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## Hybrid Genetic Deflated Newton Method for Distributed-Source Optimization

Marcus M. Noack, & Steven M. Day

Published August 15, 2016, SCEC Contribution #6754, 2016 SCEC Annual Meeting Poster #349 (PDF)

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Earthquake fault parameter inversion is a promising field of research. An accurately defined source leads in turn to accurate ground motion predictions. The promising perspective comes at a cost; local and global optimization procedures like the Newton method and the genetic algorithm offer a trade-off between accuracy and computational costs. Using the renowned Newton method cannot lead to success because the misfit function to be optimized exhibits many local optima because of the natural sine shape if a wave. Furthermore, the global optimum might not be unique. On the plus side, the Newton method is very efficient in finding a stationary point.

As a global method, the genetic algorithm suffers from high computational costs in high dimensional search spaces. Also, since no local information of the function is used, the algorithm cannot determine whether a stationary point is found. Therefore, only one solution can be found. An advantage of the genetic algorithm is, however, that the global optimum will be found eventually. Genetic algorithm and Newton methods are only examples of many local and global optimization methods but they are representative in terms of their abilities.

To join the advantages of both methods, hybrid methods have been developed. Hybrid methods are using a global optimization scheme like the genetic algorithm to explore the parameter space and a local scheme to find stationary points. One major drawback persists; one optimum can be found several times which leads to biased behavior and a premature convergence.

Recently, a new method with the name Hybrid genetic Deflated Newton method (HGDN) has been proposed which uses the advantages of a hybrid method. The new method places several individuals randomly in the search space. All individuals perform a Newton method to a stationary point. The found points are transferred to a list and the points are removed from the function by deflation. Afterwards, the entire population of individuals is set back to its starting position and the search starts again. Already found optima cannot be found again. Therefore, the individuals converge in new stationary points. The procedure continues until no more stationary points can be found in the vicinity. A genetic algorithm replaces the fittest individuals and the procedure starts over.

In this work we outline the work flow of using HGDN for fault parameter optimization, illustrating the concept for the case of a distributed acoustic source. Future work will consider the corresponding elasto-dynamic source inverse problem.

Key Words
Optimization, Inversion, Earthquake source

Citation
Noack, M. M., & Day, S. M. (2016, 08). Hybrid Genetic Deflated Newton Method for Distributed-Source Optimization. Poster Presentation at 2016 SCEC Annual Meeting.

Related Projects & Working Groups
Computational Science (CS)