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Genetic algorithms (GAs) and multi-objective genetic algorithms (MOGAs) have proven to be successful in calibrating numerical models. The limitation of using GAs and MOGAs is their expensive computational requirement. The calibration process usually needs to run the numerical model and evaluate the objective function thousands of times before converging to an acceptable solution and generating a sufficiently accurate Pareto set. However, in real world applications, there is simply not enough time and resources to perform such a huge number of model runs. In this study, a computational framework, known as GA-kNN, is presented for solving computationally expensive calibration problems. The concept of GA-kNN will be demonstrated via one novel approximate model using k-Nearest Neighbour classifier. This study also investigates Pareto ranks estimation using kNN classifier as a way to speed up multi-objective genetic algorithm search, namely NSGA-II-kNN. The approximation model is performed in predicting the form of Pareto ranks instead of running the simulation models and ranking current population. This approach can substantially reduce the number of model evaluations on computational expensive problems without compromising the good search capabilities of NSGA-II. The simulation results suggest that the proposed optimisation frameworks are able to achieve good solutions as well as provide considerable savings of the numerical model calls compared to traditional GA and NSGA-II optimisation frameworks.