## 4 Journey Profile Pareto Set Generation
### Inter-Transfer-Zone Objective Contributions (Offline)  
This section outlines how objective criteria contributions are estimated for each journey leg between each pair of transfer zones via each transport mode. For the case of open transport networks, the method is as follows. For each transfer zone, each node in that zone is set as an origin node with an initial arrival time of 0. [PERSON]'s algorithm is executed to find all of the shortest paths from the origin transfer zone to each node in every other transfer zone. The average times and distances to every other transfer zone are used to calculate the required objective criteria contributions. Let \(time(i,j,m)\), \(distance(i,j,m)\) and \(speed(i,j,m)\) denote the average shortest path times, distances and speeds, respectively, from transfer zone \(i\) to transfer zone \(j\) via transport mode \(m\). Letting \(T\) denote the set of transfer zones and \(O\) the set of open transport networks, the open-network inter-transfer-zone objective criteria contributions are calculated as follows. \[cost(i,j,m)=\left( \begin{array}{c}(time(i,j,m)\times timeCost(m,speed(i,j,m))) \\ +(distance(i,j,m)\times distanceCost(m,speed(i,j,m)))\\ +fixedCostPerUse(m)\\ +fixedCostPerDay(m)\\ +tripCost(i,j,m)\end{array} \right),\ \forall(i,j)\in T^{2}|i\
eq j,\ \forall m\in O, \tag{9}\]  
\[time(i,j,m)=time(i,j,m)+responseTime(m),\ \forall(i,j)\in T^{2}|i\
eq j,\ \forall m\in O, \tag{10}\]  
\[CO_{2}(i,j,m)=distance(i,j,m)\times distanceCO_{2}(m,speed(i,j,m)),\ \forall(i,j)\in T^{2}|i\
eq j,\ \forall m\in O, \tag{11}\]  
\[inconvenience(i,j,pedestrian)=time(i,j,pedestrian),\ \forall(i,j)\in T^{2}|i\
eq j, \tag{12}\]  
Figure 2: Transfer zones generated by Algorithm 1 for a transfer-zone sample size of 500. \[\mathit{Calories}(i,j,m)=\mathit{distance}(i,j,m)\times\mathit{ distanceCalories}(m,speed(i,j,m)),\ \forall(i,j)\in T^{2}|i\
eq j,\ \forall m\in O, \tag{13}\]  
where \(\mathit{timeCost}(m,s)\) is the cost per unit time while using transport mode \(m\) at an average speed of \(s\). \(\mathit{distanceCost}(m,s)\) is the cost per unit distance while using transport mode \(m\) at an average speed of \(s\). \(\mathit{fixedCostPerUse}(m)\) is the fixed cost per usage of transport mode \(m\). \(\mathit{responseTime}(m)\) is the response time/set up time to begin using transport mode \(m\). \(\mathit{distanceCO}_{2}(m,s)\) is the CO\({}_{2}\) emission rate per unit distance while using transport mode \(m\) at an average speed of \(s\). \(\mathit{distanceCalories}(m,s)\) is the calories used per unit distance while using transport mode \(m\) at an average speed of \(s\). \(\mathit{fixedCostPerDay}(m)\) is the fixed daily cost associated with transport mode \(m\). Finally, \(\mathit{tripCost}(i,j,m)\) is the average fare associated with a public transport trip between transfer zones \(i\) and \(j\) via transport mode \(m\). In this work, we assume a fixed daily cost model for public transport usage; see Section 6.1. The pre-calculated inter-transfer-zone objective contributions are based on static estimate average speeds of each vehicle type on each edge. Typically, transport network travel-time data come in two varieties, daily averages and real-time data. Once Pareto sets of journey profiles have been generated based on static estimates, the transfer point optimisation procedure that follows is based on real-time speed estimates accounting for current traffic conditions and disruptions. Similarly, the pre-calculated inter-transfer-zone objective contributions for public transport journey legs are based on the scheduled public transport services for the given day, and real-time disruptions can be accounted for in the transfer point optimisation procedure. Note that the inter-transfer-zone objective criteria contributions can also be updated in response to real-time changes in traffic conditions and disruptions in an ongoing update procedure.