Hill-Climbing Algorithm with a Stick for Unconstrained Optimization Problems (Advances in Applied Mathematics and Mechanics, 2018)
Inspired by the behavior of the blind for hill-climbing using a stick to detecta higher place by drawing a circle, we propose a heuristic direct search method tosolve the unconstrained optimization problems. Instead of searching a neighbourhoodof the current point as done in the traditional hill-climbing, or along specified searchdirections in standard direct search methods, the new algorithm searches on a surfacewith radius determined by the motion of the stick. The significant feature of the proposedalgorithm is that it only has one parameter, the search radius, which makes thealgorithm convenient in practical implementation. The developed method can shrinkthe search space to a closed ball, or seek for the final optimal point by adjusting searchradius. Furthermore, our algorithm possesses multi-resolution feature to distinguishthe local and global optimum points with different search radii. Therefore, it can beused by itself or integrated with other optimization methods flexibly as a mathematicaloptimization technique. A series of numerical tests, including high-dimensionalproblems, have been well designed to demonstrate its performance.