Mobility as a Service: An exploration of exact and heuristic algorithms for a new multi-modal multi-objective journey planning problem

Mobility as a Service (MaaS) is a term coined for the development and implementation of multi-modal trip planner recommendation systems. Multi-modal journeys can include public transport, private transport and hire-able e-scooters which can beneficially augment public transport journeys. This study proposes and tackles a new and more general multi-modal multi-objective journey planning problem than considered previously. Our aim is to generate Pareto sets of multi-modal journeys which minimise the objectives of cost, travel time, inconvenience, CO₂ emissions, and calorie expenditure, as well as find journeys that optimally balance the trade-offs between them. Commuters can then choose between green, cheap, fast, car-free or convenient journeys. This work proposes implicit enumeration and heuristic algorithms which are analysed in terms of their theoretical time complexity, empirically in terms of solution time and optimality gap using a series of Manhattan and random structure transport networks. We show that our algorithms can generate solutions of equal quality to RAPTOR—a prominent existing journey planning algorithm. For this problem we reveal that the number of network nodes is a huge computational bottleneck, leading to the suggestion that future research can benefit from limiting the number of network nodes that are considered as transfer points. While our heuristic can generate good quality Pareto sets quicker than the enumeration procedure for the largest instances considered, we show that the enumeration procedure with pruning rules can still be the most effective strategy for this particular problem.