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The geometry optimisation of linear and two-dimensional (2D) Yagi-Uda antenna arrays is presented. The objective from the optimisation is to increase the directivity and/or minimise the sidelobe level. The optimisation parameters are the lengths and/or the separations between the array elements for the linear array, and lengths and element locations for the 2D array. The current distribution over the array elements is found using the method of moments that takes into consideration mutual coupling between array elements. From the current distribution and the array geometry, the radiated electric field is computed, from which the directivity and other array parameters are calculated. The particle swarm optimisation (PSO) method is used in the optimisation process. Various numerical examples are presented and discussed, and the results are compared with other optimisation methods whenever possible.