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The Markov Network Fitness Model

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Markov Networks in Evolutionary Computation

Part of the book series: Adaptation, Learning, and Optimization ((ALO,volume 14))

Abstract

Fitness modelling is an area of research which has recently receivedmuch interest among the evolutionary computing community. Fitness models can improve the efficiency of optimisation through direct sampling to generate new solutions, guiding of traditional genetic operators or as surrogates for a noisy or long-running fitness functions. In this chapter we discuss the application of Markov networks to fitness modelling of black-box functions within evolutionary computation, accompanied by discussion on the relationship between Markov networks andWalsh analysis of fitness functions.We review alternative fitness modelling and approximation techniques and draw comparisons with the Markov network approach. We discuss the applicability of Markov networks as fitness surrogates which may be used for constructing guided operators or more general hybrid algorithms.We conclude with some observations and issues which arise from work conducted in this area so far.

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References

  1. Abboud, K., Schoenauer, M.: Surrogate Deterministic Mutation: Preliminary Results. In: Collet, P., Fonlupt, C., Hao, J.-K., Lutton, E., Schoenauer, M. (eds.) EA 2001. LNCS, vol. 2310, pp. 104–116. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  2. Baluja, S., Davies, S.: Using optimal dependency-trees for combinational optimization. In: ICML 1997: Proceedings of the Fourteenth International Conference on Machine Learning, pp. 30–38. Morgan Kaufmann Publishers Inc. (1997)

    Google Scholar 

  3. Bethke, A.: Genetic Algorithms as Function Optimizers. Ph.D. thesis, University of Mitchigan (1980)

    Google Scholar 

  4. Brownlee, A.E.I.: Multivariate Markov Networks for Fitness Modelling in an Estimation of Distribution Algorithm. Ph.D. thesis, Robert Gordon University, Aberdeen (2009), http://hdl.handle.net/10059/381

  5. Brownlee, A.E.I., McCall, J.A.W., Brown, D.F.: Solving the MAXSAT problem using a multivariate EDA based on Markov networks. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2007) (Late Breaking Papers), pp. 2423–2428. ACM Press, New York (2007)

    Chapter  Google Scholar 

  6. Brownlee, A.E.I., McCall, J.A.W., Shakya, S.K., Zhang, Q.: Structure Learning and Optimisation in a Markov-network based Estimation of Distribution Algorithm. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2009), pp. 447–454. IEEE Press, Trondheim (2009)

    Chapter  Google Scholar 

  7. Brownlee, A.E.I., McCall, J.A.W., Zhang, Q., Brown, D.: Approaches to Selection and their effect on Fitness Modeling in an Estimation of Distribution Algorithm. In: Proceedings of the IEEE World Congress on Computational Intelligence (CEC 2008), pp. 2621–2628. IEEE Press, Hong Kong (2008)

    Chapter  Google Scholar 

  8. Brownlee, A.E.I., Regnier-Coudert, O., McCall, J.A.W., Massie, S.: Using a Markov network as a surrogate fitness function in a genetic algorithm. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2010), pp. 4525–4532. IEEE Press, Barcelona (2010)

    Google Scholar 

  9. Brownlee, A.E.I., Wu, Y., McCall, J.A.W., Godley, P.M., Cairns, D.E., Cowie, J.: Optimisation and fitness modelling of bio-control in mushroom farming using a Markov network EDA. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2008), pp. 465–466. ACM, Atlanta (2008)

    Chapter  Google Scholar 

  10. Bui, L.T., Abbass, H.A., Essam, D.: Fitness inheritance for noisy evolutionary multi-objective optimization. In: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation, GECCO 2005, pp. 779–785. ACM, New York (2005)

    Chapter  Google Scholar 

  11. Chen, J.H., Goldberg, D., Ho, S.-Y., Sastry, K.: Fitness inheritance in multiobjective optimization. In: Proceedings of the Genetic and Evolutionary Computation COnference (GECCO 2002), pp. 319–326. ACM Press (2002)

    Google Scholar 

  12. Davarynejad, M., Ahn, C.W., Vrancken, J., van den Berg, J., Coello Coello, C.A.: Evolutionary hidden information detection by granulation-based fitness approximation. Appl. Soft Comput. 10, 719–729 (2010)

    Article  Google Scholar 

  13. Emmerich, M., Giannakoglou, K., Naujoks, B.: Single- and multiobjective evolutionary optimization assisted by gaussian random field metamodels. IEEE Transactions on Evolutionary Computation 10(4), 421–439 (2006)

    Article  Google Scholar 

  14. Furtuna, R., Curteanu, S., Leon, F.: An elitist non-dominated sorting genetic algorithm enhanced with a neural network applied to the multi-objective optimization of a polysiloxane synthesis process. Eng. Appl. Artif. Intell. 24, 772–785 (2011)

    Article  Google Scholar 

  15. Goldberg, D.: Genetic Algorithms and Walsh Functions: Part I, A Gentle Introduction. Complex Systems 3, 129–152 (1989)

    MathSciNet  MATH  Google Scholar 

  16. Goldberg, D.: Genetic Algorithms and Walsh Functions: Part II, Deception and its Analysis. Complex Systems 3, 153–171 (1989)

    MathSciNet  MATH  Google Scholar 

  17. Golubov, B., Efimov, A., Skvortsov, V.: Walsh Series and Transforms: Theory and Applications. Mathematics and Applications: Soviet Series, vol. 64. Kluwer Academic Publishers, Boston (1991)

    Book  MATH  Google Scholar 

  18. Han, S.H., Yang, H.: Screening important design variables for building a usability model: genetic algorithm-based partial least-squares approach. International Journal of Industrial Ergonomics 33(2), 159–171 (2004)

    Article  Google Scholar 

  19. Hauschild, M., Pelikan, M., Lima, C.F., Sastry, K.: Analyzing probabilistic models in hierarchical BOA on traps and spin glasses. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2007), pp. 523–530. ACM Press, New York (2007)

    Chapter  Google Scholar 

  20. Jin, Y.: A comprehensive survey of fitness approximation in evolutionary computation. Soft Computing 9(1), 3–12 (2005)

    Article  Google Scholar 

  21. Jin, Y., Sendhoff, B.: Reducing Fitness Evaluations Using Clustering Techniques and Neural Network Ensembles. In: Deb, K., et al. (eds.) GECCO 2004, Part I. LNCS, vol. 3102, pp. 688–699. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  22. Johanson, B.: Gp-music: An interactive genetic programming system for music generation with automated fitness raters. In: Proceedings of the Third Annual Conference, pp. 181–186. MIT Press (1998)

    Google Scholar 

  23. Kallel, L., Naudts, B., Reeves, R.: Properties of fitness functions and search landscapes. In: Kallel, L., Naudts, B., Rogers, A. (eds.) Theoretical Aspects of Evolutionary Computing, pp. 177–208. Springer (2000)

    Google Scholar 

  24. Larrañaga, P., Lozano, J.A.: Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Boston (2002)

    MATH  Google Scholar 

  25. Li, R., Emmerich, M., Eggermont, J., Bovenkamp, E., Back, T., Dijkstra, J., Reiber, J.: Metamodel-assisted mixed integer evolution strategies and their application to intravascular ultrasound image analysis. In: IEEE Congress on Evolutionary Computation, CEC 2008 (IEEE World Congress on Computational Intelligence), pp. 2764–2771 (2008)

    Google Scholar 

  26. Lim, D., Jin, Y., Ong, Y.S., Sendhoff, B.: Generalizing surrogate-assisted evolutionary computation. IEEE Transactions on Evolutionary Computation 14(3), 329–355 (2010)

    Article  Google Scholar 

  27. Lima, C.F., Sastry, K., Goldberg, D.E., Lobo, F.G.: Combining competent crossover and mutation operators: a probabilistic model building approach. In: Proceedings of the 2005 Conference on Genetic and Evolutionary Computation (GECCO 2005), pp. 735–742. ACM, New York (2005)

    Chapter  Google Scholar 

  28. Lucey, T.: Quantatitive Techniques: An Instructional Manual. D. P. Publications, Eastleigh (1984)

    Google Scholar 

  29. MacNish, C.: Benchmarking Evolutionary Algorithms: The Huygens Suite. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2005) (Late Breaking Papers), pp. 2423–2428. ACM Press, New York (2005)

    Google Scholar 

  30. Macready, W., Levitan, B.: Learning landscapes: regression on discrete spaces. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 1999), vol. 1, pp. 687–694 (1999)

    Google Scholar 

  31. Magnier, L., Haghighat, F.: Multiobjective optimization of building design using trnsys simulations, genetic algorithm, and artificial neural network. Building and Environment 45(3), 739–746 (2010)

    Article  Google Scholar 

  32. Michalski, R.S.: Learnable evolution model: Evolutionary processes guided by machine learning. Machine Learning 38(1-2), 9–40 (2000)

    Article  MATH  Google Scholar 

  33. Miquélez, T., Bengoetxea, E., Larrañaga, P.: Evolutionary computation based on Bayesian classifiers. International Journal of Applied Mathematics and Computer Science 14(3), 101–115 (2004)

    Google Scholar 

  34. Ochoa, A.: Opportunities for Expensive Optimization with Estimation of Distribution Algorithms. In: Tenne, Y., Goh, C.-K. (eds.) Computational Intel. in Expensive Opti. Prob. ALO, vol. 2, pp. 193–218. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  35. Ochoa, A.A., Soto, M.R.: Partial evaluation in genetic algorithms. In: Proceedings of the 10th International Conference on Industrial and Engineering Applications of Artificial Intelligence and Expert Systems, IEA/AIE 1997, pp. 217–222. Goose Pond Press (1997)

    Google Scholar 

  36. Peña, J.M., Robles, V., Larrañaga, P., Herves, V., Rosales, F., Pérez, M.S.: GA-EDA: Hybrid Evolutionary Algorithm Using Genetic and Estimation of Distribution Algorithms. In: Orchard, B., Yang, C., Ali, M. (eds.) IEA/AIE 2004. LNCS (LNAI), vol. 3029, pp. 361–371. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  37. Pelikan, M.: Hierarchical Bayesian Optimization Algorithm - Toward a New Generation of Evolutionary Algorithms. STUDFUZZ, vol. 170. Springer (2005)

    Google Scholar 

  38. Pelikan, M., Sastry, K.: Fitness Inheritance in the Bayesian Optimization Algorithm. In: Deb, K., et al. (eds.) GECCO 2004, Part II. LNCS, vol. 3103, pp. 48–59. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  39. Press, W.H., Flannery, B.P., Teukolsky, S.A., Vetterling, W.T.: Numerical Recipes: The Art of Scientific Computing. Cambridge University Press, Cambridge (1986)

    Google Scholar 

  40. Rasheed, K., Vattam, S., Ni, X.: Comparison of methods for using reduced models to speed up design optimization. In: Proceedings of the Genetic and Evolutionary Computation COnference (GECCO 2002), pp. 1180–1187. Morgan Kaufmann Publishers Inc., San Francisco (2002)

    Google Scholar 

  41. Regis, R., Shoemaker, C.: Local function approximation in evolutionary algorithms for the optimization of costly functions. IEEE Transactions on Evolutionary Computation 8(5), 490–505 (2004)

    Article  Google Scholar 

  42. 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 World on Congress on Computational Intelligence, vol. 1, pp. 360–365 (2002)

    Google Scholar 

  43. Santana, R.: A Markov Network Based Factorized Distribution Algorithm for Optimization. In: Lavrač, N., Gamberger, D., Todorovski, L., Blockeel, H. (eds.) ECML 2003. LNCS (LNAI), vol. 2837, pp. 337–348. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  44. Santana, R., Larrañaga, P., Lozano, J.A.: Mixtures of Kikuchi Approximations. In: Fürnkranz, J., Scheffer, T., Spiliopoulou, M. (eds.) ECML 2006. LNCS (LNAI), vol. 4212, pp. 365–376. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  45. Santana, R., Larrañaga, P., Lozano, J.A.: Research topics on discrete estimation of distribution algorithms. Memetic Computing 1(1), 35–54 (2009)

    Article  Google Scholar 

  46. Santana, R., Ochoa, A., Soto, M.R.: The mixture of trees factorized distribution algorithm. In: Spector, L., Goodman, E., Wu, A., Langdon, W.B., Voigt, H.M., Gen, M., Sen, S., Dorigo, M., Pezeshk, S., Garzon, M., Burke, E. (eds.) Proceedings of the Genetic and Evolutionary Computation COnference (GECCO 2001), pp. 543–550. Morgan Kaufmann Publishers (2001)

    Google Scholar 

  47. Sastry, K., Lima, C., Goldberg, D.E.: Evaluation relaxation using substructural information and linear estimation. In: Proceedings of the Genetic and Evolutionary Computation COnference (GECCO 2006), pp. 419–426. ACM Press, New York (2006)

    Chapter  Google Scholar 

  48. Schmidt, M.D., Lipson, H.: Coevolution of fitness predictors. IEEE Transactions on Evolutionary Computation 12(6), 736–749 (2008)

    Article  Google Scholar 

  49. Shakya, S., Santana, R.: A Markovianity based optimisation algorithm. Tech. Rep. EHU-KZAA-IK-3/08, Department of Computer Science and Artificial Intelligence, University of the Basque Country (2008)

    Google Scholar 

  50. Shakya, S.K.: DEUM: A framework for an estimation of distribution algorithm based on Markov random fields. Ph.D. thesis, The Robert Gordon University, Aberdeen, UK (2006), http://hdl.handle.net/10059/39

  51. Shakya, S.K., Brownlee, A.E.I., McCall, J.A.W., Fournier, F., Owusu, G.: A fully multivariate DEUM algorithm. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2009), pp. 479–486. IEEE Press (2009)

    Google Scholar 

  52. Shakya, S.K., McCall, J.A.W.: Optimization by estimation of distribution with DEUM framework based on Markov random fields. International Journal of Automation and Computing 4(3), 262–272 (2007)

    Article  Google Scholar 

  53. Shakya, S.K., McCall, J.A.W., Brown, D.F.: Incorporating a Metropolis method in a distribution estimation using Markov random field algorithm. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2005), pp. 2576–2583. IEEE Press (2005)

    Google Scholar 

  54. Shakya, S.K., McCall, J.A.W., Brown, D.F.: Solving the Ising spin glass problem using a bivariate EDA based on Markov random fields. In: Proceedings of the IEEE World Congress on Computational Intelligence (CEC 2006). IEEE Press (2006)

    Google Scholar 

  55. Shi, L., Rasheed, K.: A Survey of Fitness Approximation Methods Applied in Evolutionary Algorithms. In: Tenne, Y., Goh, C.K. (eds.) Computational Intelligence in Expensive Optimization Problems. Adaptation Learning and Optimization, vol. 2, ch.1, pp. 3–28. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  56. Smith, R.E., Dike, B.A., Stegmann, S.A.: Fitness inheritance in genetic algorithms. In: SAC 1995: Proceedings of the 1995 ACM Symposium on Applied Computing, pp. 345–350. ACM Press, New York (1995)

    Chapter  Google Scholar 

  57. Syberfeldt, A., Grimm, H., Ng, A., John, R.I.: A parallel surrogate-assisted multi-objective evolutionary algorithm for computationally expensive optimization problems. In: Wang, J. (ed.) Proceedings of the IEEE World Congress on Computational Intelligence (CEC 2008), pp. 3177–3184. IEEE Computational Intelligence Society, IEEE Press, Hong Kong (2008)

    Chapter  Google Scholar 

  58. Takahashi, S., Kita, H., Suzuki, H., Sudo, T., Markon, S.: Simulation-based optimization of a controller for multi-car elevators using a genetic algorithm for noisy fitness function. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2003), vol. 3, pp. 1582–1587 (2003)

    Google Scholar 

  59. Wallin, D., Ryan, C.: Using over-sampling in a Bayesian classifier EDA to solve deceptive and hierarchical problems. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2009), pp. 1660–1667 (2009)

    Google Scholar 

  60. Zhang, Q., Sun, J.: Iterated local search with guided mutation. In: Proceedings of the IEEE World Congress on Computational Intelligence (CEC 2006), pp. 924–929. IEEE Press (2006)

    Google Scholar 

  61. Zhang, Q., Sun, J., Tsang, E.: Combinations of estimation of distribution algorithms and other techniques. International Journal of Automation & Computing, 273–280 (2007)

    Google Scholar 

  62. Zhou, L., Haghighat, F.: Optimization of ventilation system design and operation in office environment, part i: Methodology. Building and Environment 44(4), 651–656 (2009)

    Article  Google Scholar 

  63. Zhou, Z., Ong, Y.S., Lim, M.H., Lee, B.S.: Memetic algorithm using multi-surrogates for computationally expensive optimization problems. Soft Comput. 11(10), 957–971 (2007)

    Article  Google Scholar 

  64. Zhou, Z., Ong, Y.S., Nguyen, M.H., Lim, D.: A study on polynomial regression and Gaussian process global surrogate model in hierarchical surrogate-assisted evolutionary algorithm. In: Proceedings of the IEEE Congress on Evolutionary Computation (CEC 2005), vol. 3, pp. 2832–2839 (2005)

    Google Scholar 

  65. Ziegler, J., Banzhaf, W.: Decreasing the Number of Evaluations in Evolutionary Algorithms by Using a Meta-Model of the Fitness Function. In: Ryan, C., Soule, T., Keijzer, M., Tsang, E.P.K., Poli, R., Costa, E. (eds.) EuroGP 2003. LNCS, vol. 2610, pp. 264–275. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Loughborough University, Loughborough, UK

    Alexander E. I. Brownlee

  2. Robert Gordon University, Aberdeen, UK

    John A. W. McCall

  3. Business Modelling and Operational Transformation Practice, BT Innovate & Design, Ipswich, UK

    Siddhartha K. Shakya

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  1. Alexander E. I. Brownlee
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  2. John A. W. McCall
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  3. Siddhartha K. Shakya
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Correspondence to Alexander E. I. Brownlee .

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Editors and Affiliations

  1. Transformation Practice, BT Innovate & Design, Business Modelling and Operational, Cauldwell Hall Road 172, Ipswich, IP4 5DB, United Kingdom

    Siddhartha Shakya

  2. Intelligent Systems Group, Faculty of Informatics, University of the Basque Country, Boadilla del Monte, San Sebastian, Spain

    Roberto Santana

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Brownlee, A.E.I., McCall, J.A.W., Shakya, S.K. (2012). The Markov Network Fitness Model. In: Shakya, S., Santana, R. (eds) Markov Networks in Evolutionary Computation. Adaptation, Learning, and Optimization, vol 14. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28900-2_8

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  • DOI: https://doi.org/10.1007/978-3-642-28900-2_8

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