Multi-objective optimization problem in the OptD-multi method

New measurement technologies, e.g. Light Detection And Ranging (LiDAR), generate very large datasets. In many cases, it is reasonable to reduce the number of measuring points, but in such a way that the datasets after reduction satisfy specific optimization criteria. For this purpose the Optimum Dataset (OptD) method proposed in [1] and [2] can be applied. The OptD method with the use of several optimization criteria is called OptD-multi and it gives several acceptable solutions. The paper presents methods of selecting one best solution based on the assumptions of two selected numerical optimization methods: the weighted sum method and the ε-constraint method. The research was carried out on two measurement datasets from Airborne Laser Scanning (ALS) and Mobile Laser Scanning (MLS). The analysis have shown that it is possible to use numerical optimization methods (often used in construction) to obtain the LiDAR data. Both methods gave different results, they are determined by initially adopted assumptions and – in relation to early made findings, these results can be used instead of the original dataset for various studies.

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