Dynamic routing occurs when customers are not known in advance, e.g. for real-time routing. Two heuristics are proposed that solve the balanced dynamic multiple travelling salesmen problem (BD-mTSP). These heuristics represent operational (tactical) tools for dynamic (online, real-time) routing. Several types and scopes of dynamics are proposed. Particular attention is given to sequential dynamics. The balanced dynamic closest vehicle heuristic (BD-CVH) and the balanced dynamic assignment vehicle heuristic (BD-AVH) are applied to this type of dynamics. The algorithms are applied to a wide range of test instances. Taxi services and palette transfers in warehouses demonstrate how to use the BD-mTSP algorithms in real-world scenarios. Continuous approximation models for the BD-mTSP's are derived and serve as strategic tools for dynamic routing. The models express route lengths using vehicles, customers, and dynamic scopes without the need of running an algorithm. A machine learning approach was used to obtain regression models. The mean absolute percentage error of two of these models is below 3%.

翻译：当客户事先不为人知时,就会出现动态路由,例如,实时路由。建议使用两种超常路由,解决平衡的动态多个流动销售人员问题(BD-mTSP)。这些路由是动态(在线、实时)路由的操作(战术)工具。提出了几种动态类型和范围。特别注意顺序动态。平衡的动态最接近的车辆超常(BD-CVH)和平衡的动态分配车辆超常(BD-AVH)应用到这种动态。这些算法应用到广泛的测试实例中。出租车服务和仓库的调色板传输展示了如何在现实世界情景中使用BD-mTSP算法。BD-MTSP的连续近似模型是衍生出来的,并作为动态路由的战略工具。模型表示使用车辆、客户和动态范围而不需要使用算法的路线长度。机器学习方法用于获取回归模型。两种模型的绝对百分比错误低于3 %。