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The paper first discusses the question of which objectives may be meaningful for the optimization of high‐voltage insulators, and exhaustively analyses the relationship between field strength and the geometrical properties of the boundary surfaces of a Boundary Value Problem (BVP). Afterwards a theoretical formulation of the optimization task is presented. In order to seek the parameters that may play a role in the optimization task, a formula for the global field derivative for shaping boundaries is derived. The parameters which can be determined by means of the numerical field calculation are discussed. These can be used as a point of reference for the development of an optimization procedure.