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Pure Random Search with Virtual Extension of Feasible Region

Author

Listed:
  • E. A. Tsvetkov

    (Lebedev Physical Institute of the Russian Academy of Sciences)

  • R. A. Krymov

    (Moscow Institute of Physics and Technology)

Abstract

We propose a modification of the pure random search algorithm for cases when the global optimum point can be located near the boundary of a feasible region. If the feasible region is cube-shaped, the worst case occurs when the global optimum point is located at the vertex of a cube. In these cases, the sample size for the pure random search should be increased significantly because the success probability of the single trial is decreased. The proposed modification is based on the virtual extension of the feasible region. The extended region contains $$\varepsilon $$ ε -neighbourhoods of all points of the original region. All random points that fall outside the original feasible region are mapped to the nearest points on its boundary before the values of an objective function at these points are calculated. This extension of the feasible region also leads to an increase in the sample size due to the increased volume. We compare sample sizes required to hit into the neighbourhood of the global optimum point with a given probability for the proposed method and the original pure random search algorithm with a corrected sample size. We consider ball-shaped and cube-shaped feasible regions and find the sufficient conditions for the proposed algorithm to be more efficient. We offer a practical recommendation for cases, in which the feasible region is defined by a system of linear inequalities.

Suggested Citation

  • E. A. Tsvetkov & R. A. Krymov, 2022. "Pure Random Search with Virtual Extension of Feasible Region," Journal of Optimization Theory and Applications, Springer, vol. 195(2), pages 575-595, November.
    • Handle: RePEc:spr:joptap:v:195:y:2022:i:2:d:10.1007_s10957-022-02097-w
    DOI: 10.1007/s10957-022-02097-w
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    References listed on IDEAS

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    1. Samuel H. Brooks, 1958. "A Discussion of Random Methods for Seeking Maxima," Operations Research, INFORMS, vol. 6(2), pages 244-251, April.
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    3. Donald R. Jones & Joaquim R. R. A. Martins, 2021. "The DIRECT algorithm: 25 years Later," Journal of Global Optimization, Springer, vol. 79(3), pages 521-566, March.
    4. Boris Polyak & Pavel Shcherbakov, 2017. "Why Does Monte Carlo Fail to Work Properly in High-Dimensional Optimization Problems?," Journal of Optimization Theory and Applications, Springer, vol. 173(2), pages 612-627, May.
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