In this paper, an optimization-based methodology is applied to the design of a reactor-separator-recycle system based on a measure of the extension of the domain of attraction of the operating equilibrium. The approach consists in maximizing the radius of a ball in the state space contained in the region of negative definiteness of the time derivative of a quadratic Lyapunov function. A two-level optimization strategy is proposed that solves a deterministic nonconvex global optimization problem at the inner level. To cope with the non-differentiability introduced by the inner problem, we applied a stochastic algorithm to manipulate the design variables at the outer level.