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Hill-Climbing Algorithm with a Stick for Unconstrained Optimization Problems

  • Yunqing Huang (a1) and Kai Jiang (a1)
Abstract
Abstract

Inspired by the behavior of the blind for hill-climbing using a stick to detect a higher place by drawing a circle, we propose a heuristic direct search method to solve the unconstrained optimization problems. Instead of searching a neighbourhood of the current point as done in the traditional hill-climbing, or along specified search directions in standard direct search methods, the new algorithm searches on a surface with radius determined by the motion of the stick. The significant feature of the proposed algorithm is that it only has one parameter, the search radius, which makes the algorithm convenient in practical implementation. The developed method can shrink the search space to a closed ball, or seek for the final optimal point by adjusting search radius. Furthermore our algorithm possesses multi-resolution feature to distinguish the local and global optimum points with different search radii. Therefore, it can be used by itself or integrated with other optimization methods flexibly as a mathematical optimization technique. A series of numerical tests, including high-dimensional problems, have been well designed to demonstrate its performance.

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*Corresponding author. Email: huangyq@xtu.edu.cn (Y. Q. Huang), kaijiang@xtu.edu.cn (K. Jiang)
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[1] W. Y. Sun and Y. Yuan , Optimization Theory and Methods: Nonlinear Programming, New York: Springer, 2006.

[2] A. R. Conn , N. I. M. Gould and P. L. Toint , Trust Region Methods, Philadelphia: SIAM, 2000.

[3] J. Nocedal and S. J. Wright , Numerical Optimization, Berlin: Springer-Verlag, 2nd ed., 2006.

[4] A. R. Conn , K. Scheinberg and L. N. Vicente , Introduction to Derivative-Free Optimization, Philadelphia: SIAM, 2009.

[5] L. M. Rios and N. V. Sahinidis , Derivative-free optimization: a review of algorithms and comparison of software implementations, J. Global Optim., 56 (2013), pp. 12471293.

[8] T. Wu , Y. Yang , L. Sun , and H. Shao , A heuristic iterated-subspace minimization method with pattern search for unconstrained optimization, Comput. Math. Appl., 58 (2009), pp. 20512059.

[9] Z. Zhang , Sobolev seminorm of quadratic functions with applications to derivative-free optimization, Math. Program., 146 (2014), pp. 7796.

[10] Z. Michalewicz and D. B. Fogel , How to Solve It: Modern Heuristics, Springer, 2004.

[11] Y. Lecun , Bengio , Y. Hinton and G. Hinton , Deep learning, Nature, 521 (2015), pp. 521–436.

[12] R. Hooke and T. A. Jeeves , “Direct search” solution of numerical and statistical problems, J. ACM, 8 (1961), pp. 212229.

[13] R. M. Lewis , V. Torczon and M. W. Trosset , Direct search methods: then and now, J. Comput. Appl. Math., 124 (2000), pp. 191207.

[14] J. A. Nelder and R. Mead , A simplex method for function minimization, Comput. J., 7 (1965), pp. 308313.

[15] V. Torczon , On the convergence of pattern search algorithms, SIAM J. Optim., 7 (1997), pp. 125.

[16] T. G. Kolda , R. W. Lewis and V. Torczon , Optimization by direct search: new perspectives on some classical and modern methods, SIAM Rev., 45 (2003), pp. 385482.

[17] J. E. Dennis Jr and V. Torczon , Direct search methods on parallel machines, SIAM J. Optim., 1 (1991), pp. 448474.

[18] J. M. Dieterich and B. Hartke , Empirical review of standard benchmark functions using evolutionary global optimization, Appl. Math. 3 (2012), pp. 15521564.

[19] S. Gratton , C. W. Royer , L. N. Vicente and Z. Zhang , Direct search based on probabilistic descent, SIAM J. Optim., 25 (2015), pp. 15151541.

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Advances in Applied Mathematics and Mechanics
  • ISSN: 2070-0733
  • EISSN: 2075-1354
  • URL: /core/journals/advances-in-applied-mathematics-and-mechanics
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