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3D CRS with global optimization

Author: Yujiang Lucas Xie

Description:

The software introduced three optimization algorithms to simultaneously search the 3D ZO CRS attributes, which includes the particle swarm optimization (PSO), genetic algorithm (GA) and the Powell conjugate direction (PCD) algorithm as well. The PSO used in this software is contributed by Shi and Eberhart (1998), and the codes are developed by Lucas. The GA codes are obtained from Google, and being incorporated into 3D ZO CRS by Lucas. The PCD codes are taken from the Numerical Recipes in C. Cambridge, and modified by Lucas for the 3D ZO CRS attribute search. Based on our tests, the PCD is performed well for non-smooth objective function, but might be failed in the objective semblance function which is data dependent and also might have much local maxima. The challenge of the PCD method incorporated into the 3D ZO CRS attribute search is to calculate the step length in each conjugate direction, further 3D work can focus on this. In 2D CRS case, the Coarse Grid Search (CGS) is proposed by Philipp Witte to find a close-by, relatively large maximum before the Powell method, but the CGS method is impossible to extend to 3D ZO CRS situation with eight-dimensional space.

The software has to change the initialization and constrained search space for your data set. In case you use the PSO method, the file named lucassearch8.cpp, with line 279-295 should alter the initial points with your preference. In this case, I use the midpoint in the search space to initialize for each ZO sample, but you can choose randomly initial values or the same value for all ZO samples. If you choose the GA as your algorithm, in the file named lucassearch81.cpp, the initial condition in the function initialize (int&seed), should change, such as from line 421 to 439, you have to reset your search space here.The PCD codes are more complicated, in principle, it can be used for global search, but the software designed here only consider a local optimization with guiding values from initial attributes. We have not found a good way to perform global search with the PCD method in the 3D CRS case. The usage of the software is easy as the old 3D ZO CRS software, just change the mode with different methods, more details see the source files.

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