Logistics Route Planning in Agent-Based Simulation and Its Optimization Represented in Higher-Order Markov-Chain Networks

Route planning in logistics, in which multiple pickup and delivery positions exist in a road network, is a complicated task with many choices in a path selection and their influences on the following procedures. Solving this task by multi-agent simulations, we examine the route optimization process by monitoring motions in networks based on simple or higher-order Markov chains (MCs). Agent footprints in the networks, which spread over the entire network at the initial phase, converge on small number of edges as the transportation path gets shortened. When we increase the order of MCs in agent mobilities, the MC networks are enlarged and possess a large number of nodes and edges with structural regularity so that one node contains partial trace history, while the optimized route that frequently overlaps edge groups with high transition probabilities is equivalent to a smaller and more noticeable subgraph around a local optimal solution. In other words, this localization of the traces indicates a convergence level in optimization, which can be a measure for route planning in logistics.