Abstract
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.