A Parallel Optimization Framework for Inverse Problems

Abstract

Inverse problems that are constrained by large-scale partial differential equation (PDE) systems demand significant computational resources. These problems generally require the solution of a large number of complex PDE systems. Three dimensional subsurface characterization inverse problems fall under this category. A parallel hybrid optimization framework using global search and local search (LS) techniques is developed. The global search uses genetic algorithms (GAs). For LS several non-gradient based algorithms such as Nelder-Meade simplex, Hooke-Jeeves pattern search and Powell's method of conjugate directions and a gradient based algorithm namely, Fletcher-Reeves conjugate gradient method are implemented in the framework. Subsurface inverse characterization problems are posed as optimization problems and solved using this framework. The GA or hybrid GA-LS optimizer is employed to drive a parallel finite-element (FEM) groundwater transport simulator. Multilevel parallelism opportunities exist at the coarse-grained optimization level and the fine-grained function evaluation level. Coarse-grained parallelism (task parallelism) in the optimizer is exploited using a self-scheduling algorithm. Fine-grained parallelism (data parallelism) in the FEM transport simulator is achieved through a domain decomposition strategy. The MPI (Message Passing Interface) communication library is used for the parallel implementation. Parallelism is enhanced for local searches by enabling concurrent execution of multi-start or multi-type local searches. Performance results for convergence are examined for different test problems including biological activity zone identification, contaminant source zone identification (location and concentration) and contaminant sources release history reconstruction problems showing the applicability of the proposed approach. The size and complexity of problems solved in this research far exceed what has been reported to date in the literature. The implementation has been extensively tested on a single supercomputer and on the grid (TeraGrid). This research illustrates that the hybrid approaches are generally more effective than either standalone GA or LS for solving inverse problems.