Accelerating value function approximations for dynamic dial-a-ride problems via dimensionality reductions

As the success of ride-sharing mobility service providers shows, customer demand for shared mobility services is increasing. The availability of mobile devices enables the constant accessibility of mobility apps and the immediate placement of transport requests. To provide such a dynamic dial-a-ride service, an effective control of the fleet is necessary. One promising solution approach is the value function approximation (VFA), which on the one hand convinces through good performance, but on the other hand also stands out through fast response times for a request. Training a VFA can be a challenging task since, among other things, the dimensionality of the state space plays a decisive role. If many variables to describe a state are used, a high amount of information can produce good performance after completion of the learning process. If the state space is too high-dimensional, there is also a risk that the method will not be able to find a reasonable solution. In contrast, if the number of variables is reduced, the learning speed can be accelerated, but the eventual performance may suffer from the associated loss of information. Furthermore, not all variables are equally relevant, as they contain different amounts of information. This paper presents a hybrid strategy, temporarily lowering the dimensionality of the problem using dimension reduction methods and subsequently increasing it by mapping the lower-dimensional state representations back onto a high-dimensional state space in order to exploit the advantages of both space dimensionalities. VFA in itself results in competitive performance for the dynamic dial-a-ride problem with shared rides. The proposed hybrid state representation can outperform the reference state representations by 3%, which corresponds to a meaningful acceleration in VFA learning speed.