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%.

动态路由发生在客户不知道的情况下，例如实时路由。提出了两种启发式方法来解决平衡动态多旅行商问题（BD-mTSP）。这些启发式代表用于动态（在线、实时）路由的操作（战术）工具。提出了几种类型和范围的动力学。特别注意顺序动态。平衡动态最近车辆启发式 (BD-CVH) 和平衡动态分配车辆启发式 (BD-AVH) 应用于此类动态。该算法适用于广泛的测试实例。出租车服务和仓库中的调色板传输演示了如何在真实场景中使用 BD-mTSP 算法。

BD-mTSP 的连续逼近模型被导出并用作动态路由的战略工具。这些模型使用车辆、客户和动态范围来表达路线长度，而无需运行算法。机器学习方法用于获得回归模型。其中两个模型的平均绝对百分比误差低于 3%。