Skip to main content
Log in

Study of the Practical Convergence of Evolutionary Algorithms for the Optimal Program Control of a Wheeled Robot

Journal of Computer and Systems Sciences International Aims and scope

Cite this article


Evolutionary algorithms for solving the problem of the optimal program control are considered. The most popular evolutionary algorithms, the genetic algorithm (GA), the differential evolution (DE) algorithm, the particle swarm optimization (PSO), the bat-inspired algorithm (BIA), the bees algorithm (BA), and the grey wolf optimizer (GWO) algorithm are described. An experimental analysis of these algorithms and their comparison with gradient methods are given. An experiment was carried out to solve the problem of the optimal control of a mobile robot with phase constraints. Indicators of the best objective functional value, the average value for several startups, and the standard deviation were used to compare the algorithms.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions


  1. Yu. G. Evtushenko, Optimization and Rapid Automatic Differentiation (VTs RAN, Moscow, 2013) [in Russian].

    Google Scholar 

  2. E. Polak, Computational Methods in Optimization. A Unified Approach (Academic, New York, 1971; Moscow, Mir, 1974).

    MATH  Google Scholar 

  3. N. N. Moiseev, “Methods of dynamic programming in the theory of optimum controls. I. Systems which permit the use of a control scale,” Zh. Vychisl. Mat. Mat. Fiz. 4, 485–494 (1964).

    Google Scholar 

  4. N. N. Moiseev, “Optimization and control (evolution of ideas and perspectives),” Izv. AN SSSR, Tekh. Kibernet., No. 4, 3–16 (1974).

    Google Scholar 

  5. N. I. Grachev and Yu. G. Evtushenko, “Software library for solving problems of optimal control,” Zh. Vychisl. Mat. Mat. Fiz. 19, 367–387 (1979).

    MathSciNet  Google Scholar 

  6. A. P. Karpenko, Modern Algorithms of Search Engine Optimization. Nature–Inspired Optimization Algorithms (Mosk. Gos. Tekh. Univ. im. N. E. Baumana, Moscow, 2014) [in Russian].

    Google Scholar 

  7. J. N. Holland, Adaptation in Natural and Artificial Systems (Univ. Michigan Press, Michigan, 1975).

    Google Scholar 

  8. A. B. Ragimov, “One approach to solving optimal control problems on piecewise constant, piecewise linear, and piecewise given function classes,” Vestn. Tomsk. Univ., Upravl., Vychisl. Tekh. Inform., No. 2, 20–30 (2012).

    Google Scholar 

  9. F. P. Vasil’ev, Numerical Methods for Extremal Problems Solution (Nauka, Moscow, 1988) [in Russian].

    Google Scholar 

  10. M. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear Programming: Theory and Algorithms (Wiley–Interscience, New York, 2006).

    Book  MATH  Google Scholar 

  11. V. G. Karmanov, Mathematical Programming (Fizmatlit, Moscow, 2008; Mir, Moscow, 1989).

    MATH  Google Scholar 

  12. A. V. Panteleev and T. A. Letova, Optimization Methods in Examples and Problems (Vyssh. Shkola, Moscow, 2005) [in Russian].

    Google Scholar 

  13. E. B. Lee and L. Markus, Foundations of Optimal Control Theory (Krieger, Malabar, FL, 1986; Moscow, Nauka, 1972).

    Google Scholar 

  14. B. V. Sobol’, B. Ch. Meskhi, and G. I. Kanygin, Optimization Methods, Practical Guide (Feniks, Rostov–on–Don, 2009) [in Russian].

    Google Scholar 

  15. D. P. Kingma and J. Ba, “Adam: a method for stochastic optimization,” in Proceedings of the 3rd International Conference for Learning Representations, San Diego, 2015, arXiv:1412.6980v8 [cs.LG].

    Google Scholar 

  16. D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison–Wesley, Reading, MA, 1989).

    MATH  Google Scholar 

  17. A. V. Panteleev, D. V. Skavinskaya, and E. A. Aleshina, Metaheuristic Algorithms for Finding the Optimal Program Control (INFRA–M, Moscow, 2016) [in Russian].

    Book  Google Scholar 

  18. R. Storn and K. Price, “Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces,” J. Global Optimiz., No. 11, 341–359 (1997).

    Article  MathSciNet  MATH  Google Scholar 

  19. J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks IV, Perth, 1995, pp. 1942–1948.

    Chapter  Google Scholar 

  20. A. P. Karpenko and E. Yu. Seliverstov, “Global optimization by the particle swarm method. Review,” Inform. Tekhnol., No. 2, 25–34 (2010).

    Google Scholar 

  21. D. T. Pham, A. Ghanbarzadeh, E. Koc, et al., “The bees algorithm—a novel tool for complex optimisation problems,” in Intelligent Production Machines and Systems, Proceedings of the 2nd I*PROMS Virtual International Conference (Elsevier, Amsterdam, 2006), pp. 454–459.

    Chapter  Google Scholar 

  22. A. A. Grishin and A. P. Karpenko, “Efficiency investigation of the bees algorithm into global optimization problem,” Nauka Obrazov., No. 8 (2010).

  23. X. S. Yang, “A new metaheuristic bat–inspired algorithm,” Studies Comput. Intell. 284, 65–74 (2010).

    MATH  Google Scholar 

  24. S. Mirjalili, S. M. Mirjalili, and A. Lewis, “Grey wolf optimizer,” Adv. Eng. Software 69, 46–61 (2014).

    Article  Google Scholar 

  25. L. B. Rapoport, “Estimation of attraction domains in wheeled robot control,” Autom. Remote Control 67, 1416 (2006).

    Article  MathSciNet  MATH  Google Scholar 

  26. A. V. Pesterev, “A linearizing feedback for stabilizing a car–like robot following a curvilinear path,” J. Comput. Syst. Sci. Int. 52, 819 (2013).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to A. I. Diveev.

Additional information

Original Russian Text © A.I. Diveev, S.V. Konstantinov, 2018, published in Izvestiya Akademii Nauk, Teoriya i Sistemy Upravleniya, 2018, No. 4.

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Diveev, A.I., Konstantinov, S.V. Study of the Practical Convergence of Evolutionary Algorithms for the Optimal Program Control of a Wheeled Robot. J. Comput. Syst. Sci. Int. 57, 561–580 (2018).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: