Abstract: Continuous global climate change brought severe meteorological disasters and adverse weather events to every country in recent years, and there was no exception to China. Those meteorological hazards greatly influence road safety and traffic operation, so road weather management programs are popularized in many western countries and road weather information system is developed to monitor, predict, and warn major meteorological events on the road network. This kind of system is a part of smart highway construction and intelligent meteorological support service, and its effectiveness greatly depends on the layout of road weather information system (RWIS) stations. However, locating RWIS station is not so straightforward because it is related to lots of internal and external influencing factors. For example, decision-makers are faced with the uncertain average annual transport demand for each road segment in 5 to 15 years to come, the inconsistent spacing standards of RWIS station location due to fuzzy weather information requirements for smart applications, and the investment budget uncertainty due to weak world economic growth. These uncertainties from smart transport system and economic growth increase the difficulty of optimizing RWIS station layout. This study applies robust concept to existing RWIS stations’ siting problem by modelling uncertain transport demand as a polyhedral uncertainty set. Moreover, this research also gives a case study of Zibo highway network to demonstrate the effectiveness of the proposed methodology, which can also be applied to other places.
In this study, a polyhedral uncertainty set is introduced to describe the uncertainty of highway transport demand, and a robust siting model for RWIS stations is proposed under three assumptions. The robust optimization model aims to maximize the total freight turnover serviced by RWIS station network, and it includes two special constraints such as minimum station spacing related with smart highway level and investment budget in the context of weak investment willingness. Because the objective function of the proposed model has max set operation, the equivalence between the inside max optimization subproblem and its min dual optimization subproblem is firstly proved, then the original robust model is further transformed into an equivalent mixed integer programming problem in the manner of the work of BERTSIMAS and SIM (2004). Besides, the nonlinear minimum station spacing constraint is converted to its equivalent linear constraint using logic constraint and big M method. As a result, an equivalent mixed integer linear programming (MILP) problem is derived from the original robust model. Because CPLEX solver can deal with the large-scale MILP problem efficiently, it is integrated into master control solving program written by Python programming language in PYCHARM.
A data preparation of case study includes three parts: First, the static information about the planned Zibo highway network and candidate RWIS station in 2025 is collected as well as some major model parameters are configured. Second, both average annual passenger transport demand and average annual cargo transport demand from 2021 to 2035 are predicted as nominal values. Third, the proportion of disturbance and the level of uncertainty are determined according to existing studies. Then several numerical analyses are carried out and some findings are concluded as follows: (1)The proposed model is shown to be sensitive to the proportion of disturbance and the level of uncertainty of transport demand. When there is neither disturbance nor uncertainty in transport demand, the optimal value of objective, that is, the total freight turnover serviced, reaches its peak at 77141.5 million ton-kilometers from 2021 to 2035. It is also suggested that when the level of uncertainty of transport demand increases, the total freight turnover serviced will decrease. (2)In the worst uncertainty of transport demand, the effect of the minimum station spacing on optimal layout plan is investigated which indicates that the former may have impact on the latter. However, that effect shows heterogeneity on different types of highways with various topography and intelligence. (3)In the worst uncertainty of transport demand, the effect analysis of the investment budget on optimal objective value and road section coverage rate shows that a progressive increase in investment budget from 3.0 to 3.4 million Yuan would improve optimal objective value and road section coverage rate. Nevertheless, when the budget exceeds 3.4 million Yuan, both optimal objective value and road section coverage will remain stable.
The proposed model may be improved to consider other influencing factors and develop heuristic algorithm, and it is necessary to study how to jointly optimize RWIS layout problem with other ones like meteorological station maintenance resources scheduling and highway intelligence upgrading decision-making.

Key words: smart highway, road weather information system station, robust optimization, mixed integer linear programming, demand uncertainty

摘要： 公路交通气象观测站布设是智慧高速公路建设和智慧气象保障服务的重要内容之一,也是各方关注面临的难题。然而交通运输需求不确定性更增加了布局优化的困难。本文引入多面体不确定集合刻画路段交通运输需求的不确定性,同时考虑最小站点间距及投资预算限制等约束,构建一个以被服务总货运周转量最大化为目标的公路交通气象站鲁棒选址模型。利用鲁棒优化理论,将模型转化为等价的混合整数线性规划问题,通过PYCHARM软件编程并调用CPLEX求解器求解。最后,以淄博市高速公路网交通气象站布设为例,验证模型和求解方法的可行性和鲁棒性。结果表明,公路交通运输需求的扰动比例和不确定水平对公路交通气象站的选址方案和最优目标值有一定影响;最小站点间距会对选址方案和最优目标值有一定影响,其影响大小与高速公路的地形和智慧化等级有关;总投资预算在一定范围内会影响布设方案和最优目标值,但当超过某个阈值,这种影响将不起作用。

关键词: 智慧高速公路, 交通气象观测站, 鲁棒优化, 混合整数线性规划, 需求不确定性