The navigation relayed by multiple stations (NRMS) is an advanced cooperative navigation technology which relies on multiple different stations to sequentially guide a vehicle to its destination. This paper addresses the optimal path planning problem for the vehicle navigated by the NRMS technology (OPP-V-NRMS) which is a challenging hierarchical mixed-variable constrained optimization problem involving two coupling levels. To solve OPP-V-NRMS, we present two decoupling methods: the accurate method and the approximation method. The accurate method performs path planning for all possible arrangements, which is accurate but time-consuming. The approximation method only selects a few arrangements for path planning, which achieves a better tradeoff between solution quality and computational cost. In both decoupling methods, a differential evolution based (DE-based) path planning algorithm is proposed for path planning. Comparative experiments show that both methods can find a feasible and high-quality path for the vehicle while the approximation method brings about much lower computational cost.
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