(558e) Efficient Adaption of Simulated Annealing and Genetic Algorithms to Atmospheric Inverse-Source Problems

In the present work, simulated annealing and genetic algorithms are examined to determine their most efficient implementations in atmospheric inverse-source problems. The inverse problem is comprised of retrieving the spatial coordinates (x, y, and z), source strength, wind speed, and the wind direction at the source, given certain sensor locations, and concentration values at these sensor locations. The solution methodologies developed work for arbitrary atmospheric inverse-source problems, given a forward model and the limits of estimation of the sensors. In the current work, the Gaussian plume model (GPM) is adopted as the forward model due to its theoretical and computational simplicity. Seven out of the eight model parameters in the GPM were retrieved, thus making the inverse problem seven dimensional (7D).

Atmospheric inverse-source problems suffer from sparse number of sensor measurements in general, and very few non-zero measurements in particular. Therefore, the first step in the solution procedure was the development of a misfit function that takes into account both zero and non-zero measurements, and treats both of them equally. The new misfit function developed is based on the reciprocal of the L1-norm of an indicator function, with the indicator function taking the value one when the base 10 logarithm of the observed and predicted data at a certain receptor falls within certain (derived) bounds. The inverse-source problem is cast as a minimization problem and the final source parameters correspond to the model parameters for which the misfit function is minimized. Since the misfit function for atmospheric source inversion problems is characterized by several local minima, stochastic search algorithms such as SA and GA are employed.

In the current work, SA with the inhomogeneous Metropolis algorithm is implemented. In theory, even though SA is an optimization algorithm (asymptotically converges to set of global minima with probability one), in any implementation, heuristic choices need to be made. This is because the necessary and sufficient conditions for convergence are computationally intractable for large state spaces and hence cannot be implemented. Consequently, heuristic versions of SA were developed which do not necessarily satisfy the conditions for weak ergodicity. One of the objectives of the present work is the identification of a feasible annealing algorithm for atmospheric inverse-source problems. Therefore, the performance of several variants of SA was examined. The variants considered include classical SA, Cauchy annealing, very fast SA, adaptive SA, and generalized SA with Tsallis statistics (GSA-TS). These variants were implemented with several neighborhood generation mechanisms and temperature reduction schedules. Since the atmospheric inverse-problem is a formulated as a continuous minimization problem, a continuous GA (CGA) was implemented. In the CGA, the effect of the various parameters such as the initial population size, selection ratio, and mutation rate, and the mechanisms that can be used in the selection, mating, crossover, and mutation procedures, and their effect on the final solution obtained is investigated. At the conference, the performance of the various versions of SA and GA will be presented. Based on the results, the most feasible version will be identified.