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A novel multi-objective quantum particle swarm algorithm for suspension optimization

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Abstract

In this paper, a novel multi-objective archive-based Quantum Particle Optimizer (MOQPSO) is proposed for solving suspension optimization problems. The algorithm has been adapted from the well-known single objective QPSO by substantial modifications in the core equations and implementation of new multi-objective mechanisms. The novel algorithm MOQPSO and the long-established NSGA-II and COGA-II (Compressed-Objective Genetic Algorithm with Convergence Detection) are compared. Two situations are considered in this paper: a simple half-car suspension model and a bus suspension model. The numerical model of the bus allows complex dynamic interactions not considered in previous studies. The suitability of the solution is evaluated based on vibration-related ISO Standards, and the efficiency of the proposed algorithm is tested by dominance comparison. For a specifically chosen Pareto front solution found by MOQPSO in the second case, the passengers and driver accelerations attenuated about 50% and 33%, respectively, regarding non-optimal suspension parameters. All solutions found by NSGA-II are dominated by those found by MOQPSO, which presented a Pareto front noticeably wider for the same number of objective function calls.

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(adapted from Sekulic et al. (2013))

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Adapted from ISO (1999)

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References

  • Ahmadian MT, Sharifi SR and Abdollahpour R (2005) Application of car active suspension in a vertical acceleration reduction of vehicle due to road excitation and its effect on human health. In: 5th International conference on multibody systems, nonlinear dynamics, and control, California, USA, vol 6, pp 375–382. ISBN: 0-7918-4806-X

  • Al-Baity H (2015) A quantum behaved particle swarm approach to multiobjective optimization. Ph.D. Thesis, The University of Birmingham

  • Boonlong K (2013) Multiobjective optimization of a vehicle vibration model using the improved compressed-objective genetic algorithm with convergence detection. Hindawi Publishing Corporation. Adv Mech Eng. https://doi.org/10.1155/2013/131495

    Article  Google Scholar 

  • Branke J, Mostaghim S (2006) About selecting the personal best in multiobjective particle swarm optimization. Parallel Probl Solv Nat PPSN IX 4196:523–532

    Google Scholar 

  • Chen S, Shi T, Wang D, Chen J (2015) Multiobjective optimization of the vehicle ride comfort based on Kriging approximate model and NSGA-II. J Mech Sci Technol 29(3):1007–1018. https://doi.org/10.1007/s12206-015-0215-x

    Article  Google Scholar 

  • Coello CAC, Lamont GB, van Veldhuizen DA (2007) Evolutionary algorithms for solving multiobjective problems-second edition. Springer, New York, pp 175–228 (ISBN: 978-0-387-33254-3)

    Google Scholar 

  • Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evolut Comput. https://doi.org/10.1109/4235.996017

    Article  Google Scholar 

  • Fan Z, Wang TJ, Chen Z, Li G (2017) An improved multiobjective particle swarm optimization algorithm using minimum distance of point to line. Shock Vib 2017(5):1–16. https://doi.org/10.1155/2017/8204867

    Article  Google Scholar 

  • Florea A, Cofaru II, Roamn L (2017) Applying the multiobjective optimization techniques in the design of suspension systems. J Dig Inf Manag 14(6):351–367

    Google Scholar 

  • Gadhvia B, Savsania V, Patel V (2016) Multiobjective optimization of vehicle passive suspension system using NSGA-II, SPEA2 and PESA-II. Proc Technol 23:361–368. https://doi.org/10.1016/j.protcy.2016.03.038

    Article  Google Scholar 

  • Goh CK, TanKC Liu DS, Chiam SC (2012) A competitive and cooperative co-evolutionary approach to multi-objective particle swarm optimization algorithm design. Eur J Oper Res 202:42–54

    Article  Google Scholar 

  • Gomes HM (2016) Multi-objective optimization of quarter car passive suspension design in the frequency domain based on PSO. Eng Comput Int J Comput Aided Eng Softw 33(5):1422–1423. https://doi.org/10.1108/EC-01-2015-0021

    Article  Google Scholar 

  • Griffin MJ (1990) Handbook of human vibration. Academic Press Limited, London. ISBN 978-0-12-303040-5

    Google Scholar 

  • Hassani K, Lee W (2015) Multiobjective design of state feedback controllers using reinforced quantum-behaved particle swarm optimization. Appl Soft Comput 41:66–76. https://doi.org/10.1016/j.asoc.2015.12.024

    Article  Google Scholar 

  • Havelka F, Musil M (2014) Multiobjective optimization of vehicle suspension parameters considering various road classes. In: Scientific proceedings 2014, Faculty of Mechanical Engineering, SUT in Bratislava, vol 22, pp 26–31. https://doi.org/10.2478/stu-2014-0005

  • ISO 8608:1995 (1995) Mechanical vibration—road surface profiles—reporting of measured data. ISO/TC108/SC2, International Organization for Standardization, Geneva, Switzerland

  • ISO 3888:1999 (1999) Test Track for a severe lane-change maneuver part 1: double lane change. ISO/TC 22/SC 33, International Organization for Standardization, Geneva, Switzerland

  • ISO 5982 (2001) Mechanical vibration and shock—Range of idealized values to characterize seated-body biodynamic response under vertical vibration. ISO/TC108/SC4, International Organization for Standardization, Geneva, Switzerland

  • ISO 2631-1:1997 (1997) Mechanical vibration and shock-evaluation of human exposure to whole-body vibration. ISO/TC108/SC4, International Organization for Standardization, Geneva, Switzerland

  • Ji X, Eger TR, Dickey JP (2017) Evaluation of the vibration attenuation properties of an air-inflated cushion with two different heavy machinery seats in multi-axis vibration environments including jolts. Appl Ergon 59:293–301. https://doi.org/10.1016/j.apergo.2016.06.011

    Article  Google Scholar 

  • Knowles J, Corne D (1999) The Pareto archived evolution strategy: a new baseline algorithm for Pareto multiobjective optimisation. In: Proceedings of the 1999 congress on evolutionary computation, 1999. (CEC 99), vol 1. IEEE 1999. https://doi.org/10.1109/cec.1999.781913

  • Koulocheris D, Papaioannou G, Christodoulou D (2017) An approach for multiobjective optimization of vehicle suspension system. IOP Conf Ser Mater Sci Eng. https://doi.org/10.1088/1757-899x/252/1/012037

    Article  Google Scholar 

  • Lee CK, Cheng YC (2014) Application of uniform design and QPSO in the sensitivity problem a railway vehicle system. Proc Eng 79:427–436. https://doi.org/10.1016/j.proeng.2014.06.364

    Article  Google Scholar 

  • Mahmoodabadi MJ, Safaie A, Bagheri A, Nariman-zadeh N (2013) A novel combination of Particle Swarm Optimization and Genetic Algorithm for Pareto optimal design of a five-degree of freedom vehicle vibration model. Appl Soft Comput 13:2577–2591. https://doi.org/10.1016/j.asoc.2012.11.028

    Article  Google Scholar 

  • Mitra CA, Desai JG, Patwardhan RS, Shirke HP, Kurne MHW, Banerjee N (2016) Optimization of passive vehicle suspension system by genetic algorithm. Proc Eng 144:1158–1166

    Article  Google Scholar 

  • Nariman-Zadeh N, Salehpour M, Jamali A, Haghgoo E (2010) Pareto optimization of a five-degree of freedom vehicle vibration model using a multi-objective uniform-diversity genetic algorithm (MUGA). Eng Appl Artif Intell 23:543–551. https://doi.org/10.1016/j.engappai.2009.08.008

    Article  Google Scholar 

  • Nawayseh N (2015) Effect of the seating condition on the transmission of vibration through the seat pan and backrest. Int J Ind Ergon 45:82–90. https://doi.org/10.1016/j.ergon.2014.12.005

    Article  Google Scholar 

  • Omkar SN, Khanderlwal R, Ananth TVS, Narayana NG, Gopalakrishnan S (2009) Quantum behaved Particle Swarm Optimization (QPSO) for multiobjective design optimization of composite structures. Expert Syst Appl 36:11312–11322. https://doi.org/10.1016/j.eswa.2009.03.006

    Article  Google Scholar 

  • Rill G (2012) Road vehicle dynamics: fundamentals and modeling, 1a edn. Taylor and Francis Group, Boca Raton

    Google Scholar 

  • Sammonds GM, Fray M, Mansfield NJ (2017) Effect of long term driving on driver discomfort and its relationship with seat fidgets and movements. Appl Ergon 58:119–127. https://doi.org/10.1016/j.apergo.2016.05.009

    Article  Google Scholar 

  • Sekulic D, Dedovic V, Rusov S, Salinic S, Obradovic A (2013) Analysis of vibration effects on the comfort of intercity bus users by oscillatory model with ten degrees of freedom. Appl Math Model 37:8629–8644

    Article  Google Scholar 

  • Sert E, Boyraz P (2017) Optimization of suspension system and sensitivity analysis for improvement of stability in a midsize heavy vehicle. Eng Sci Technol Int J 20(2017):997–1012

    Article  Google Scholar 

  • Sharp RS, Crolla DA (1987) Road vehicle suspension system design—a review. Veh Syst Dyn Int J Veh Mech Mobil 16(3):167–192. https://doi.org/10.1080/00423118708968877

    Article  Google Scholar 

  • Spentzas K, Kanarachos SA (2002) Design of a non-linear hybrid car suspension system using neural networks. Math Comput Simul 60(3–5):369–378. https://doi.org/10.1016/S0378-4754(02)00029-0

    Article  MathSciNet  MATH  Google Scholar 

  • Sun J, Feng B and Xu W (2004) Particle swarm optimization with particles having quantum behavior. In: Proceedings of congress on evolutionary computation, Portland, OR, USA, pp 325–331

  • Sun J, Xu W, Feng B (2004) A global search strategy of quantum-behaved particle swarm optimization. In: Cybernetics and intelligent systems, 2004 IEEE conference, vol 1, pp 111–116

  • Sun J, Lai C-H, Wu X-J (2011) Particle Swarm Optimization: classical and quantum perspectives. CRC Press Ed, Chapman & Hall/CRC Numerical Analysis and Scientific Computing Series

  • Xu S-H, Mu X-D, Chai D, Zhao P (2016) Multiobjective quantum-behaved particle swarm optimization algorithm with double potential well and share learning. Optik 127:4921–4927. https://doi.org/10.1016/j.ijleo.2016.02.049

    Article  Google Scholar 

  • Yang X, Shi P, Shen W, Jiang K, Pang S (2013) Multiobjective quantum-behaved particle swarm optimization with entropy-based density assessment and chaotic mutation operator. J Comput Inf Syst 9(10):3873–3881

    Google Scholar 

  • Zamanian A, Nikravesh A, Monazzam MR, Hassanzadeh J, Fararouei M (2014) Short-term exposure with vibration and its effect on attention. J Environ Health Sci Eng 12(1):135. https://doi.org/10.1186/s40201-014-0135-1

    Article  Google Scholar 

  • Zhan S, Qing-Wei C (2011) Multi-objective quantum-behaved particle swarm optimization algorithm based on QPSO and crowding distance sorting. Control Decis 26(4):540–547

    MathSciNet  Google Scholar 

  • Zhang X, Qiu Y, Griffin MJ (2015) Transmission of vertical vibration through a seat: effect of thickness of foam cushions at the seat pan and the backrest. Int J Ind Ergon 48:36–45. https://doi.org/10.1016/j.ergon.2015.03.006

    Article  Google Scholar 

  • Zhou D-Z, Li Y, Jiang B, Wang J (2016) A novel multiobjective quantum-behaved particle swarm optimization based on the ring model. Math Probl Eng 2016:1–15. https://doi.org/10.1155/2016/4968938

    Article  MATH  Google Scholar 

Download references

Funding

Funding was provided by National Council for Scientific and Technological Development CNPq (Grant no. 301719-2017-9) and Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (Grant no. 001).

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Authors and Affiliations

  1. Federal University of Rio Grande do Sul, Porto Alegre, Rio Grande do Sul, Brazil

    Ewerton Grotti, Douglas Makoto Mizushima, Artur Dieguez Backes, Marcos Daniel de Freitas Awruch & Herbert Martins Gomes

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  1. Ewerton Grotti
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  2. Douglas Makoto Mizushima
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  3. Artur Dieguez Backes
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  4. Marcos Daniel de Freitas Awruch
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  5. Herbert Martins Gomes
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Correspondence to Herbert Martins Gomes.

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Communicated by Hector Cancela.

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Grotti, E., Mizushima, D.M., Backes, A.D. et al. A novel multi-objective quantum particle swarm algorithm for suspension optimization. Comp. Appl. Math. 39, 105 (2020). https://doi.org/10.1007/s40314-020-1131-y

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