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Volume 9, Issue 2
Hill-Climbing Algorithm with a Stick for Unconstrained Optimization Problems

Yunqing Huang & Kai Jiang

Adv. Appl. Math. Mech., 9 (2017), pp. 307-323.

Published online: 2018-05

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  • 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.

  • AMS Subject Headings

90C56, 90C30, 56K05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-9-307, author = {Huang , Yunqing and Jiang , Kai}, title = {Hill-Climbing Algorithm with a Stick for Unconstrained Optimization Problems}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {9}, number = {2}, pages = {307--323}, 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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.2016.m1481}, url = {http://global-sci.org/intro/article_detail/aamm/12150.html} }
TY - JOUR T1 - Hill-Climbing Algorithm with a Stick for Unconstrained Optimization Problems AU - Huang , Yunqing AU - Jiang , Kai JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 307 EP - 323 PY - 2018 DA - 2018/05 SN - 9 DO - http://doi.org/10.4208/aamm.2016.m1481 UR - https://global-sci.org/intro/article_detail/aamm/12150.html KW - Direct search algorithm, stick hill-climbing algorithm, search radius. AB -

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.

Huang , Yunqing and Jiang , Kai. (2018). Hill-Climbing Algorithm with a Stick for Unconstrained Optimization Problems. Advances in Applied Mathematics and Mechanics. 9 (2). 307-323. doi:10.4208/aamm.2016.m1481
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