Embedded multiple shooting methodology in a genetic algorithm framework for parameter estimation and state identification of complex systems

Inverse problem studies of biochemical systems with structure identification of S-systems by embedding training functions in a genetic algorithm

“…We include the second term in Eq. (5) because the discontinuities in MS simulated profiles ( Section 2.2 ) could mislead the search direction in its initial stages [37] .…”

“…The complete details of the implementation of the MS training function are given in Sarode et al [37] . In the MS approach [45][46][47][48] …”

“…, n ms ) along with ˆ X − is trained using the MS function (described in Section 2.2 ) to obtain new estimates in ˆ P ms,m and ˆ X P ms,m , respectively [B6]. After performing the MS training function for all members ∈ P ms , we obtain new populations of parameter estimates ˆ P ms and state estimates ˆ X P ms [B7] [37] . The second subpopulation P d [B8] is used as an initial population for a GA optimization using the decomposition approach (described in Section 2.3 ).…”

“…Crossover and mutation operators are then applied on the selected members P S to obtain other parts of the next generation population P C and P M with n c and n m number of members, respectively. For the crossover and mutation operators, we have followed the GA mechanisms described in [37,44] . We also applied a new mechanism in the GA to form the additional subpopulation P R [B13], by using the slope regression method ( Eq.…”

“…The methodology of embedded multiple shooting in a genetic algorithm (EMSGA) has shown advantages in parameter estimation and simultaneous state identification of inverse problems in complex nonlinear systems [37] . The approach is seen to handle practical data related challenges including noise, missing data points and recovering the dynamics of unmonitored state variable(s).…”