Pareto-based evolutionary algorithms for the calculation of transformation parameters and accuracy assessment of historical maps

•Historical map data involves transformation of the coordinates to the current system.•The main problem is that the quality of historical data is heterogeneous.•Sometimes it is necessary to discard some of the historical input data.•The proposed method is Pareto front based on evolutionary genetic algorithms.•This method reduces linear error by 40% by eliminating only 2% of the points used.

When historical map data are compared with modern cartography, the old map coordinates must be transformed to the current system. However, historical data often exhibit heterogeneous quality. In calculating the transformation parameters between the historical and modern maps, it is often necessary to discard highly uncertain data. An optimal balance between the objectives of minimising the transformation error and eliminating as few points as possible can be achieved by generating a Pareto front of solutions using evolutionary genetic algorithms. The aim of this paper is to assess the performance of evolutionary algorithms in determining the accuracy of historical maps in regard to modern cartography. When applied to the 1787 Tomas Lopez map, the use of evolutionary algorithms reduces the linear error by 40% while eliminating only 2% of the data points. The main conclusion of this paper is that evolutionary algorithms provide a promising alternative for the transformation of historical map coordinates and determining the accuracy of historical maps in regard to modern cartography, particularly when the positional quality of the data points used cannot be assured.

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