R5 Multimodal Routing Engine

• R5 Multimodal Routing Engine is a unified multimodal routing architecture that integrates various transport modes using a single graph with mode-specific cost multipliers.
• It generates distinct intermodal alternatives by dynamically adjusting mode weights, offering tailored solutions for both passenger MaaS and freight synchromodality.
• Its flexible objective function enables customizable routing preferences, allowing adaptive responses to real-world urban mobility and logistical constraints.

The R5 Multimodal Routing Engine refers to a new class of routing engine architectures and algorithms designed to seamlessly integrate multiple modes of transport, leverage heterogeneous optimization criteria, and produce practical, interpretable routing solutions in real-world logistical and mobility scenarios. The R5 architecture, as developed in the context of intermodal and synchromodal passenger and freight routing systems, provides flexible, objective-driven, and adaptive routing by merging unified graph modeling, explicit multimodality, objective customization, and robust alternative generation methodologies.

1. Integrated Multimodal Graph and Routing Formulation

The R5 engine is characterized by its use of a single unified multimodal graph, as opposed to layered or pre-segmented networks. In this formulation, the graph represents all traversable routes and segments across different transport modes—car, public transit, walking, biking, freight, etc.—with each edge explicitly annotated by its set of allowed modes. The routing process is performed on this integrated graph, enabling dynamic traversal across available modes without ex-ante selection or manual interchange point specification (Prandtstetter et al., 2020).

Each edge's cost is dynamically computed using a mode-specific multiplier:

$w_i' = w_i \cdot \mu_{\text{mode}(i)}$

where:

• $w_i$ is the intrinsic weight (e.g., travel time or distance) on edge $i$,
• $\mu_{\text{mode}(i)}$ is the user- or system-defined multiplier reflecting the perceived impedance or preference for the particular mode.

The total travel cost for a path is then:

$T = \sum_{i=1}^n w_i \cdot \mu_{\text{mode}(i)}$

where $n$ is the number of edges in the path. Minimization of $T$ yields the optimal multimodal route under the user’s customized cost perception.

2. Real Intermodal Route Alternatives

R5 is notable for generating genuine intermodal alternatives—routes that differ not just in timing but in their underlying modal composition and trade-offs. Instead of outputting trivial variations (e.g., alternate departure times or similar mode splits), the algorithm systematically varies the mode multipliers $\mu_{\text{mode}}$, thereby producing distinct alternatives aligned with user-defined preferences and possible real-world constraints (Prandtstetter et al., 2020). For example, increasing the multiplier for walking relative to transit will produce alternatives that minimize walking legs, favoring transit-heavy combinations.

This approach enables:

• Passenger-focused scenario planning (car+public transit+walk, bike+transit, or car all the way)
• Freight synchromodality, where shipments dynamically switch between trucks, trains, or vessels according to performance metrics and availability

3. Objective Function and Optimization Flexibility

The R5 framework generalizes the route search by making the objective function explicitly customizable. The cost function remains a minimization of perceived travel time, but mode multipliers introduce user or operator value functions directly into the optimization process:

$T = \min \sum_{i=1}^n (t_i \times \mu_i)$

where $t_i$ is the segment’s original travel time and $\mu_i$ is the multiplier for the edge’s mode. This mechanism allows user preferences, accessibility requirements, sustainability incentives, and regulatory considerations to be encoded through simple parameter adjustments, providing an operationally tractable form of multi-criteria optimization within the classical Dijkstra shortest-path context.

4. Application Scenarios: MaaS, Synchromodality, and Specialized Routing

The R5 engine’s unified graph and alternative generation mechanisms lend themselves to two central applications:

• Mobility-as-a-Service (MaaS): Users may specify permissible or preferred modes for certain journey legs. For example, R5 can suggest switching from a personal vehicle to transit at a park-and-ride, then walking to the final destination, with all viable alternatives scored and presented for user choice.
• Synchromodality in Freight: The engine’s flexibility supports real-time freight logistics by dynamically selecting optimal modal handoffs for goods, taking into account evolving network conditions (e.g., traffic or availability).

A specialized showcase in the algorithm’s development is the motorhome routing scenario. Here, R5 produces three tailored alternatives: (1) long-haul motorhome use with transfer to local modes at a parking area; (2) optimized car routing and mode transfer at suitable facilities; (3) direct motorhome routing through potentially suboptimal routes, catering to user willingness for risk or inconvenience (Prandtstetter et al., 2020).

Use Case	Routing Output	Decision Logic Example
Passenger MaaS	Route with mode switches	Multipliers encode walking aversion
Freight Synchromodality	Route with modal transitions	Minimize time, adjust mode weights
Motorhome Routing	3 alternatives considering vehicle access and transfer points	Edge restrictions, parking constraints

5. Theoretical and Algorithmic Principles

The R5 methodology leverages a modified Dijkstra’s algorithm adapted for explicit multimodality. Standard Dijkstra’s shortest path calculation is modified such that only edges that match the allowed set of modes (as selected by the user or system for each stage) are considered at each step. The cost function at each search node dynamically incorporates the active mode multiplier.

This approach is robust to the presence of arbitrary combinations of modes, does not require the specification of interchange points in advance, and supports direct, interpretable trade-offs between alternatives (since each leg’s mode and cost factor are explicit in the returned solutions).

6. Practical Implications and System Integration

The R5 routing engine exemplifies advances in practical routing systems by supporting:

• Real-time intermodal journey planning without excessive preprocessing or mode-specific network segmentation
• Flexible integration with travel demand platforms and urban mobility operators for agile, user-centered recommendations
• Adaptive response to external conditions (e.g., temporary mode restrictions, vehicle size constraints, or policy shifts)

Furthermore, the explicit nature of the mode multipliers and alternative generation process enables easy policy intervention and sensitivity analysis for urban and transportation planners, making R5 architectures attractive for both operational deployment and research.

7. Limitations and Open Research

The R5 framework’s principal limitations are tied to the assumption that cost trade-offs between modes can be fully captured with static or piecewise-constant multipliers. This abstraction may not reflect dynamic, context-dependent utility shifts (e.g., weather-sensitive walking costs, congestion pricing), though the algorithmic machinery can be straightforwardly extended, for instance by incorporating dynamic multipliers or multi-criteria post-filtering.

Challenges also remain in the precise calibration of the user’s perceived mode costs, the computational burden of supporting rich real-time constraints in very large networks, and the necessity for robust, up-to-date multimodal network data.

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In summary, the R5 Multimodal Routing Engine delivers a principled, unified approach to intermodal and synchromodal routing. Its integrated graph representation, mode-annotated cost multipliers, and capacity for true alternative generation constitute a flexible foundation for both passenger MaaS solutions and dynamic freight logistics, with proven adaptability to real-world constraints and operational complexity (Prandtstetter et al., 2020).