Nonlinear numerical optimization technique based on genetic algorithm for inverse problem

Organizationally complex nonlinear systems, such as metabolic pathways and gene-circuit systems, are comprised of numerous, richly interacting system components. In the case where the details of the process that govern interactions among system components (state variables) are not well known, however, how do we represent mathematical model for such complex nonlinear processes? Estimation of the interaction mechanism among system components by using the experimentally observed dynamic responses (time-courses) of some of the system components is generally a so-called "inverse problem." The "S-system," which belongs to power-law formalism, is one of the best representations to solve this inverse problem; the S-system is rich enough in structure to capture all relevant dynamics. This formalism has, however, a major disadvantage in that it includes large number of parameters to be estimated; the estimation of these parameter-values is almost never straightforward, and almost always a real challenge. In this paper, for the purpose of solving the inverse problem, we introduce the Genetic Algorithm and propose an efficient procedure for estimation (optimization) of large numbers of parameters in S-system formalism.