GPU Accelerated Parameter Estimation by Global Optimization using Interval Analysis

Mads B. Eriksen, Soren Rasmussen
School of ICT, Aalborg University
Aalborg University, Student report, 2013


   title={GPU Accelerated Parameter Estimation by Global Optimization using Interval Analysis},

   author={Eriksen, Mads B and Rasmussen, S{o}ren},



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This master thesis treats the topic of non-linear parameter estimation using global optimization methods based on interval analysis (IA), accelerated by parallel implementation on a Graphics Processing Unit (GPU). Global optimization using IA is a mathematically rigorous Branch & Bound-type method, capable of reliably solving global optimization problems with continuously differentiable objective functions, even in the presence of rounding errors. The structure of the problems and methods considered is parallel by nature and fit the parallel architecture of modern GPUs well. Methods for efficiently exploiting this parallelism are presented, based on which a parallel GPU accelerated global optimization algorithm is implemented. A set of algorithmic variations of the parallel GPU accelerated algorithm are benchmarked and compared to corresponding sequential CPU based implementations. Results show speedups ranging from 1.43 to 60.4 times for the test problems and problem sizes used. Analysis shows that the GPU accelerated implementations do not utilize the GPU hardware fully. It is assessed that further utilization and speedup can be obtained by introducing an additional level parallelism. It is concluded that for problems with large numbers of measurements, use of the method presented has the potential of yielding significant speedups.
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