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Self-adaptive differential evolution applied to combustion engine calibration

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Abstract

In this paper, a new population-based stochastic optimization algorithm called Hybrid Self-Adaptive Differential Evolution (HSADE) is proposed. The algorithm addresses unconstrained global optimization problems, exploring and combining the best features of some Differential Evolution (DE), obtaining a good balance between exploration and exploitation. These approaches are important for increasing the accuracy and efficiency of a population-based stochastic algorithm and for adapting the control parameter values during the optimization process. Further, they are crucial for increasing the convergence speed and reducing the risk of search stagnation. To verify the performance of the HSADE, 25 benchmark functions were tested presenting an optimal performance when compared to some state-of-the-art DEs algorithms. Furthermore, an experimental problem in an automotive sector, related to automatic internal combustion engine calibration, was used adjusting 300 decision variables. The HSADE achieved a reliable calibration, reducing the time required to perform approximately 90% when comparing to other optimization algorithms.

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Notes

  1. \( F_{i} \) and \( {\text{CR}}_{i} \) are considered to be successful if the trial vector \( \vec{U}_{i,G} \) is better than its corresponding target vector \( \vec{X}_{i,G} \).

References

  • Ayala HVH, Keller P, Morais MF, Mariani VC, Coelho LS, Rao RV (2016) Design of heat exchangers using a novel multiobjective free search differential evolution paradigm. Appl Therm Eng 94(5):170–177

    Article  Google Scholar 

  • Brest J, Greiner S, Boskovic B, Mernik M, Zumer V (2006) Self-adapting control parameters in differential evolution: a comparative study on numerical benchmark problems. IEEE Trans Evol Comput 10(6):646–657

    Article  Google Scholar 

  • Brest J, Maučec MP, Bošković B (2016) iL-SHADE: improved L-SHADE algorithm for single objective real-parameter optimization. In: IEEE congress on evolutionary computation (CEC), Vancouver, BC, Canada

  • Coelho LS, Souza RCT, Mariani VC (2009) Improved differential evolution approach based on cultural algorithm and diversity measure applied to solve economic load dispatch problems. Math Comput Simul 79(10):3136–3147

    Article  MathSciNet  MATH  Google Scholar 

  • Coelho LS, Ayala HVH, Mariani VC (2014a) A self-adaptive chaotic differential evolution algorithm using gamma distribution for unconstrained global optimization. Appl Math Comput 234(15):452–459

    MathSciNet  MATH  Google Scholar 

  • Coelho LS, Bora TC, Mariani VC (2014b) Differential evolution based on truncated Lévy-type flights and population diversity measure to solve economic load dispatch problems. Int J Electr Power Energy Syst 57:178–188

    Article  Google Scholar 

  • Cook JA, Sun J, Buckland JH, Kolmanovsky IV, Peng H, Grizzle JW (2006) Automotive powertrain control: a survey. Asian J Control 8(3):237–260

    Article  MathSciNet  Google Scholar 

  • Cui L, Li G, Zhu Z, Wen Z, Lu N, Lu J (2018) A novel differential evolution algorithm with a self-adaptation parameter control method by differential evolution. Soft Comput 22(8):6171–6190

    Article  Google Scholar 

  • Deng LB, Wang S, Qiao LW, Zhang BQ (2018) DE-RCO: rotating crossover operator with multiangle searching strategy for adaptive differential evolution. IEEE Access 6:2970–2983

    Article  Google Scholar 

  • Derrac J, Garcia S, Molina D, Herrera F (2011) A practical tutorial on the use of nonparametric statistical tests as a methodology for comparing evolutionary and swarm intelligence algorithms. Swarm Evolut Comput 1(1):3–18

    Article  Google Scholar 

  • Fan Q, Zhang Y (2016) Self-adaptive differential evolution algorithm with crossover strategies adaptation and its application in parameter estimation. Chemometr Intell Lab Syst 151:164–171

    Article  Google Scholar 

  • Gamperle R, Muller SD, Koumoutsakos P (2002) A parameter study for differential evolution. In: Grmela A, Mastorakis NE (eds) Advances in intelligent systems, fuzzy systems, evolutionary computation. WSEAS Press, Interlaken, pp 293–298

    Google Scholar 

  • Hosny KM, Khalid AM, Mohamed ER (2020) Efficient compression of volumetric medical images using Legendre moments and differential evolution. Soft Comput 24:409–427

    Article  Google Scholar 

  • Langouët KH, Metivier L, Sinoquet D, Tran QH (2008) Optimization for engine calibration. In: International conference on engineering optimization, Rio de Janeiro, Brazil 1–10

  • Li YX, Gou J, Wang C, Luo W, Cai YQ (2017) Improved differential evolution with a modified orthogonal learning strategy. IEEE Access 5:9699–9716

    Article  Google Scholar 

  • Mallipeddi R, Suganthan PN, Pan QK, Tasgetiren MF (2011) Differential evolution algorithm with ensemble of parameters and mutation strategies. Appl Soft Comput 11(2):1679–1696

    Article  Google Scholar 

  • Mariani VC, Coelho LS, Sahoo PK (2011) Modified differential evolution approaches applied in exergoeconomic analysis and optimization of a cogeneration system. Expert Syst Appl 38(11):13886–13893

    Google Scholar 

  • Moussa TM, Awotunde AA (2018) Self-adaptive differential evolution with a novel adaptation technique and its application to optimize ES-SAGD recovery process. Comput Chem Eng 118:64–76

    Article  Google Scholar 

  • Novoa-Hernández P, Corona CC, Pelta DA (2013) Self-adaptive, multipopulation differential evolution in dynamic environments. Soft Comput 17(10):1861–1881

    Article  Google Scholar 

  • Opara KR, Arabas J (2019) Differential evolution: a survey of theoretical analyses. Swarm Evolut Comput 44:546–558

    Article  Google Scholar 

  • Piotrowski AP (2017) Review of differential evolution population size. Swarm Evolut Comput 32:1–24

    Article  Google Scholar 

  • Piotrowski AP, Napiorkowski JJ (2018) Step-by-step improvement of JADE and SHADE-based algorithms: success or failure? Swarm Evolut Comput 44:88–108

    Article  Google Scholar 

  • Poláková R, Tvrdík J, Bujok P (2019) Differential evolution with adaptive mechanism of population size according to current population diversity. Swarm Evolut Comput (in press)

  • Qin AK, Huang VL, Suganthan PN (2009) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417

    Article  Google Scholar 

  • Rahnamayan S, Tizhoosh HR, Salama MMA (2008) Opposition-based differential evolution. IEEE Trans Evol Comput 12(1):64–79

    Article  Google Scholar 

  • Storn R, Price K (1997) Differential evolution: a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11:341–359

    Article  MathSciNet  MATH  Google Scholar 

  • Suganthan PN, Hansen N, Liang JJ, Deb K, Chen YP, Auger A, Tiwari S (2005) Problem definitions and evaluation criteria for the CEC 2005 special session on real-parameter optimization, Nanyang Technology University, Singapore, IIT Kanpur, Kanpur, India, Technical report, KanGAL

  • Tanabe R, Ishibuchi H (2019) Review and analysis of three components of the differential evolution mutation operator in MOEA/D-DE. Soft Comput 23(23):12843–12857

    Article  Google Scholar 

  • Vasconcelos Segundo EH, Amoroso AL, Mariani VC, Coelho LS (2017) Thermodynamic optimization design for plate-fin heat exchangers by Tsallis JADE. Int J Therm Sci 113:136–144

    Article  Google Scholar 

  • Vasconcelos Segundo EH, Mariani VC, Coelho LS (2019) Design of heat exchangers using falcon optimization algorithm. Appl Therm Eng 156:119–144

    Article  Google Scholar 

  • Vossoughi GR, Rezazadeh S (2005) Optimization of the calibration for an internal combustion engine management system using multi-objective genetic algorithms. In: IEEE congress on evolutionary computation, Edinburgh, Scotland, UK, 2, pp 1254–1261

  • Wang Y, Cai Z, Zhang Q (2011) Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans Evol Comput 15(1):55–66

    Article  Google Scholar 

  • Zhang J, Sanderson AC (2009) JADE: adaptive differential evolution with optional external archive. IEEE Trans Evol Comput 13(5):945–958

    Article  Google Scholar 

  • Zhao X, Xu G, Rui L, Liu D, Liu H, Yuan J (2019) A failure remember-driven self-adaptive differential evolution with top-bottom strategy. Swarm Evolut Comput 45:1–14

    Article  Google Scholar 

Download references

Funding

This study was funded by the National Council of Scientific and Technologic Development of Brazil—CNPq (Grants: 307958/2019-1-PQ, 307966/2019-4-PQ, 405101/2016-3-Univ, 404659/2016-0-Univ, and PRONEX Fundação Araucária (Grant Number 042/2018).

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Authors and Affiliations

  1. Department of Electrical Engineering, Electrical Engineering Graduate Program (PPGEE), Federal University of Parana, Curitiba, PR, Brazil

    José Márcio Fachin, Viviana Cocco Mariani & Leandro dos Santos Coelho

  2. Industrial and Systems Engineering Graduate Program (PPGEPS), Pontifical Catholic University of Parana, Curitiba, PR, Brazil

    Gilberto Reynoso-Meza & Leandro dos Santos Coelho

  3. Department of Mechanical Engineering, Pontifical Catholic University of Parana, Curitiba, PR, Brazil

    Viviana Cocco Mariani

Authors
  1. José Márcio Fachin
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  2. Gilberto Reynoso-Meza
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  3. Viviana Cocco Mariani
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  4. Leandro dos Santos Coelho
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Corresponding author

Correspondence to Viviana Cocco Mariani.

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Author José Márcio Fachin declares that he has no conflict of interest. Author Gilberto Reynoso Meza declares that he has no conflict of interest. Author Viviana Cocco Mariani declares that she has no conflict of interest. Author Leandro dos Santos Coelho declares that he has no conflict of interest.

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This article does not contain any studies with human participants performed by any of the authors. This article does not contain any studies with animals performed by any of the authors.

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Communicated by A. Di Nola.

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Fachin, J.M., Reynoso-Meza, G., Mariani, V.C. et al. Self-adaptive differential evolution applied to combustion engine calibration. Soft Comput 25, 109–135 (2021). https://doi.org/10.1007/s00500-020-05469-4

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