Skip to main content
SpringerLink
Log in

Why Is Optimization Difficult?

  • Chapter
Nature-Inspired Algorithms for Optimisation

Part of the book series: Studies in Computational Intelligence ((SCI,volume 193))

Abstract

This chapter aims to address some of the fundamental issues that are often encountered in optimization problems, making them difficult to solve. These issues include premature convergence, ruggedness, causality, deceptiveness, neutrality, epistasis, robustness, overfitting, oversimplification, multi-objectivity, dynamic fitness, the No Free Lunch Theorem, etc. We explain why these issues make optimization problems hard to solve and present some possible countermeasures for dealing with them. By doing this, we hope to help both practitioners and fellow researchers to create more efficient optimization applications and novel algorithms.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ackley, D.H.: A connectionist machine for genetic hillclimbing. The Springer International Series in Engineering and Computer Science, vol. 28. Kluwer Academic Publishers, Dordrecht (1987)

    Google Scholar 

  2. Altenberg, L.: The schema theorem and price’s theorem. Foundations of Genetic Algorithms 3, 23–49 (1994)

    Google Scholar 

  3. Altenberg, L.: Genome growth and the evolution of the genotype-phenotype map. In: Evolution and Biocomputation – Computational Models of Evolution, pp. 205–259. Springer, Heidelberg (1995)

    Google Scholar 

  4. Altenberg, L.: Nk fitness landscapes. In: Handbook of Evolutionary Computation, ch.. B2.7.2. Oxford University Press, Oxford (1996)

    Google Scholar 

  5. Altenberg, L.: Fitness distance correlation analysis: An instructive counterexample. In: Proceedings of the International Conference on Genetic Algorithms, ICGA, pp. 57–64 (1997)

    Google Scholar 

  6. Amitrano, C., Peliti, L., Saber, M.: Population dynamics in a spin-glass model of chemical evolution. Journal of Molecular Evolution 29(6), 513–525 (1989)

    Article  Google Scholar 

  7. Amor, H.B., Rettinger, A.: Intelligent exploration for genetic algorithms: Using self-organizing maps in evolutionary computation. In: Genetic and Evolutionary Computation Conference, GECCO, pp. 1531–1538 (2005) doi:10.1145/1068009.1068250

    Google Scholar 

  8. Angeline, P.J., Pollack, J.: Evolutionary module acquisition. In: The Second Annual Conference on Evolutionary Programming, Evolutionary Programming Society, pp. 154–163 (1993)

    Google Scholar 

  9. Aragón, V.S., Esquivel, S.C.: An evolutionary algorithm to track changes of optimum value locations in dynamic environments. Journal of Computer Science & Technology (JCS&T) 4(3), 127–133 (2004); invited paper

    Google Scholar 

  10. Bachmann, P.G.H.: Die Analytische Zahlentheorie / Dargestellt von Paul Bachmann, Zahlentheorie: Versuch einer Gesamtdarstellung dieser Wissenschaft in ihren Haupttheilen, vol. Zweiter Theil. B. G. Teubner, Leipzig, Germany (1894)

    Google Scholar 

  11. Bäck, T., Hammel, U.: Evolution strategies applied to perturbed objective functions. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, vol. 1, pp. 40–45 (1994) doi:10.1109/ICEC.1994.350045

    Google Scholar 

  12. Bak, P., Sneppen, K.: Punctuated equilibrium and criticality in a simple model of evolution. Physical Review Letters 71, 4083–4086 (1993)

    Article  Google Scholar 

  13. Baldwin, J.M.: A new factor in evolution. The American Naturalist 30, 441–451 (1896)

    Article  Google Scholar 

  14. Barnett, L.: Tangled webs: Evolutionary dynamics on fitness landscapes with neutrality. Master’s thesis, School of Cognitive Science, University of East Sussex, Brighton, UK (1997)

    Google Scholar 

  15. Barnett, L.: Ruggedness and neutrality – the nkp family of fitness landscapes. In: Artificial Life VI: Proceedings of the sixth international conference on Artificial life, pp. 18–27 (1998)

    Google Scholar 

  16. Bateson, W.: Mendel’s Principles of Heredity. Cambridge University Press, Cambridge (1909)

    Google Scholar 

  17. Beaudoin, W., Verel, S., Collard, P., Escazut, C.: Deceptiveness and neutrality the nd family of fitness landscapes. In: Genetic and Evolutionary Computation Conference, GECCO, pp. 507–514 (2006) doi:10.1145/1143997.1144091

    Google Scholar 

  18. Beerenwinkel, N., Pachter, L., Sturmfels, B.: Epistasis and shapes of fitness landscapes. Eprint arXiv:q-bio/0603034 (Quantitative Biology, Populations and Evolution) (accessed 2007-08-05) (2006), http://arxiv.org/abs/q-bio.PE/0603034

  19. Bergman, A., Feldman, M.W.: Recombination dynamics and the fitness landscape. Physica D: Nonlinear Phenomena 56, 57–67 (1992)

    Article  MATH  Google Scholar 

  20. Bethke, A.D.: Genetic algorithms as function optimizers. PhD thesis, University of Michigan, Ann Arbor, MI, USA (1980)

    Google Scholar 

  21. Beyer, H.-G.: Toward a theory of evolution strategies: Some asymptotical results from the (1, + λ)-theory. Evolutionary Computation 1(2), 165–188 (1993)

    Article  Google Scholar 

  22. Beyer, H.-G.: Toward a theory of evolution strategies: The (μ, λ)-theory. Evolutionary Computation 2(4), 381–407 (1994)

    Article  MathSciNet  Google Scholar 

  23. Blackwell, T.: Particle swarm optimization in dynamic environments. In: Evolutionary Computation in Dynamic and Uncertain Environments, ch. 2, pp. 29–52. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  24. Bledsoe, W.W., Browning, I.: Pattern recognition and reading by machine. In: Proceedings of the Eastern Joint Computer Conference (EJCC) – Papers and Discussions Presented at the Joint IRE - AIEE - ACM Computer Conference, pp. 225–232 (1959)

    Google Scholar 

  25. Blum, C., Roli, A.: Metaheuristics in combinatorial optimization: Overview and conceptual comparison. ACM Computing Surveys 35(3), 268–308 (2003)

    Article  Google Scholar 

  26. Bonner, J.T.: On Development: The Biology of Form, new ed edn. Commonwealth Fund Publications, Harvard University Press (1974)

    Google Scholar 

  27. Bornberg-Bauer, E., Chan, H.S.: Modeling evolutionary landscapes: Mutational stability, topology, and superfunnels in sequence space. Proceedings of the National Academy of Science of the United States of Americs (PNAS) – Biophysics 96(19), 10689–10694 (1999)

    Article  Google Scholar 

  28. Bosman, P.A.N., Thierens, D.: Multi-objective optimization with diversity preserving mixture-based iterated density estimation evolutionary algorithms. International Journal Approximate Reasoning 31(3), 259–289 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  29. Bosman, P.A.N., Thierens, D.: A thorough documentation of obtained results on real-valued continuous and combinatorial multi-objective optimization problems using diversity preserving mixture-based iterated density estimation evolutionary algorithms. Tech. Rep. UU-CS-2002-052, Institute of Information and Computing Sciences, Utrecht University, P.O. Box 80.089, 3508 TB Utrecht, The Netherlands (2002)

    Google Scholar 

  30. Brameier, M.F., Banzhaf, W.: Explicit control of diversity and effective variation distance in linear genetic programming. In: Foster, J.A., Lutton, E., Miller, J., Ryan, C., Tettamanzi, A.G.B. (eds.) EuroGP 2002. LNCS, vol. 2278, pp. 37–49. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  31. Branke, J.: Creating robust solutions by means of evolutionary algorithms. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 119–128. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  32. Branke, J.: Memory enhanced evolutionary algorithms for changing optimization problems. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, vol. 3, pp. 1875–1882 (1999) doi:10.1109/CEC.1999.785502

    Google Scholar 

  33. Branke, J.: The moving peaks benchmark. Tech. rep., Institute AIFB, University of Karlsruhe, Germany (accessed 2007-08-19) (1999), http://www.aifb.uni-karlsruhe.de/~jbr/MovPeaks/ Presented in [32]

  34. Branke, J.: Evolutionary optimization in dynamic environments. PhD thesis, Universität Karlsruhe (TH), Fakultät für Wirtschaftswissenschaften (2000)

    Google Scholar 

  35. Branke, J.: Evolutionary Optimization in Dynamic Environments. Genetic Algorithms and Evolutionary Computation, vol. 3. Kluwer Academic Publishers, Dordrecht (2001)

    Google Scholar 

  36. Branke, J., Salihoğlu, E., Uyar, Ş.: Towards an analysis of dynamic environments. In: Genetic and Evolutionary Computation Conference, GECCO, pp. 1433–1440 (2005)

    Google Scholar 

  37. Bremermann, H.J.: Optimization through evolution and recombination. Self-Organizing systems pp. 93–100 (1962)

    Google Scholar 

  38. Burke, E.K., Gustafson, S.M., Kendall, G.: Survey and analysis of diversity measures in genetic programming. In: Genetic and Evolutionary Computation Conference, GECCO, pp. 716–723 (2002)

    Google Scholar 

  39. Burke, E.K., Gustafson, S.M., Kendall, G., Krasnogor, N.: Is increasing diversity in genetic programming beneficial? an analysis of the effects on fitness. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, pp. 1398–1405 (2003)

    Google Scholar 

  40. Burke, E.K., Gustafson, S.M., Kendall, G.: Diversity in genetic programming: An analysis of measures and correlation with fitness. IEEE Transactions on Evolutionary Computation 8(1), 47–62 (2004)

    Article  Google Scholar 

  41. Cantú-Paz, E., Pelikan, M., Goldberg, D.E.: Linkage problem, distribution estimation, and bayesian networks. Evolutionary Computation 8(3), 311–340 (2000)

    Article  Google Scholar 

  42. Carlisle, A.J.: Applying the particle swarm optimizer to non-stationary environments. PhD thesis, Graduate Faculty of Auburn University (2002)

    Google Scholar 

  43. Carlisle, A.J., Dozier, G.V.: Tracking changing extrema with adaptive particle swarm optimizer. In: Proceedings of the 5th Biannual World Automation Congress, WAC 2002, Orlando, Florida, USA, vol. 13, pp. 265–270 (2002) doi:10.1109/WAC.2002.1049555

    Google Scholar 

  44. Carroll, C.W.: An operations research approach to the economic optimization of a kraft pulping process. PhD thesis, Institute of Paper Chemistry, Appleton, Wisconsin, USA (1959)

    Google Scholar 

  45. Ceollo Coello, C.A., Lamont, G.B., van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems, Genetic and Evolutionary Computation. Genetic and Evolutionary Computation (1st edn., 2002, 2nd edn., 2007), vol. 5. Kluwer Academic Publishers, Springer (2007)

    Google Scholar 

  46. Chen, Y.p.: Extending the Scalability of Linkage Learning Genetic Algorithms – Theory & Practice. Studies in Fuzziness and Soft Computing, vol. 190. Springer, Heidelberg (2006)

    MATH  Google Scholar 

  47. Cohoon, J.P., Hegde, S.U., Martin, W.N., Richards, D.: Punctuated equilibria: a parallel genetic algorithm. In: Proceedings of the Second International Conference on Genetic algorithms and their Application, pp. 148–154 (1987)

    Google Scholar 

  48. Courant, R.: Variational methods for the solution of problems of equilibrium and vibrations. Bulletin of the American Mathematical Society 49(1), 1–23 (1943)

    Article  MATH  MathSciNet  Google Scholar 

  49. Cousins, S.H.: Species diversity measurement: Choosing the right index. Trends in Ecology and Evolution (TREE) 6(6), 190–192 (1991)

    Article  Google Scholar 

  50. Das, I., Dennis, J.E.: A closer look at drawbacks of minimizing weighted sums of objectives for pareto set generation in multicriteria optimization problems. Structural optimization 14(1), 63–69 (1997)

    Article  Google Scholar 

  51. Davidor, Y.: Epistasis variance: A viewpoint on GA-hardness. In: Proceedings of the First Workshop on Foundations of Genetic Algorithms, pp. 23–35 (1990)

    Google Scholar 

  52. Dawkins, R.: The evolution of evolvability. In: ALIFE – Artificial Life: Proceedings of the Interdisciplinary Workshop on the Synthesis and Simulation of Living Systems, pp. 201–220 (1987)

    Google Scholar 

  53. de Jong, E.D., Watson, R.A., Pollack, J.B.: Reducing bloat and promoting diversity using multi-objective methods. In: Genetic and Evolutionary Computation Conference, GECCO, pp. 11–18 (2001)

    Google Scholar 

  54. de Lamarck, J.B.P.A.d.C.: Philosophie zoologique – ou Exposition des considérations relatives à l’histoire naturelle des Animaux. Dentu / G. Baillière, Paris, France/Harvard University (1809)

    Google Scholar 

  55. Deb, K.: Genetic algorithms in multimodal function optimization. Master’s thesis, The Clearinghouse for Genetic algorithms, University of Alabama, Tuscaloosa, tCGA Report No. 89002 (1989)

    Google Scholar 

  56. Deb, K.: Solving goal programming problems using multi-objective genetic algorithms. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, pp. 77–84 (1999) doi:10.1109/CEC.1999.781910

    Google Scholar 

  57. Deb, K.: Genetic algorithms for optimization. KanGAL Report 2001002, Kanpur Genetic Algorithms Laboratory (KanGAL), Kanpur, PIN 208 016, India (2001)

    Google Scholar 

  58. Deb, K.: Nonlinear goal programming using multi-objective genetic algorithms. Journal of the Operational Research Society 52(3), 291–302 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  59. Deb, K., Goldberg, D.E.: Analyzing deception in trap functions. In: Foundations of Genetic Algorithms 2, pp. 93–108 (1993)

    Google Scholar 

  60. Deb, K., Goldberg, D.E.: Sufficient conditions for deceptive and easy binary functions. Annals of Mathematics and Artificial Intelligence 10(4), 385–408 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  61. Deb, K., Agrawal, S., Pratab, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Proceedings of the International Conference on Parallel Problem Solving from Nature, PPSN, pp. 849–858 (2000); KanGAL Report No. 200001

    Google Scholar 

  62. Deb, K., Pratab, A., Agrawal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)

    Article  Google Scholar 

  63. Deb, K., Sinha, A., Kukkonen, S.: Multi-objective test problems, linkages, and evolutionary methodologies. In: Genetic and Evolutionary Computation Conference, GECCO, pp. 1141–1148. ACM, New York (2006)

    Chapter  Google Scholar 

  64. Dietterich, T.: Overfitting and undercomputing in machine learning. ACM Computing Surveys (CSUR) 27(3), 326–327 (1995)

    Article  Google Scholar 

  65. Droste, S., Wiesmann, D.: On representation and genetic operators in evolutionary algorithms. Tech. Rep. CI–41/98, Fachbereich Informatik, Universität Dortmund (1998)

    Google Scholar 

  66. Eiben, Á.E., Schippers, C.A.: On evolutionary exploration and exploitation. Fundamenta Informaticae 35(1-4), 35–50 (1998)

    MATH  Google Scholar 

  67. Eldredge, N., Gould, S.J.: Punctuated equilibria: an alternative to phyletic gradualism. In: Schopf, T.J.M. (ed.) Models in Paleobiology, ch. 5, pp. 82–115. W.H. Freeman, New York (1972)

    Google Scholar 

  68. Eldredge, N., Gould, S.J.: Punctuated equilibria: The tempo and mode of evolution reconsidered. Paleobiology 3(2), 115–151 (1977)

    Google Scholar 

  69. Eshelman, L.J., Schaffer, J.D.: Preventing premature convergence in genetic algorithms by preventing incest. In: Proceedings of the International Conference on Genetic Algorithms, ICGA, pp. 115–122 (1991)

    Google Scholar 

  70. Eshelman, L.J., Caruana, R.A., Schaffer, J.D.: Biases in the crossover landscape. In: Proceedings of the third international conference on Genetic algorithms, pp. 10–19 (1989)

    Google Scholar 

  71. Feo, T.A., Resende, M.G.C.: Greedy randomized adaptive search procedures. Journal of Global Optimization 6(2), 109–133 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  72. Festa, P., Resende, M.G.: An annotated bibliography of grasp. AT&T Labs Research Technical Report TD-5WYSEW, AT&T Labs (2004)

    Google Scholar 

  73. Fiacco, A.V., McCormick, G.P.: Nonlinear Programming: Sequential Unconstrained Minimization Techniques. John Wiley & Sons Inc., Chichester (1968)

    MATH  Google Scholar 

  74. Fisher, S.R.A.: The correlations between relatives on the supposition of mendelian inheritance. Philosophical Transactions of the Royal Society of Edinburgh 52, 399–433 (1918)

    Google Scholar 

  75. Fitzpatrick, J.M., Grefenstette, J.J.: Genetic algorithms in noisy environments. Machine Learning 3(2–3), 101–120 (1988)

    Google Scholar 

  76. Fonseca, C.M., Fleming, P.J.: Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization. In: Proceedings of the 5th International Conference on Genetic Algorithms, pp. 416–423 (1993)

    Google Scholar 

  77. Forst, C.V., Reidys, C., Weber, J.: Evolutionary dynamics and optimization: Neutral networks as model-landscapes for RNA secondary-structure folding-landscapes. In: European Conference on Artificial Life, pp. 128–147 (1995)

    Google Scholar 

  78. Friedberg, R.M.: A learning machine: Part i. IBM Journal of Research and Development 2, 2–13 (1958)

    MathSciNet  Google Scholar 

  79. Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Series of Books in the Mathematical Sciences. W. H. Freeman & Co., New York (1979)

    MATH  Google Scholar 

  80. Geman, S., Bienenstock, E., Doursat, R.: Neural networks and the bias/variance dilemma. Neural Computation 4(1), 1–58 (1992)

    Article  Google Scholar 

  81. Glover, F.: Tabu search – part ii. Operations Research Society of America (ORSA) Journal on Computing 2(1), 190–206 (1990)

    Google Scholar 

  82. Glover, F., Taillard, É.D., de Werra, D.: A user’s guide to tabu search. Annals of Operations Research 41(1), 3–28 (1993)

    Article  MATH  Google Scholar 

  83. Gobb, H.G., Grefenstette, J.J.: Genetic algorithms for tracking changing environments. In: Proceedings of the International Conference on Genetic Algorithms, ICGA, pp. 523–529 (1993)

    Google Scholar 

  84. Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley Longman Publishing Co., Amsterdam (1989)

    MATH  Google Scholar 

  85. Goldberg, D.E., Richardson, J.: Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of the Second International Conference on Genetic algorithms and their Application, pp. 41–49 (1987)

    Google Scholar 

  86. Goldberg, D.E., Deb, K., Korb, B.: Messy genetic algorithms: motivation, analysis, and first results. Complex Systems 3, 493–530 (1989)

    MATH  MathSciNet  Google Scholar 

  87. Greiner, H.: Robust filter design by stochastic optimization. Proceedings of SPIE (The International Society for Optical Engineering) 2253, 150–161 (1994)

    Google Scholar 

  88. Greiner, H.: Robust optical coating design with evolutionary strategies. Applied Optics 35, 5477–5483 (1996)

    Article  Google Scholar 

  89. Gruau, F., Whitley, L.D.: Adding learning to the cellular development of neural networks: Evolution and the baldwin effect. Evolutionary Computation 1(3), 213–233 (1993)

    Article  Google Scholar 

  90. Guntsch, M., Middendorf, M.: Pheromone modification strategies for ant algorithms applied to dynamic TSP. In: Boers, E.J.W., Gottlieb, J., Lanzi, P.L., Smith, R.E., Cagnoni, S., Hart, E., Raidl, G.R., Tijink, H. (eds.) EvoIASP 2001, EvoWorkshops 2001, EvoFlight 2001, EvoSTIM 2001, EvoCOP 2001, and EvoLearn 2001. LNCS, vol. 2037, pp. 213–222. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  91. Guntsch, M., Middendorf, M., Schmeck, H.: An ant colony optimization approach to dynamic TSP. In: Genetic and Evolutionary Computation Conference, GECCO, pp. 860–867 (2001)

    Google Scholar 

  92. Gurin, L.S., Rastrigin, L.A.: Convergence of the random search method in the presence of noise. Automation and Remote Control 26, 1505–1511 (1965)

    Google Scholar 

  93. Gustafson, S.M.: An analysis of diversity in genetic programming. PhD thesis, University of Nottingham, School of Computer Science & IT (2004)

    Google Scholar 

  94. Gustafson, S.M., Ekárt, A., Burke, E.K., Kendall, G.: Problem difficulty and code growth in genetic programming. Genetic Programming and Evolvable Machines 5(3), 271–290 (2004)

    Article  Google Scholar 

  95. Hadj-Alouane, A.B., Bean, J.C.: A genetic algorithm for the multiple-choice integer program. Tech. Rep. 92-50, Department of Industrial and Operations Engineering, The University of Michigan, Ann Arbour, MI 48109-2117, USA (1992)

    Google Scholar 

  96. Hammel, U., Bäck, T.: Evolution strategies on noisy functions: How to improve convergence properties. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 159–168. Springer, Heidelberg (1994)

    Google Scholar 

  97. Han, L., He, X.: A novel opposition-based particle swarm optimization for noisy problems. In: ICNC 2007: Proceedings of the Third International Conference on Natural Computation, vol. 3, pp. 624–629 (2007) doi:10.1109/ICNC.2007.119

    Google Scholar 

  98. Handa, H., Lin, D., Chapman, L., Yao, X.: Robust solution of salting route optimisation using evolutionary algorithms. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, pp. 3098–3105 (2006) doi:10.1109/CEC.2006.1688701

    Google Scholar 

  99. Harik, G.R.: Learning gene linkage to efficiently solve problems of bounded difficulty using genetic algorithms. PhD thesis, University of Michigan, Ann Arbor (1997)

    Google Scholar 

  100. Hinton, G.E., Nowlan, S.J.: How learning can guide evolution. Complex Systems 1, 495–502 (1987)

    MATH  Google Scholar 

  101. Hinton, G.E., Nowlan, S.J.: How learning can guide evolution. In: Adaptive individuals in evolving populations: models and algorithms, pp. 447–454. Addison-Wesley Longman Publishing Co., Inc., Amsterdam (1996)

    Google Scholar 

  102. Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. The University of Michigan Press, Ann Arbor (1975); reprinted by MIT Press, NetLibrary, Inc. (April 1992)

    Google Scholar 

  103. Holland, J.H.: Genetic algorithms. Scientific American 267(1), 44–50 (1992)

    Article  Google Scholar 

  104. Horn, J., Nafpliotis, N., Goldberg, D.E.: A niched pareto genetic algorithm for multiobjective optimization. In: Proceedings of the First IEEE Conference on Evolutionary Computation, vol. 1, pp. 82–87 (1994) doi:10.1109/ICEC.1994.350037

    Google Scholar 

  105. Huynen, M.A.: Exploring phenotype space through neutral evolution. Journal of Molecular Evolution 43(3), 165–169 (1996)

    Article  Google Scholar 

  106. Huynen, M.A., Stadler, P.F., Fontana, W.: Smoothness within ruggedness: The role of neutrality in adaptation. Proceedings of the National Academy of Science, USA 93, 397–401 (1996)

    Article  Google Scholar 

  107. Igel, C.: Causality of hierarchical variable length representations. In: Proceedings of the 1998 IEEE World Congress on Computational Intelligence, pp. 324–329 (1998)

    Google Scholar 

  108. Igel, C., Toussaint, M.: On classes of functions for which no free lunch results hold. Information Processing Letters 86(6), 317–321 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  109. Igel, C., Toussaint, M.: Recent results on no-free-lunch theorems for optimization. ArXiv EPrint arXiv:cs/0303032 (Computer Science, Neural and Evolutionary Computing) (accessed 2008-03-28) (2003), http://www.citebase.org/abstract?id=oai:arXiv.org:cs/0303032

  110. Ingber, L.: Adaptive simulated annealing (asa): Lessons learned. Control and Cybernetics 25(1), 33–54 (1996)

    MATH  Google Scholar 

  111. Joines, J.A., Houck, C.R.: On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with ga’s. In: Proceedings of the First IEEE Conference on Evolutionary Computation, pp. 579–584 (1994) doi:10.1109/ICEC.1994.349995

    Google Scholar 

  112. Jones, T.: Evolutionary algorithms, fitness landscapes and search. PhD thesis, The University of New Mexico (1995)

    Google Scholar 

  113. Kauffman, S.A.: Adaptation on rugged fitness landscapes. In: Stein, D.L. (ed.) Lectures in the Sciences of Complexity: The Proceedings of the 1988 Complex Systems Summer School. Santa Fe Institute Studies in the Sciences of Complexity, vol. Lecture I, pp. 527–618. Addison-Wesley, Reading (1988)

    Google Scholar 

  114. Kauffman, S.A.: The Origins of Order: Self-Organization and Selection in Evolution. Oxford University Press, Oxford (1993)

    Google Scholar 

  115. Kauffman, S.A., Levin, S.A.: Towards a general theory of adaptive walks on rugged landscapes. Journal of Theoretical Biology 128(1), 11–45 (1987)

    Article  MathSciNet  Google Scholar 

  116. Kearns, M.J., Mansour, Y., Ng, A.Y., Ron, D.: An experimental and theoretical comparison of model selection methods. In: COLT 1995: Proceedings of the eighth annual conference on Computational learning theory, pp. 21–30. ACM Press, New York (1995)

    Chapter  Google Scholar 

  117. Kirkpatrick, S., Gelatt Jr., C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  118. Kirschner, M., Gerhart, J.: Evolvability. Proceedings of the National Academy of Science of the USA (PNAS) 95(15), 8420–8427 (1998)

    Article  Google Scholar 

  119. Kita, H., Sano, Y.: Genetic algorithms for optimization of noisy fitness functions and adaptation to changing environments. In: 2003 Joint Workshop of Hayashibara Foundation and 2003 Workshop on Statistical Mechanical Approach to Probabilistic Information Processing (SMAPIP) (2003)

    Google Scholar 

  120. Kolarov, K.: Landscape ruggedness in evolutionary algorithms. In: Proceedings of the IEEE Conference on Evolutionary Computation, pp. 19–24 (1997)

    Google Scholar 

  121. Köppen, M., Wolpert, D.H., Macready, W.G.: Remarks on a recent paper on the “no free lunch” theorems. IEEE Transactions on Evolutionary Computation 5(3), 295–296 (2001)

    Article  Google Scholar 

  122. Landau, E.: Handbuch der Lehre von der Verteilung der Primzahlen. B. G. Teubner, Leipzig (1909); reprinted by Chelsea, New York (1953)

    Google Scholar 

  123. Laumanns, M., Thiele, L., Deb, K., Zitzler, E.: On the convergence and diversity-preservation properties of multi-objective evolutionary algorithms. Tech. Rep. 108, Computer Engineering and Networks Laboratory (TIK), Department of Electrical Engineering, Swiss Federal Institute of Technology (ETH) Zurich and Kanpur Genetic Algorithms Laboratory (KanGAL), Department of Mechanical Engineering, Indian Institute of Technology Kanpur (2001)

    Google Scholar 

  124. Lawrence, S., Giles, C.L.: Overfitting and neural networks: Conjugate gradient and backpropagation. In: Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks (IJCNN 2000), vol. 1, pp. 1114–1119. IEEE Computer Society, Los Alamitos (2000)

    Google Scholar 

  125. Lee, J.Y.B., Wong, P.C.: The effect of function noise on gp efficiency. In: Progress in Evolutionary Computation, pp. 1–16 (1995)

    Google Scholar 

  126. Li, X., Branke, J., Blackwell, T.: Particle swarm with speciation and adaptation in a dynamic environment. In: Genetic and Evolutionary Computation Conference, GECCO, pp. 51–58 (2006) doi:10.1145/1143997.1144005

    Google Scholar 

  127. Liepins, G.E., Vose, M.D.: Deceptiveness and genetic algorithm dynamics. In: Proceedings of the First Workshop on Foundations of Genetic Algorithms (FOGA), pp. 36–50 (1991)

    Google Scholar 

  128. Ling, C.X.: Overfitting and generalization in learning discrete patterns. Neurocomputing 8(3), 341–347 (1995)

    Article  Google Scholar 

  129. Lohmann, R.: Structure evolution and neural systems. In: Dynamic, Genetic, and Chaotic Programming: The Sixth-Generation, pp. 395–411. Wiley Interscience, Hoboken (1992)

    Google Scholar 

  130. Lohmann, R.: Structure evolution and incomplete induction. Biological Cybernetics 69(4), 319–326 (1993)

    Article  Google Scholar 

  131. Luke, S., Panait, L.: A comparison of bloat control methods for genetic programming. Evolutionary Computation 14(3), 309–344 (2006)

    Article  Google Scholar 

  132. Lush, J.L.: Progeny test and individual performance as indicators of an animal’s breeding value. Journal of Dairy Science 18(1), 1–19 (1935)

    Google Scholar 

  133. Magurran, A.E.: Biological diversity. Current Biology Magazine 15, R116–R118 (2005)

    Article  Google Scholar 

  134. Martin, W.N., Lienig, J., Cohoon, J.P.: Island (migration) models: Evolutionary algorithms based on punctuated equilibria. In: Handbook of Evolutionary Computation, ch. 6.3. Oxford University Press, Oxford (1997)

    Google Scholar 

  135. Mendes, R., Mohais, A.S.: Dynde: a differential evolution for dynamic optimization problems. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, vol. 3, pp. 2808–2815 (2005)

    Google Scholar 

  136. Miller, B.L., Goldberg, D.E.: Genetic algorithms, tournament selection, and the effects of noise. IlliGAL Report 95006, Illinois Genetic Algorithms Laboratory, Department of General Engineering, University of Illinois (1995)

    Google Scholar 

  137. Miller, B.L., Goldberg, D.E.: Genetic algorithms, selection schemes, and the varying effects of noise. Evolutionary Computation 4(2), 113–131 (1996)

    Article  Google Scholar 

  138. Miller, B.L., Shaw, M.J.: Genetic algorithms with dynamic niche sharing for multimodal function optimization. IlliGAL Report 95010, Department of General Engineering, University of Illinois at Urbana-Champaign (1995)

    Google Scholar 

  139. Mitchell, M., Forrest, S., Holland, J.H.: The royal road for genetic algorithms: Fitness landscapes and GA performance. In: Towards a Practice of Autonomous Systems: Proceedings of the First European Conference on Artificial Life, pp. 245–254 (1991)

    Google Scholar 

  140. Mitchell, T.M.: Generalization as search. In: Webber, B.L., Nilsson, N.J. (eds.) Readings in Artificial Intelligence, 2nd edn., pp. 517–542. Tioga Pub. Co. Press, Morgan Kaufmann Publishers, Elsevier Science & Technology Books (1981)

    Google Scholar 

  141. Mitchell, T.M.: Generalization as search. Artificial Intelligence 18(2), 203–226 (1982)

    Article  MathSciNet  Google Scholar 

  142. Mori, N., Kita, H., Nishikawa, Y.: Adaptation to a changing environment by means of the thermodynamical genetic algorithm. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 513–522. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  143. Mori, N., Imanishi, S., Kita, H., Nishikawa, Y.: Adaptation to changing environments by means of the memory based thermodynamical genetic algorithm. In: Proceedings of the International Conference on Genetic Algorithms, ICGA, pp. 299–306 (1997)

    Google Scholar 

  144. Mori, N., Kita, H., Nishikawa, Y.: Adaptation to a changing environment by means of the feedback thermodynamical genetic algorithm. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 149–158. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  145. Morrison, R.W.: Designing evolutionary algorithms for dynamic environments. PhD thesis, George Mason University, USA (2002)

    Google Scholar 

  146. Morrison, R.W.: Designing Evolutionary Algorithms for Dynamic Environments. Natural Computing 24(1), 143–144 (2004)

    Google Scholar 

  147. Morrison, R.W., De Jong, K.A.: A test problem generator for non-stationary environments. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, vol. 3, pp. 2047–2053 (1999) doi:10.1109/CEC.1999.785526

    Google Scholar 

  148. Morrison, R.W., De Jong, K.A.: Measurement of population diversity. In: Collet, P., Fonlupt, C., Hao, J.-K., Lutton, E., Schoenauer, M. (eds.) EA 2001. LNCS, vol. 2310, pp. 1047–1074. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  149. Mostaghim, S.: Multi-objective evolutionary algorithms: Data structures, convergence and, diversity. PhD thesis, Fakultät für Elektrotechnik, Informatik und Mathematik, Universität Paderborn, Deutschland, Germany (2004)

    Google Scholar 

  150. Munetomo, M., Goldberg, D.E.: Linkage identification by non-monotonicity detection for overlapping functions. Evolutionary Computation 7(4), 377–398 (1999)

    Article  Google Scholar 

  151. Munetomo, M., Goldberg, D.E.: Linkage identification by non-monotonicity detection for overlapping functions. IlliGAL Report 99005, Illinois Genetic Algorithms Laboratory (IlliGAL), University of Illinois at Urbana-Champaign (1999)

    Google Scholar 

  152. Muttil, N., Liong, S.-Y.: Superior exploration–exploitation balance in shuffled complex evolution. Journal of Hydraulic Engineering 130(12), 1202–1205 (2004)

    Article  Google Scholar 

  153. Naudts, B., Verschoren, A.: Epistasis on finite and infinite spaces. In: Proceedings of the 8th International Conference on Systems Research, Informatics and Cybernetics, pp. 19–23 (1996)

    Google Scholar 

  154. Naudts, B., Verschoren, A.: Epistasis and deceptivity. Bulletin of the Belgian Mathematical Society 6(1), 147–154 (1999)

    MATH  MathSciNet  Google Scholar 

  155. Newman, M.E.J., Engelhardt, R.: Effect of neutral selection on the evolution of molecular species. Proceedings of the Royal Society of London B (Biological Sciences) 256(1403), 1333–1338 (1998)

    Google Scholar 

  156. Oei, C.K., Goldberg, D.E., Chang, S.J.: Tournament selection, niching, and the preservation of diversity. IlliGAl Report 91011, Illinois Genetic Algorithms Laboratory (IlliGAL), Department of Computer Science, Department of General Engineering, University of Illinois at Urbana-Champaign (1991)

    Google Scholar 

  157. Olsen, A.L.: Penalty functions and the knapsack problem. In: Proceedings of the First IEEE Conference on Evolutionary Computation, vol. 2, pp. 554–558 (1994)

    Google Scholar 

  158. Osman, I.H.: An introduction to metaheuristics. In: Lawrence, M., Wilsdon, C. (eds.) Operational Research Tutorial Papers, pp. 92–122. Stockton Press, Hampshire (1995); publication of the Operational Research Society, Birmingham, UK

    Google Scholar 

  159. Paenke, I., Branke, J., Jin, Y.: On the influence of phenotype plasticity on genotype diversity. In: First IEEE Symposium on Foundations of Computational Intelligence (FOCI 2007), pp. 33–40 (2007)

    Google Scholar 

  160. Pan, G., Dou, Q., Liu, X.: Performance of two improved particle swarm optimization in dynamic optimization environments. In: ISDA 2006: Proceedings of the Sixth International Conference on Intelligent Systems Design and Applications (ISDA 2006), vol. 2, pp. 1024–1028. IEEE Computer Society Press, Los Alamitos (2006)

    Chapter  Google Scholar 

  161. Pan, H., Wang, L., Liu, B.: Particle swarm optimization for function optimization in noisy environment. Applied Mathematics and Computation 181(2), 908–919 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  162. Pelikan, M., Goldberg, D.E., Cantú-Paz, E.: Boa: The bayesian optimization algorithm. In: Genetic and Evolutionary Computation Conference, GECCO, pp. 525–532 (1999)

    Google Scholar 

  163. Phillips, P.C.: The language of gene interaction. Genetics 149(3), 1167–1171 (1998)

    Google Scholar 

  164. Pohlheim, H.: Geatbx introduction – evolutionary algorithms: Overview, methods and operators. Tech. rep., documentation for GEATbx version 3.7 (2005) (accessed, 2007-07-03), http://www.GEATbx.com

  165. Purshouse, R.C.: On the evolutionary optimisation of many objectives. PhD thesis, Department of Automatic Control and Systems Engineering, The University of Sheffield (2003)

    Google Scholar 

  166. Radcliffe, N.J.: Non-linear genetic representations. In: Proceedings of the International Conference on Parallel Problem Solving from Nature, PPSN, pp. 259–268. Elsevier, Amsterdam (1992)

    Google Scholar 

  167. Radcliffe, N.J.: The algebra of genetic algorithms. Annals of Mathematics and Artificial Intelligence 10(4) (1994) doi:10.1007/BF01531276

    Google Scholar 

  168. Radcliffe, N.J., Surry, P.D.: Fundamental limitations on search algorithms: Evolutionary computing in perspective. In: van Leeuwen, J. (ed.) Computer Science Today. LNCS, vol. 1000, pp. 275–291. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  169. Rayward-Smith, V.J.: A unified approach to tabu search, simulated annealing and genetic algorithms. In: Rayward-Smith, V.J. (ed.) Applications of Modern Heuristic Methods – Proceedings of the UNICOM Seminar on Adaptive Computing and Information Processing, Brunel University Conference Centre, London, UK, vol. I, pp. 55–78. Alfred Waller Ltd / Nelson Thornes Ltd / Unicom Seminars Ltd (1994)

    Google Scholar 

  170. Rechenberg, I.: Evolutionsstrategie: Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog Verlag, Stuttgart (1973)

    Google Scholar 

  171. Rechenberg, I.: Evolutionsstrategie 1994. Werkstatt Bionik und Evolutionstechnik, vol. 1. Frommann Holzboog (1994)

    Google Scholar 

  172. Reidys, C.M., Stadler, P.F.: Neutrality in fitness landscapes. Applied Mathematics and Computation 117(2–3), 321–350 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  173. Richter, H.: Behavior of evolutionary algorithms in chaotically changing fitness landscapes. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 111–120. Springer, Heidelberg (2004)

    Google Scholar 

  174. Riedl, R.J.: A systems-analytical approach to macroevolutionary phenomena. Quarterly Review of Biology, 351–370 (1977)

    Google Scholar 

  175. Robbins, H., Monro, S.: A stochastic approximation method. Annals of Mathematical Statistics 22(3), 400–407 (1951)

    Article  MATH  MathSciNet  Google Scholar 

  176. Ronald, S.: Preventing diversity loss in a routing genetic algorithm with hash tagging. Complexity International 2 (1995) (accessed 2008-12-07), http://www.complexity.org.au/ci/vol02/sr_hash/

  177. Ronald, S.: Genetic algorithms and permutation-encoded problems. diversity preservation and a study of multimodality. PhD thesis, University Of South Australia. Department of Computer and Information Science (1996)

    Google Scholar 

  178. Ronald, S.: Robust encodings in genetic algorithms: A survey of encoding issues. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, pp. 43–48 (1997) doi:10.1109/ICEC.1997.592265

    Google Scholar 

  179. Rosca, J.P.: An analysis of hierarchical genetic programming. Tech. Rep. TR566, The University of Rochester, Computer Science Department (1995)

    Google Scholar 

  180. Rosca, J.P., Ballard, D.H.: Causality in genetic programming. In: Proceedings of the International Conference on Genetic Algorithms, ICGA, pp. 256–263 (1995)

    Google Scholar 

  181. Rosin, P.L., Fierens, F.: Improving neural network generalisation. In: Proceedings of the International Geoscience and Remote Sensing Symposium, Quantitative Remote Sensing for Science and Applications, IGARSS 1995, vol. 2, pp. 1255–1257. IEEE, Los Alamitos (1995)

    Chapter  Google Scholar 

  182. Rothlauf, F.: Representations for Genetic and Evolutionary Algorithms, 2nd edn. Physica-Verlag (2006) (1st edn., 2002)

    Google Scholar 

  183. Routledge, R.D.: Diversity indices: Which ones are admissible? Journal of Theoretical Biology 76, 503–515 (1979)

    Article  MathSciNet  Google Scholar 

  184. Rudnick, W.M.: Genetic algorithms and fitness variance with an application to the automated design of artificial neural networks. PhD thesis, Oregon Graduate Institute of Science & Technology (1992)

    Google Scholar 

  185. Rudolph, G.: Self-adaptation and global convergence: A counter-example. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, vol. 1, pp. 646–651 (1999)

    Google Scholar 

  186. Rudolph, G.: Self-adaptive mutations may lead to premature convergence. IEEE Transactions on Evolutionary Computation 5(4), 410–414 (2001)

    Article  Google Scholar 

  187. Rudolph, G.: Self-adaptive mutations may lead to premature convergence. Tech. Rep. CI–73/99, Fachbereich Informatik, Universität Dortmund (2001)

    Google Scholar 

  188. Sano, Y., Kita, H.: Optimization of noisy fitness functions by means of genetic algorithms using history of search. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000. LNCS, vol. 1917, pp. 571–580. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  189. Sano, Y., Kita, H.: Optimization of noisy fitness functions by means of genetic algorithms using history of search with test of estimation. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, pp. 360–365 (2002)

    Google Scholar 

  190. Sarle, W.: What is overfitting and how can i avoid it? Usenet FAQs: compaineural-nets FAQ 3: Generalization(3) (2007)

    Google Scholar 

  191. Sarle, W.S.: Stopped training and other remedies for overfitting. In: Proceedings of the 27th Symposium on the Interface: Computing Science and Statistics, pp. 352–360 (1995)

    Google Scholar 

  192. Schaffer, J.D., Eshelman, L.J., Offutt, D.: Spurious correlations and premature convergence in genetic algorithms. In: Proceedings of the First Workshop on Foundations of Genetic Algorithms (FOGA), pp. 102–112 (1990)

    Google Scholar 

  193. Sendhoff, B., Kreutz, M., von Seelen, W.: A condition for the genotype-phenotype mapping: Causality. In: Proceedings of the International Conference on Genetic Algorithms, ICGA, pp. 73–80 (1997)

    Google Scholar 

  194. Shackleton, M., Shipman, R., Ebner, M.: An investigation of redundant genotype-phenotype mappings and their role in evolutionary search. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, pp. 493–500 (2000)

    Google Scholar 

  195. Shekel, J.: Test functions for multimodal search techniques. In: Proceedings of the Fifth Annual Princeton Conference on Information Science and Systems, pp. 354–359. Princeton University Press, Princeton (1971)

    Google Scholar 

  196. Shipman, R.: Genetic redundancy: Desirable or problematic for evolutionary adaptation? In: Proceedings of the 4th International Conference on Artificial Neural Nets and Genetic Algorithms, pp. 1–11 (1999)

    Google Scholar 

  197. Shipman, R., Shackleton, M., Ebner, M., Watson, R.: Neutral search spaces for artificial evolution: a lesson from life. In: Bedau, M., McCaskill, J.S., Packard, N.H., Rasmussen, S., McCaskill, J., Packard, N. (eds.) Artificial Life VII: Proceedings of the Seventh International Conference on Artificial Life. The MIT Press, Bradford Books, Complex Adaptive Systems (2000)

    Google Scholar 

  198. Shipman, R., Shackleton, M., Harvey, I.: The use of neutral genotype-phenotype mappings for improved evolutionary search. BT Technology Journal 18(4), 103–111 (2000)

    Article  Google Scholar 

  199. Siedlecki, W.W., Sklansky, J.: Constrained genetic optimization via dynamic reward-penalty balancing and its use in pattern recognition. In: Proceedings of the third international conference on Genetic algorithms, pp. 141–150 (1989)

    Google Scholar 

  200. Singh, G., Deb, K.: Comparison of multi-modal optimization algorithms based on evolutionary algorithms. In: Genetic and Evolutionary Computation Conference, GECCO, pp. 1305–1312 (2006)

    Google Scholar 

  201. Smith, A.E., Coit, D.W.: Penalty functions. In: Handbook of Evolutionary Computation, ch. 5.2. Oxford University Press, Oxford (1997)

    Google Scholar 

  202. Smith, M.: Neural Networks for Statistical Modeling. John Wiley & Sons, Inc. International Thomson Computer Press (1993/1996)

    Google Scholar 

  203. Smith, S.S.F.: Using multiple genetic operators to reduce premature convergence in genetic assembly planning. Computers in Industry 54(1), 35–49 (2004)

    Article  Google Scholar 

  204. Smith, T., Husbands, P., Layzell, P., O’Shea, M.: Fitness landscapes and evolvability. Evolutionary Computation 10(1), 1–34 (2002)

    Article  Google Scholar 

  205. Spatz, B.M., Rawlins, G.J.E. (eds.): Proceedings of the First Workshop on Foundations of Genetic Algorithms. Morgan Kaufmann Publishers, Inc., San Francisco (1990)

    Google Scholar 

  206. Spieth, C., Streichert, F., Speer, N., Zell, A.: Utilizing an island model for ea to preserve solution diversity for inferring gene regulatory networks. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, vol. 1, pp. 146–151 (2004)

    Google Scholar 

  207. Stagge, P., Igel, C.: Structure optimization and isomorphisms. In: Theoretical Aspects of Evolutionary Computing, pp. 409–422. Springer, Heidelberg (2000)

    Google Scholar 

  208. Stewart, T.: Extrema selection: accelerated evolution on neutral networks. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, vol. 1 (2001)

    Google Scholar 

  209. Taguchi, G.: Introduction to Quality Engineering: Designing Quality into Products and Processes. Asian Productivity Organization / American Supplier Institute Inc. / Quality Resources / Productivity Press Inc., translation of Sekkeisha no tame no hinshitsu kanri (1986)

    Google Scholar 

  210. Taillard, É.D., Gambardella, L.M., Gendrau, M., Potvin, J.-Y.: Adaptive memory programming: A unified view of metaheuristics. European Journal of Operational Research 135(1), 1–16 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  211. Tetko, I.V., Livingstone, D.J., Luik, A.I.: Neural network studies, 1. comparison of overfitting and overtraining. Journal of Chemical Information and Computer Sciences 35(5), 826–833 (1995)

    Google Scholar 

  212. Thierens, D.: On the scalability of simple genetic algorithms. Tech. Rep. UU-CS-1999-48, Department of Information and Computing Sciences, Utrecht University (1999)

    Google Scholar 

  213. Thierens, D., Goldberg, D.E., Pereira, Â.G.: Domino convergence, drift, and the temporal-salience structure of problems. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, pp. 535–540 (1998), doi:10.1109/ICEC.1998.700085

    Google Scholar 

  214. Toussaint, M., Igel, C.: Neutrality: A necessity for self-adaptation. In: Proceedings of the IEEE Congress on Evolutionary Computation, CEC, pp. 1354–1359 (2002)

    Google Scholar 

  215. Trelea, I.C.: The particle swarm optimization algorithm: convergence analysis and parameter selection. Information Processing Letters 85(6), 317–325 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  216. Trojanowski, K.: Evolutionary algorithms with redundant genetic material for non-stationary environments. PhD thesis, Instytut Podstaw Informatyki PAN, Institute of Computer Science, Warsaw, University of Technology, Poland (1994)

    Google Scholar 

  217. Tsutsui, S., Ghosh, A.: Genetic algorithms with a robust solution searching scheme. IEEE Transactions on Evolutionary Computation 1, 201–208 (1997)

    Article  Google Scholar 

  218. Tsutsui, S., Ghosh, A., Fujimoto, Y.: A robust solution searching scheme in genetic search. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 543–552. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  219. Ursem, R.K.: Models for evolutionary algorithms and their applications in system identification and control optimization. PhD thesis, Department of Computer Science, University of Aarhus, Denmark (2003)

    Google Scholar 

  220. Vaessens, R.J.M., Aarts, E.H.L., Lenstra, J.K.: A local search template. In: Proceedings of the International Conference on Parallel Problem Solving from Nature, PPSN, pp. 67–76 (1992)

    Google Scholar 

  221. Vaessens, R.J.M., Aarts, E.H.L., Lenstra, J.K.: A local search template. Computers and Operations Research 25(11), 969–979 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  222. van Nimwegen, E., Crutchfield, J.P.: Optimizing epochal evolutionary search: Population-size dependent theory. Machine Learning 45(1), 77–114 (2001)

    Article  MATH  Google Scholar 

  223. van Nimwegen, E., Crutchfield, J.P., Huynen, M.: Neutral evolution of mutational robustness. Proceedings of the National Academy of Science of the United States of Americs (PNAS) – Evolution 96(17), 9716–9720 (1999)

    Article  Google Scholar 

  224. van Nimwegen, E., Crutchfield, J.P., Mitchell, M.: Statistical dynamics of the royal road genetic algorithm. Theoretical Computer Science 229(1–2), 41–102 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  225. Wagner, A.: Robustness and Evolvability in Living Systems. Princeton Studies in Complexity. Princeton University Press, Princeton (2005)

    Google Scholar 

  226. Wagner, A.: Robustness, evolvability, and neutrality. FEBS Lett 579(8), 1772–1778 (2005)

    Article  Google Scholar 

  227. Wagner, G.P., Altenberg, L.: Complex adaptations and the evolution of evolvability. Evolution 50(3), 967–976 (1996)

    Article  Google Scholar 

  228. Watanabe, S.: Knowing and Guessing: A Quantitative Study of Inference and Information. John Wiley & Sons, Chichester (1969)

    MATH  Google Scholar 

  229. Weicker, K.: Evolutionäre Algorithmen. Leitfäden der Informatik, B. G. Teubner GmbH (2002)

    Google Scholar 

  230. Weicker, K., Weicker, N.: Burden and benefits of redundancy. In: Sixth Workshop on Foundations of Genetic Algorithms (FOGA), pp. 313–333. Morgan Kaufmann, San Francisco (2000)

    Google Scholar 

  231. Weise, T., Zapf, M., Geihs, K.: Rule-based Genetic Programming. In: Proceedings of BIONETICS 2007, 2nd International Conference on Bio-Inspired Models of Network, Information, and Computing Systems (2007)

    Google Scholar 

  232. Weise, T., Niemczyk, S., Skubch, H., Reichle, R., Geihs, K.: A tunable model for multi-objective, epistatic, rugged, and neutral fitness landscapes. In: Genetic and Evolutionary Computation Conference, GECCO, pp. 795–802 (2008)

    Google Scholar 

  233. Whitley, L.D., Gordon, V.S., Mathias, K.E.: Lamarckian evolution, the baldwin effect and function optimization. In: Davidor, Y., Männer, R., Schwefel, H.-P. (eds.) PPSN 1994. LNCS, vol. 866, pp. 6–15. Springer, Heidelberg (1994)

    Google Scholar 

  234. Wiesmann, D., Hammel, U., Bäck, T.: Robust design of multilayer optical coatings by means of evolutionary algorithms. IEEE Transactions on Evolutionary Computation 2, 162–167 (1998)

    Article  Google Scholar 

  235. Wiesmann, D., Hammel, U., Bäck, T.: Robust design of multilayer optical coatings by means of evolutionary strategies. Sonderforschungsbereich (sfb) 531, Universität Dortmund (1998)

    Google Scholar 

  236. Wilke, C.O.: Evolutionary dynamics in time-dependent environments. PhD thesis, Fakultät für Physik und Astronomie, Ruhr-Universität Bochum (1999)

    Google Scholar 

  237. Wilke, C.O.: Adaptive evolution on neutral networks. Bulletin of Mathematical Biology 63(4), 715–730 (2001)

    Article  MathSciNet  Google Scholar 

  238. Wilke, D.N., Kok, S., Groenwold, A.A.: Comparison of linear and classical velocity update rules in particle swarm optimization: notes on diversity. International Journal for Numerical Methods in Engineering 70(8), 962–984 (2007)

    Article  MathSciNet  Google Scholar 

  239. Williams, G.C.: Pleiotropy, natural selection, and the evolution of senescence. Evolution 11(4), 398–411 (1957)

    Article  Google Scholar 

  240. Winter, P.C., Hickey, G.I., Fletcher, H.L.: Instant Notes in Genetics, 3rd edn. Springer, New York (2006) (1st edn. 1998, 2nd edn. 2002)

    Google Scholar 

  241. Wolpert, D.H., Macready, W.G.: No free lunch theorems for search. Tech. Rep. SFI-TR-95-02-010, The Santa Fe Institute (1995)

    Google Scholar 

  242. Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 1(1), 67–82 (1997)

    Article  Google Scholar 

  243. Wu, N.: Differential evolution for optimisation in dynamic environments. Tech. rep., School of Computer Science and Information Technology, RMIT University (2006)

    Google Scholar 

  244. Yang, S., Ong, Y.S., Jin, Y.: Evolutionary Computation in Dynamic and Uncertain Environments. Studies in Computational Intelligence, vol. 51(XXIII). Springer, Heidelberg (2007)

    MATH  Google Scholar 

  245. Zakian, V.: New formulation for the method of inequalities. Proceedings of the Institution of Electrical Engineers 126(6), 579–584 (1979)

    Article  Google Scholar 

  246. Žilinskas, A.: Algorithm as 133: Optimization of one-dimensional multimodal functions. Applied Statistics 27(3), 367–375 (1978)

    Article  MATH  Google Scholar 

  247. Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm. Tech. Rep. 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich (2001)

    Google Scholar 

  248. Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Evolutionary Methods for Design, Optimisation and Control with Application to Industrial Problems. Proceedings of the EUROGEN 2001 Conference, pp. 95–100 (2001)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Distributed Systems Group, University of Kassel, Wilhelmshöher Allee 73, 34121, Kassel, Germany

    Thomas Weise & Michael Zapf

  2. School of Computing & Design, Swinburne University of Technology (Sarawak Campus), 93350, Kuching, Sarawak, Malaysia

    Raymond Chiong

  3. Dept. Lenguajes y Ciencias de la Computación, ETSI Informática, University of Málaga, Campus de Teatinos, 29071, Málaga, Spain

    Antonio J. Nebro

Authors
  1. Thomas Weise
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michael Zapf
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Raymond Chiong
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Antonio J. Nebro
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Swinburne University of Technology, Sarawak Campus, Jalan Simpang Tiga, 93350, Kuching, Sarawak, Malaysia

    Raymond Chiong

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Weise, T., Zapf, M., Chiong, R., Nebro, A.J. (2009). Why Is Optimization Difficult?. In: Chiong, R. (eds) Nature-Inspired Algorithms for Optimisation. Studies in Computational Intelligence, vol 193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00267-0_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-00267-0_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00266-3

  • Online ISBN: 978-3-642-00267-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation