Comparison study on nature-inspired optimization algorithms for optimization back analysis of underground engineering

  • 37 Accesses


Optimization back analysis is the most common approach to displacement back analysis for underground engineering. However, this is a non-convex problem that requires the use of nature-inspired global optimization algorithms. Therefore, the present study will investigate on the suitability of six state-of-the-art nature-inspired algorithms for elastic back analysis and elastic–plastic back analysis. These algorithms include improved genetic algorithm, immunized evolutionary programming, particle swarm optimization, continuous ant colony optimization, artificial bee colony and black hole algorithm. Numerical results indicate that immunized evolutionary programming is overall the best algorithm followed by the black hole algorithm; while, the improved genetic algorithm is the worst optimizer. Meanwhile, using elastic back analysis, the sensitivity analysis of the main input parameters for these nature-inspired optimization algorithms has been conducted. At last, the comparative results have been verified by using in one real underground roadway in Huainan coal mine of China.

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

Access options

Buy single article

Instant unlimited access to the full article PDF.

US$ 39.95

Price includes VAT for USA

Subscribe to journal

Immediate online access to all issues from 2019. Subscription will auto renew annually.

US$ 99

This is the net price. Taxes to be calculated in checkout.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23
Fig. 24
Fig. 25
Fig. 26
Fig. 27


  1. 1.

    Chen SH, Chen SF, Shahrour I (2001) The feedback analysis of excavated rock slope. Rock Mech Rock Eng 34(1):39–56

  2. 2.

    Dorigo M, Maniezzo V, Colorni A (1996) Ant system: optimization by a colony of cooperating agents. IEEE T Syst Man Cy B 26(1):29–41

  3. 3.

    Fogel, D. B. (1995). Evolutionary Computation: Toward a New Philosophy of Machine Intelligence, IEEE Press, New York, U.S.A

  4. 4.

    Fogel, L. J., Owens, A. J., and Walsh, M. J. (1966). Artificial Intelligence Through Simulated Evolution, John Wiley, New York, U.S.A

  5. 5.

    Gao, W. (2003). “An Improved Fast-convergent Genetic Algorithm.” Proc. Inter. Conf. on Robotics, Intelligent Systems and Signal Processing, Xi, N. and Liu, Y. H., ed., IEEE Press, New York, 1197–1202

  6. 6.

    Gao W (2015) Slope stability analysis based on immunised evolutionary programming. Environ Earth Sci 74:3357–3369

  7. 7.

    Gao W (2016) Displacement back analysis for underground engineering based on immunized continuous ant colony optimization. Eng Optim 48(5):868–882

  8. 8.

    Gao W (2016) Inverse back analysis based on evolutionary neural network for underground engineering. Neural Process Lett 44(1):81–101

  9. 9.

    Gao W, Liu QS (2009) Back analysis of underground engineering based on bionics computation intelligence-methods and applications. Science Press, Beijing (in Chinese)

  10. 10.

    Gao W, Yin ZX (2011) Modern intelligent bionics algorithm and its applications. Science Press, Beijing (in Chinese)

  11. 11.

    Gopalakrishnan K, Kim S (2010) Global optimization of pavement structural parameters during back-calculation using hybrid shuffled complex evolution algorithm. J Comput Civ Eng 24(5):441–451

  12. 12.

    Grossauer K, Schubert W (2009) Back-analysis of tunnel response using simulated annealing. In: Proc., SINOROCK2009, Hudson JA, Tham LG, Feng XT, Kwong AKL (ed) The University of Hong Kong, Hong Kong, 145–149

  13. 13.

    Hatamlou A (2013) Black hole: a new heuristic optimization approach for data clustering. Inf Sci 222:175–184

  14. 14.

    Jiang AN, Li P (2011) Back-analysis of mechanics parameters of tunnel based on particle swarm optimization and numerical simulation. Key Eng Mater 474–476:1373–1376

  15. 15.

    Kang F, Li JJ, Li HJ (2013) Artificial bee colony algorithm and pattern search hybridized for global optimization. Appl Soft Comput 13:1781–1791

  16. 16.

    Kang F, Li JJ, Ma ZY (2011) Rosenbrock artificial bee colony algorithm for accurate global optimization of numerical functions. Inf Sci 181:3508–3531

  17. 17.

    Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39:459–471

  18. 18.

    Karaboga D, Basturk B (2008) On the performance of artificial bee colony (ABC) algorithm. Appl Soft Comput 8:687–697

  19. 19.

    Kennedy J, Eberhart RC, Shi YH (2001) Swarm intelligence. Morgan Kaufmann Publishers, San Francisco

  20. 20.

    Khamesi H, Torabi S, Mirzaei-Nasirabad H, Ghadiri Z (2015) Improving the performance of intelligent back analysis for tunneling using optimized fuzzy systems: case study of the Karaj Subway line 2 in Iran. J Comput Civ Eng.,05014010

  21. 21.

    Kowalczyk T, Furukawa T, Yoshimura S, Yagawa G (1998) An extensible evolutionary algorithm approach for inverse problems. In: Tanaka M, Dulikravich GS (eds) Inverse problems in engineering mechanics. Elsevier, Oxford, pp 541–550

  22. 22.

    Kumar S, Datta D, Singh SK (2015) Black hole algorithm and its applications. In: Azar AT, Vaidyanathan S (eds) Computational intelligence applications in modelling and control. Springer International Publishing, Switzerland, pp 147–170

  23. 23.

    Levasseur S, Mal´ecot Y (2008) Soil parameter identification using a genetic algorithm. Int J Numer Anal Met 32(2):189–213

  24. 24.

    Michalewicz Z (1996) Genetic algorithms + data structures = evolution programs. Springer, New York

  25. 25.

    Miranda T, Dias D, Eclaircy-Caudron S, Gomes Correia A, Costa L (2011) Back analysis of geomechanical parameters by optimisation of a 3D model of an underground structure. Tunn Undergr Sp Technol 26(6):659–673

  26. 26.

    Moreira N, Miranda T, Pinheiro M, Fernandes P, Dias D, Costa L, Sena-Cruz J (2013) Back analysis of geomechanical parameters in underground works using an Evolution Strategy algorithm. Tunn Undergr Sp Technol 33:143–158

  27. 27.

    Nogueira C, Azevedo R, Zornberg J (2011) Validation of coupled simulation of excavations in saturated clay: camboinhas case history. Int J Geomech 11(3):202–210

  28. 28.

    Oreste P (2005) Back-analysis techniques for the improvement of the understanding of rock in underground constructions. Tunn Undergr Sp Technol 20(1):7–21

  29. 29.

    Papon A, Riou Y, Dano C, Hicher PY (2012) Single- and multi-objective genetic algorithm optimization for identifying soil parameters. Int J Numer Anal Met 36(5):597–618

  30. 30.

    Shao Y, Macari E (2008) Information feedback analysis in deep excavations. Int J Geomech 8(1):91–103

  31. 31.

    Sun J, Huang W (1995) An optimization method for elasto-plastic inversion of parameters in rock mechanics. Chin J Rock Mech Eng 14(3):394–400

  32. 32.

    Xu F, Wang K, Su JD, Xiong Z (2011) Back analysis of displacement based on support vector machine and continuous tabu search. In: He XM (ed) Proc., Inter. Conf. Electric Technology and Civil Engineering, IEEE Press, New York, 2016–2019

  33. 33.

    Yang CX, Wu YH, Hon T (2010) A no-tension elastic-plastic model and optimized back-analysis technique for modeling nonlinear mechanical behavior of rock mass in tunneling. Tunn Undergr Sp Technol 25(3):279–289

  34. 34.

    Yang LD (1996) Theory and applications of back analysis in geotechnical engineering. Science Press, Beijing (in Chinese)

  35. 35.

    Yang ZF, Wang SJ, Feng ZL, Liu HH, Xue L, Wang ZY (2002) Principles and applications of back analysis in geotechnical engineering. Earthquake Press, Beijing (in Chinese)

  36. 36.

    Yen KK (1998) System identification-tutorial. In: Proc., Inter. Workshop on Artificial Intelligence and Mathematical Methods in Pavement and Geomechanical Systems, Attoh-Okine, ed., Balkema, Rotterdam, 179–193

  37. 37.

    Zhang LQ, Yue ZQ, Yang ZF, Qi JX, Liu FC (2006) A displacement-based back-analysis method for rock mass modulus and horizontal in situ stress in tunnelling-Illustrated with a case study. Tunn Undergr Sp Technol 21:636–649

  38. 38.

    Zhang SK, Yin SD, Wang FM, Zhao HB (2017) Characterization of in situ stress state and joint properties from extended leak-off tests in fractured reservoirs. J Geomech, Int.,04016074

  39. 39.

    Zhang SK, Yin SD, Yuan YG (2015) Estimation of fracture stiffness, in situ stresses, and elastic parameters of naturally fractured geothermal reservoirs. J. Geomech, Int.,04014033

  40. 40.

    Zheng YR, Zhu HH, Fang ZC, Liu HH (2012) The stability analysis and design theory of surrounding rock of underground engineering. China Communications Press, Beijing (in Chinese)

  41. 41.

    Zhu CX, Zhao HB, Zhao M (2014) Back analysis of geomechanical parameters in underground engineering using artificial bee colony. Sci World J.,693812

  42. 42.

    Zhu WS, Zhao J (2004) Stability analysis and modelling of underground excavations in fractured rocks. Elsevier Science, Amsterdam

Download references

Author information

Correspondence to Wei Gao.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gao, W. Comparison study on nature-inspired optimization algorithms for optimization back analysis of underground engineering. Engineering with Computers (2020).

Download citation


  • Underground engineering
  • Displacement measurement data
  • Optimization back analysis
  • Nature-inspired algorithms
  • Elastic behavior
  • Elastic–plastic behavior