[IEEE 2007 International Bhurban Conference on Applied Sciences & Technology - Islamabad, Pakistan...

Automated Design of Mechatronic Systems using

Bond-Graph Modeling and Simulation and GeneticProgramming

Saheeb Ahmed Kayani and Muhammad Afzaal Malik"Department of Mechanical Engineering, College ofE&ME, National University of Sciences and Technology, Rawalpindi, Pakistan

*saheebk(hotmail.com, **mafzmlk(hotmail.com

Abstract - All modern dynamic engineering systems can becharacterized as mechatronic systems. The multi-domain nature ofa mechatronic system makes it difficult to model using a singlemodeling technique over the whole system as varying sets of systemvariables are required. Bond-Graphs offer an advanced objectoriented modeling and simulation technique. They are domainindependent allowing straight forward and efficient modelcomposition, classification and analysis. Bond-Graph model of themechatronic system can be directly simulated on a digital computerusing simulation softwares like 20-Sim and Modelica graphically ormanipulated mathematically to yield state equations using asimplified set of power and energy variables. The simulationscheme can be augmented to synthesize designs for mechatronicsystems using genetic programming as a tool for open ended search.This research paper presents results of experiments conducted tocombine Bond-Graph modeling and simulation with geneticprogramming. A comprehensive review of the methodology is alsoincluded and the results are compared using different simulationsoftwares and conclusions drawn by research groups working onmechatronic systems and genetic programming internationally.

I. INTRODUCTION

Mechatronics refers to a synergetic combination ofdisciplines like mechanics, electronics, pneumatics, hydraulicsand thermodynamics etc. This field of technology is relativelynew and addresses the issues related with design anddevelopment of modem dynamic engineering systemsemploying electronics based control schemes. As most oftoday's machines ranging from house hold devices to automatedindustrial manufacturing systems are multi-disciplinarycombinations in design or hybrid systems in nature so the termand the technology field mechatronics has been put to use for thestudy and analysis of these so called multi-domain systems.Traditionally a mechatronic system has been defined as amechanical system being electronically controlled. This conceptcan be extended and any dynamic multi-domain systemcombining mechanical, electrical, hydraulic, pneumatic andthermal components etc. can be considered as a mechatronicsystem.

Incidentally we can hardly find any significant modemengineering application without digital control or not having

multi-domain character. In Fig. 1 we can see that a generalengineering system may consist of sets of sensors and actuatorsselected according to the design requirements in the particularsystem domain. [1] The output signal from the sensor is passedon to the signal conditioning block. Depending upon its nature aespecially employed circuit processes and transfers it to thedigital control architecture block where this conditionedinformation is interpreted and a command is issued which isagain transformed into a signal that is suitable for driving anactuator employed in the particular system. Also if there is avisual display the reading is refreshed based on most recentlyavailable information. The digital parts be it signal collectionfrom sensors, signal conditioning, data interpretation,implementation of control scheme or signal communication foractuators all contribute significantly towards rendering a generalmulti-domain engineering system to a mechatronic system.

A GENERAL ENGINEERING SYSTEMSystem Model & Dynamic Response

ACTUATORS SENSORS INPUT SIGNALi.e. Solenoids, Voice i.e. Switches, Strain CONDITIONINGCoils, DC Motors, Gauges, Potentiometers, & INTERFACINGStepper Motors, Thermocouples, i.e. Discrete CircuitsServo Motors, Photoelectronics, Filters ADC DACHydraulics, Accelerometers, Digital v

DAC,

Pneumatics etc. Encoders, MEMS etc. Amplifiers etc.

- _-|-_ _l

OUTPUT SIGNAL DIGITAL CONTROLCONDITIONING ARCHITECTURES

GRAPHICAL & INTERFACING i.e. Logic Circuits,DISPLAYS i.e. ADC, DAC, Microcontrollers, SBC, PLC,

i.e. LED, LCD, Digital Amplifiers, PWM, Sequencing and Timing,Displays, CRT etc. Power Transistors, Logic and Arithmetic,

Power Operational Control Algorithms,Amplifiers etc. Communication etc.

Fig. 1. A Mechatronic System.

This understanding also extends the range of application ofBond-Graphs [2], [3] to hybrid systems as they can handle alldomains fairly easily owing to the universal nature of theirmodeling paradigm. As explained earlier from cars to washing

Proceedings of International Bhurban Conference on Applied Sciences & TechnologyIslamabad, Pakistan, 8th- 11th January, 2007

104

machines and from mirrors for laser surgery to control surfacesfor space shuttles virtually every engineering system is acandidate for electronic control. To perform correctly thesemechatronic systems all depend on the interaction of sensors,computers or microcontrollers and actuators. Yet takingcomplicated dynamic systems all the way from concept toprototype requires mathematical models. Such models caninclude those whose equations the modeler derives directly.They can also include equations the modeler develops withsoftware that holds the mathematics in the background like 20-Sim. Generally mechatronic systems use sensors to convertmechanical measures into electrical signals. Sensors aredynamic and sometimes must themselves be modeled. Computeralgorithms issue commands to actuators based on sensor outputs.The actuators convert electrical inputs to mechanical motions.To model a mechatronic system all these sub-systems must beconnected and all non-linearities typical of a specific energydomain must be accounted for. To do this a language is neededto describe the different energy domains in communal terms.Using such a language sub-models can be connected in anoverall system model which can then be simulated on acomputer. Interacting physical systems store, transport anddissipate energy among sub-systems. Only Bond-Graphs canprovide a concise pictorial representation of these interactingdynamic systems down to the topological level. [4]

*JR

Fig. 2. A Mechatronics Network.

When using Bond-Graphs for mechatronic systemrepresentation we can assume that the mechatronic system underconsideration is an n-port mechatronics network with el and £being system input effort and flow signals and en and f, beingsystem output effort and flow signals respectively. [5]

II. REVIEW OF AUTOMATED DESIGN OFMECHATRONIC SYSTEMS

The basic idea of automated design is to replace the role ofdomain knowledge with the cheap computational resourcesavailable today. By combining unified modeling and analysiscapabilities of Bond-Graphs with powerful topologically openended synthesis and search capability of genetic programming asoftware system and methodology that is able to evolveinnovative mechatronic design solutions represented as Bond-Graphs has been developed with ever improving performance inan iterative loop of synthesis, analysis and feedback to thedesign process. [6] Extensive development on this automateddesign approach has been carried out at Genetic Algorithms

Research and Applications Group, College of Engineering,Michigan State University, East Lansing, MI, USA under theguidance of Dr. Erik Goodman and Dr. Bill Punch since 1993.Genetic programming based techniques are capable ofsynthesizing designs of arbitrary complexity as therepresentation of designs is entirely open ended. The synthesisoperators will allow the algorithm to combine building blocks ofarbitrary size and shape from one design to insert into anotherbased on what it has learned about the performance from Bond-Graph analysis and simulation of both designs. This synthesisprocess is made more efficient because the Bond-Graph designscan be evaluated in two stages. The first determines whether thecomponent connections in the candidate design satisfy certainrules of causality in their pattern of inter-connection and this canbe determined quickly using the researcher's existing Bond-Graph analysis tools. Then for designs which pass that criterionmore expensive calculation of their performance in fulfilling thespecified design objectives is done again using existing toolswhich the researchers need only adapt to this use. [7]

Fig. 3. Automated Design using Bond-Graphs and Genetic Programming.

For mechatronic systems the term automated design orautomated synthesis of design has been interchangeably used inavailable literature. In engineering design usually refers toassigning and finding numerical values to variables inmathematical models of a system while the whole process isbeing guided by a criteria based on design requirements. Whenthe design process is automated the first Bond-Graph designentered by the user is in fact in an embryonic state. The designsystem based on genetic programming improves the embryo andcreates newer versions of it called generations. In doing so thedesign process is automatically synthesizing newer generationsof the embryo while the whole process is being conducted within the limits specified by the fitness function which serves as aquality criterion for each new generation. Fig. 4 suggests adesign approach for generating mechatronic systems identifiedby Jiachuan Wang et al. [5] in 2005. According to thismethodology for any mechatronic system a start up design isspecified at the initial stage. Then Bond-Graph representation isdeveloped and it is transferred to the genetic programming toolwhich generates initial population, evaluates it according to the


105

4* modlaftork

A Wm*

fitness function, reconfigures the population and repeats theprocess until the design criteria are met. The successfulconceptual design candidates are transformed into final designagain represented as Bond-Graph models. During this wholeprocess information is extensively exchanged with knowledgecaches and incorporated in initial and final stages of the designprocess. The methodology involves increased human-computerinteraction. Also with in the knowledge library storedinformation is updated and enhanced as the design proceeds.The knowledge library serves as a dynamic data base of domainknowledge which is constantly updated and the contents areverified continuously to remove any errors or omissions throughan automated system. The input source to the knowledge libraryis the set of successful conceptual design candidates whichmeans that only the best of all sorted information is stored forfurther reference and improvement.

Knowledge Incorporation

KnowledgeI

I Library

" I I+ \Human _

taluation Computer AccumulationI Interaction

/ ,'

I Verification

I [

Kw| Knowledge ||i|Library

KnowledgeeExtractionn

Final Design 4Realization

Knowledge Incorporation

Fig. 4. Automated Design Methodology for Mechatronic Systems.

Multi-domain dynamic system design differs fromconventional design of electronic circuits, mechanical systemsand fluid power systems etc. partially because of the need tointegrate several types of energy behavior as part of the basicdesign. Multi-domain design is difficult because such systemstend to be complex and most current simulation tools operateover only a single domain. Bond-Graphs allow us to capture theenergy behavior underlying the physical aspects as opposed tothe information aspects of mechatronic systems in a uniformly

effective way across different domains. They enable the analysisof multi-domain systems with a unified inter domain tool.Search techniques can be used to generate improved designs ofsystems represented as Bond-Graph models like a variationaldesign method which means that a complete Bond-Graph modelis developed first and then it is changed topologically using agenetic algorithm [8] yielding new design alternatives. Geneticprogramming is an effective way to generate design candidatesin an open ended but statistically structured manner. A criticalaspect of the procedure is a fitness or a performance measurewhich must guide the evolution of candidate designs towards asuitable result in a reasonable time. [6] There have been anumber of research efforts aimed at exploring the combinationof genetic programming with physical systems modeling to findimproved engineering designs like the work of Dr. John R. Koza[9]-[11] considered a pioneer in this field. He presents a singleuniform approach using genetic programming for the automaticsynthesis of both the topology and sizing of a suite of variousprototype analog circuits including low pass filters, operationalamplifiers and controllers etc. But this means that his approachrequires a different simulation code or tool for each application.Writing a simulation code for an application is a very timeconsuming and tedious job. If the design applications ordomains are different one must be able to write or link to asimulation code for each new application. [7]

III. REVIEW OF AUTOMATED AND UNIFIED METHODOLOGYFOR MECHATRONIC SYSTEM DESIGN

Due to complexity of the engineering design problem theneed for efficiency in the design methodology is greatlyincreased. The most critical issues are automation of the designprocess and use of a unified design tool. Most design tools ormethodologies require user interaction so the developer mustmake many decisions during the design process. This makesthe design procedure more complex and often introducesthe need for trial and error iterations. The other issue is theneed for a unified design tool that can be applied to severaldomain areas. Designers some times have to consume largeamounts of time to prepare new analysis tools or methods. Adesign methodology that combines Bond-Graphs and geneticprogramming can provide both capabilities. The Bond-Graphwith genetic programming or BG/GP design methodologyrequires only an embryo model and a fitness definition in itsinitial stage as illustrated in the design example and theremaining procedures are automatically executed by geneticprogramming search. [7]

The multi-domain system representation is quitecomplicated and detailed due to different energy domainsinvolved as in addition to appropriate drivers or sources even thesimplest lumped parameter dynamic mechanical system modelstypically include at least masses, springs and dampers while thesimple RLC electric circuit includes resistors, inductors and


106

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I

-1IYI,VLAIVtV

capacitors. The most difficult aspect of the research inautomated system design is to develop a method that can explorethe design space in a topologically open ended manner yet findappropriate configurations efficiently enough to be useful.Bond-Graphs are ideal and most suitable candidates forcombining mechatronic system models with geneticprogramming as a means of exploring the design space. [7] In anattempt to automate design Danielson et al. [12] used Bond-Graphs and genetic algorithms to design a two strokecombustion engine. They started from a preliminary design andfound near optimal values for fifteen physical parameters for acombustion engine but without allowing topological variations.The approach developed by Erik Goodman et al. [6], [7], [13]enables analysis of multi-energy domain systems with a unifiedinter domain tool. It also allows unlimited search for atopologically open ended solution. Moreover efficient and rapidevaluation of individual designs is provided by using a two stageprocedure: a. Causal analysis of the Bond-Graph model. b.Appropriate detailed calculation using a derived state-spacemodel. Also a dynamic library of useful model performanceevaluation tools can be embedded as need arises since the use ofthese tools is encapsulated in the overall process. Even controlsystems related problems like eigen value search can beimplemented using this approach. It is a remarkable fact thatmodels based on apparently diverse branches of engineeringscience and knowledge can be expressed using Bond-Graphnotation based on energy and information flow. Using thislanguage one may construct models of electrical, mechanical,magnetic, hydraulic, pneumatic, thermal, acoustic, socio-economic, environmental and other systems using only a rathersmall set of ideal elements as building blocks. As a special formof evolutionary computation genetic programming is a powerfulapproach for creating and evolving novel design structures in anopen ended manner. Through definition of a set of basicconstruction functions a genotype tree is created for everyindividual in each generation. The process of evaluating thegenotype tree maps it into a phenotype which is an abstracttopological description of the design of the multi-domain systemusing Bond-Graphs. Physical realization is carried out to relateeach abstract element of the Bond-Graph model to thecorresponding components in various energy domains. [13]

IV. IMPLEMENTATION OF A METHODOLOGY FOR AUTOMATEDSYSTEM DESIGN

The experiments included in this research paper wereconducted as part of a postgraduate research thesis. Theseexperiments were based on the methodology for automateddesign of mechatronic systems identified by Kisung Seo et al. in[6] and Dr. Jianjun Hu in [14].

A. Summary ofthe MethodologyA brief summary of the methodology followed for

implementing the automated design scheme is included. a. ABond-Graph model is specified. b. First population of geneticprogramming tree is created. c. Each individual is evaluated forfitness using fitness function. d. Genetic programmingoperations i.e. selection, reproduction, crossover and mutationare performed for each population. e. Physical design is realizedif termination condition of genetic programming run is satisfied.f. Otherwise the process is repeated starting from fitnessevaluation of each individual.

B. Evaluation ofBond-Graph ModelsIn [6] a two step process is employed for evaluation of

Bond-Graph models. First each model is analyzed for causalityand then state equations are derived identifying whether thesystem is linear or not. In the next step the fitness of the model isanalyzed using fitness criterion.

C. Problem FormulationThe experiment was designed to be as simple as possible

because the C language code that was used for implementing themethodology became very complicated and difficult to handle.In all previous applications of this methodology by variousresearchers lil-gp 1.01 [15] a Java based genetic programmingsoftware has been used. But for the first time GeneticProgramming Studio [16] is employed in this application whichuses the lil-gp 1.01 kernel but offers a visual platform forexecuting genetic programming code. The code has been writtenusing MS Visual C++ 6.0. Six different code files are developed.1. protoapp.h contains prototypes of functions that app.cincludes. 2. appdef.h contains #defines of the application. 3.app.h contains global data and any other function defined byuser. 4. app.c contains software specific functions that help ininput/output procedures. 5. function.h contains prototypes offunctions and terminals of the problem. 6. function.c containsfunctions and terminals that are used for building the individual.Also files like epgdll.h, epgdll.c, defines.h, types.h, syscon.h andsyscon.c are included for creating DLL or dynamic linkedlibrary files. These files are software kernel files and are not tobe modified. The genetic programming parameters are saved inthe problem set file with the extension .EPG. This software alsooffers a simulation tool which can be used for representing theindividuals in LISP format. In case of Bond-Graph basedindividuals the final design requires simplification andreduction. The code is compiled and the DLL file is generatedthrough MS Visual C++ 6.0. The problem implemented is aneigen value design problem from [6]. Two target eigen valuesselected are -1±2j represented by cross marks x on complexplane and a Bond-Graph model with these eigen values is to begenerated.


107

mI4

x f2

IIi1

RR

Fig. 5. Representation of -1±2j on Complex Plane.

D. Bond-Graph EmbryoAn embryo Bond-Graph model is specified with only one

modifiable site represented by a dashed square box called thewrite head. The resistors are given same impedance values(R1:250, R2:500) as in [6] to achieve comparable results. Theembryo is allowed only one modifiable site to keep the designprocess and programming simple and less complicated toimplement and interpret.

R1 :250

R

| :-------- R2:500

Se A 1 +' 0- - R

Fig. 6. The Embryo Bond-Graph Model with One Modifiable Site.

E. Fitness FunctionThe fitness function includes two parameters namely raw

fitness and normalized fitness. Raw fitness FitnessRaw is the sumof distances between target eigen values and the nearest solutioneigen values after they have been paired. Normalized fitnessFitnessNorm is calculated according to the relation:

FitnessNOr 0.5 +I

1 + Fitness Raw(1)

F. Function and Terminal SetA list of genetic programming functions and terminals along

with their descriptions appears in Table I. The function f add Rrequires an additional parameter value called ephemeral randomconstant or ERC. An ERC is a special terminal whose value isfixed. When an ERC terminal is generated either during thefilling of the initial population or by mutation later in the run avalue is attached to that terminal and is unchanged bysubsequent operations. [15]

TABLE IFUNCTION AND TERMINAL DESCRIPTIONS

Function Descriptionf tree Generate a tree model

f add_C Add a C element to ajunctionf add_R Add a R element to ajunctionf add_I Add an I element to ajunction

f insert-JO Insert a zero junction in a bondf insert_JI Insert a one junction in a bondreplace C Replace with C elementreplace R Replace with R elementreplace_I Replace with I element

f add_ERC Add two ERCsf del_ERC Delete two ERCsend_A End terminal for add elementend_I End terminal for insert elementend_R End terminal for replace elementERC Ephemeral Random Constant

G. Experimental SetupThe genetic programming parameters used in the

experiment have been included in Table II. The software wasinstalled and run on a DELL/Pentium-1Il1.OGHz and 256MBRAM personal computer with Windows XP/2002/SP-1. Threedifferent random seeds were used and the experiment wasrepeated three times with population sizes of 100, 1000 and2500 with different number of generations.

TABLE IIGENETIC PROGRAMMING PARAMETERS

Number of Generations 100-500Population Size 100-2500

Initial Population Half and HalfSub Populations 10Maximum Nodes 300

Initial Depth 3-6Maximum Depth 17

Selection TournamentSize 7

Crossover 0.9Mutation 0.1

H. Experimental Results andAnalysisWhen different Bond-Graph functions can be applied to the

same write head this technique is termed as strongly typedgenetic programming. Add functions can only be applied to ajunction while insert functions are only applied to a bond.Replace functions change the type of the Bond-Graph elementand are node specific. Arithmetic functions of addition andsubtraction are carried out by f add_ERC and f del_ERCrespectively. The construction procedure for a Bond-Graphmodel is identified by the genetic programming tree. Using LISPformat of representing genetic programming trees the simulation


108

............... ... .... ....... ........... .................. -pp

xt

tool of Genetic Programming Studio is used to print long handversions of such genetic programming trees which need to besimplified for extracting meaningful information. One geneticprogramming tree represents one individual.

Rl :250

R

11:0 35

R3:0 922

1 ,r R

R2:500

Se 1 *,0 ,-'RLFI

C

Cl :0.42

Fig. 7. The Final Simplified Bond-Graph Model.

The average distance error e between target and solutioneigen values is calculated using distance formula for two pairs ofnumbers (x1, Yl) and (x2, Y2) given as:

e = [(x2 - X ±)2+ (Y2 -YI)21/2 (2)

The best solution eigen values compared to target eigenvalues are included in Table III along with average distanceerror. This table also contains number of R, C, I and junctionelements added to the write head. Numerical values of one portelements are also shown.

It is to be noted that the eigen values are determined usingthe A matrix of the Bond-Graph model (when state-spaceequations are written in matrix form assuming the system islinear) containing state variables contributed by the energystoring C and I elements.

dydt

:y[A] + u[B] (3)

In above equation y is the vector of states, A is an nxnsquare matrix, u is the array of sources and B is a matrix ofdimensions nxm where n is the number of states and m is thenumber of sources.

TABLE IIISUMMARY OF RESULTSTarget Eigen Values

-1±2jSolution Eigen Values

-0.82±1.941j

Average Distance Error0.18

Evolved Structure on Write HeadR Elements 1C Elements 1I Elements 1Junctions 1Bonds 4

Bond-Graph Element ValuesR Element 0.922C Element 0.42I Element 0.35

The values achieved in this experiment are slightly differentfrom the values in [6]. Short comings in the code used forgenerating the Bond-Graph model and fitness evaluation may bethe reason which can be removed with more rigorous and carefuleffort devoted towards code development.

V. CONCLUSION

Automated design of mechatronic systems using Bond-Graphs and genetic programming requires intensive effort forimplementation and code development. The technique has theadvantage of synthesizing topology and other design attributesusing the simplified and universal representation scheme offeredby Bond-Graphs and open ended search capabilities of geneticprogramming as illustrated by the eigen value design problem.This field has immense potential for exploring new researchideas pertaining to automated, unified and evolutionary design.When Bond-Graphs are used for system representation theautomated design methodology can cover problems in single andmulti-energy domains equally. This leads to application of thedesign approach to far more complicated problems compared toprevious efforts without using Bond-Graphs. The robustness ofthe approach lies in compactness of the genetic programmingcode and fitness evaluation of the evolved designs. Theinterpretation of the results can be simplified in further researchefforts.

ACKNOWLEDGMENT

We thank Dr. Abdul Ghafoor, Dr. Ijaz Ahmed Malik, RajaAmer Azim and Mr. Akhtar Khurshid for taking interest in thiswork. Also Mr. Ali Hassan/DCE and Mr. Wasim Baig/OICLibrary deserve our regards for their help in exploring availableliterature on Bond-Graph modeling and simulation and geneticprogramming.


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REFERENCES

[1] Michael B. Histand, David G. Alciatore, Introduction to Mechatronics andMeasurement Systems, McGraw Hill, New York, 1998.

[2] Dean C. Karnopp, Donald L. Margolis, Ronald C. Rosenberg, SystemDynamics - Modeling and Simulation of Mechatronic Systems, 3rd Edition,John Wiley, New York, 2000.

[3] Amalendu Mukherjee, Ranjit Karmakar, Modeling and Simulation ofEngineering Systems through Bond-Graphs, Narosa, New Delhi, 2000.

[4] Dean C. Karnopp, Donald L. Margolis, "The Language of Interaction", MEMagazine, American Society of Mechanical Engineers, January 2001, pp.1-4.

[5] Jiachuan Wang, Zhun Fan, Janis P. Terpenny, Erik D. Goodman,"Knowledge Interaction with Genetic Programming in MechatronicSystems Design using Bond-Graphs", IEEE Transactions on Systems, Manand Cybernetics, Part C: Applications and Reviews, Vol. 35, No. 2, May2005, pp. 172-182.

[6] Kisung Seo, Jianjun Hu, Zhun Fan, Erik D. Goodman, Ronald C.Rosenberg, "Automated Design Approaches for Multi-Domain DynamicSystems using Bond-Graphs and Genetic Programming", The InternationalJournal of Computers, Systems and Signals, Vol. 3, No. 1, 2002, pp. 55-70.

[7] Erik D. Goodman, Kisung Seo, Zhun Fan, Jianjun Hu, Ronald C.Rosenberg, "Automated Design of Mechatronic Systems: Novel SearchMethods and Modular Primitives to Enable Real World Applications",Proceedings of NSF Design, Service and Manufacturing Grantees andResearch Conference, Alabama, January 6-9, 2003, pp. 1-19.

[8] David E. Goldberg, Genetic Algorithms in Search, Optimization andMachine Learning, Addison Wesley, New York, 1989.

[9] John R. Koza, Martin A. Keane, Matthew J. Streeter, "What's Al Done forMe Lately? - Genetic Programming's Human Competitive Results", IEEEIntelligent Systems, 18(3), 2003, pp. 25-3 1.

[10] Haym Hirsh, Wolfgang Banzhaf, John R. Koza, Conor Ryan, Lee Spector,Christian Jacob, "Genetic Programming", IEEE Intelligent Systems, 15(3),2000, pp. 74-84.

[11] John R. Koza, Forrest H. Bennett, Jason Lohn, Frank Dunlap, Martin A.Keane, David Andre, "Automated Synthesis of Computational Circuitsusing Genetic Programming", Proceedings of IEEE InternationalConference on Evolutionary Computation, Indianapolis, 1997, pp. 447-452.

[12] B. Danielson, J. Foster, D. Frincke, "GABSys: Using Genetic Algorithmsto Breed a Combustion Engine", Proceedings of IEEE InternationalConference on Evolutionary Computation, Anchorage, May 4-9, 1998, pp.259-264.

[13] Zhun Fan, Kisung Seo, Ronald C. Rosenberg, Jianjun Hu, Erik D.Goodman, "Computational Synthesis of Multi-Domain Systems",Proceedings of AAAI Spring Symposium on Computational Synthesis,Stanford, March 24-26, 2003, pp. 59-66.

[14] Jianjun Hu, "Sustainable Evolutionary Algorithms and ScalableEvolutionary Synthesis of Dynamic Systems", PhD Dissertation,Department of Computer Science and Engineering, Michigan StateUniversity, MI, USA, 2004, pp. 69-80.

[15] Douglas Zongker, Bill Punch, lil-gp 1.01 User Manual, Michigan StateUniversity, MI, USA, 1996.

[16] Genetic Programming Studio, Version 1.0, Copyright (C Andres del CampoNovales, University of Cordoba, 1998, Spain.


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