This article proposes a new problem which is called the Stochastic Travelling Advisor Problem (STAP) in network optimization, and it is defined for an advisory group who wants to choose a subset of candidate workplaces comprising the most profitable route within the time limit of day working hours. A nonlinear binary mathematical model is formulated and a real application case study in the occupational health and safety field is presented. The problem has a stochastic nature in travelling and advising times since the deterministic models are not appropriate for such real-life problems. The STAP is handled by proposing suitable probability distributions for the time parameters and simulating the problem under such conditions. Many application problems like this one are formulated as nonlinear binary programming models which are hard to be solved using exact algorithms especially in large dimensions. A novel binary version of the recently developed gaining-sharing knowledge-based optimization algorithm (GSK) to solve binary optimization problems is given. GSK algorithm is based on the concept of how humans acquire and share knowledge during their life span. The binary version of GSK (BGSK) depends mainly on two stages that enable BGSK for exploring and exploitation of the search space efficiently and effectively to solve problems in binary space. The generated simulation runs of the example are solved using the BGSK, and the output histograms and the best-fitted distributions for the total profit and for the route length are obtained.

中文翻译：

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带有案例研究的随机旅行顾问问题仿真：一种新的基于知识的二进制获取共享知识的优化算法

本文提出了一个在网络优化中称为随机旅行顾问问题（STAP）的新问题，该问题是为希望在日常工作时间内选择一部分获利最多的候选工作场所的咨询小组定义的小时。建立了非线性二元数学模型，并提出了在职业健康安全领域的实际应用案例。该问题在旅行和建议时间中具有随机性，因为确定性模型不适用于此类现实问题。通过为时间参数提出合适的概率分布并在这种条件下模拟问题来处理STAP。诸如此类的许多应用问题被表述为非线性二进制编程模型，这些问题很难使用精确的算法来解决，尤其是在大尺寸情况下。给出了一种新近开发的基于增益共享知识的优化算法（GSK）的二进制版本，用于解决二进制优化问题。GSK算法基于人类在生命周期中如何获取和共享知识的概念。GSK（BGSK）的二进制版本主要取决于两个阶段，这些阶段使BGSK能够有效地探索和利用搜索空间来有效解决二进制空间中的问题。使用BGSK求解示例的生成模拟运行，并获得输出直方图和总利润和路径长度的最佳拟合分布。