## 6 Results
### ML-TZSA Query Response Results  
Figure 8 provides average query response information based on 2000 commuter queries, each varying by origin, destination and departure time. The top row of bar charts provides the average number of non-dominated journey profiles generated and average number of non-dominated multi-modal journeys generated from those journey profiles, for a range of different transfer-zone sample sizes. The bottom row of bar charts provides corresponding average query times expressed in orders of magnitude of seconds (1 = 10 s, 0 = 1 s, \(-\)1 = 0.1 s, \(-\)2 = 0.01 s, \(-\)3 = 0.001 s). The first column limits the available transport modes to walking and public transport; for this we include results for RAPTOR [9]. The second column limits the available transport modes to walking, public transport and e-scooters. For this, we include results for RAPTOR-ES, which is RAPTOR where e-scooters can be used via e-scooter racks at the beginning and/or end of public transport journeys as well as to make connections between consecutive public transport services. The third column limits the available transport modes to walking, public transport, e-scooters and taxis. Figure 8 reveals several general trends. The average journey profile Pareto set sizes increase the more transport modes there are available, as do average total query times. On average, half of the journey profiles lead to non-dominated journeys, which can be attributed to the aggregated and approximate nature of the journey profile generation procedure with respect to exact query departure times, origin and destination locations, but which are accounted for in the transfer point and path optimisation procedure. Average total query times remain between 0.1 s and 10 s in all cases, i.e., acceptable for real-time applications. The largest average total query times are 3.34 s for RAPTOR-ES (for the case of walking, public transport and e-scooters being available) and 3.21 s for ML-TZSA (10) (for the case of walking, public transport, e-scooters and taxis being available). Figure 8 also shows that ML-TZSA average total query times are somewhat independent of transfer-zone sample size. Although the number of solutions generated increases with transfer-zone sample size, the time required to optimise the paths and transfer points of individual journey profiles decreases. The transfer point solution space, constrained by the transfer-zone sequences, decreases within increasing transfer-zone sample size. Average individual journey profile transfer point optimisation times range between 0.575 s for the case of 10 transfer zones and 0.0189 s for the case of 500 transfer zones. This is a positive result, meaning that we need not worry about finding a compromise transfer-zone sample size and simply make it as large as possible. The bottleneck regarding the maximum transfer-zone sample size is the memory space required to store the pre-processed information, which becomes unmanageable for a current standard desktop computer for transfer-zone sample sizes in excess of 500. For the case of walking, public transport and e-scooters being available, ML-TZSA can generate Pareto sets of journey profiles in a time ranging from 1.4 to 10.8 ms. Transfer point optimisation accounts for the vast majority of total query time. Figure 8: Average numbers of solutions and query times for ML-TZSA and RAPTOR methodologies for different sets of available modes, based on 2000 examples, commuter queries. Figure 8 showed that ML-TZSA can generate many more solutions than two different versions of RAPTOR in roughly equal query times. The main reason for this is that RAPTOR's objective is to minimise travel time and transfers, which is an objective function that generally characterises a smaller Pareto set of journeys. Figure 9 provides results for a comparison between ML-TZSA and RAPTOR based on the best objective values found for each criteria for each of the 2000 test queries.