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In this paper, an original modification of the generalised robust estimation of deformation from observation differences (GREDOD) method is presented with the application of two evolutionary optimisation algorithms, the genetic algorithm (GA) and generalised particle swarm optimisation (GPSO), in the procedure of robust estimation of the displacement vector. The iterative reweighted least-squares (IRLS) method is traditionally used to perform robust estimation of the displacement vector, i.e., to determine the optimal datum solution of the displacement vector. In order to overcome the main flaw of the IRLS method, namely, the inability to determine the global optimal datum solution of the displacement vector if displaced points appear in the set of datum network points, the application of the GA and GPSO algorithms, which are powerful global optimisation techniques, is proposed for the robust estimation of the displacement vector. A thorough and comprehensive experimental analysis of the proposed modification of the GREDOD method was conducted based on Monte Carlo simulations with the application of the mean success rate (MSR). A comparative analysis of the traditional approach using IRLS, the proposed modification based on the GA and GPSO algorithms and one recent modification of the iterative weighted similarity transformation (IWST) method based on evolutionary optimisation techniques is also presented. The obtained results confirmed the quality and practical usefulness of the presented modification of the GREDOD method, since it increased the overall efficiency by about 18% and can provide more reliable results for projects dealing with the deformation analysis of engineering facilities and parts of the Earth's crust surface.