This work aims to assess the suitability of different formulations of normalization techniques within multi-criteria decision-making (MCDM) for applying to final design selection from the obtained Pareto frontier. The MCDM methods are applied as the post-optimization process for decision-making about the selection of final design among the non-dominated solutions for a case study. The Pareto front of a hull layout design problem for a ship is considered as the available set of alternatives that are obtained by multi-objective optimization. The selection of the final design is defined as an MCDM problem, and widely used methods of decision-making are adopted to select the final design. Different normalization formulations are applied to transfer the solution values of the Pareto frontier to the required data range for the input of MCDM methods. The effect of the normalization methods is discussed in a comparative study in the decision-making of the internal ship design problem. The results are assessed by comparison of top-ranked alternatives and by evaluating the correlation coefficients of obtained rank for all the alternatives. The normalization methods that are able to keep the dominancy order of the alternatives mostly resulted in similar final design selection.

这项工作旨在评估多准则决策制定（MCDM）中不同规格化标准化技术的适用性，以应用于从获得的帕累托边界进行最终设计选择。MCDM方法被用作后优化过程，用于在案例研究的非主导解决方案中选择最终设计的决策。船舶的船体布局设计问题的Pareto前沿被认为是通过多目标优化获得的一组可用替代方案。最终设计的选择被定义为MCDM问题，并且采用了广泛采用的决策方法来选择最终设计。应用了不同的归一化公式，以将帕累托边界的解值转移到MCDM方法输入所需的数据范围。在对内部船舶设计问题的决策进行比较研究中，讨论了标准化方法的效果。通过比较排名靠前的替代方案和评估所有替代方案获得的等级的相关系数来评估结果。能够保持替代方案的优势顺序的归一化方法主要导致了相似的最终设计选择。