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Identifying the optimal design for an RO membrane network is not straightforward when significant fouling occurs. The most robust optimal network design will feature the minimal capital and operating costs over the anticipated lifetime of the plant, and is therefore strongly dependent on the fouling behaviour and associated mitigation. This study considers the case where the likely fouling behaviour is known and investigates how to incorporate this knowledge into the design and operation of a network. The optimisation task is complicated by the highly non-linear nature of the problem owing to membrane behaviour, fouling behaviour, network interactions and operating parameter constraints (pressures and flows). In this work, fouling is modelled as an exponential decay in membrane permeability. Three optimisation approaches are used to evaluate candidate networks: (i) laborious comparison of pre-selected individual network designs; (ii) deterministic gradient search methods, and (iii) a simulated-annealing-based hybrid stochastic-deterministic method. All of the approaches consider various configurations of a two-stage network with a maximum of three membrane units in each stage, represented in a superstructure model. The results from the approaches are compared and the most effective method for network design is discussed. [ABSTRACT FROM AUTHOR]