Simultaneous synthesis and design of integrated reaction-separation processes using rigorous models is highly desirable to improve process performance. However, it often leads to a large-scale highly nonlinear nonconvex mixed-integer nonlinear programming model, which is difficult to solve. In this work, we propose a computationally-efficient optimization framework for simultaneous synthesis and design using rigorous models. The reactor and separation network are modelled using generalized disjunctive programming (GDP), which is reformulated into a mixed-integer nonlinear programming model using the convex-hull method. The activeness and inactiveness of a tray in a distillation column is modelled using the bypass efficiency method without introduction of integer variables, leading to significant reduction in the number of integer variables. To solve the model to local optimality, a systematic solution approach is proposed in which the pseudo-transient continuation model is used to generate a good starting point for optimization. The complementary conditions are added step by step to avoid infeasibility and ensure bypass efficiency variables be 0 or 1 only. An example from literature is solved to illustrate the capacity of the proposed optimization framework. The computational results demonstrate that the proposed optimization framework generates the local optimal solution of 2.13 M$/year within 58 CPU seconds. Significant reduction in computational efforts by 85% and improvement in solution quality by 5% are achieved compared to the existing approach.