Application Of Numerical Optimization Technique Based On Real-coded Genetic Algorithm To Inverse Problem In Biochemical Systems

Real-coded Genetic Algorithms (RCGA) attract attention as numerical optimization methods for nonlinear systems. One of the crossover operators for RCGA called unimodal normal distribution crossover (UNDX) has shown good performance in optimization of various functions including multi-modal ones and benchmark functions with epistasis among parameters (Ono and Kobayashi, 1997). The UNDX generates new population lie on some ponds or along some valleys in order to focus the search on promising areas from a viewpoint of searching efficiency. Especially when the function has epistasis among parameters, namely valleys that are not parallel to coordinate axis, the UNDX can efficiently optimize it. Simple GA is one of the well-known generation alternation models, however, it has two problems. One is early convergence in the fast stage of search and the other is evolutionary stagnation in the last stage of it. A new generation alternation model called minimal generation gap (MGG) was proposed to overcome the above problems (Sato et al., 1997, Ono et al., 2000). The MGG has all advantages of convention models and the ability of avoiding the early convergence and suppressing the evolutionary stagnation. Here, we applied the combination method (MGG+UNDX) to the optimization of real-valued parameters in the form of the S-system that is a type of power-law formalism and is suitable for description of organizationally complex systems such as gene expression networks (Maki et al., 2001) and metabolic pathways (nonlinear biochemical systems). The S-system is based on a particular type of ordinary differential equation in which such component processes are characterized by power-law functions as follows: ∏ ∏ = = − = n