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Metaheuristics for Optimization Problems

  • Lídice Camps Echevarría
  • Orestes Llanes Santiago
  • Haroldo Fraga de Campos Velho
  • Antônio José da Silva Neto
Chapter
Part of the Studies in Computational Intelligence book series (SCI, volume 763)

Abstract

An introduction to metaheuristics for optimization problems is presented in this chapter. In Sect. 3.1 a classification of metaheuristics is put forward. The metaheuristics Differential Evolution (DE); Particle Collision Algorithm (PCA); Ant Colony Optimization (ACO) in its version for continuous problems; and Particle Swarm Optimization (PSO) are described in Sects. 3.2, 3.3, 3.4 and 3.5, respectively. These metaheuristics were applied to he benchmark problems diagnosis described in Chap.  2, based on Fault Diagnosis-Inverse Problem Methodology (FD-IPM) as described in Chap.  2.

References

  1. 3.
    Angeline, P.J.: Chapter Evolutionary optimization versus particle swarm optimization: philosophy and performance differences. In: Evolutionary Programming VII: Proceeding of the Seventh Annual Conference on Evolutionary Programming (EP98). Lecture Notes in Computer Science, vol. 1447, pp. 601–611. Springer, New York (1998)Google Scholar
  2. 4.
    Baeck, T.: Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford University Press, Oxford (1996)Google Scholar
  3. 7.
    Becceneri, J.C., Zinober, A.: Extraction of energy in a nuclear reactor. In: XXXIII Simposio Brasileiro de Pesquisa Operacional. Campos do Jordão, SP, Brazil (2001)Google Scholar
  4. 8.
    Becceneri, J.C., Sandri, S., Luz, E.F.P.: Using ant colony systems with pheromone dispersion in the traveling salesman problem. In: Proceedings of the 11th International Conference of the Catalan Association for Artificial Intelligence. Sant Martí d’Empúries (2008)Google Scholar
  5. 10.
    Beielstein, T., Parsopoulos, K.E., Vrahatis, M.N.: Tuning PSO parameters through sensitivity analysis. Tech. rep., Reihe Computational Intelligence CI 124/02, Collaborative Research Center (SFB 531), Department of Computer Science and University of Dortmund (2002)Google Scholar
  6. 11.
    Beni, G., Wang, J.: Swarm intelligence. In: Seventh Annual Meeting of the Robotics Society of Japan. RSJ Press, Tokyo (1989)Google Scholar
  7. 12.
    Bertsekas, D.P.: Nonlinear Programming. Athena Scientific, Belmont, MA (1999)Google Scholar
  8. 13.
    Blum, C.: Ant colony optimization: introduction and recent trends. Phys. Life Rev. 2(4), 353–373 (2005)CrossRefGoogle Scholar
  9. 14.
    Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Oxford University Press, Oxford (1999)Google Scholar
  10. 15.
    Brest, J., Greiner, S., Boscovic, B., Mernik, M., Zumer, V.: Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans. Evol. Comput. 10(8), 646–657 (2006)CrossRefGoogle Scholar
  11. 19.
    Camps Echevarría, L., Llanes-Santiago, O., Silva Neto, A.J.: A proposal to fault diagnosis in industrial systems using bio-inspired strategies. Ingeniare. Revista chilena de ingeniería 19(2), 240–252 (2011)CrossRefGoogle Scholar
  12. 23.
    Carlisle, A., Dozier, G.: An off-the-self PSO. In: Proceedings of the Particle Swarm Optimization Workshop, Indiana, pp. 1–6 (2001)Google Scholar
  13. 26.
    Clerc, M., Kennedy, J.: The particle swarm-explosion, stability and convergence in a multidimensional complex space. IEEE Trans. Evol. Comput. 6(2), 58–73 (2002)CrossRefGoogle Scholar
  14. 27.
    Das, S., Abraham, A., Uday, K.C., Konar, A.: Differential evolution using a neighborhood-based mutation operator. IEEE Trans. Evol. Comput. 13(3), 526–553 (2009)CrossRefGoogle Scholar
  15. 28.
    Dawkins, R.: The Selfish Gene. Clarendon Press, Oxford (1976)Google Scholar
  16. 30.
    Derrac, J., García, S., Molina, D., Herrera, F.: A practical tutorial on the use of nonparametric statistical test as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evol. Comput. 1(1), 3–18 (2011)CrossRefGoogle Scholar
  17. 32.
    Dorigo, M.: Ottimizzazione, apprendimento automatico, ed algoritmi basati su metafora naturale. Ph.D. thesis, Politécnico di Milano (1992)Google Scholar
  18. 33.
    Dorigo, M., Blum, C.: Ant colony optimization theory: a survey. Theor. Comput. Sci. 344(2–3), 243–278 (2005)MathSciNetCrossRefGoogle Scholar
  19. 34.
    Dorigo, M., Maniezzo, V., Colorni, A.: The ant system: optimization by a colony of cooperating agents. IEEE Trans. Syst. Man Cybern. Part B 26(1), 29–41 (1996)CrossRefGoogle Scholar
  20. 37.
    Eberhart, R., Shi, Y.: Chapter Comparison between Genetic Algorithms and Particle Swarm Optimization. In: Evolutionary Programming VII: Proceeding of the Seventh Annual Conference on Evolutionary Programming (EP98). Lecture Notes in Computer Science, vol. 1447, pp. 611–619. Springer, Berlin (1998)Google Scholar
  21. 38.
    Eberhart, R.C., Shi, Y.H.: Comparing inertia weights and constriction factors in particle swarm optimization. In: Proceeding of the IEEE Congress on Evolutionary Computation, pp. 84–88 (2001)Google Scholar
  22. 45.
    García, S., Molina, D., Lozano, M., Herrera, F.: A study on the use of non-parametric tests for analyzing the evolutionary algorithms behaviour: a case study on the CEC 2005 Special Session on Real Parameter Optimization. J. Heuristics 15(6), 617–644 (2009)CrossRefGoogle Scholar
  23. 46.
    Glover, F.: Tabu search: a tutorial. Tech. rep., Center for Applied Artificial Intelligence, University of Colorado (1990)Google Scholar
  24. 47.
    Goldberg, D.E.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading, MA (1989)Google Scholar
  25. 48.
    Gomez, Y.: Two step swarm intelligence to solve the feature selection problem. J. Univ. Comput. Sci. 14(15), 2582–2596 (2008)Google Scholar
  26. 49.
    Gong, W., Cai, Z., Ling, C.X., Li, H.: A real-coded biogeography-based optimization with mutation. Appl. Math. Comput. 216(9), 2749–2758 (2010)MathSciNetCrossRefGoogle Scholar
  27. 50.
    Gong, W., Cai, Z., Ling, C.X.: DE/BBO a hybrid differential evolution with biogeography-based optimization for global numerical optimization. Soft Comput.: Fusion Found. Methodol. Appl. Arch. 15(4), 645–665 (2010)CrossRefGoogle Scholar
  28. 52.
    Hart, W.E., Krasnogor, N., Smith, J.E.: Recent Advances in Memetic Algorithms. Studies in Fuzziness and Soft Computing. Springer (2005). http://books.google.com.br/books?id=LYf7YW4DmkUC
  29. 65.
    Kameyama, K.: Particle swarm optimization – a survey. IEICE Trans. Inf. Syst. E92-D(7), 1354–1361 (2009)CrossRefGoogle Scholar
  30. 67.
    Karaboga, D., Akay, B.: A survey: algorithms simulating bee swarm intelligence. Artif. Intell. Rev. 31(1), 61–85 (2009)CrossRefGoogle Scholar
  31. 69.
    Kennedy, J.: The particle swarm: social adaptation of knowledge. In: IEEE International Conference on Evolutionary Computation, pp. 303–308. IEEE, Piscataway, NJ (1997)Google Scholar
  32. 70.
    Kennedy, J.: Chapter The behavior of particles. In: Evolutionary Programming VII: Proceeding of the Seventh Annual Conference on Evolutionary Programming (EP98). Lecture Notes in Computer Science, vol. 1447, pp. 581–590. Springer, New York (1998)Google Scholar
  33. 71.
    Kennedy, J., Eberhart, R.: Particle swarm optimization. In: IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948. IEEE, Perth (1995)Google Scholar
  34. 72.
    Kiran, M., Ozceylan, E., Gunduz, M., Paksoy, T.: A novel hybrid approach based on particle swarm optimization and ant colony algorithm to forecast energy demand of Turkey. Energy Convers. Manag. 53(2), 75–83 (2012)Google Scholar
  35. 73.
    Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)MathSciNetCrossRefGoogle Scholar
  36. 75.
    Krasnogor, N., Smith, J.: A tutorial for competent memetic algorithms: model, taxonomy, and design issues. IEEE Trans. Evol. Comput. 9(5), 474–488 (2005)CrossRefGoogle Scholar
  37. 79.
    Larrañaga, P., Lozano, J.: Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Genetic Algorithms and Evolutionary Computation, vol. 2. Kluwer Academic Publishers, Boston (2002)Google Scholar
  38. 81.
    Liang, J.J., Qin, A.K., Suganthan, P.N., Baskar, S.: Comprehensive learning particle swarm optimizer for global optimization of multimodal functions. IEEE Trans. Evol. Comput. 10(3), 281–295 (2006)CrossRefGoogle Scholar
  39. 83.
    Liu, L., Yang, S., Wang, D.: Particle Swarm Optimization with Composite Particle in Dynamic Environments. IEEE Trans. Syst. Man Cybern. Part B: Cybern. 40(6), 1634–1638 (2010)Google Scholar
  40. 87.
    Luz, E.F.P., Becceneri, J.C., De Campos Velho, H.F.F.: A new multiparticle collision algorithm for optimization in a high-performance environment. J. Comput. Interdiscip. Sci. 1(1), 3–10 (2008)Google Scholar
  41. 90.
    Metropolis, N., Rosenbluth, A.W., Teller, E.: Equations of state calculations by fast computing machines. J. Chem. Phys. 21(6), 1087–1092 (1953)Google Scholar
  42. 91.
    Mezura-Montes, E., Velázquez-Reyes, J., Coello-Coello, C.: A comparative study of differential evolution variants for global optimization. In: GECCO 06, Seattle, Washington (2006)Google Scholar
  43. 100.
    Price, K.V., Storn, R.M., Lampinen, J.A.: Differential Evolution: A Practical Approach to Global Optimization. Springer, Berlin (2005)Google Scholar
  44. 101.
    Puris, A., Bello, R., Herrera, F.: Analysis of the efficacy of a two-step methodology for ant colony optimization: case of study with TSP and QAP. Expert Syst. Appl. 37(7), 5443–5453 (2010)CrossRefGoogle Scholar
  45. 102.
    Qin, A., Huang, V.L., Suganthan, P.N.: Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans. Evol. Comput. 13(2), 398–417 (2009)CrossRefGoogle Scholar
  46. 104.
    Sacco, W.F., Oliveira, C.R.E.: A new stochastic optimization algorithm based on particle collisions. In: 2005 ANS Annual Meeting, Transactions of the American Nuclear Society (2005)Google Scholar
  47. 105.
    Sacco. W.F. Oliveira, C.R.E., Pereira, C.M.N.A.: Two stochastic optimization algorithms applied to nuclear reactor core design. Prog. Nucl. Energy 48(6), 525–539 (2006)CrossRefGoogle Scholar
  48. 107.
    Seckiner, S., Eroglu, Y., Emrullah, M., Dereli, T.: Ant colony optimization for continuous functions by using novel pheromone updating. Appl. Math. Comput. 219, 4163 (2013)MathSciNetCrossRefGoogle Scholar
  49. 108.
    Shah-Hosseini, H.: The intelligent water drops algorithm: a nature-inspired swarm-based optimization algorithm. Int. J. Bio-Inspired Comput. 1(1/2), 71–79 (2009)CrossRefGoogle Scholar
  50. 110.
    Shelokar, P.S., Siarry, P., Jayaraman, V.K., Kulkarni, B.D.: Particle swarm and ant colony algorithms hybridized for improved continuous optimization. Appl. Math. Comput. 188(1), 129–142 (2007)MathSciNetCrossRefGoogle Scholar
  51. 111.
    Silva Neto, A.J., Becceneri, J.C., Campos Velho, H.F. (eds.): Computational Intelligence Applied to Inverse Problems in Radiative Transfer. EdUERJ, Rio de Janeiro, Brazil (2016)Google Scholar
  52. 112.
    Silva Neto, A.J., Lugon Jr., J., Soliro, F.J.C.P., Biondi Neto, L., Santana, C.C., Lobato, F.S., Steffen Jr., V., Campos Velho, H.F., Souza, A.F., Camara L, D.T., Assis, E.G., Silva, F.M., Oliveira, G.P., Camps Echevarría, L., Llanes-Santiago, O.: Direct and Inverse Problems with Applications in Engineering – Research Collection. InTech, Rijeka, Croatia (2016)Google Scholar
  53. 113.
    Silva Neto, A.J., Llanes-Santiago, O., Silva, G.N. (eds.): Mathematical Modelling and Computational Intelligence in Engineering Applications. Springer, Cham (2016)zbMATHGoogle Scholar
  54. 118.
    Socha, K.: Ant colony optimization for continuous and mixed-variable domains. Ph.D. thesis, Université Libre de Bruxelles (2008)Google Scholar
  55. 119.
    Socha, K., Dorigo, M.: Ant colony optimization for continuous domains. Eur. J. Oper. Res. 185(3), 1155–1173 (2008)MathSciNetCrossRefGoogle Scholar
  56. 121.
    Sousa, F.L.: Generalized extremal optimization: a new stochastic algorithm for optimal design. Ph.D. thesis, Graduate Program in Applied Computation, Instituto Nacional de Pesquisas Espaciais, INPE-9564-TDI/836 (2003). (In Portuguese)Google Scholar
  57. 122.
    Souto, R.P., Stephany, S., Becceneri, J.C., Campos Velho, H.F., Silva Neto, A.J.: On the use of the ant colony system for radiative properties estimation. In: 5th International Conference on Inverse Problems in Engineering – Theory and Practice (V ICIPE), vol. 3, pp. 1–10. Leeds University Press, Leeds, Inglaterra (2005)Google Scholar
  58. 123.
    Storn, R., Price, K.: Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces. Tech. Rep. 12, International Computer Science Institute (1995)Google Scholar
  59. 124.
    Storn, R., Price, K.: Differential evolution: a simple and efficient adaptive heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)CrossRefGoogle Scholar
  60. 125.
    Suganthan, P., Hansen, N., Liang, J., Deb, K., Chen, Y.P., Auger, A., Tiwari, S.: Problem definitions and evaluation criteria for the CEC 2005 special session on real parameter optimization. Tech. rep., Nanyang Technological University (2005)Google Scholar
  61. 129.
    Tvrdik, J.: Adaptation in differential evolution: a numerical comparison. Appl. Soft Comput. 9(3), 1149–1155 (2009)MathSciNetCrossRefGoogle Scholar
  62. 138.
    Yang, X.S.: Firefly algorithm, stochastic test functions and design optimisation. Int. J. Bio-Inspired Comput. 2(2), 78–84 (2010)CrossRefGoogle Scholar
  63. 139.
    Yang, X.: Nature – Inspired Optimization Algorithms. Elsevier, Amsterdam (2014)zbMATHGoogle Scholar
  64. 141.
    Yang, X.S., Deb, S.: Engineering Optimisation by Cuckoo Search. Int. J. Math. Model. Numer. Optim. 1(4), 330–343 (2010)zbMATHGoogle Scholar
  65. 144.
    Yang, Z., Tang, K., Yao, X.: Self-adaptive differential evolution with neighborhood search. In: IEEE Congress on Evolutionary Computation (CEC2008), Hong Kong, pp. 1110–1116 (2008)Google Scholar
  66. 145.
    Yew-Soon, O., Meng-Hiot, L., Ning, Z., Kok-Wai, W.: Classification of adaptive memetic algorithms: a comparative study. Syst. Man Cybern. Part B: Cybern. 36(1), 141–152 (2006)CrossRefGoogle Scholar
  67. 146.
    Zaharie, D.: Influence of crossover on the behavior of differential evolution algorithms. Appl. Soft Comput. 9(3), 1126–1138 (2009)CrossRefGoogle Scholar
  68. 147.
    Zhan, Z.H., Zhang, J., Li, Y., Shi, Y.H.: Orthogonal learning particle swarm optimization. IEEE Trans. Evol. Comput. 15(6), 832–847 (2011)CrossRefGoogle Scholar
  69. 148.
    Zhang, J.: Adaptive differential evolution with optional external archive. IEEE Trans. Evol. Comput. 13(5), 945–958 (2009)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2019

Authors and Affiliations

  • Lídice Camps Echevarría
    • 1
  • Orestes Llanes Santiago
    • 2
  • Haroldo Fraga de Campos Velho
    • 3
  • Antônio José da Silva Neto
    • 4
  1. 1.Centro de Estudios de MatemáticaUniversidad Tecnológica de La Habana José, Antonio Echeverría, CUJAEMarianaoCuba
  2. 2.Dpto. de Automática y ComputaciónUniversidad Tecnológica de La Habana José, Antonio Echeverría, CUJAEMarianaoCuba
  3. 3.National Institute for Space Research, INPESão José dos CamposBrazil
  4. 4.Instituto PolitécnicoUniversidade do Estado do Rio de Janeiro, UERJNova FriburgoBrazil

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