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Solving metameric variable-length optimization problems using genetic algorithms

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Abstract

In many optimization problems, one of the goals is to determine the optimal number of analogous components to include in the system. Examples include the number of sensors in a sensor coverage problem, the number of turbines in a wind farm problem, and the number of plies in a laminate stacking problem. Using standard approaches to solve these problems requires assuming a fixed number of sensors, turbines, or plies. However, if the optimal number is not known a priori this will likely lead to a sub-optimal solution. A better method is to allow the number of components to vary. As the number of components varies, so does the dimensionality of the search space, making the use of gradient-based methods difficult. A metameric genetic algorithm (MGA), which uses a segmented variable-length genome, is proposed. Traditional genetic algorithm (GA) operators, designed to work with fixed-length genomes, are no longer valid. This paper discusses the modifications required for an effective MGA, which is then demonstrated on the aforementioned problems. This includes the representation of the solution in the genome and the recombination, mutation, and selection operators. With these modifications the MGA is able to outperform the fixed-length GA on the selected problems, even if the optimal number of components is assumed to be known a priori.

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References

  1. G.D. Edgecombe, G. Giribet, Evolutionary biology of centipedes (Myriapoda: Chilopoda). Annu. Rev. Entomol. 52, 151–170 (2007)

    Article  Google Scholar 

  2. C. Kettle, J. Johnstone, T. Jowett, H. Arthur, W. Arthur, The pattern of segment formation, as revealed by engrailed expression, in a centipede with a variable number of segments. Evol. Dev. 5(2), 198–207 (2003)

    Article  Google Scholar 

  3. W. Banzhaf, P. Nordin, R.E. Keller, F.D. Francone, Genetic Programming—An Introduction (Morgan Kaufmann, San Francisco, 1998)

    Book  MATH  Google Scholar 

  4. D.E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison-Wesley, Reading, 1989)

    MATH  Google Scholar 

  5. M. Mitchell, An Introduction to Genetic Algorithms (The MIT Press, Cambridge, 1998)

    MATH  Google Scholar 

  6. A.E. Eiben, J.E. Smith, Introduction to Evolutionary Computing, 2nd edn. (Springer, Berlin Heidelberg, 2015)

    Book  MATH  Google Scholar 

  7. T.M. Chan, K.F. Man, K.S. Tang, S. Kwong, A Jumping-Genes Paradigm for Optimizing Factor WLAN Network. IEEE Ind. Inform. 3(1), 33–43 (2007)

    Article  Google Scholar 

  8. G. Soremekun, Z. Gürdal, R.T. Haftka, L.T. Watson, Composite laminate design optimization by genetic algorithm with generalized elitist selection. Comput. Struct. 79(2), 131–143 (2001)

    Article  Google Scholar 

  9. C.H. Park, W.I. Lee, W.S. Han, A. Vautrin, Improved genetic algorithm for multidisciplinary optimization of composite laminates. Comput. Struct. 86(19–20), 1894–1903 (2008)

    Article  Google Scholar 

  10. R. Le Riche, R.T. Haftka, Improved genetic algorithm for minimum thickness composite laminate design. Compos. Eng. 5(2), 143–161 (1995)

    Article  Google Scholar 

  11. C.H. Park, W.I. Lee, W.S. Han, A. Vautrin, Multiconstraint optimization of composite structures manufactured by resin transfer molding process. J. Compos. Mater. 39(4), 347–374 (2005)

    Article  Google Scholar 

  12. J.A. Hageman, R. Wehrens, H.A. van Sprang, L.M.C. Buydens, Hybrid genetic algorithm-tabu search approach for optimizing multilayer optical coatings. Anal. Chim. Acta 490, 211–222 (2003)

    Article  Google Scholar 

  13. A. Gad, O. Abdelkhalik, Hidden genes genetic algorithm for multi-gravity-assist trajectories optimization. J. Spacecr. Rockets 48(4), 629–641 (2011)

    Article  Google Scholar 

  14. S. Bandyopadhyay, U. Maulik, Genetic clustering for automatic evolution of clusters and application to image classification. Pattern Recogn. 35, 1197–1208 (2002)

    Article  MATH  Google Scholar 

  15. S. Das, A. Abraham, A. Konar, Automatic clustering using an improved differential evolution algorithm. IEEE Trans. Syst. Man Cybern. A 38(1), 218–237 (2008)

    Article  Google Scholar 

  16. S. Das, S. Sil, Kernel-induced fuzzy clustering of image pixels with an improved differential evolution algorithm. Inform. Sci. 180, 1237–1256 (2010)

    Article  MathSciNet  Google Scholar 

  17. S.-M. Pan, K.-S. Cheng, Evolution-based tabu search approach to automatic clustering. IEEE Trans. Syst. Man Cybern. C 37(5), 827–838 (2007)

    Article  Google Scholar 

  18. R.S. Zebulum, M.A. Pacheco, M. Vellasco, Variable length representation in evolutionary electronics. Evol. Comput. 8(1), 93–120 (2000)

    Article  Google Scholar 

  19. N.J. Radcliffe, Forma analysis and random respectful recombination, in ICGA’91 (Morgan-Kaufmann, San Mateo, 1991), pp. 222–229

  20. H. Kargupta, K. Deb, D.E. Goldberg, Ordering genetic algorithms and deception, in PPSN II (Elsevier, Amsterdam, 1999), pp. 47–56

  21. M. Ryerkerk, R. Averill, K. Deb, E. Goodman, Optimization for variable-size problems using genetic algorithms, in Proceedings of the 14th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference (AIAA, Indianapolis, 2012)

  22. X. Han, X. Cao, E.L. Lloyd, C-C. Shen, Deploying directional sensor networks with guaranteed connectivity and coverage, in SECON’08 (IEEE, San Francisco, 2008), pp. 153–160

  23. S.S. Dhillon, K. Chakrabarty, Sensor placement for effective coverage and surveillance in distributed sensor networks, in WCNC’03, vol. 3 (IEEE, New Orleans, 2003), pp. 1609–1614

  24. X. Boukerche, A. Fei, Coverage-preserving scheme for wireless sensor network with irregular sensing range. Ad Hoc Netw. 5(8), 1303–1316 (2007)

    Article  Google Scholar 

  25. C.-F. Huang, Y.-C. Tseng, The coverage problem in a wireless sensor network. Mobile Netw. Appl. 10(4), 519–528 (2005)

    Article  Google Scholar 

  26. Y-C. Wang, C-C. Hu, Y-C. Tseng, Efficient deployment algorithms for ensuring coverage and connectivity of wireless sensor networks, in WICON’05 (IEEE, Budapest, 2005), pp. 114–121

  27. M. Younis, K. Akkaya, Strategies and techniques for node placement in wireless sensor networks: a survey. Ad Hoc Netw. 6(4), 621–655 (2008)

    Article  Google Scholar 

  28. J. Jia, J. Chen, G. Chang, Z. Tan, Energy efficient coverage control in wireless sensor networks based on multi-objective genetic algorithm. Comput. Math. Appl. 57(11–12), 1756–1766 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  29. R. Kershner, The number of circles covering a set. Am. J. Math. 61(3), 665–671 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  30. X. Bai, S. Kumar, D. Xuan, Z. Yun, T.H. Lai, Deploying wireless sensors to achieve both coverage and connectivity, in MobiHoc’06 (ACM, Florence, 2006), pp. 131–142

  31. K.J. Nurmela, P.R.J. Östergård, Covering a Square with up to 30 Equal Circles, Helsinki University of Technology, Laboratory for Theoretical Computer Science, Research Report A62 (Espoo, Finland, 2000)

    Google Scholar 

  32. N.A.A. Aziz, K.A. Aziz, W.Z.W. Ismail, Coverage strategies for wireless sensor networks. World Acad. Sci. Eng. Technol. 50, 145–150 (2009)

    Google Scholar 

  33. C.-H. Wu, K.-C. Lee, Y.-C. Chung, A delaunay triangulation based method for wireless sensor network deployment. Comput. Commun. 30(14), 2744–2752 (2007)

    Article  Google Scholar 

  34. Z. Yangyang, J. Chunlin, Y. Ping, L. Manlin, W. Chaojin, W. Guangxing, Particle swarm optimization for base station placement in mobile communication, in ICNSC ‘04 (IEEE, Taipei, 2004), pp. 428–432

  35. C.-K. Ting, C.-N. Lee, H.-C. Chang, J.-S. Wu, Wireless heterogeneous transmitter placement using multiobjective variable-length genetic algorithm. IEEE Ttans. Syst. Man Cybern. B 39(4), 945–958 (2009)

    Article  Google Scholar 

  36. D.B. Jourdan, O.L. de Weck, Layout optimization for a wireless sensor network using a multi-objective genetic algorithm, in VTC ‘04-Spring (IEEE, Milan, 2004), pp. 2466–2470

  37. M. Marks, A survey of multi-objective deployment in wireless sensor networks. J. Telecommun. Inform. Technol. 3, 36–41 (2010)

    Google Scholar 

  38. A. Tonda, E. Lutton, G. Squillero, A benchmark for cooperative coevolution. Memet. Comp. 4(4), 262–277 (2012)

    Google Scholar 

  39. G. Mosetti, C. Poloni, B. Diviacco, Optimization of wind turbine positioning in large windfarms by means of a genetic algorithm. J. Wind Eng. Ind. Aerod. 51(1), 105–116 (1994)

    Article  Google Scholar 

  40. S.A. Grady, M.Y. Hussaini, M.M. Abdullah, Placement of wind turbines using genetic algorithms. Renew. Energy 30(2), 259–270 (2010)

    Article  Google Scholar 

  41. H-S. Huang, Distributed genetic algorithm for optimization of wind farm annual profits, in ISAP’07 (IEEE, Kaohsiung, 2007), pp. 418–423

  42. S. Şişbot, Ö. Turgut, M. Tunç, Ü. Çamdali, Optimal positioning of wind turbines on Gökçeada using multi-objective genetic algorithm. Wind Energy 13(4), 297–306 (2010)

    Article  Google Scholar 

  43. A. Emami, P. Noghreh, New approach on optimization in placement of wind turbines within wind farm by genetic algorithms. Renew. Energy 35(7), 1559–1564 (2010)

    Article  Google Scholar 

  44. Duan, J. Wang, H. Gu, Modified genetic algorithm for layout optimization of multi-type wind turbines, in ACC 2014 (IEEE, Portland, 2014), pp. 3633–3638

  45. J.C. Mora, J.M.C. Barón, J.M.R. Santos, M.B. Payán, An evolutive algorithm for wind farm optimal design. Neurocomputing 70(16), 2651–2658 (2007)

    Article  Google Scholar 

  46. J.S. González, A.G.G. Rodriguez, J.C. Mora, J.R. Santos, M.B. Payán, Optimization of wind farm turbines layout using an evolutive algorithm. Renew. Energy 35(8), 1671–1681 (2010)

    Article  Google Scholar 

  47. J.S. González, A.G.G. Rodriguez, J.C. Mora, M.B. Payán, J.R. Santos, Overall design optimization of wind farms. Renew. Energy 36(7), 1973–1982 (2011)

    Article  Google Scholar 

  48. Wan, J. Wang, G. Yang, X. Zhang, Optimal micro-siting of wind farms by particle swarm optimization, in ICSI 2010 (Springer, Beijing, 2010), pp. 198–205

  49. S. Saavedra-Moreno, A. Salcedo-Sans, L. Paniagua-Tineo, A. Prieto, Portilla-Figueras, seeding evolutionary algorithms with heuristics for optimal wind turbines positioning in wind farms. Renew. Energy 36(11), 2838–2844 (2011)

    Article  Google Scholar 

  50. B.L. DuPont, J. Cagan, An extended pattern search approach to wind farm layout optimization. J. Mech. Des. 134(081002), 081002-18 (2012)

    Google Scholar 

  51. M. Wagner, J. Day, F. Neumann, A fast and effective local search algorithm for optimizing the placement of wind turbines. Renew. Energy 51, 64–70 (2013)

    Article  Google Scholar 

  52. J.F. Herbert-Acero, O. Probst, P.-E. Réthoré, G.C. Larsen, K.K. Castillo-Villar, A review of methodological approaches for the design and optimization of wind farms. Energies 7(11), 6930–7016 (2014)

    Article  Google Scholar 

  53. J.S. González, M.B. Payán, J.R. Santos, F. González-Langatt, A review and recent developments in the optimal wind-turbine micro-siting problem. Renew. Sust. Energy Rev. 30, 133–144 (2014)

    Article  Google Scholar 

  54. N.O. Jensen, A note of wind generator interaction, Risø National Laboratory, Technical report Riso-M-2411 (Roskilde, 1983)

  55. S. Frandsen, On the wind speed reduction in the center of large clusters of wind turbines. J. Wind Eng. Ind. Aerod. 39(1), 251–265 (1992)

    Article  Google Scholar 

  56. S. Venkataraman, R.T. Haftka, Optimization of composite panels—a review, in Proceedings of the 14th Annual Technical Conference of the American Society of Composites (Dayton, 1999), pp. 479–488

  57. L.A. Schmit, B. Farshi, Optimum design of laminated fibre composite plates. Int. J. Numer. Method Eng. 11(4), 623–640 (1977)

    Article  MATH  Google Scholar 

  58. S.N. Omkar, R. Khandelwal, S. Yathindra, G.N. Naik, S. Gopalakrishnan, Artificial immune system for multi-objective design optimization of composite structures. Eng. Appl. Artif. Intel. 21(8), 1416–1429 (2008)

    Article  Google Scholar 

  59. I.M. Daniel, O. Ishai, Engineering Mechanics of Composite Materials, 2nd edn. (Oxford University Press, New York, 2006)

    Google Scholar 

  60. A.R.M. Rao, N. Arvind, A scatter search algorithm for stacking sequence optimization of laminate composites. Compos. Struct. 70(4), 383–402 (2005)

    Article  Google Scholar 

  61. F.-X. Irisarri, D.H. Bassir, N. Carrere, J.-F. Maire, Multiobjective stacking sequence optimization for laminated composite structures. Compos. Sci. Technol. 69(7–8), 983–990 (2009)

    Article  Google Scholar 

  62. D.R. Dasgupta, S.G.A. Mcgregor, A structured genetic algorithm, University of Strathclyde, Department of Computer Science, Technical report IKBS-8-92 (Glasgow, 1992)

  63. D.M. Cherba, W. Punch, Crossover gene selection by spatial location, in GECCO’06 (ACM, Seattle, 2006), pp. 1111–1116

  64. B. Hutt, K. Warwick, Synapsing variable-length crossover: meaningful crossover for variable-length genomes. IEEE Trans. Evolut. Comput. 11(1), 118–131 (2007)

    Article  Google Scholar 

  65. K. Deb, Multi-Objective Optimization Using Evolutionary Algorithms (Wiley, Chichester, 2001)

    MATH  Google Scholar 

  66. K.O. Stanley, R. Miikkulainen, Efficient reinforcement learning through evolving neural network topologies, in GECCO’02 (Morgan Kaufmann Publishers, New York, 2002), pp. 569–577

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Acknowledgments

This material is based in part upon work supported by the National Science Foundation under Cooperative Agreement No. DBI-0939454 to BEACON Center for the Study of Evolution in Action. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

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  1. Michigan State University, East Lansing, MI, 48823, USA

    Matthew L. Ryerkerk, Ronald C. Averill, Kalyanmoy Deb & Erik D. Goodman

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  1. Matthew L. Ryerkerk
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Correspondence to Matthew L. Ryerkerk.

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Ryerkerk, M.L., Averill, R.C., Deb, K. et al. Solving metameric variable-length optimization problems using genetic algorithms. Genet Program Evolvable Mach 18, 247–277 (2017). https://doi.org/10.1007/s10710-016-9282-8

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