找到总成本最小的不相交图

Question

This is an optimization / minimum flow problem. For this directed graph, I would like all vertices to be visited exactly once, but this graph can exist multiple disjoint paths, and each path has constraints on its total cost. The goal of this problem is to minimize the total cost of all disjoint paths.

I only know how to find Dijkstra shortest path, and I am not sure if similar principle can be applied. Please help me out and share your thoughts on this.

Thank you so much!

Answer 1

It sounds to me you are describing a vehicle routing problem, where each route is constrained eg by the vehicle capacity or maximum travel time. Have a look at https://en.wikipedia.org/wiki/Vehicle_routing_problem .