Multi-objective optimization of biological systems represented by S-system models

This paper considers multi-objective optimization problems of biological systems. The biological system is represented by the S-system formalism. The advantage of this representation is that the steady-state equations are linear when the variables of the models are expressed in logarithmic coordinates. Profiting from this special property of S-system models, we transform the original nonlinear problem into a multi-objective linear programming. The obtained problem is then reformulated as a new multi-objective programming that has no equality or inequality constraints. The example of tryptophan biosynthesis is performed to the proposed framework and shown to the effectiveness of the approach. The simulation is also studied to give a performance comparison between the proposed and nonlinear approaches.