Combinatorial models for optimisation of placement of refuelling stations and routing for alternative fuel vehicles in road network

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Alternative fuel vehicles (AFV's), in particular, electric and hybrid vehicles, play an increasing role in road transport networks. Despite their advantages, currently there are many challenges associated with their usage. For example, electric vehicles usually have a relatively short cruising range, require significant battery charging time, and normally are attached to the existing capacities of the electric grid. In general, a strong interest in development of AFV's and corresponding technologies is motivated by limited resources of hydrocarbons and large-scale environmental issues associated with usage of internal combustion engines. The main ideas behind AFV's are to have them more energy efficient, environmentally friendly and, whenever possible, using renewable energy resources. Problems and challenges associated with AFV's and corresponding technologies include where and how to fuel AFV's, how to use them in an efficient way, and how to make them publicly adopted. The main objective of this PhD project is to develop new mathematical models and combinatorial optimisation techniques for smart and efficient development of road network infrastructure for navigation of vehicles using new types of energies, e.g. electric, biofuel, hydrogen, and to advise on efficient routing with respect to the existing infrastructure. This will be based on development of more subtle mathematical models using graphs and digraphs and done by algorithmically solving the corresponding combinatorial optimisation problems, obtaining related analytical and structural results. We will examine new models on weighted graphs and digraphs using different types of dominating set concepts, subsequently developing new methodologies to provide efficient and effective algorithmic solution techniques. Special attention will be paid to scaling of the models to large-size road networks.