A hybrid algorithm of evolutionary optimization, called hybrid differential evolution (HDE), is developed in this study. The acceleration phase and migration phase are embedded into the original algorithm of differential evolution (DE). These two phases are used to improve the convergence speed without decreasing the diversity among individuals. With some assumptions, this hybrid method is shown as a method using N-p parallel processors of the two member evolution strategy, where N-p is the number of individuals in the solution space. The multiplier updating method is introduced in the proposed method to solve the constrained optimization problems. The topology of the augmented Lagrange function and the necessary conditions for the approach are also inspected. The method is then extended to solve the optimal control and optimal parameter selection problems., A fed-batch fermentation example is used to investigate the effectiveness of the proposed method. For comparison, several alternate methods are also employed to solve this process.