Procedure used for Solving the MIMOO Problem

By setting the time-derivative of each metaboUte concentration to zero under pseudo-stationary assumption, the set of differential equations for mass balance equations is converted into a system of algebraic equations (see the E-coli.txt file in the folder Chapter 13 on the attached compact disk). Each nonlinear equation contains several rate expressions and terms. The glucose impulse term, fpuise, in the mass balance equation 

Chassagnole et al. (2002) is used to generate transient profiles using the 

Using the glucose-6-phosphate dehydrogenase (G6PDH) enzymatic sub-system as an example, reaction rate of G6PDH (i.e., rate of reaction facilitated by G6PDH) is given as  

NSGA-II parameters used in this study are maximum number of generations (up to 500), population size (100 chromosomes), probability of crossover (0.85), probability of mutation (0.05), distribution index for the simulated crossover operation (10), distribution index for the simulated mutation operation (20) and random seed (0.6). Except for the first and last parameter listed here, rest of the NSGA-II parameter values are taken from Tarafder et al. (2005). Values for maximum number of generations and random seed are obtained by trial and error. Our preliminary gene manipulation optimization runs show convergence within 500 generations for the random seed of 0.6. 

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