臺灣博碩士論文加值系統

全域性最佳化(global optimization)可應用於各種領域，如工程、自然科學、經濟、生物資訊、及商業等領域上。本論文提出一新的演化式方法論，稱為家族競爭演化式方法(FCEA)，此方法可應用於解全域性最佳化問題及實際的問題上。此方法以家族競爭(family competition)及調適規則(adaptive rules)為基礎，並整合遞減式(decreasing-based)及自我調整式(self-adaptive)的突變(mutation)，使FCEA能具有區域性最佳化及全域性最佳化的搜尋策略。這些策略能緊密結合，因此FCEA具有平衡區域性搜尋及全域性搜尋的能力，使得FCEA解全域性最佳化問題時能獲得好的結果。接著我們應用FCEA於函數最佳化(function optimization)及限制性最佳化(constrained optimization)的問題，實證結果顯示FCEA皆能獲得良好的結果，並優於遺傳演算法(genetic algorithms)、演化式策略(evolution strategies)及演化式規劃(evolutionary programming)等演化式方法。
我們已成功的應用FCEA於類神經網路(neural network)、光學薄膜設計(optical thin-film design)及結構化藥物設計(structure-based drug design)等實際的問題上，並獲得良好的成果。在類神經網路學習上，FCEA可訓練向前回饋式(feed forward)類神經網路解分類問題(classification benchmarks)，如雙螺旋問題(two-spiral problem)及採礦聲納問題( sonar classification)等。FCEA也可訓練回饋式 (recurrent)類神經網路解人工智慧的問題，如人工螞蟻(artificial ant problems)及規則化語言辨識(regular language recognition)等。接著我們設計FCEA成為光學薄膜設計的結合方法(synthesis method)，FCEA已成功設計反反射薄膜問題(antireflection coatings)、光束分歧器(beam splitter)、窄頻濾波(narrowband filter)、及邊界濾波( edge filter)等四種最重要的光學薄膜設計問題。光學薄膜設計能廣泛的應用於各種重要的領域上，如科學器具製造、醫學、及太空科學等。最後FCEA應用於彈性蛋白質結合(flexible ligand docking)問題上，此問題是結構化藥物設計的重要課題。
FCEA在上面五種應用領域上皆能獲得令人滿意的結果，因此我們認為FCEA具有一些良好的特性，我們也分析FCEA的收斂特性、搜尋行為及參數設定等特性。FCEA解全域性最佳化問題時具備彈性和穩定性，因此我們相信FCEA是有效之全域性最佳化的方法論。

Global optimization problems arise in many practical applications, such as engineering, natural sciences, economics, bioinformatics, and business. In this dissertation, a new evolutionary algorithm, called family competition evolutionary approach (FCEA), is proposed not only as the answer to global optimization, but also to be used for several practical applications. Based on family competition and adaptive rules, the proposed approach consists of global and local strategies by integrating decreasing-based mutations and self-adaptive mutations. These smoothly integrated strategies enable FCEA to balance the exploration and exploitation to achieve robust performance for global optimization. FCEA is then applied to certain areas of global optimization such as the function optimization and general constrained optimization problems. The experiments show that the proposed approach is more robust than other comparative evolutionary algorithms, including genetic algorithms, evolution strategies, and evolutionary
programming
FCEA has produced promising results in a number of applications,
including training neural networks, optical thin-film coatings,
and flexible ligand docking. For neural networks, FCEA is able to train feedforward neural networks for classification benchmarks, such as two-spiral problem and sonar classification. FCEA also gives promising recurrent neural networks for artificial intelligence problems, such as artificial ant problems and regular language recognition. FCEA is a good synthesis answer for the most important thin-film designs, including antireflection coatings, beam splitter, narrowband filters, and edge filters. Optical thin-film coatings have numerous remarkable applications in many branches of science and technology, such as scientific instrument manufacturing, spectroscope, medicine, and astronomy. Finally, it is verified that FCEA is able to generate low-energy solutions for flexible ligand docking problems, the molecular recognition between two molecules, which are are important for structure-based drug design
With the encouraging results shown, FCEA can imply certain
characteristics. This thesis has also analyzed the global
convergence property, search behaviors, and the parameter setting of FCEA. We believe that the flexibility and robustness of FCEA make it an effective tool for global optimization problems.

1 Introduction
1.1 Evolutionary Algorithms
1.2 Thesis Overview
2 The Family Competition Evolutionary Approach
2.1 Introduction
2.2 Overview
2.3 Family Competition
2.4 Chromosome Representation
2.5 Recombination Operators
2.6 Mutation Operators
2.7 Adaptive Rules
2.8 Global Convergence of FCEA
2.8.1 Markov Model
2.8.2 The Proof of Global Convergence
3 Functions Optimization Problems
3.1 Introduction
3.2 Analysis of FCEA
3.2.1 Parameters of FCEA
3.2.2 The Effectiveness of Multiple Operators and Family Competition
3.2.3 Controlling Step Sizes
3.3 Comparison with Other Methods
3.4 Testing Functions from the International Contests on Evolutionary Optimization
3.5 Building a Better Test Suite
3.6 Summary
4 Constrained Optimization Problems
4.1 Introduction
4.2 Problem Formulation
4.3 Experimental Results and Discusses
5 Training Neural Networks 58
5.1 Introduction
5.2 Artificial Neural Networks
5.3 Boolean Functions Learning
5.4 Inducing Regular Languages
5.5 The Parity Problems
5.6 Classification Problems
5.6.1 The Sonar Classification
5.6.2 The Two-spiral Problem
5.7 The Ant Problems
5.8 A Study of FCEA on Training Neural Networks
5.9 Summary
6 The Thin-film Synthesis of Optical Coatings 79
6.1 Introduction
6.2 Problem Definition
6.3 Homogeneous Coatings at Normal Light Incidence with Two Materials
6.3.1 Infrared Antireflection Coating
6.3.2 Filter with 0.0, 0.5, and 1.0 Transmission Regions
6.3.3 Tristimulus Filter
6.4 Inhomogeneous Coatings at Normal Light Incidence
6.4.1 Beam Splitter
6.4.2 Narrowband Reflector Filter
6.5 Coatings at Oblique Light Incidence
6.5.1 Long-wave-pass Filter
6.5.2 Short-wave-pass Filter
6.5.3 Nonpolarized Edge Filters
6.6 Investigation of FCEA on Thin-film Designs
6.6.1 Parameters of FCEA
6.6.2 The Effectiveness of Multiple Operators and Family Competition
6.7 Summary
7 Flexible Ligand Docking for Structure-based Drug Design
7.1 Introduction
7.2 Problem Description
7.3 Molecular Binding Experiments
7.4 Summary
8 Conclusions
8.1 Summary
8.2 Major Contributions
8.3 Future Works
A List of Publications

Bibliography
[1] Aguilera, J. A., Aguilera, J., Baumeister, P., Bloom, A., Coursen, D.,
Dobrowolski, J. A., Goldstein, F. T., Gustafson, D. E., and Kemp, R. A.
Antireflection coatings for germanium IR optics: a comparison of numerical design
methods. Applied Optics 27, 14 (1988), 2832--2840.
[2] Angeline, P. J., Saunders, G. M., and Pollack, J. B. An evolutionary algo?
rithm that constructs recurrent neural networks. IEEE trans. on Neural Networks 5,
1 (1994), 54--65.
[3] Angluin, D., and Smith, C. H. Inductive inference: theory and methods. Com?
puting Surveys 15, 3 (1983), 237--269.
[4] B?ack, T. Evolutionary Algorithms in Theory and Practice. Oxford University Press,
New York, USA, 1996.
[5] B?ack, T., Hammel, U., and Schwefel, H.-P. Evolutionary computation: Com?
ments on the history and current state. IEEE trans. Evolutionary Computation 1, 1
(1997), 3--17.
[6] B?ack, T., Hoffmeister, F., and Schwefel, H.-P. A survey of evolution strate?
gies. In Proc. Fourth Int. Conf. on Genetic Algorithms (1991), pp. 2--9.
[7] B?ack, T., and Sch?utz, M. Evolution strategies for mix-integer optimization of
optical multilayer systems. In Proc. of the 4th Annu. Conf. on Evolutionary Program?
ming (1995), D. B. Fogel and W. Atmar, Eds., Evolutionary Programming Society,
San Diego, CA, pp. 33--51.
[8] B?ack, T., and Schwefel, H.-P. An overview of evolution algorithms for parameter
optimization. Evolutionary Computation 1, 1 (1993), 1--23.
[9] Bengio, Y., Simard, P., and Frasconi, P. Learning long-term dependencies with
gradient descent is difficult. IEEE trans. on Neural Networks 5, 2 (1994), 157--166.
[10] Bersini, H., Dorigo, M., Langerman, S., Seront, G., and Gambardella,
L. Results of the first international content on evolutionary optimization (1st ICEO).
In Proc. of the IEEE Int. Conf. on Evolutionary Computation (1996), pp. 611--614.
[11] Bethke, A. D. Genetic algorithms as function optimizer. PhD thesis, University of
Michigan, 1990.
[12] Beyer, H. G. Toward a theory of evolution strategies: On the benefit of sex?
the theory. Evolutionary Computation 3, 1 (1995), 81--111.
[13] Bovard, B. G. Derivation of a matrix describing a rugate dielectric thin film. Applied
Optics 27, 10 (1988), 1998--2005.
[14] Clark, D. E., and Westhead, D. R. Evolutionary algorithms in computer-aided
molecular design. Journal of Computer-aided Molecular Design 10 (1996), 337--358.
[15] Clark, K. P., and Ajay. Flexible ligand docking without parameter adjustment
across four ligand-receptor complexes. Journal of Computational Chemistry 16, 10
(1995), 1210--1226.
[16] Cornell, W. D., Cieplak, P., Bayly, C. I., Gould, I. R., Merz, K. M. J.,
Ferguson, D. M., Spellmeyer, D. C., Fox, T., Caldwell, J. W., and Koll?
man, P. A. A second generation force field for the simulation of proteins and nucleic
acids. Journal of the American Chemical Society 117 (1995), 5179--5197.
[17] D. A. Matthews, et. al. Dihydrofolate reductase from lactobacillus casei : X-ray
structure of the enzyme methotrexate nadph complex. Journal of Biological Chemistry
253, 19 (1978), 6946--6954.
[18] Davis, L. Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York, 1991.
[19] De Jong, K. A. An Analysis of the Behavior of a Class of Genetic Adaptive Systems.
PhD thesis, University of Michigan, 1975.
[20] De Jong, K. A. Genetic algorithms are NOT function optimizers. In Forrest [33],
pp. 5--17.
[21] Deb, K., and Agrawal, R. B. Simulated binary crossover for continuous search
space. Complex Systems 9 (1995), 115--148.
[22] Deb, K., and Beyer, H.-P. Self-adaptation in real-parameter genetic algorithms
with simulated binary crossover. In Genetic and Evolutionary Computation Conf.
(GECCO?9) (1999), pp. 172--179.
[23] Deb, K., and Goldberg, D. E. An investigation of niche and species formation
in genetic function optimization. In Proc. of the Third International Conf. on Genetic
Algorithms (1989), pp. 42--50.
[24] Dobrowolski, J. A. Comparison of the fourier transform and flip-flop thin-film
synthesis methods. Applied Optics 25, 12 (1986), 1966--1972.
[25] Dobrowolski, J. A. Merit function for more effective thin film calculations. Applied
Optics 28, 14 (1989), 2824--2831.
[26] Dobrowolski, J. A. Optical properties of films and coatings. In Handbook of Optics,
M. Bass, Ed. McGraw-hill, New York, 1995, ch. 42, pp. 2824--2831.
[27] Dobrowolski, J. A. Numerical methods for optical thin films. Optics and Photonics
News 8, 6 (June 1997), 24--33.
[28] Dobrowolski, J. A., and Kemp, R. A. Refinement of optical multilayer systems
with different optimization procedures. Applied Optics 29, 19 (1990), 2876--2893.
[29] Dobrowolski, J. A., Tikhonravov, A. V., Trubetskov, M. K., Sullivan,
B. T., and Verly, P. G. Optimal single-band normal-incidence antireflection coat?
ings. Applied Optics 35, 4 (1996), 644--658.
[30] Druessel, J., and Grantham, J. Optimal phase modulation for gradient-index
optical filters. Optics Letters 18, 19 (1993), 1583--1585.
[31] Eisenhammer, T., Lazarov, M., Leutbecher, M., Sch?offel, U., and Siz?
mann, R. Optimization of interference filters with genetic algorithms applied to silver?
based heat mirrors. Applied Optics 32, 31 (1993), 6310--6315.
[32] Eshelman, L. J. The CHC adaptive search algorithm: How to have safe search when
engaging in nontraditional genetic recombination. In Foundation of Genetic Algorithms
1, G. J. Rawlins, Ed. Morgan Kaufmann Publishers, Inc., San Mateo, CA, USA, 1991,
pp. 265--283.
[33] Eshelman, L. J., and Schaffer, J. D. Crossover''s niche. In Proc. of the Fifth
International Conf. on Genetic Algorithms (July 17?1 1993), S. Forrest, Ed., Morgan
Kaufmann Publishers, Inc., pp. 9--14.
[34] Eshelman, L. J., and Schaffer, J. D. Real-coded genetic algorithms and interval?
schemata. In Foundation of Genetic Algorithms 2, L. D. Whitley, Ed. Morgan Kauf?
mann Publishers, Inc., 1993, pp. 187--202.
[35] Fahlamn, S. E., and Lebiere, C. The cascade-correlation learning architecture. In
Advances in Neural Information Processing Systems II (1990), D. S. Touretzky, Ed.,
CA:Morgan-maufmann, pp. 524--532.
[36] Floudas, C. A., and Pardalos, P. M. A collection of test problems for constrained
global optimization algorithm, vol. 455 of Lecture Notes in Computer Science. Springer?
Verlag, New York, USA ; Berlin, 1987.
[37] Fogel, D. B. An analysis of evolutionary programming. In Proc. of the 1st Annu.
Conf. on Evolutionary Programming (1992), pp. 43--51.
[38] Fogel, D. B. An introduction to simulated evolutionary optimization. IEEE trans.
Neural Networks 5, 1 (1994), 3--14.
[39] Fogel, D. B. A comparison of evolutionary programming and genetic algorithm on
selected constrained optimization problems. Simulation (1995), 397--404.
[40] Fogel, D. B. Evolutionary Computation: Toward a New Philosophy of Machine
Intelligent. NJ:IEEE Press, Piscataway, 1995.
[41] Fogel, D. B., and Atmar, W. Comparing genetic operators with gaussian muta?
tions in simulated evolutionary processes using linear systems. Biological Cybernetics
63 (1990), 111--114.
[42] Fogel, D. B., Fogel, L. J., and Porto, V. W. Evolving neural networks.
Biological Cybernetics 63 (1990), 487--493.
[43] Fogel, L. J., Owens, A. J., and Walsh, M. J. Artificial intelligence through
simulated evolution. Wiley, New York, 1966.
[44] Forrest, S. Genetic algorithms: Principles of natural selection applied to computa?
tion. Science 261 (1993), 872--878.
[45] Gehlhaar, D. K., Verkhivker, G. M., Rejto, P., Sherman, C. J., Fogel,
D. B., Fogel, L. J., and Freer, S. T. Molecular recognition of the inhibitor
AG?343 by HIV? protease: conformationally flexible docking by evolutionary pro?
gramming. Chemistry and Biology 2, 5 (1995), 317--324.
[46] Giles, C. Learning and extracting finite state automata with second-order recurrent
networks. Neural Computation 4 (1992), 393--405.
[47] Goldberg, D. E. Genetic Algorithms in Search, Optimization and Machine Learning.
Addison-Wesley Publishing Company, Inc., Reading, MA, USA, 1989.
[48] Goodsell, D. S., and Olson, A. J. Automated docking of substrates to proteins
by simulated annealing. Proteins Structure Function and Genetics 8 (1990), 195--202.
[49] Gordon, V. S., and Whitley, D. Serial and parallel genetic algorithms as function
optimizers. In Forrest [33], pp. 177--183.
[50] Gorman, R. P., and Sejnowski, T. J. Analysis of hidden units in a layered
network trained to classify sonar targets. Neural Networks 1 (1988), 75--89.
[51] Greniner, H. Robust optical coating design with evolutionary strategies. Applied
Optics 36, 28 (1996), 5477--5482.
[52] Hart, W. E. Adaptive global optimization with local search. PhD thesis, University
of California, San Diego, 1994.
[53] Hart, W. E. Comparing evolutionary programs and evolutionary pattern search
algorithms: A drug docking application. In Genetic and Evolutionary Computation
Conf. (GECCO?9) (1999).
[54] Himmelblau, D. M. Applied nonlinear programming. McGraw-Hill, New York, 1972.
[55] Hock, W., and Schittkowski, K. Test examples for Nonlinear Programming
Codes, vol. 187 of Lecture Notes in Economics and Mathematical systems. Springer?
Verlag, New York, USA ; Berlin, 1981.
[56] Holland, J. H. Adaptation in natural and artificial systems. The University of
Michigan Press, Ann Arbor, MI, 1975.
[57] Homaifar, A. S., Lai, H.-Y., and Qi, X. Constrained optimization via genetic
algorithms. Simulation 62, 4 (1994), 242--254.
[58] Hornik, K. Approximation capabilities of multilayer feedforward networks. Neural
Networks 4 (1991), 251--257.
[59] Hwang, J.-N., You, S.-S., Lay, S.-R., and Jou, I.-C. The cascade-correlation
learning: A projection pursuit learning perspective. IEEE trans. on Neural Networks
7, 2 (1996), 278--289.
[60] Janikow, C. Z., and Michalewicz, Z. An experimental comparison of binary and
floating point representations in genetic. In Proc. of the Fourth International Conf. on
Genetic Algorithms (1991), pp. 31--36.
[61] Jefferson, D., Collins, R., Dyer, C. C. M., Flowers, M., Korf, R., Tay?
lor, C., and Wang, A. Evolution as a theme in artificial life: The genesys/tracker
system. In Artificial Life II: Proc. of the Workshop on Artificial Life (1990), pp. 549--
577.
[62] Joines, J. A., and Houck, C. R. On the use of nonstationary penalty functions
to solve nonlinear constrained optimization problems with ga''s. In Proc. of the IEEE
Int. Conf. on Evolutionary Computation (1994), pp. 579--584.
[63] Judson, R. S., Tan, Y. N., Mori, E., Melius, C., Jaeger, E. P., Treasury?
wala, A. M., and Mathiowetz, A. Docking flexible molecules: A case study of
three proteins. Journal of Computational Chemistry 16, 11 (1995), 1405--1419.
[64] Juill'' u, H., and Pollack, J. B. Co-evolving intertwined spirals. In Proc. of the
Fifth Annual Conf. on Evolutionary Programming (1996), pp. --.
[65] Kim, J.-H., and Myung, H. Evolutionary programming techniques for constrained
problems. IEEE trans. on Evolutionary Computation 1, 2 (1997), 129--140.
[66] Kirkpatrick, S., Gelatt, Jr., C. D., and Vecchi, M. P. Optimization by
simulated annealing. Science 220, 4598 (1983), 671--680.
[67] Kitano, H. Empirical studies on the speed of the convergence of neural network
training using genetic algorithms. In Proc. of the Int. Conf. on Artificial Intelligence
(1990), pp. 789--795.
[68] Koza, J. Genetic evolution and co-evolution of computer programs. In Artificial Life
II: Proc. of the Workshop on Artificial Life (1990), pp. 603--629.
[69] Koza, J. Genetic Programming: On the Programming of Computers by Means of
Natural Selection. MA:MIT Press, Cambridge, 1992.
[70] Kuntz, I. D. Structure-based strategies for drug design and discovery. Science 257
(1992), 1078--1082.
[71] Kuntz, I. D., Blaney, J. M., Oatley, S. J., Langridge, R., and Ferrin,
T. E. A geometric approach to macromolecular-ligand interactions. Journal of Com?
putational Biology 161 (1982), 269--288.
[72] Kuyper, L. Receptor-based design of dihydrofolate reductase inhibitors: Comparison
of crystallgraphically determined enzyme binding with enzyme affinity in a series of
carboxy-substituted trimethoprim analogues. Journal of Med. Chem. (1982), 1120--
1122.
[73] Lang, K. J., and Witbrock, M. J. Learning to tell two spirals apart. In Proc. of
the 1988 Connections Models Summer School (1988), Morgan Kaufmann, pp. 52--59.
[74] Li, L., and Dobrowolski, J. A. Computation speeds of different optical thin-film
synthesis methods. Applied Optics 31, 19 (1992), 3790--3799.
[75] Lin, F.-T., Kao, C.-Y., and Hsu, C.-C. Applying the genetic approach to simu?
lated annealing in solving some np-hard problems. IEEE trans. on System, Man, and
Cybernetics 23 (1993), 1752--1767.
[76] Macleod, H. A. Thin film optical filters. McGraw-Hill, New York, 1986.
[77] Martin, S., Rivory, J., and Schoeanauer, M. Synthesis of optical multilayer
systems using genetic algorithms. Applied Optics 34, 13 (1995), 2247--2254.
[78] Mathias, K. E., and Whitley, L. D. Changing representations during search: A
comparative study of delta coding. Evolutionary Computation 2, 3 (1994), 249--278.
[79] Michalewicz, Z. Genetic algorithms, numerical optimization, and constraints. In
Proc. of the Sixth International Conf. on Genetic Algorithms (University of Pittsburgh,
July 15?9 1995), L. J. Eshelman, Ed., Office of Naval Research, Naval Research Lab?
oratory, Philips Laboratory, North American Philips Corporation and International
Society for Genetic Algorithms, Morgan Kaufmann Publishers, Inc., pp. 151--158.
[80] Montana, D. J., and Davis, L. Training feedforward neural networks using genetic
algorithms. In Proc. of Eleventh Int. Joint Conf. on Artificial Intelligence (1989),
pp. 762--767.
[81] Morris, G. M., Goodsell, D. S., Halliday, R. S., Huey, R., Hart, W. E.,
Belew, R. K., and Olson, A. J. Automated docking using a lamarckian ge?
netic algorithm and empirical binding free energy function. Journal of Computational
Chemistry 19 (1998), 1639--1662.
[82] Morris, G. M., Goodsell, D. S., Huey, R., and Olson, A. J. Distributed
automated docking of flexible ligands to proteins: Parallel applications of autodock
2.4. Journal of Computer-aided Molecular Design 10 (1996), 293--304.
[83] M?uhlenbein, H., and Schlierkamp-Hoosen, D. Predictive models for the
breeder genetic algorithm I. continuous parameters optimization. Evolutionary Com?
putation 1, 1 (1993), 24--49.
[84] M?uhlenbein, H., Schomisch, M., and Born, J. The parallel genetic algorithm
as function optimizer. Parallel Computing 17 (1991), 619--632.
[85] Myung, H., and Kim, J. H. Constrained optimization using two-phase evolutionary
algorithm. In Proc. of the IEEE Int. Conf. on Evolutionary Computation (1996),
pp. 262--267.
[86] Myung, H., Kim, J. H., and Fogel, D. Preliminary investigations into a two?
stage method of evolutionary optimization on constrained problems. In Proc. of the
4th Annu. Conf. on Evolutionary Programming (1995), pp. 449--463.
[87] Neveu, J. Mathematical foundations of the calculus of probability. Holden-lay Inc.,
San Franciso, 1965.
[88] Nummelin, E. General irreducible Markov chains and non-iegative operators. Cam?
bridge University Press, Cambridge, 1984.
[89] Orvosh, D., and Davis, L. Shall we repair? genetic algorithms, combinatorial
optimization, and feasibility constraints. In Proc. of the Fifth International Conf. on
Genetic Algorithms (1993), p. 650.
[90] Oshiro, C. M., Kuntz, I. D., and Dixon, J. S. Flexible ligand docking using a
genetic algorithm. Journal of Computer-aided Molecular Design 9 (1995), 113--130.
[91] Ouh-Young, M. PhD thesis, University of North Carolina at Chapel Hill, 1990.
[92] Paredis, J. Co-evolutionary constraint satisfaction. In Parallel Problem Solving
form Nature-PPSN III, Int. Conf. on Evolutionary Computation (Lecture Notes in
Computer Science, vol. 866) (1994), pp. 46--55.
[93] Pattabiraman, N., Levitt, M., Ferrin, T. E., and Langridge, R. Computer
graphics and drug design: Real time docking, energy calculation and minimization.
Journal of Computational Chemistry 6 (1985), 432--436.
[94] Pollack, J. B. The induction of dynamical recognizers. Machine Learning 7 (1991),
227--252.
[95] Powell, D., and Skolnick, M. M. Using genetic algorithms in engineering design
optimization with non-linear constraints. In Forrest [33], pp. 424--430.
[96] Radcliffe, N. J. Equivalence class analysis of genetic algorithms. Complex Systems
5, 2 (1991), 183--206.
[97] Revuz, D. Markov chains. North-holland publishing Company, New York, 1975.
[98] Rudolph, G. Convergence properties of canonical genetic algorithms. IEEE trans.
on Neural Networks 5, 1 (1994), 96--101.
[99] Rudolph, G. Convergence of evolutionary algorithms in general search spaces. In
Proc. of the Third IEEE Conf. on Evolutionary Computation (1996), pp. 50--54.
[100] Rudolph, G. Local convergence rates of simple evolutionary algorithms with cauchy
mutations. IEEE trans. on Evolutionary Computation 1, 4 (1997), 249--258.
[101] Rudolph, G. Finite markov chain results in evolutionary computation: A tour
d''horizon. Fundamenta Informaticae 35, 1? (1998), 67--89.
[102] Rumelhart, D. E., Hinton, G. E., and Williams, R. J. Learning internal
representations by error propagation. In Parallel Distributed Processing: Explorations
in the Microstructures of Cognition (1986), D. Rumelhart and J. L. McClelland, Eds.,
Cambridge, MA: MIT Press, pp. 318--362.
[103] Salomon, R. Reevaluating genetic algorithm performance under coordinate rotation
of benchmark functions; a survey of some theoretical and practical aspects of genetic
algorithms. BioSystems 39, 3 (1996), 263--278.
[104] Saravanan, N., and Fogel, D. B. Multi-operator evolutionary programming: A
preliminary on function optimization. In Proc. of the 6th Annu. Conf. on Evolutionary
Programming (Lecture Notes in Computer Science, vol. 1213) (1997), P. J. Angeline,
et. al., Ed., pp. 215--222.
[105] Schaffer, J. D., Whitley, D., and Eshelman, L. J. Combinations of genetic
algorithms and neural networks: A survey of the state of the art. In Proc. of Int.
workshop on Combinations of Genetic Algorithms and Neural Networks (1992), pp. 1--
37.
[106] Scholz, M. A learning strategy for neural networks based on a modified evolution?
ary strategy. In Parallel Problem Solving form Nature proc. 1st Workshop PPSN 1.
(Lecture Notes in Computer Science, vol. 496) (1991), vol. 496, pp. 314--318.
[107] Schutz, M., and Sprave, J. Application of parallel mixed-integer evolutionary
strategies with mutation rate pooling. In Proc. of the 5th Annu. Conf. on Evolutionary
Programming (1996), pp. 345--354.
[108] Schwefel, H.-P. Numerical optimization of computer models. Chichester: Wiley,
1981.
[109] Sherman, C. J., Ogden, R. C., and Freer, S. T. De Novo design of enzyme
inhibitors by monte carlo ligand generation. Journal of Medicinal Chemistry 38, 3
(1995), 466--472.
[110] ''
Smieja, F. The pandemonium system of reflective agents. IEEE trans. on Neural
Networks 7, 1 (1996), 97--106.
[111] Snyman, J. A., and Fatti, L. P. A multi-start global minimization algorithm with
dynamic search trajectories. Journal of Optimization Theory and Applications 54, 1
(1987), 121--142.
[112] Southwell, W. H. Coating design using very thin high?and low-index layers.
Applied Optics 24 (1985), 457--460.
[113] Srinivas, M., and Patnaik, L. M. Adaptive probabilities of crossover and mutation
in genetic algorithms. IEEE trans. Systems, Man, and Cybernetics 24, 4 (1994), 656--
667.
[114] Sullivan, B. T., and Dobrowolski, J. A. Implementation of a numerical needle
method for thin-film design. Applied Optics 35, 28 (1996), 5484--5492.
[115] Syswerda, G. Uniform crossover in genetic algorithms. In Proc. of the Third Inter?
national Conf. on Genetic Algorithms (1989), pp. 2--9.
[116] Tesauro, G., and Janssens, B. Scaling relationships in back-bropagation learning.
Complex Systems 2 (1988), 39--84.
[117] Tikhonravov, A. V. Some theoretical aspects of thin-film optics and their applica?
tions. Applied Optics 32, 28 (1993), 5417--5426.
[118] Tikhonravov, A. V., Trubetsko, M. K., and Debell, G. W. Application of
the needle optimization technique to design of optical coatings. Applied Optics 35, 28
(1996), 5493--5508.
[119] Tomita, M. Dynamic construction of finite-state automata from examples using hill?
climbing. In Proc. of the Fourth Annual Cognitive Science Conf. (1982), pp. 105--108.
[120] T?orn, A., and ?
Zilinskas, A. Global Optimization, vol. 350 of Lecture Notes in
Computer Science. Springer-serlag, New York, USA ; Berlin, 1989.
[121] Wang, L.-H. Molecular binding in structure-based drug design:a case study of the
population-based annealing genetic algorithms. PhD thesis, National Taiwan University,
1997.
[122] Wang, L.-H., Kao, C.-Y., Ouh-Young, M., and Chen, W. C. Molecular bind?
ing: a case study of the population-based annealing genetic algorithms. 50--55.
[123] Watrous, R. L., and Kuhn, G. M. Induction of finite-state languages using
second-order recurrent networks. Neural Computation 4 (1992), 406--414.
[124] Weiner, S. J., Kollman, P. A., Case, D. A., Singh, U. C., Ghio, C., Alag?
ona, G., S. Jr, P., and Weiner, P. A new force field for molecular mechanical
simulation of nucleic acids and proteins. Journal of the American Chemical Society
106 (1984), 765--784.
[125] Weiner, S. J., Kollman, P. A., Nguyen, D. T., and Case, D. A. An all atom
force field for simulations of proteins and nucleic acids. Journal of Computational
Chemistry 7 (1986), 266--278.
[126] Whitley, D., Mathias, K., Rana, S., and Dzubera, J. Building better test
functions. In Proc. of the Sixth Int. Conf. on Genetic Algorithms (1995), pp. 239--246.
[127] Whitley, D., Starkweather, T., and Bogart, C. Genetic algorithms and
neural networks: Optimizing connections and connectivity. Parallel Computing 14
(1990), 347--361.
[128] Willy, R. A. Predicting achievable design performance of broadband antireflective
coating. Applied Optics 32, 28 (1993), 5447--5451.
[129] Wolpert, D. H., and Macready, W. G. No free lunch theorems for optimization.
IEEE trans. on Evolutionary Computation 1 (1997), 67--82.
[130] Xiao, J., Michalewicz, Z., Zhang, L., and Trojanowski, K. Adaptive evolu?
tionary planner/navigator for mobile robots. IEEE trans. on Evolutionary Computa?
tion 1, 1 (1997), 18--28.
[131] Xiao, Y. L., and Williams, D. E. Genetic algorithms for docking of actinomycin D
and deoxyguanosine molecules with comparison to the crystal structure of actinomycin
D-deoxyguanosine complex. The Journal of Physical Chemistry 98, 29 (1994), 7191--
7200.
[132] Yang, J.-M., Chen, Y.-P., Horng, J.-T., and Kao, C.-Y. Applying family
competition to evolution strategies for constrained optimization. In Lecture Notes
in Computer Science (1997), P. J. Angeline, R. G. Reynolds, J. R. McDonnell, and
R. Eberhart, Eds., vol. 1213, pp. 201--211.
[133] Yang, J.-M., Horng, J.-T., and Kao, C.-Y. A genetic algorithm with adaptive
mutations and family competition for training neural networks. International Journal
of Neural Systems 10, 5 (2000), 333--352.
[134] Yang, J.-M., and Kao, C.-Y. A combined simulated evolutionary algorithm for
real parameter optimization. In Proc. IEEE Int. Conf. on Evolutionary Computation
(1996), pp. 732--737.
[135] Yang, J.-M., and Kao, C.-Y. An evolutionary algorithm for synthesizing optical
thin-film designs. In Lecture Notes in Computer Science (1998), vol. 1498, pp. 947--958.
[136] Yang, J.-M., and Kao, C.-Y. An evolutionary algorithm for continuous global
optimization. In Genetic and Evolutionary Computation Conf. (GECCO?9) (1999),
pp. 930--937.
[137] Yang, J.-M., and Kao, C.-Y. An evolutionary algorithm for the synthesis of oblique
incidence optical coatings. In IEEE Int. Conf. on Industrial Electronics, Control and
Instrumentation (2000).
[138] Yang, J.-M., and Kao, C.-Y. An evolutionary algorithm to training neural net?
works for a two-spiral problem. In Genetic and Evolutionary Computation Conf.
(GECCO?000) (2000), pp. 1025--1032.
[139] Yang, J.-M., and Kao, C.-Y. A family competition evolutionary algorithm for au?
tomated docking of flexible ligands to proteins. IEEE trans. on Information Technology
in Biomedicine 4, 3 (2000), 225--237.
[140] Yang, J.-M., and Kao, C.-Y. Flexible ligand docking using a robust evolutionary
algorithm. Journal of Computational Chemistry 21, 11 (2000), 988--998.
[141] Yang, J.-M., and Kao, C.-Y. Flexible ligand docking using a robust evolutionary
algorithm. In Evolutionary Design and Manufacture, I. C. Parmee, Ed. Springer, 2000,
pp. 95--106.
[142] Yang, J.-M., and Kao, C.-Y. Integrating adaptive mutations and family com?
petition into genetic algorithms as function optimizer. Soft Computing 4, 2 (2000),
89--102.
[143] Yang, J.-M., and Kao, C.-Y. A robust evolutionary algorithm for training neural
networks. Neural Computing and Application (2001, to appear).
[144] Yang, J.-M., Kao, C.-Y., and Horng, J.-T. Evolving neural induction regular
languages using combined evolutionary algorithms. In Proc. of the 9th Int. Conf. on
Artificial Intelligence (1996), pp. 162--169.
[145] Yang, J.-M., Kao, C.-Y., and Horng, J.-T. A continuous genetic algorithm for
global optimization. In Proc. of the Seventh Int. Conf. on Genetic Algorithms (1997),
pp. 230--237.
[146] Yang, J.-M., Kao, C.-Y., and Horng, J.-T. A new evolutionary approach to
developing neural autonomous agents. In IEEE Int. Conf. on Robotics and Automation
(1998), pp. 1411--1416.
[147] Yang, J.-M., Kao, C.-Y., and Horng, J.-T. Incorporation of a multi-operator
with family competition to training neural networks using a novel evolutionary algo?
rithm. In Proc. of the Congress of Evolutionary Computation (1999), pp. 1994--2001.
[148] Yang, J.-M., Kao, C.-Y., and Horng, J.-T. A robust evolutionary algorithm
for optical thin-film designs. In Proc. of the Congress of Evolutionary Computation
(2000), pp. 978--985.
[149] Yao, X., and Liu, Y. Fast evolutionary programming. In Proc. of the Fifth Annual
Conf. on Evolutionary Programming (1996), pp. 451--460.
[150] Yao, X., and Liu, Y. A new evolutionary system for evolving artificial neural
networks. IEEE trans. on Neural Networks (1996).
[151] Yao, X., and Liu, Y. Fast evolution strategies. In Proc. of the 6th Annu. Conf.
on Evolutionary Programming (Lecture Notes in Computer Science, vol. 1213) (1997),
P. J. Angeline, R. G. Reynolds, J. R. McDonnell, and R. Eberhart, Eds., pp. 151--161.
[152] Yen, J., Liao, J. C., Lee, B., and Randoph, D. A hybrid approach to modeling
metabolic systems using a genetic algorithm and simplex method. IEEE trans. on
Systems, Man, and Cybernetics part B 28, 2 (1998), 173--191.
[153] Yip, P. P. C., and Pao, Y. H. Combinatorial optimization with use of guided
evolutionary simulated annealing. IEEE trans. on Neural Networks 6, 2 (1995), 290--
195.