عنوان مقاله [English]
Conventional methods for solving the problem of site location for booster chlorination stations have assumed the use of linear superposition principle for first-order kinetics of chlorine decay in water distribution systems in order to speed up the process of evolutionary algorithms. However, examination of this assumption in this paper shows that it causes a non-trivial error, especially when the order of chlorine decay rate is more than one. This paper presents a novel meta-model for solving the multi-objective optimization problem of optimal locations for booster chlorination stations for the nonlinear order of chlorine decay rate. In the proposed model, the meta-model is the water quality simulation model quantified by the principle of linear superposition for nonlinear kinetics of chlorine decay. To do so, residual chlorine concentration is calculated from the injection unit chlorine concentration at each node in the network as offline outside the optimisation loop. Then, within the optimization loop, the residual chlorine concentration in the network obtained for the optimal solutions is calculated as the combined chlorine injected from different locations and at different concentrations based on the linear superposition meta-model of the previous part. Objective functions of the optimisation solutions are quickly evaluated by this meta-model. In order to mitigate the significant error due to the estimation of this meta-model, the fitness of the best solutions are again evaluated using the real water quality simulation model (nonlinear chlorine decay rate) and replaced with the evaluations previously approximated by the meta-model. The results show the desirable accuracy of the proposed model and the high speed in the run time of the hybrid optimisation model.