Application of the differential evolution method to solving inverse transport problems

The differential evolution method, a powerful stochastic optimization algorithm that mimics the process of evolution in nature, is applied to inverse transport problems with several unknown parameters of mixed types, including interface location identification, source composition identification, and material mass density identification, in spherical and cylindrical radioactive source/shield systems. In spherical systems, measurements of leakages of discrete gamma-ray lines are assumed, while in cylindrical systems, measurements of scalar fluxes of discrete lines at points outside the system are assumed. The performance of the differential evolution algorithm is compared to the Levenberg-Marquardt method, a standard gradient-based technique, and the covariance matrix adaptation evolution strategy, another stochastic technique, on a variety of numerical test problems with several (i.e., three or more) unknown parameters. Numerical results indicate that differential evolution is the most adept method for finding the global optimum for these problems. In spherical geometry, differential evolution implemented serially is run-time competitive with gradient-based methods, while a parallel version of differential evolution would be run-time competitive with gradient-based techniques in cylindrical geometry. A hybrid differential evolution/Levenberg- Marquardt method is also introduced, and numerical results indicate that it can be a fast and robust optimizer for inverse transport problems.