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Many networked systems involve multiple modes of transport. Such systems arecalled multimodal, and examples include logistic networks, biomedicalphenomena, manufacturing process and telecommunication networks. Existingtechniques for determining optimal paths in multimodal networks have eitherrequired heuristics or else application-specific constraints to obtaintractable problems, removing the multimodal traits of the network duringanalysis. In this paper weighted coloured--edge graphs are introduced to modelmultimodal networks, where colours represent the modes of transportation.Optimal paths are selected using a partial order that compares the weights ineach colour, resulting in a Pareto optimal set of shortest paths. This approachis shown to be tractable through experimental analyses for random and realmultimodal networks without the need to apply heuristics or constraints.

Partial order approach to compute shortest paths in multimodal networks