Optimization for process design in the chemical engineering industry has been important for energy efficiency and economic feasibility. Because many industries perform optimization with a commercial process simulator such as the Aspen HYSYS, an optimization methodology for expensive black-box functions is needed. Thus, the development of derivative free optimization algorithms has long been studied and the deterministic global search algorithm DIRECT (DIviding a hyper-RECTangle) was suggested. In this paper, a modified DIRECT algorithm with a sub-dividing step for considering hidden constraints is proposed. The effectiveness of the algorithm is exemplified by its application to a cryogenic mixed refrigerant process using a single mixed refrigerant for natural gas liquefaction and its comparison with a well-known stochastic algorithm (GA, PSO, SA), and model based search algorithm (SNOBFIT), local solver (GPS, GSS, MADS, active-set, interior-point, SQP), and other hidden constraint handling methods, including the barrier approach and the neighborhood assignment strategy. Optimal solution calculated by the proposed algorithms decreases the specific power required for natural gas liquefaction to 18.9% compared to the base case.
- Derivative-free optimization
- Hidden constraint
- Single mixed refrigerant (SMR)