Geomechanics and Engineering

  • 제27권1호
  • /
  • Pages.63-74
  • /
  • 2021
  • /
  • 2005-307X(pISSN)
  • /
  • 2092-6219(eISSN)
테크노프레스 (Techno-Press)
권호 표지
DOI QR코드

DOI QR Code

Pareto optimality and game theory for pile design having conflicting objectives

  • Hati, Shantanu (Department of Civil Engineering, Indian Institute of Technology (ISM) Dhanbad) ;
  • Panda, Sarat K. (Department of Civil Engineering, Indian Institute of Technology (ISM) Dhanbad)
  • 투고 : 2021.03.06
  • 심사 : 2021.09.29
  • 발행 : 2021.10.10
⟨ 이전 논문 다음 논문 ⟩

초록

Based on concept of Pareto-optimal solution and game theory associated with Nash non-cooperative and cooperative solution, a mathematical procedure is presented for optimum design of axially loaded pile structure. The decision making situation is formulated as a constrained optimization problem with two objectives of contradictory in nature. The factor of safety is taken as the design variable. Geometric constraints are considered by imposing a lower and upper bound on the design variable. Two objectives considered are: maximization of ultimate load carrying capacity of pile and minimization of associated cost. The generation of Pareto-optimal solution and methodology based on game theory concept is described. The design problem is mathematically formulated as two-person game. To obtain the starting point of game, Nash non-cooperative solution or Nash equilibrium solution is evaluated for an irrational play. For cooperative game, a negotiation model is developed for overall benefit of all players. Game is terminated when the optimal trade-off between two objectives is reached with maximization of supercriterion. Two numerical examples of practical interest are solved to demonstrate the methodology.

키워드

참고문헌

  1. Abusharar, S.W., Zheng, J.J., Chen, B.G. and Yin, J.H. (2009), "A simplified method for analysis of a piled embankment reinforced with geosynthetics", Geotext. Geomembranes, 27(1), 39-52. https://doi.org/10.1016/j.geotexmem.2008.05.002.
  2. Adali, S. (1983), "Pareto optimal design of beams subjected to support motions", Comput. Struct., 16, 297-303. https://doi.org/10.1016/0045-7949(83)90169-4 .
  3. Arai, K., Ohta, H. and Yasui, T. (1983), "Simple optimization techniques for evaluating deformation moduli from field observations", Soils Found., 24(4), 95-108. https://doi.org/10.3208/sandf1972.23.107.
  4. Azadi, M., Ghasemi, S.H. and Mohammadi, M. (2020), "Reliability analysis of tunnels with consideration of the earthquakes extreme events", Geomech. Eng., 22(5), 433-439. https://doi.org/10.12989/gae.2020.22.5.433.
  5. Balachandran, M. and Gero, J.S. (1984), "A comparison of three methods for generating the pareto optimal set", Eng. Optimiz., 7, 319-336. https://doi.org/10.1080/03052158408960646.
  6. Bhattacharya, G. (1990), "Sequential unconstrained minimization technique in slope stability analysis", Ph.D. Dissertation, Indian Institute of Technology, Kanpur, India.
  7. Brajevic, I. and Ignjatovic, J. (2019), "An upgraded firefly algorithm with feasibility-based rules for constrained engineering optimization problems", J. Intell. Manufact., 30(6), 2545-2574. https://doi.org/10.1007/s10845-018-1419-6.
  8. Chan, C.M., Zhang, L.M. and Ng, J.T. (2009), "Optimization of pile groups using hybrid genetic algorithms", J. Geotech. Geoenviron. Eng., 135(4), 497-505. https://doi.org/10.1061/(ASCE)1090-0241(2009)135:4(497).
  9. Chen, L. (2001), "Multiobjective design optimization based on satisfaction metrics", Eng. Optimiz., 33(5), 601-617. https://doi.org/10.1080/03052150108940935.
  10. Cheng, F.Y. (1999), "Multiobjective optimum design of structures with genetic algorithm and game theory: Application to life-cycle cost design", Comput. Mech. Struct. Eng., 1-16. https://doi.org/10.1016/B978-008043008-9/50039-9.
  11. Dey, A. and Basudhar, P.K. (2012), "Estimation of burger model parameters using inverse formulation", Int. J. Geotech. Eng., 6(3), 261-274. https://doi.org/10.3328/IJGE.2012.06.03.261-274.
  12. Ding, J., Wang, Q., Zhang, Q., Ye, Q. and Ma, Y. (2019), "A hybrid particle swarm optimization-cuckoo search algorithm and its engineering applications", Math. Probl. Eng., https://doi.org/10.1155/2019/5213759.
  13. Domaszewski, M., Bassir, H., and Zhang, W. H. (1999), "Stress, displacement and weight minimization by multicriteria optimization and game theory approach", WIT T. Built Environ., 40. https://doi.org/10.2495/OP990161.
  14. Duckstein, L. (1981), "Multiobjective optimization in structural design: the model choice problem", Proceedings of the International Symposium on Optimum Structural Design, the 11th ONR Naval Structural Mechanics Symposium, Tucson, Arizona, U.S.A., October.
  15. Grandhi, R., Bharatram, G. and Venkayya, V. (1993), "Multiobjective optimization of large-scale structures", AIAA J., 31(7). https://doi.org/10.2514/3.11771.
  16. Guido, V.A., Kneuppel, J.D. and Sweeney, M.A. (1987), "Plate loading tests on geogrid reinforced earth slabs", Proceedings of Geosynthetics Conference, New Orleans, U.S.A.
  17. Hati, S. and Panda, S.K. (2021), "Game theory approach for optimum design of an aged structure with multiple objectives," Structures, 31, 205-215. https://doi.org/10.1016/j.istruc.2021.01.097.
  18. Hewlett, W.J. and Randolph, M.F. (1988), "Analysis of piled embankments", Ground Eng., 21(3), 12-18.
  19. Ho, Y. C. (1970), "Differential games, dynamic optimization and generalized control theory", J. Optimiz. Theory App., 6(3), 179-209. https://doi.org/10.1007/BF00926600.
  20. Hwang, C.L. and Masud, A.S.M. (1979), Multiple Objective Decision Making-Methods and Applications, Springer, Berlin, Germany.
  21. Kalemci, E. N. and Ikizler, S.B. (2020), "Rao-3 algorithm for the weight optimization of reinforced concrete cantilever retaining wall", Geomech. Eng., 20(6), 527-536. https://doi.org/doi.org/10.12989/gae.2020.20.6.527.
  22. Karen, I., Yildiz, A. R., Kaya, N., Ozturk, N. and Ozturk, F. (2006), "Hybrid approach for genetic algorithm and Taguchi's method based design optimization in the automotive industry", Int. J. Prod. Res., 44(22), 4897-4914. https://doi.org/10.1080/00207540600619932.
  23. Khalkhali, A., Sarmadi, M., Khakshournia, S. and Jafari, N. (2016), "Probabilistic multi-objective optimization of a corrugated-core sandwich structure", Geomech. Eng., 10(6), 709-726. https://doi.org/10.12989/gae.2016.10.6.709.
  24. Koski, J. (1981), "Multicriterion optimization in structural design", Proceedings of the International Symposium on Optimum Structural Design, the 11th ONR Naval Structural Mechanics Symposium, Tucson, Arizona, U.S.A., October.
  25. Koski, J. and Silvennoinen, R. (1982), "Pareto optima of isostatic trusses", Comput. Meth. Appl. Mech. Eng., 31, 265-279. https://doi.org/10.1016/0045-7825(82)90008-1.
  26. Kuhn, H. W. and Tucker, A. W. (1951), "Nonlinear programming", Proceedings of the 2nd Berkeley Symposium on Mathematical Statistics and Probability, Berkeley, California, U.S.A.
  27. Liu, J., Luan, H., Zhang, Y., Sakaguchi, O. and Jiang, Y. (2020), "Prediction of unconfined compressive strength ahead of tunnel face using measurement-while-drilling data based on hybrid genetic algorithm", Geomech. Eng., 22(1), 81-95. https://doi.org/10.12989/gae.2020.22.1.081.
  28. Masutti, T.A.S. and De Castro, L.N. (2017), "Bee-inspired algorithms applied to vehicle routing problems: A survey and a proposal", Math. Probl. Eng. https://doi.org/10.1155/2017/3046830.
  29. Meng, R., Ye, Y. and Xie, N. (2010), "Multi-objective optimization design methods based on game theory", Proceedings of the 8th World Congress on Intelligent Control and Automation, Jinan, China, July.
  30. Mirzaei, Z., Akbarpour, A., Khatibinia, M. and Siuki, A. K. (2015), "Optimal design of homogeneous earth dams by particle swarm optimization incorporating support vector machine approach", Geomech. Eng., 9(6), 709-727. https://doi.org/10.12989/gae.2015.9.6.709.
  31. Misra, A. (2010), "A multicriteria based quantitative framework for assessing sustainability of pile foundations", M.Sc. Dissertation, University of Connecticut, U.S.A.
  32. Nash, J. (1950), "The bargaining problem", Econometrica J. Economet. Soc., 18(2), 155-162. https://doi.org/10.2307/1907266
  33. Nash, J. (1951), "Non-cooperative games", Annal. Math., 54(2), 286-295. https://doi.org/10.2307/1969529.
  34. Nash, J. (1953), "Two-person cooperative games", Econometrica J. Economet. Soc., 21(1), 128-140. https://doi.org/10.2307/1906951.
  35. Raju, P. (1999), "Parameters estimation from in-situ pile load test results using non-linear programming and neural networks: an inverse analysis," Ph.D. Dissertation, Indian Institute of Technology, Kanpur, India.
  36. Rao, S.S. (1984), "Design of vibration isolation systems using multiobjective optimization techniques", American Society of Mechanical Engineers, Paper No. 84-DET-60.
  37. Rao, S.S. (1987), "Game theory approach for multiobjective structural optimization", Comput. Struct., 25(1), 119-127. https://doi.org/10.1016/0045-7949(87)90223-9.
  38. Ravichandran, N., Shrestha, S. and Piratla, K. (2018), "Robust design and optimization procedure for piled-raft foundation to support tall wind turbine in clay and sand", Soil Found., 58, 744-755. https://doi.org/10.1016/j.sandf.2018.02.027.
  39. Ray, T., Tai, K., and Seow, K.C. (2001), "Multiobjective design optimization by an evolutionary algorithm", Eng. Optimiz., 33(4), 399-424. https://doi.org/10.1080/03052150108940926.
  40. Reddy, M.J. and Kumar, D. N. (2007), "An efficient multiobjective optimization algorithm based on swarm intelligence for engineering design", Eng. Optimiz., 39(1), 49-68. https://doi.org/10.1080/03052150600930493.
  41. Salgado, R. (2006), The Engineering of Foundation, McGraw-Hill.
  42. Salgado, R. and Prezzi, M. (2007), "Computation of cavity expansion pressure and penetration resistance in sands", Int. J. Geomech., 7(4), 251-265. https://doi.org/10.1061/(ASCE)1532-3641(2007)7:4(251).
  43. Stadler, W. (1986), "Multicriteria optimization in mechanics (a survey)", J. Appl. Mech., 37, 277-286.
  44. Von Neumann, J., and Morgenstern, O. (1947), Theory of Games and Economic Behavior, Princeton University Press, Princeton, New Jersey, U.S.A.
  45. Wang, S., Wang, Q., An, P., Yang, Y., Qi, J. and Liu, F. (2019), "Optimization of hydraulic section of irrigation canals in cold regions based on a practical model for frost heave", Geomech. Eng., 17(2),133-143. https://doi.org/10.12989/gae.2019.17.2.133.
  46. Yamagami, T. and Ueta, Y. (1987), "Optimization techniques for back analysis of failed slopes", Proceedings of the 8th Asian Regional Conference, Kyoto, Japan.
  47. Yang, X. and Gandomi, A.H. (2012), "Bat algorithm: A novel approach for global engineering optimization", Eng. Comput., 29(5), 464-483. https://doi.org/10.1108/02644401211235834.
  48. Yu, Y., Wang, Z. and Sun, H. (2020), "Optimal design of stone columns reinforced soft clay foundation considering design robustness", Geomech. Eng., 22(4), 305-318. https://doi.org/10.12989/gae.2020.22.4.305.