A Memetic Algorithm for Global Optimization in Chemical Process Synthesis Problems

Design optimization problems in chemical engineering and in many other engineering domains are characterized by the presence of a large number of discrete and continuous decision variables, complex nonlinear models that restrict the search space, nonlinear cost functions, and the presence of many local optima. The classical approach to such problems are mixed integer nonlinear program solvers that work on a superstructure formulation which explicitly represents all design alternatives. The structural decisions lead to a large number of discrete variables and an exponential increase in the computational effort. The mathematical programming (MP) methods which are usually employed to solve the continuous subproblems that arise by fixing the discrete variables provide only one local optimum which depends strongly on the initialization. Thus standard methods may not find the global optimum despite long computation times. In this contribution we introduce a memetic algorithm (MA) for the global optimization of a computational demanding real-world design problem from the chemical engineering domain. The MA overcomes the problem of getting stuck in local optima by the use of an evolution strategy (ES) which addresses the global optimization of the design decisions, whereas a robust MP solver is used to handle complex nonlinear constraints as well as to improve the individuals of the ES by performing a local search in continuous sub-spaces in an integrated fashion. The MA is discussed in detail, the novel decomposition of the problem class at hand is analyzed and the MA is tested for the example of the optimal design of a reactive distillation column with several thousand decision variables. The MA is the only algorithm that finds the global solution in reasonable computation times. The introduction of structural decisions and additional constraints and discontinuous penalty terms lead only to a moderate increase in the computational effort which demonstrates the potential of this class of memetic algorithms in real-world design optimization problems.