Equivalent dipole parameter estimation using simulated annealing.

Equivalent-electrical dipole source modeling of evoked potential signals requires complicated non-linear multivariate optimization. Newton and non-linear simplex optimization methods often converge to a local minimum, and their results are affected by the procedure's starting parameter estimates. This paper describes simulated annealing, a more robust and resistant global optimization method. As an illustrative example, both the simplex and simulated annealing algorithms were used for parameter estimation in modeling wave V of the brain-stem auditory evoked potential (BAEP) using a single decaying sinusoid dipole source. Data for a single subject from 3000 responses to stimuli on each of 2 days were recorded, with modeling performed on 1000 response subaverages. Each estimation problem was run with 5 different sets of starting parameters. Simulated annealing always converged to the global minimum regardless of the starting parameter estimates while simplex often converged to markedly different solutions for different starting parameter estimates. No association was apparent between the simplex's converging to a local minimum and the closeness of the starting estimates to the true parameter values. Implementation of simulated annealing is discussed in terms of cooling schedules and other procedure parameters.