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The tuning of parameters in climate models is essential to provide reliable long-term forecasts of Earth system behaviour. In this paper we present the first application of the multiobjective non-dominated sorting genetic algorithm (NSGA-II) to the GENIE-1 Earth System Model (ESM). Twelve model parameters are tuned to improve four objective measures of fitness to observational data. Grid computing and data handling technology is harnessed to perform the concurrent simulations that comprise the generations of the genetic algorithm. Recent advances in the method exploit Response Surface Modelling to provide surrogate models of each objective. This enables more extensive and efficient searching of the design space. We assess the performance of the NSGA-II using surrogates by repeating a tuning exercise that has been performed using a proximal analytical centre plane cutting method and the Ensemble Kalman Filter on the GENIE-1 model. We find that the multiobjective algorithm locates Pareto-optimal solutions which are of comparable quality to those obtained using the single objective optimisation methods.