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.
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Yu. G. Evtushenko, Optimization and Rapid Automatic Differentiation (VTs RAN, Moscow, 2013) [in Russian].
E. Polak, Computational Methods in Optimization. A Unified Approach (Academic, New York, 1971; Moscow, Mir, 1974).
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).
N. N. Moiseev, “Optimization and control (evolution of ideas and perspectives),” Izv. AN SSSR, Tekh. Kibernet., No. 4, 3–16 (1974).
N. I. Grachev and Yu. G. Evtushenko, “Software library for solving problems of optimal control,” Zh. Vychisl. Mat. Mat. Fiz. 19, 367–387 (1979).
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].
J. N. Holland, Adaptation in Natural and Artificial Systems (Univ. Michigan Press, Michigan, 1975).
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).
F. P. Vasil’ev, Numerical Methods for Extremal Problems Solution (Nauka, Moscow, 1988) [in Russian].
M. Bazaraa, H. D. Sherali, and C. M. Shetty, Nonlinear Programming: Theory and Algorithms (Wiley–Interscience, New York, 2006).
V. G. Karmanov, Mathematical Programming (Fizmatlit, Moscow, 2008; Mir, Moscow, 1989).
A. V. Panteleev and T. A. Letova, Optimization Methods in Examples and Problems (Vyssh. Shkola, Moscow, 2005) [in Russian].
E. B. Lee and L. Markus, Foundations of Optimal Control Theory (Krieger, Malabar, FL, 1986; Moscow, Nauka, 1972).
B. V. Sobol’, B. Ch. Meskhi, and G. I. Kanygin, Optimization Methods, Practical Guide (Feniks, Rostov–on–Don, 2009) [in Russian].
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].
D. E. Goldberg, Genetic Algorithms in Search, Optimization, and Machine Learning (Addison–Wesley, Reading, MA, 1989).
A. V. Panteleev, D. V. Skavinskaya, and E. A. Aleshina, Metaheuristic Algorithms for Finding the Optimal Program Control (INFRA–M, Moscow, 2016) [in Russian].
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).
J. Kennedy and R. Eberhart, “Particle swarm optimization,” in Proceedings of the IEEE International Conference on Neural Networks IV, Perth, 1995, pp. 1942–1948.
A. P. Karpenko and E. Yu. Seliverstov, “Global optimization by the particle swarm method. Review,” Inform. Tekhnol., No. 2, 25–34 (2010).
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.
A. A. Grishin and A. P. Karpenko, “Efficiency investigation of the bees algorithm into global optimization problem,” Nauka Obrazov., No. 8 (2010).
X. S. Yang, “A new metaheuristic bat–inspired algorithm,” Studies Comput. Intell. 284, 65–74 (2010).
S. Mirjalili, S. M. Mirjalili, and A. Lewis, “Grey wolf optimizer,” Adv. Eng. Software 69, 46–61 (2014).
L. B. Rapoport, “Estimation of attraction domains in wheeled robot control,” Autom. Remote Control 67, 1416 (2006).
A. V. Pesterev, “A linearizing feedback for stabilizing a car–like robot following a curvilinear path,” J. Comput. Syst. Sci. Int. 52, 819 (2013).
Original Russian Text © A.I. Diveev, S.V. Konstantinov, 2018, published in Izvestiya Akademii Nauk, Teoriya i Sistemy Upravleniya, 2018, No. 4.
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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). https://doi.org/10.1134/S106423071804007X