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Empirical distribution-based framework for improving multi-parent crossover algorithms

  • Methodologies and Application
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Abstract

Multi-parent crossover algorithms (MCAs) are widely used in solving optimization problems in many fields relying on encoding, crossover, variation and choice operators to produce iterative offspring chromosome. In this paper, a real-coded schema to support this genetic optimization process is considered. At each crossover stage, a linear combination of coefficients at the same scale hybridizes a fixed number of parent chromosomes. If parent chromosomes are iteratively selected, then coefficients will indicate these parent chromosomes: how to propagate. Essentially, all MCAs differentiate one algorithm from others through coefficient restriction. However, little work exists on analyzing techniques that efficiently create within-bound coefficients. The existing MCAs build coefficients following a uniform distribution, but at the same time, these coefficients violate constraints, thus propagating error. The error will cascade exponentially as the hybrid scale rises even slightly, leading to increased time consumption. To address this problem, an empirical distribution-based framework (EDBF) is proposed which takes multiple MCAs as its constituent members. Numerical results showed that proposed EDBF outperforms its members in terms of time consumption. As a general framework rather than a specific algorithm, EDBF is easy to implement and can easily accommodate any existing MCA.

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References

  • Ahmed ZH (2015) A multi-parent genetic algorithm for the quadratic assignment problem. Opsearch 52(4):714–732

    Article  MathSciNet  Google Scholar 

  • Brits R, Engelbrecht AP, Van den Bergh F (2002) A niching particle swarm optimizer. In: Proceedings of the 4th Asia-Pacific conference on simulated evolution and learning, vol 2, pp 692–696

  • Caboussat A, Glowinski R, Pons V (2009) Numerical methods for non-smooth L1 optimization: applications to free surface flows and image denoising. Int J Numer Anal Model 6(3):355–374

    MathSciNet  MATH  Google Scholar 

  • Davis L (1991) Handbook of genetic algorithms. Van Nostrand Reinhold, New York

    Google Scholar 

  • Deep K, Thakur M (2007) A new mutation operator for real coded genetic algorithms. Appl Math Comput 193(1):211–230

    MathSciNet  MATH  Google Scholar 

  • Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: MHS’95. Proceedings of the sixth international symposium on micro machine and human science, pp 39–43

  • Eiben AE, Back T (1997) Empirical investigation of multiparent recombination operators in evolution strategies. Evol Comput 5(3):347–365

    Article  Google Scholar 

  • Eiben ÁE, Schippers CA (1996) Multi-parent’s niche: n-ary crossovers on NK-landscapes. In: International conference on parallel problem solving from nature, pp 319–328

  • Eiben AE, Raue PE, Ruttkay Z (1994) Genetic algorithms with multi-parent recombination. In: International conference on parallel problem solving from nature, pp 78–87

  • Eiben ÁE, van Kemenade CH, Kok JN (1995) Orgy in the computer: multi-parent reproduction in genetic algorithms. In: European conference on artificial life, pp 934–945

  • Eshelman LJ, Schaffer JD (1993) Real-coded genetic algorithms and interval-schemata. In: Foundations of genetic algorithms, vol 2 pp 187–202

  • Franken M, Rumpf M, Wirth B (2011) A phase field based PDE constraint optimization approach to time discrete Willmore flow. Int J Numer Anal Model

  • Goldberg DE (1991) Real-coded genetic algorithms, virtual alphabets, and blocking. Complex Syst 5(2):139–167

    MathSciNet  MATH  Google Scholar 

  • Herrera F, Lozano M, Verdegay JL (1998) Tackling real-coded genetic algorithms: operators and tools for behavioural analysis. Artif Intell Rev 12(4):265–319

    Article  Google Scholar 

  • Holland JH (1992) Genetic algorithms. Sci Am 267(1):66–73

    Article  Google Scholar 

  • Janikow CZ, Michalewicz Z (1991) An experimental comparison of binary and floating point representations in genetic algorithms. In: ICGA, pp 31–36

  • Jia R, He D (2012) Hybrid artificial bee colony algorithm for solving nonlinear system of equations. In: 2012 Eighth international conference on computational intelligence and security, pp 56–60

  • Jiang D, Lin J (2010) A unified multi-parent combination algorithm. Huazhong Keji Daxue Xuebao(Ziran Kexue Ban)/J Huazhong Univ Sci Technol (Nat Sci Ed) 38(12):98–101 (in Chinese)

    Google Scholar 

  • Michalewicz Z (2013) Genetic algorithms + data structures = evolution programs. Springer Science & Business Media

  • Ono I, Kobayashi S (1999) A real-coded genetic algorithm for function optimization using unimodal normal distribution. In: Proceedings of international conference on genetic algorithms, pp 246–253

  • Phyu SPTP, Srijuntongsiri G (2016) A binary coded multi-parent genetic algorithm for shuttle bus routing system in a college campus. In: 2016 international conference on advanced informatics: concepts, theory and application (ICAICTA), pp 1–5

  • Qin AK, Suganthan PN (2005) Self-adaptive differential evolution algorithm for numerical optimization. In: 2005 IEEE congress on evolutionary computation, vol 2, pp 1785–1791

  • Qin AK, Huang VL, Suganthan PN (2008) Differential evolution algorithm with strategy adaptation for global numerical optimization. IEEE Trans Evol Comput 13(2):398–417

    Article  Google Scholar 

  • Shi Y, Eberhart R (1998) A modified particle swarm optimizer. In: 1998 IEEE international conference on evolutionary computation proceedings. IEEE world congress on computational intelligence (Cat. No. 98TH8360), pp 69–73

  • Storn R, Price K (1997) Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J Global Optim 11(4):341–359

    Article  MathSciNet  Google Scholar 

  • Tao G, Li-shan K (1999) A new evolutionary algorithm for function optimization. Wuhan Univ J Nat Sci 4(4):409–414. https://doi.org/10.1007/bf02832273

    Article  MathSciNet  MATH  Google Scholar 

  • Toth P, Vigo D (eds) (2014) Vehicle routing: problems, methods, and applications. Society for Industrial and Applied Mathematics, Philadelphia

    MATH  Google Scholar 

  • Tsutsui S, Ghosh A (1998) A study on the effect of multi-parent recombination in real coded genetic algorithms. In: 1998 IEEE international conference on evolutionary computation proceedings. IEEE World Congress on Computational Intelligence (Cat. No. 98TH8360), pp 828–833

  • Wright AH (1991) Genetic algorithms for real parameter optimization. In: Foundations of genetic algorithms, vol 1, pp 205–218

  • Wu Z, Kang L, Zou X (2002) A parallel global-local mixed evolutionary algorithm for multimodal function optimization. In: Fifth international conference on algorithms and architectures for parallel processing, 2002. Proceedings, pp 247–250

  • Wu Z, Kang L, Zou X (2003) An elite subspace evolutionary algorithm for solving function optimization problems. Comput Appl 23(2):13–15 (in Chinese)

    Google Scholar 

  • Wu Z, Tang Z, Kang L (2003) A parallel global-local mixed evolutionary algorithm for multimodal function optimization based on domain decomposition. Wuhan Univ J Nat Sci 8(1):253–258

    Article  Google Scholar 

  • Xu X, Zhang J (2007) An improved immune evolutionary algorithm for multimodal function optimization. In: Third international conference on natural computation (ICNC 2007), vol 3, pp 641–646

  • Xu Y, Zou J (2017) A convergent adaptive edge element method for an optimal control problem in magnetostatics. ESAIM Math Model Numer Anal 51(2):615–640

    Article  MathSciNet  Google Scholar 

  • Yang Z, Yao X, He J (2007) Making a difference to differential evolution. In: Advances in metaheuristics for hard optimization, pp 397–414

  • Yang Z, Tang K, Yao X (2008) Self-adaptive differential evolution with neighborhood search. In: 2008 IEEE congress on evolutionary computation (IEEE World Congress on Computational Intelligence), pp 1110–1116

  • Zhang Y, Gong DW, Sun XY, Geng N (2014) Adaptive bare-bones particle swarm optimization algorithm and its convergence analysis. Soft Comput 18(7):1337–1352

    Article  Google Scholar 

  • Zhang Y, Song XF, Gong DW (2017) A return-cost-based binary firefly algorithm for feature selection. Inf Sci 418:561–574

    Article  Google Scholar 

  • Zhao L, Huang S, Sun Y, Yan L, Dissanayake G (2015) Parallaxba: bundle adjustment using parallax angle feature parametrization. Int J Robot Res 34(4–5):493–516

    Article  Google Scholar 

  • Zhu W, Duan H (2014) Chaotic predator–prey biogeography-based optimization approach for UCA V path planning. Aerosp Sci Technol 32(1):153–161

    Article  Google Scholar 

  • Zuo Z, Wu Z, Sun Y, Zhang R, Yan L (2020) Accelerating the generation of coefficient vectors in elite multiparent crossover algorithm by using empirical probability density curve. Eng J Wuhan Univ 53(08):728–733 (in Chinese). https://doi.org/10.14188/j.1671-8844.2020-08-011

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Funding

This study was funded by National Key R & D Program of China (2017YFB0503004).

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Authors and Affiliations

  1. School of Earth and Space Science, Peking University, Beijing, 100871, China

    Zhengkang Zuo, Lei Yan, Sana Ullah, Yiyuan Sun, Ruihua Zhang & Hongying Zhao

Authors
  1. Zhengkang Zuo
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  2. Lei Yan
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  3. Sana Ullah
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  4. Yiyuan Sun
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  5. Ruihua Zhang
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  6. Hongying Zhao
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Correspondence to Hongying Zhao.

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Authors declare no competing interests.

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Communicated by V. Loia.

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Appendix

Appendix

See Tables 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30 and 31.

Table 18 Benchmark function
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Table 19 Efficiency comparison among EMCA, − EDBF, UMCA, − EDBF1 and − EDBF2 on Ackley problem (D = 2)
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Table 20 Efficiency comparison among EMCA, − EDBF, UMCA, − EDBF1 and − EDBF2 on exponential problem (D = 2)
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Table 21 Efficiency comparison among EMCA, − EDBF, UMCA, − EDBF1 and − EDBF2 on Rastrigin problem (D = 3)
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Table 22 Efficiency comparison among EMCA, − EDBF, UMCA, − EDBF1 and − EDBF2 on Schwefel problem (D = 2)
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Table 23 Efficiency comparison among EMCA, − EDBF, UMCA, − EDBF1 and − EDBF2 on Paviani problem (D = 10)
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Table 24 Efficiency comparison among EMCA, − EDBF, UMCA, − EDBF1 and − EDBF2 on Sphere problem (D = 3)
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Table 25 Efficiency comparison among EMCA, − EDBF, UMCA, − EDBF1 and − EDBF2 on Rosenbrock problem (D = 3)
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Table 26 Efficiency comparison among EMCA, − EDBF, UMCA, − EDBF1 and − EDBF2 on Ellipsoidal problem (D = 3)
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Table 27 Efficiency comparison among EMCA, − EDBF, UMCA, − EDBF1 and − EDBF2 on Schewefel3 problem (D = 10)
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Table 28 Efficiency comparison among EMCA, − EDBF, UMCA, − EDBF1 and − EDBF2 on axis parallel hyper ellipsoid problem (D = 10)
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Table 29 Parameters setting of EMCA and − EDBF among 10 classical test functions
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Table 30 Parameters setting of ABPSO among 10 classical test functions
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Table 31 Parameters setting of RcBBFA among 10 classical test functions
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Zuo, Z., Yan, L., Ullah, S. et al. Empirical distribution-based framework for improving multi-parent crossover algorithms. Soft Comput 25, 4799–4822 (2021). https://doi.org/10.1007/s00500-020-05488-1

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