
tions as arcs, with travel times defined by a mono-
tonic function f
e
(t) of the departure time. This en-
sures consistent travel times and avoids logical incon-
sistencies. However, the model assumes deterministic
travel times, and does not account for delays and un-
certainties inherent in real-world systems. Since PT
is often affected by operational disruptions, delays,
and fluctuating traffic conditions, the time-dependent
approach may struggle to accurately capture the real-
time dynamics of transport networks. Conversely, the
time-expanded model (Pyrga et al., 2008) introduces
a temporal dimension by duplicating each node for
every vehicle departure and arrival event, offering a
more detailed representation of schedules and trans-
fers. However, a major drawback is the substantial in-
crease in graph size, as the number of nodes and arcs
grows exponentially with the number of time inter-
vals considered. This makes the model computation-
ally expensive and challenging to scale for large, real-
world networks. Despite these limitations, the time-
expanded model is particularly valuable for capturing
variable schedules and the multimodal nature of jour-
neys (Bast et al., 2015; Lienkamp and Schiffer, 2024;
Goel et al., 2016).
This study presents an innovative approach to
route planning, introducing additional considerations
associated with the integration of soft and active mo-
bility. By incorporating both SSAM and PSAM into
a generic model capable of accommodating any num-
ber of SAM, the proposed approach enhances flexi-
bility in selecting transport modes throughout a jour-
ney. The challenges are then to manage transitions
between personal and shared SAMs and optimize
their usage based on the user’s travel requirements.
This approach demands a more nuanced analysis of
transport mode choices, temporal constraints, transfer
times, and the feasibility of journey continuity, par-
ticularly for certain SAMs that require specific autho-
rizations, such as bringing a bicycle onto a bus. This
work forms part of the ”Mon Trajet Vert” (Mon Trajet
Vert, 2025) initiative, which aims to provide dynamic,
multimodal, and sustainable route planning solutions
tailored to the specific needs of students. To ensure
the essential punctuality demanded by students with
strict time constraints and to address the temporal
complexity and multimodal integration of intermodal
journey planning, this work adopts a time-expanded
model as an appropriate approach. The problem is
described in Section 2, along with the correspond-
ing modeling approach 3. The algorithm developed
to solve it is detailed in Section 4. Its results are given
in section 5, using real-world data derived from stu-
dents’ schedules, offering a practical alternative to the
random data generation methods often employed in
existing studies. Finally, section 6 concludes the pa-
per by presenting perspectives and directions for fur-
ther research.
2 PROBLEM DESCRIPTION
The main challenge of this research is to design a
route planning system for the students, that is able of
seamlessly integrating various modes of SAM within
the multimodal solution of the PT. This includes
the integration of SSAM, which requires availability
nearby, and PSAM, that provides flexibility without
the need for retrieval. We propose to categorize SAM
into two types:
• Heavy SAM (HSAM) corresponds to devices
such as bicycles or scooters, which are not always
allowed on PT and cannot be carried in a bag. For
instance, trains and trams often have designated
areas for hanging bicycles. When these spaces
are full, boarding the train with a bicycle is no
longer permitted. Similarly, during peak passen-
ger traffic times, boarding public transport with an
HSAM may be restricted.
• Light SAM (LSAM) is the rollerblades or skate-
boards, and are devices that are unconditionally
allowed on PT and can be easily combined with
HSAM.
Several assumptions are considered in this work:
1. SSAM lies in the HSAM category.
2. We cannot use two HSAM simultaneously, nor
carry one while using the other.
3. PSAM can be Heavy (HPSAM) or Light (LP-
SAM).
4. Because of assumption 1, 2, and 3, SSAM cannot
be used with HPSAM. Indeed, it is useless for a
user that already have a personal bicycle to rent
another bicycle.
Each student has a specific request type, which
can be categorized as either campus-to-home or
home-to-campus. This distinction allows for tailored
optimization of route planning:
• For a home-to-campus request, the objective is to
maximize the departure time while guaranteeing
arrival at a fixed time, such as the start of classes.
• For a campus-to-home request, the goal is to min-
imize the arrival time while respecting a fixed de-
parture time, such as the end of classes or activi-
ties.
Given that our target audience is students, the re-
liability of routes becomes a crucial consideration for
Multimodal Route Planning Integrating Soft Mobility: A Real-World Case Study for Student Mobility
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