Modal choice models used for freight transportation studies covering inter-regional or international areas are difficult to set up because of the dearth of information about explanatory factors. While cost and transit time are known as being important explanatory variables, they are generally correlated to each other, and their coefficient computed with a Logit model can have unexpected signs. 

Box-Cox transformations (BCT) of the independent variables can help to overcome this problem. If solutions to identify the BCT parameter that maximises the likelihood of a model are well known, the process is not straightforward once it must respect the constraints that the variables’ coefficient estimators take the expected signs.

This paper presents a shotgun hill climbing meta-heuristic with backtracking capabilities, able to quickly identify Box-Cox λ parameters to use when multiple variables must be transformed. The algorithm appears to be efficient and effective and produces stable and statistically valid solutions.

由于缺乏有关解释因素的信息，用于跨区域或国际区域的货运研究的模式选择模型难以建立。虽然成本和运输时间被认为是重要的解释变量，但它们通常相互关联，并且使用 Logit 模型计算的系数可能会出现意想不到的迹象。 

自变量的 Box-Cox 变换 (BCT) 可以帮助克服这个问题。如果识别使模型的可能性最大化的 BCT 参数的解决方案是众所周知的，那么一旦它必须尊重变量的系数估计器采用预期符号的约束，该过程就不是直截了当的。

本文提出了一种具有回溯能力的猎枪爬山元启发式算法，能够在必须转换多个变量时快速识别要使用的 Box-Cox λ 参数。该算法似乎是高效和有效的，并产生稳定和统计有效的解决方案。