The optimization of biological systems, which is a branch of metabolic engineering, has generated a lot of industrial and academic interest for a long time. In the last decade, metabolic engineering approaches based on mathematical optimizations have been used extensively for the analysis and manipulation of metabolic networks. In practical optimization of metabolic reaction networks, designers have to manage the nature of uncertainty resulting from qualitative characters of metabolic reactions, e.g., the possibility of enzyme effects. A deterministic approach does not give an adequate representation for metabolic reaction networks with uncertain characters. Fuzzy optimization formulations can be applied to cope with this problem. A fuzzy multi-objective optimization problem can be introduced for finding the optimal engineering interventions on metabolic network systems considering the resilience phenomenon and cell viability constraints. The accuracy of optimization results depends heavily on the development of essential kinetic models of metabolic networks. Kinetic models can quantitatively capture the experimentally observed regulation data of metabolic systems and are often used to find the optimal manipulation of external inputs. To address the issues of optimizing the regulatory structure of metabolic networks, it is necessary to consider qualitative effects, e.g., the resilience phenomena and cell viability constraints. Combining the qualitative and quantitative descriptions for metabolic networks makes it possible to design a viable strain and accurately predict the maximum possible flux rates of desired products. Considering the resilience phenomena in metabolic networks can improve the predictions of gene intervention and maximum synthesis rates in metabolic engineering. Two case studies will present in the conference to illustrate the phenomena.
 R. B. Bellman and L. A. Zadeh, "Decision-making in a fuzzy environment,” Management Science, vol. 17, no. 4, pp. 141–164, 1970.
 W. J. Sutherland, "The best solution,” Nature, vol. 435, p. 569, Jun. 2005.
 E. O. Voit, "Optimization in integrated biochemical systems,” Biotechnology and Bioengineering, vol. 40, no. 5, pp. 572–582, Aug. 1992.
 R. Curto, E. O. Voit, A. Sorribas, and M. Cascante, "Mathematical models of purine metabolism in man,” Mathematical Biosciences, vol. 151, no. 1, pp. 1–49, Jul. 1998.
 D. Segrè, D. Vitkup, and G. M. Church, "Analysis of optimality in natural and perturbed metabolic networks,” Proceedings of the National Academy of Sciences, vol. 99, no. 23, pp. 15112–15117, Jun. 2002.
 T. Shlomi, O. Berkman, and E. Ruppin, "Regulatory on/off minimization of metabolic flux changes after genetic perturbations,” Proceedings of the National Academy of Sciences, vol. 102, no. 21, pp. 7695–7700, Feb. 2005.
 W. H. Wu, F. S. Wang, and M. S. Chang, "Multi-objective Optimization of Enzyme Manipulations in Metabolic Networks Considering Resilience Effects,” BMC Systems Biology, vol. 5, p. 145, Sep. 2011.
 J. Vera, R. Curto, M. Cascante, and N. V. Torres, "Detection of potential enzyme targets by metabolic modelling and optimization: application to a simple enzymopathy,” Bioinformatics, vol. 23, no. 17, pp. 2281–2289, Sep. 2007.
 K. C. Hsu and F. S. Wang, "Fuzzy Optimization for Detecting Enzyme Targets of Human Uric Acid Metabolism,” Bioinformatics, vol. 29, no. 24, pp. 3191–3198, Dec. 2013.
 J. P. Chiou and F. S. Wang, "Hybrid Method of Evolution Algorithms for Static and Dynamic Optimization Problems with Application to A Fedbatch Fermentation Process,” Computers & Chemical Engineering, vol. 23, no. 9, pp. 1277–1291, Nov. 1999.