### Fuzzy Multi-Objective Optimization for Metabolic Reaction Networks by Mixed-Integer Hybrid Differential Evolution

Abstract

The ultimate goal of metabolic engineering optimization is to find the optimal modulation strategy for improving productivity. In practical optimization of metabolic reaction networks, designers have to manage the nature of uncertainty resulting from qualitative characters of metabolic reactions, for example 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.

This chapter introduces a generalized fuzzy multi-objective optimization problem (GFMOOP) for finding optimal engineering interventions on metabolic network systems considering the resilience phenomenon and cell-viability constraints. This approach first formulates a constrained MOOP that considers the resilience effects and minimum set of manipulated enzymes simultaneously by combining the concepts of minimization of metabolic adjustment (MOMA) and regulatory on/off minimization (ROOM) into an optimization framework. In addition, the nonlinear kinetic equations are directly included in the optimization formulation, to formulate a constrained mixed-integer nonlinear programming (MINLP) problem. The mixed-integer hybrid differential evolution (MIHDE), which is a population-based evolution algorithm for solving unconstrained MINLP optimization problems, is extended to solve constrained MINLP problems through the implementation of constraint-handling techniques. The fuzzy goal attainment approach implemented in MIHDE is used to solve GFMOOPs for the identification of optimal genetic manipulation strategies on metabolic reaction networks, and can directly find a satisfactory solution in the Pareto-optimal set without yielding the Pareto frontier.