Using Limited Concentration Data for the Determination of Rate Constants with the Genetic Algorithm

Abstract

A computational strategy is presented that uses limited concentration vs time data to iteratively determine rate constants for a postulated reaction mechanism. These rate constants, once found, can be used to compute complete concentration profiles as a function of time and can be transferred to other reaction mechanisms that contain common reaction steps. The computational algorithm presented here maps this iterative rate constant search onto a problem of functional optimization, where the values of the rate constants themselves are optimized in order to minimize a well-defined error function. This error function contains multiple minima, which obviates the use of conventional computational methods of functional optimization such as conjugate gradient and Simplex methods. Alternatively, the genetic algorithm is found to be extremely robust in its ability to find solutions near enough to the global minimum to yield meaningful results without getting “stuck” in local minima. The algorithm presented here uses the Genetic Algorithm to get near a minimum that is close to a useful local minimum and then uses the Simplex method to polish the solutions, i.e., to find this minimum. The usefulness of the algorithm is demonstrated on two model problems each based on an environmentally relevant chemical reaction system.