Multi-objective optimization of reverse osmosis desalination units using different adaptations of the non-dominated sorting genetic algorithm (NSGA)

Multi-objective optimization using genetic algorithm (GA) is carried out for the desalination of brackish and sea water using spiral wound or tubular modules. A few sample optimization problems involving two and three objective functions are solved, both for the operation of an existing plant (which is almost trivial), as well as, for the design of new plants (associated with a higher degree of freedom). The possible objective functions are: maximize the permeate throughput, minimize the cost of desalination, and minimize the permeate concentration. The operating pressure difference, ΔP, across the membrane is the only important decision variable for an existing unit. In contrast, for a new plant, ΔP, the active area, A, of the membrane, the membrane to be used (characterized by the permeability coefficients for salt and water), and the type of module to be used (spiral wound/tubular, as characterized by the mass transfer coefficient on the feed-side), are the important decision variables. Sets of non-dominated (equally good) Pareto solutions are obtained for the problems studied. The binary coded elitist non-dominated sorting genetic algorithm (NSGA-II) is used to obtain the solutions. It is observed that for maximum throughput, the permeabilities of both the salt and the water should be the highest for those cases studied where there is a constraint on the permeate concentration. If one of the objective functions is to minimize the permeate concentration, the optimum permeability of salt is shifted towards its lower limit. The membrane area is the most important decision variable in designing a spiral wound module for desalination of brackish water as well as seawater, whereas ΔP is the most important decision variable in designing a tubular module for the desalination of brackish water (where the quality of the permeate is of prime importance). The results obtained using NSGA-II are compared with those from recent, more efficient, algorithms, namely, NSGA-II-JG and NSGA-II-aJG. The last of these techniques appears to converge most rapidly.