Experience in Using Stochastic Optimization Methods for Determining Numerical Parameters of Models in Materials Structurization Management Systems

  • Authors

    • Korneev Andrey Mastislavovich
    • Buzina Olga Petrovna
    • Sukhanov Andrey Vladimirovich
    • Shipulin Ilya Andreevich
    2018-07-07
    https://doi.org/10.14419/ijet.v7i3.5.15196
  • Optimization, Random value, Normal distribution, Stochastic search, Simulation method for annealing
  • Abstract

    The task of intellectual support of the process of composition formation for materials with a composite structure occurs when designing and operating automated control systems for multi-stage production processes. Such automated systems function in direct interaction with the external environment, and should promptly return the results of processing to the environment in the form of corrective actions or as messages to the user. The need for correct and complete mathematical models and fast, accurate algorithms that solve multistage problems often arises when structuring composite materials. In this case, mathematical models contain sets of numerical parameters and the search for exact values for them presents a complex optimization problem. The purpose of this paper is to investigate the possibility of using stochastic optimization methods to determine the exact numerical values of the calculated parameters of mathematical models that mimic the behavior of a structured composite material with given physico-mechanical characteristics under operating conditions. To carry out the research, special software has been created that implements algorithms for searching for extreme values for functions of several variables. The functional purpose of the software is intellectual support for decision-making in the formation of chemical compositions of cast iron alloys. Another developed system is designed to make effective decisions when designing the composition and structure of composite materials containing discrete fibers. Optimization of the calculated parameters was performed on a definite and fixed search area, which is a hyperparallelepiped. The program implements ten modifications of the simulation algorithm for annealing, allowing for a finite number of steps to make an estimate of the optimal value of the input elements of the function under study on a multidimensional space. In particular, modification of A, B and B algorithm schemes using the Boltzmann and Cauchy distribution functions, as well as the superfast annealing algorithm and the Xin Yao algorithm are implemented. The obtained data allowed to draw conclusions about the advantages and disadvantages of each modification of the stochastic search algorithm..

     

     

  • References

    1. [1] Zhiglyavsky A.A, (1985), Mathematical theory of global random search. L .: Izd-vo Leningr. University, ,p. 296.

      [2] Zhiglyavsky AA, Zhilinskas, AG, (1991), Methods of searching for a global extremum. - M .: Nauka.

      [3] Lopatin, AS, (2005), Annealing method, Stochastic optimization in informatics. SPb .: Publishing house SPbGU, No. 1, pp. 133-149.

      [4] Tikhomirov AS, (2009), About fast variants of the annealing algorithm (simulated annealing), Stochastic optimization in computer science, T. 46, No. 3, pp. 379-394.

      [5] Tikhomirov A.S, (2007), On the rate of convergence of a homogeneous Markov monotonic search for an extremum, Journal of Computational Mathematics and Mathematical Physics, T. 47, No. 5, pp. 817-828.

      [6] Gribanova E.B, (2017), Stochastic search algorithm. Gribanova, Applied in-formatics, Journal of applied informatics, No. 2 (68), pp. 130-134.

      [7] Panteleev A.V, (2009), Metaheuristic algorithms for finding the global extremum. Moscow: MAI, p. 160.

      [8] Shmyrin A.M, (2017), Study of skill-computing systems using a neighborhood approach, Ð.Ðœ. Shmyrin, A.M. Korneev, V.V. Kavygin, A.G. Kuznetsov, Bulletin of the Lipetsk State Technical University, No. 3 (33), pp. 18-21.

      [9] Korneev A.M, (2016), Modeling of the technological process of recrystallization annealing, Ð.Ðœ. Korneev, G.M.Sh. Al-Sabri, Bulletin of the Lipetsk State Technical University. No. 2 (28), pp. 12-16.

      [10] Korneev A.M, (2015), Formation of closed sets of parameters of complex shape and trees of perspective subsets, A.M. Korneev, L.S. Abdullah, T.A. Smetannikova, Co-temporary problems of science and education, No. 1, p. 158.

      [11] Ingber L, (1995), Adaptive simulated annealing (ASA): Lessons learned, Journal Control and Cybernetics.

      [12] Ingber L, (1989), Very fast simulated re-annealing, Mathematical and Computer Modelling, No. 12, pp. 967-973.

  • Downloads

  • How to Cite

    Andrey Mastislavovich, K., Olga Petrovna, B., Andrey Vladimirovich, S., & Ilya Andreevich, S. (2018). Experience in Using Stochastic Optimization Methods for Determining Numerical Parameters of Models in Materials Structurization Management Systems. International Journal of Engineering & Technology, 7(3.5), 32-36. https://doi.org/10.14419/ijet.v7i3.5.15196

    Received date: 2018-07-06

    Accepted date: 2018-07-06

    Published date: 2018-07-07