genetic Algorithm to Optimize Fitness Function withSampling Error and its Application to Financial OptimizationProblemMasaru Tezuka, Masaharu Munetomo, Kiyoshi Akama . . . . . . . . . . . . . . . . 419

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Contents XVII

Part IV Search for Robust Solutions

19 Single/Multi-objective Inverse Robust EvolutionaryDesign Methodology in the Presence of UncertaintyDudy Lim, Yew-Soon Ong, Meng-Hiot Lim, Yaochu Jin . . . . . . . . . . . . . . . 439

20 Evolving the Tradeoffs between Pareto-Optimality andRobustness in Multi-Objective Evolutionary AlgorithmsChi Keong Goh, Kay Chen Tan . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

21 Evolutionary Robust Design of Analog Filters UsingGenetic ProgrammingJianjun Hu, Shaobo Li, Erik Goodman . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 481

22 Robust Salting Route Optimization Using EvolutionaryAlgorithmsHisashi Handa, Lee Chapman, Xin Yao . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499

23 An Evolutionary Approach For Robust Layout Synthesisof MEMSZhun Fan, Jiachuan Wang, Min Wen, Erik Goodman, Ronald Rosenberg 521

24 A Hybrid Approach Based on Evolutionary Strategies andInterval Arithmetic to Perform Robust DesignsClaudio M. Rocco S., Daniel E. Salazar A. . . . . . . . . . . . . . . . . . . . . . . . . . . 545

25 An Evolutionary Approach for Assessing the Degree ofRobustness of Solutions to Multi-Objective ModelsCarlos Barrico, Carlos Henggeler Antunes . . . . . . . . . . . . . . . . . . . . . . . . . . 567

26 Deterministic Robust Optimal Design Based on StandardCrowding Genetic AlgorithmQing Ling, Gang Wu, Qiuping Wang . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 585

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 601

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List of Contributors

Hussein A. AbbassArtificial Life and Adaptive RoboticsLaboratorySchool of Information Technologyand Electrical EngineeringThe University of New South WalesAustralian Defence Force AcademyCanberra ACT 2600, [email protected]

Adrian AgoginoUC Santa CruzNASA Ames Research CenterMailstop 269-3Moffett Field, CA 94035, [email protected]

Kiyoshi AkamaInformation Initiative CenterHokkaido UniversityKita 11 Nishi 5Sapporo, 060-0811, [email protected]

Carlos Henggeler AntunesDepartment of Electrical Engineeringand ComputersUniversity of Coimbra3000-033 Coimbra, [email protected]

Steven William ArmfieldSchool of Aerospace, Mechanical andMechatronic EngineeringUniversity of SydneySydney NSW 2006, [email protected]

Carlos BarricoDepartment of InformaticsUniversity of Beira Interior6201-001 Covilha, [email protected]

Tim BlackwellDepartment of ComputingGoldsmiths CollegeUniversity of LondonNew Cross, London SE14 6NW, [email protected]

Peter A. N. BosmanCentre for Mathematics andComputer Science (CWI)P.O. Box 940791090 GB Amsterdam, [email protected]

Lee ChapmanSchool of Geography, Earth, andEnvironmental ScienceThe University of BirminghamEdgbastonBirmingham B15 2TT, [email protected]

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XX List of Contributors

Constantin ChiriacSolveIT SoftwarePO Box 3161Adelaide, SA 5000, [email protected]

Carlos A. Coello CoelloCINVESTAV-IPN (EvolutionaryComputation Group)Departamento de IngenierıaElectrica, Seccion ComputacionAv. IPN No. 2508Col. San Pedro ZacatencoMexico D.F. 07360, [email protected]

Hai H. DamArtificial Life and Adaptive RoboticsLaboratorySchool of Information Technologyand Electrical EngineeringThe University of New South WalesAustralian Defence Force AcademyCanberra ACT 2600, [email protected]

Kalyanmoy DebKanpur Genetic AlgorithmsLaboratory (KanGAL)Dept. of Mechanical EngineeringIndian Institute of TechnologyKanpurKanpur, PIN 208 016, [email protected]

Lixin DingState Key Laboratory of SoftwareEngineeringWuhan UniversityWuhan 430072, Hubei, P. R. China.lx [email protected]

Zhun FanTechnical University of DenmarkDept. of Mechanical EngineeringLynby, 2800, [email protected]

Tushar Goel231 MAE-A, P.O. Box 116250Mechanical and Aerospace Engineer-ing DepartmentUniversity of FloridaGainesville, FL 32611-6250, [email protected]

Chi Keong GohDepartment of Electrical andComputer EngineeringNational University of Singapore4 Engineering Drive 3Singapore [email protected]

Erik Goodman2120 Engineering BuildingMichigan State UniversityEast Lansing, MI 48824, [email protected]

Raphael Haftka231 MAE-A, P.O. Box 116250Mechanical and Aerospace Engineer-ing DepartmentUniversity of FloridaGainesville, FL 32611-6250, [email protected]

Hisashi HandaGraduate School of Natural Scienceand TechnologyOkayama University,Tsushima-Naka 3-1-1,Okayama, 700-8530, [email protected]

Jianjun HuMCB 403DUniversity of Southern CaliforniaLos Angeles, CA, 90089, [email protected]

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List of Contributors XXI

Yaochu JinHonda Research Institute EuropeCarl-Legien-Str 3063073 Offenbach am Main, [email protected]

Lishan KangState Key Laboratory of SoftwareEngineeringWuhan UniversityWuhan 430072, Hubei, P. R. China.kang [email protected]

Shaobo LiCAD/CIMS InstituteGuizhou UniversityGuiyang 550003, Guizhou,P. R. [email protected]

Dudy LimSchool of Computer EngineeringNanyang Technological UniversityNanyang Avenue, Singapore [email protected]

Meng-Hiot LimSchool of Electrical and ElectronicsEngineeringNanyang Technological UniversityNanyang Avenue, Singapore [email protected]

Qing LingDepartment of AutomationUniversity of Science and Technologyof ChinaHefei 230026, P. R. [email protected]

Chris LokanArtificial Life and Adaptive RoboticsLaboratorySchool of Information Technologyand Electrical EngineeringThe University of New South WalesAustralian Defence Force AcademyCanberra ACT 2600, [email protected]

Yolanda Mack231 MAE-A, P.O. Box 116250Mechanical and Aerospace Engineer-ing DepartmentUniversity of FloridaGainesville, FL 32611-6250, [email protected]

Raino A. E. MakinenDipartimento di Elettrotecnica edElettronicaPolitecnico di BariVia E. Orabona 4, 70125Bari, [email protected]

Geraldo Robson MateusComputer Science DepartmentUniversidade Federal de MinasGerais (UFMG)Av. Antonio Carlos, 6627Belo Horizonte, MG, [email protected]

Matthew MichalewiczSolveIT SoftwareP.O. Box 3161Adelaide, SA 5000, [email protected]

Zbigniew MichalewiczSchool of Computer ScienceUniversity of AdelaideAdelaide, SA 5005, [email protected]

Masaharu MunetomoInformation Initiative CenterHokkaido UniversityKita 11 Nishi 5Sapporo, 060-0811, [email protected]

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XXII List of Contributors

Pawan K. S. NainKanpur Genetic AlgorithmsLaboratory (KanGAL)Dept. of Mechanical EngineeringIndian Institute of TechnologyKanpurKanpur, PIN 208 016, [email protected]

Fabıola Guerra NakamuraComputer Science DepartmentUniversidade Federal de MinasGerais (UFMG)Av. Antonio Carlos, 6627Belo Horizonte, MG, [email protected]

Ferrante NeriDepartment of MathematicalInformation Technology,P.O. Box 35 (Agora), FI-40014University of Jyvaskyla, [email protected]

Yew-Soon OngSchool of Computer EngineeringNanyang Technological UniversityBlk N4, 2b-39Nanyang Avenue, Singapore [email protected]

Frederico Paiva QuintaoComputer Science DepartmentUniversidade Federal de MinasGerais (UFMG)Av. Antonio Carlos, 6627Belo Horizonte, MG, [email protected]

Margarita Reyes-SierraCINVESTAV-IPN (EvolutionaryComputation Group)Departamento de IngenierıaElectrica, Seccion ComputacionAv. IPN No. 2508Col. San Pedro ZacatencoMexico D.F. 07360, [email protected]

Claudio M. Rocco S.Facultad de IngenierıaUniversidad Central de VenezuelaApartado Postal 47937Los ChaguaramosCaracas 1041A, [email protected]

Ronald RosenbergDepartment of Electrical andComputer EngineeringMichigan State UniversityEast Lansing, MI 48823, [email protected]

Daniel E. Salazar A.Instituto de Sistemas Inteligentes yAplicaciones Numericas enIngenierıa (IUSIANI)Universidad de Las Palmas de GranCanariaEdif. Central del Parque Cientıfico yTecnologico2 planta, Campus de Tafira BajaLas Palmas 35017, [email protected]

Martin SchmidtSolveIT SoftwareP.O. Box 3161Adelaide, SA 5000, [email protected]

Lutz SchonemannDepartment of Computer ScienceUniversity of DortmundD-44221 Dortmund, [email protected]

Hui ShiSchool of Computer ScienceChina University of GeoSciencesWuhan 430074, Hubei, P. R. [email protected]

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List of Contributors XXIII

Wei ShyyDept. of Aerospace EngineeringUniversity of Michigan1320 Beal AvenueAnn Arbor, MI 48109-2140, [email protected]

Wenbin SongSchool of Engineering SciencesUniversity of SouthamptonUniversity RoadSouthampton SO17 1BJ, [email protected]

Kay Chen TanDepartment of Electrical andComputer EngineeringNational University of Singapore4 Engineering Drive 3Singapore [email protected]

Yoel TenneSchool of Aerospace, Mechanical andMechatronic EngineeringUniversity of SydneySydney NSW 2006, [email protected]

Masaru TezukaResearch and Development SectionHitachi East Japan Solutions Ltd.2-16-10, Honcho, AobaSenadi, 980-0014, [email protected]

Renato TinosDepartamento de Fısica eMatematicaUniversidade de Sao Paulo (USP)Av. Bandeirantes 3900Ribeirao Preto, SP, 14040-901, [email protected]

Kagan TumerNASA Ames Research CenterMailstop 269-4Moffett Field, CA 94035, [email protected]

Jiachuan WangSystems DepartmentUnited Technologies Research CenterEast Hartford, 06128, [email protected]

Qiuping WangNational Synchrotron RadiationLaboratoryUniversity of Science and Technologyof ChinaHefei 230026, P. R. [email protected]

Min WenTechnical University of DenmarkDepartment of Informatics andMathematical ModellingLynby, 2800, [email protected]

Gang WuDepartment of AutomationUniversity of Science and Technologyof ChinaHefei 230026, P. R. [email protected]

Shengxiang YangDepartment of Computer ScienceUniversity of LeicesterUniversity RoadLeicester LE1 7RH, [email protected]

Xin YaoCERCIASchool of Computer ScienceThe University of BirminghamEdgbaston,Birmingham B15 2TT, [email protected]

Sanyou ZengSchool of Computer ScienceChina University of GeoSciencesWuhan 430074, Hubei, P. R. [email protected]

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