Bounded implicit enumeration for wastewater-treatment systems

A wastewater-treatment system can be represented by a multistage configuration consisting of a variety of unit processes from various stages. The number of treatment combinations may be very large when the number of unit processes in a stage and the number of stages in a system increase. Enumeration techniques, e.g., total enumeration and implicit enumeration, have been used to eliminate infeasible treatment combinations and to identify the least-cost treatment system. A bounded implicit enumeration approach is proposed to make the implicit enumeration more efficient. A lower bound is calculated at each stage and added to the up-to-date objective function value to eliminate more combinations before reaching the final stage. The results for two wastewater-treatment-system-synthesis models indicate that the bounded implicit enumeration is consistently more efficient than the total and implicit enumeration approaches in identifying least-cost and feasible treatment alternatives.