Parallelizing Nonlinear Least-Squares Regression with Application to Analyses of Microalgae

ABSTRACTNonlinear least-squares regression is a valuable tool for gaining chemical insights into complex systems. Yet, the success of nonlinear regression as measured by residual sum of squares (RSS), correlation, and reproducibility of fit parameters strongly depends on the availability of a good initial solution. Without such, iterative algorithms quickly become trapped in an unfavorable local RSS-minimum. For determining an initial solution, a high-dimensional parameter space needs to be screened, a process that is very time-consuming but can be parallelized. Another advantage of parallelization is equally important: After determining initial solutions, the used processors can be tasked to each optimize an initial guess. Even if several of these optimizations become stuck in a shallow local RSS-minimum, other processors continue and improve the regression outcome. A software package for parallel processing-based constrained nonlinear regression (RegressionLab) has been developed, implemented, and teste...