Hybrid Genetic Algorithm with an Adaptive Penalty Function for Fitting Multimodal Experimental Data: Application to Exchange-Coupled Non-Kramers Binuclear Iron Active Sites

Abstract

A Genetic Algorithm (GA) is a stochastic optimization technique based on the mechanisms of biological evolution. These algorithms have been successfully applied in many fields to solve a variety of complex nonlinear problems. While they have been used with some success in chemical problems such as fitting spectroscopic and kinetic data, many have avoided their use due to the unconstrained nature of the fitting process. In engineering, this problem is now being addressed through incorporation of adaptive penalty functions, but their transfer to other fields has been slow. This study updates the Nanakorrn Adaptive Penalty function theory, expanding its validity beyond maximization problems to minimization as well. The expanded theory, using a hybrid genetic algorithm with an adaptive penalty function, was applied to analyze variable temperature variable field magnetic circular dichroism (VTVH MCD) spectroscopic data collected on exchange coupled Fe(II)Fe(II) enzyme active sites. The data obtained are described by a complex nonlinear multimodal solution space with at least 6 to 13 interdependent variables and are costly to search efficiently. The use of the hybrid GA is shown to improve the probability of detecting the global optimum. It also provides large gains in computational and user efficiency. This method allows a full search of a multimodal solution space, greatly improving the quality and confidence in the final solution obtained, and can be applied to other complex systems such as fitting of other spectroscopic or kinetics data.