Structural and Multidisciplinary Optimization

, Volume 59, Issue 1, pp 131–151 | Cite as

Multiobjective backtracking search algorithm: application to FSI

  • R. El Maani
  • B. Radi
  • A. El Hami


Fluid-structure interaction (FSI) problems play an important role in many technical applications, for instance, wind turbines, aircraft, injection systems, or pumps. Thus, the optimization of such kind of problems is of high practical importance. Optimization algorithms aim to find the best values for a system’s parameters under various conditions. In this paper, we present a new Backtracking Search Optimization Algorithm for multiobjective optimization, named BSAMO, a new evolutionary algorithm (EA) for solving real-valued numerical optimization problems. EAs are popular stochastic search algorithms that are widely used to solve nonlinear, nondifferentiable and complex numerical optimization problems. In order to test the performance of this algorithm, a well known benchmark multiobjective problem has been chosen from the literature, and for FSI optimization, using a partitioned coupling procedure. The method has been tested through a 2D plate and a 3D wing subjected to aerodynamic loads. The obtained Pareto solutions are then presented and compared to those of the Non-dominated Sorting Genetic Algorithm-II (NSGA-II). The numerical results demonstrate the efficiency of BSAMO and also its best performance in tackling real-world multiphysics problems.


Fluid-structure interaction Aerodynamic Multiobjective optimization Evolutionary algorithm 



  1. Benra F, Dohmen H, Pei J, Schuster S, Wan B (2011) A comparison of one-way and two-way coupling methods for numerical analysis of fluid structure interactions. J Appl Math 2011:40–56MathSciNetzbMATHCrossRefGoogle Scholar
  2. Bonilla-Petriciolet A, Segovia-Hernandez JG (2009) Particle swarm optimization for phase stability and equilibrium calculations in reactive systems. Comput Aid Ch 26:635–640Google Scholar
  3. Bosman PAN, Thierens D (2003) The balance between proximity and diversity in multiobjective evolutionary algorithms. IEEE Trans Evol Comput 7(2):174–188CrossRefGoogle Scholar
  4. Civicioglu P (2013) Backtracking search optimization algorithm for numerical optimization problems. Appl Math Comput 219:8121–8144MathSciNetzbMATHGoogle Scholar
  5. Civicioglu P, Besdok E (2013) A conceptual comparison of the Cuckoo-search, particle swarm optimization, differential evolution and artificial bee colony algorithms. Artif Intell Rev 39:315–346CrossRefGoogle Scholar
  6. Coello CAC (2006) Evolutionary multi-objective optimization: a historical view of the field. Comput Intell Mag IEEE 1(1):28–36MathSciNetCrossRefGoogle Scholar
  7. Deb K, Pratab A, Agrawal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182–197CrossRefGoogle Scholar
  8. Deb K (2014) Multi-objective optimization. In: Search methodologies. Springer, US, pp 403–449Google Scholar
  9. El Hami A, Radi B (2013) Uncertainty and optimization in structural mechanics. Wiley-ISTE, LondonCrossRefGoogle Scholar
  10. El Hami A, Radi B (2017) Fluid-structure interactions and uncertainties: ansys and fluent tools. Wiley-ISTE, LondonCrossRefGoogle Scholar
  11. El Maani R, Makhloufi A, Radi B, El Hami A (2017a) RBDO analysis of the aircraft wing based aerodynamic behavior. Struct Eng Mech 61(4):441–451CrossRefGoogle Scholar
  12. El Maani R, Radi B, El Hami A (2017b) Vibratory reliability analysis of an aircraft’s wing via fluid-structure interactions, journal of aerospace. Multidiscip Digit Publ Inst 4(3):40Google Scholar
  13. El Maani R, Makhloufi A, Radi B, El hami A (2018) Reliability-based design optimization with frequency constraints using new safest point approach. Eng Optim 50(10):1715–1732MathSciNetCrossRefGoogle Scholar
  14. Erfani T, Utyuzhnikov SV, KOLO B (2013) A modified directed search domain algorithm for multiobjective engineering and design optimization. Struct Multidiscip Optim 48(6):1129–1141MathSciNetCrossRefGoogle Scholar
  15. Fonseca CM, Flemming PJ (1998) Multiobjective optimization and multiple constraint handling with evolutionary algorithms, part ii: application example. IEEE Trans Syst Man Cybern 28:38–47CrossRefGoogle Scholar
  16. Guney K, Durmus A, Basbug S (2014) Backtracking search optimization algorithm for synthesis of concentric circular antenna arrays. Int J Antennas Propag 2014:1–11Google Scholar
  17. He Q, Wang L (2007) An effective co-evolutionary particle swarm optimization for constrained engineering design problems. Eng Appl Artif Intell 20:89–99CrossRefGoogle Scholar
  18. Igel C, Hansen N, Roth S (2007) Covariance matrix adaptation for multi-objective optimization. Evol Comput 15:1–28CrossRefGoogle Scholar
  19. Ishibuch H, Yoshida T, Murata T (2003) Balance between genetic search and local search in memetic algorithms for multiobjective permutation flowshop scheduling. IEEE Trans Evol Comput 7(2):204–223CrossRefGoogle Scholar
  20. Jeong K, Ahn B, Lee S (2001) Modal analysis of perforated rectangular plates in contact with water. Struct Eng Mech 12(2):189–200CrossRefGoogle Scholar
  21. Karaboga D, Basturk B (2007) A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J Global Optim 39:459–471MathSciNetzbMATHCrossRefGoogle Scholar
  22. Karaboga D, Akay B (2009) A comparative study of artificial bee colony algorithm. Appl Math Comput 214:108–132MathSciNetzbMATHGoogle Scholar
  23. Konak A, Coit DW, Smith AE (2006) Multi-objective optimization using genetic algorithms: a tutorial. Reliab Eng Syst Saf 91(9):992–1007CrossRefGoogle Scholar
  24. Kursawe F (1990) A variant of evolution strategies for vector optimization. In: Proceedings of the parallel problem solving from nature first workshop PPSN I. Lecture notes in computer science, vol 496, Berlin, pp 193–207Google Scholar
  25. Lin J (2015) Oppositional backtracking search optimization algorithm for parameter identification of hyperchaotic systems. Nonlinear Dyn 80(1):209–219MathSciNetCrossRefGoogle Scholar
  26. Lund E, Moller H, Jakobsen L (2003) Shape design optimization of stationary fluid-structure interaction problems with large displacements and turbulence. Struct Multidiscip Optim 25:383–392CrossRefGoogle Scholar
  27. Maoguo G, Licheng J, Haifeng D, Liefeng B (2008) Multi-objective Immune Algorithm with Nondominated Neighbor-Based Selection. Evol Comput 16(2):225–255CrossRefGoogle Scholar
  28. Martins RRA, Lambe AB (2013) Multidisciplinary design optimization: a survey of architectures. AIAA J 51:2049–2075CrossRefGoogle Scholar
  29. Maute K, Nikbay M, Farhat C (2003) Sensitivity analysis and design optimization of three-dimensional non-linear aeroelastic systems by the adjoint method. Int J Numer Methods Eng 56:911–933zbMATHCrossRefGoogle Scholar
  30. Maute K, Allen M (2004) Conceptual design of aeroelastic structures by topology optimization. Struct Multidiscip Optim 1:27–42CrossRefGoogle Scholar
  31. Neri F, Tirronen V (2010) Recent advances in differential evolution: a survey and experimental analysis. Artif Intell Rev 33:61–106CrossRefGoogle Scholar
  32. Osyczka A, Kundu S (1995) A new method to solve generalized multicriteria optimization problems using the simple genetic algorithm. Struct Multidiscip Optim 10(2):94–99CrossRefGoogle Scholar
  33. Ourique CO, Biscaia EC, Pinto JC (2002) The use of particle swarm optimization for dynamical analysis in chemical processes. Comput Chem Eng 26:1783–1793CrossRefGoogle Scholar
  34. Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. IEEE Trans Evol Comput 3:1785–1791Google Scholar
  35. Salman AA, Ahmad I, Omran MGH, Mohammad G (2010) Frequency assignment problem in satellite communications using differential evolution. Comput Oper Res 37:2152–2163MathSciNetzbMATHCrossRefGoogle Scholar
  36. Schmitt V, Charpin F (1979) Pressure distributions on the onera m6 wing at transonic mach numbers, Agard-ar-138-experimental data base for computer program assessmentGoogle Scholar
  37. Schott JR (1995) Fault tolerant design using single and multicriteria genetic algorithm optimization. Masters thesis, Departmentt Aeronautics and Astronautics, Massachussets Institue of TechnologyGoogle Scholar
  38. Slater JW, Abbott JM, Cavicchi RH (2002) Validation of wind for a series of inlet flows. AIAA JournalGoogle Scholar
  39. Souli M, Benson DJ (2010) Arbitrary lagrangian-eulerian and fluid-structure interaction. ISTE Ltd and John Wiley SonsGoogle Scholar
  40. Storn R, Price K (1997) Differential evolution - a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359MathSciNetzbMATHCrossRefGoogle Scholar
  41. Tanaka M (1995) Ga-based decision support system for multi-criteria, optimization. In: Proceedings of the international conference on systems, Man and cybernetics-2. Piscataway, pp 1556–1561Google Scholar
  42. Veldhuizen DAV, Lamont GB (1998) Multiobjective evolutionary algorithm research: a history and analysis, Report TR-98-03. Department of Electrical and Computer Engineering, Graduate School of Engineering, Air Force Institute of Technology Wright-Patterson AFB, pp 45433–7765Google Scholar
  43. Yang X, Deb P (2013) Multiobjective cuckoo search for design optimization. Comput Oper Res 40 (6):1616–1624MathSciNetzbMATHCrossRefGoogle Scholar
  44. Yun Z, Hui Y (2011) Coupled fluid structure flutter analysis of a transonic fan. Chin J Aeronaut 24:258–264CrossRefGoogle Scholar
  45. Zeine AT, El Hami A, Ellaia R, Pagnacco E (2017) Backtracking search algorithm for multi-objective design optimisation. Int J Math Modell Numer Optim 8(2):93–107Google Scholar
  46. Zhang J, Xie L, Wang S (2006) Particle swarm for the dynamic optimization of biochemical processes. Comput Aid Ch 21:497–502Google Scholar
  47. Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13:945–958CrossRefGoogle Scholar
  48. Zitzler E (1998) Evolutionary algorithms for multiobjective optimization: methods and applications, Doctoral dissertation ETH 13398. Swiss Federal Institute of Technology (ETH), ZurichGoogle Scholar
  49. Zitzler E, Thiele L (1998) Multiobjective optimization using evolutionary algorithms a comparative case study, (Eds.): Parallel Problems Solving from Nature, Springer, 1498:292–301Google Scholar
  50. Zitzler E, Laumanns M, Thiele L (2002) SPEA2: improving the strength pareto evolutionary algorithm. Optimization and Control with Applications to Industrial Problems, Athens, pp 95–100Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.LSMIENSAM MeknèsMeknesMorocco
  2. 2.LIMIIFST Settatroute de CasablancaMorocco
  3. 3.LMNINSA RouenSaint Etienne de RouvrayFrance

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