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Heuristic Optimal Meeting Point Algorithm for Car-Sharing in Large Multi-modal Road Networks

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Abstract

For several decades, the use of private vehicles has exploded, leading to an increase in traffic congestion, pollution and accidents. Various solutions exist but ride-sharing seems to be the most viable alternative for users in terms of economy, ecology and comfort. Car-sharing can be described as a shared transport system in which users take a common route and vehicle to reach their different, or common, destinations. However, as the authors of point out, in the majority of car-sharing systems proposed today users have to explicitly specify the pickup and drop locations. This research introduces a new version of the car-sahring problem, focusing on finding optimal meeting points (OMP) in large multi-modal road networks. The goal is to automatically define a rendezvous points that ensure fair travel times for the all the users.
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The widespread use of private vehicles has led to traffic congestion,
pollution, and safety concerns. While public transport offers a
solution, not all areas have comprehensive systems, making car-
sharing an attractive alternative. However, current car-pooling
solutions often prioritize profitability over fairness. This research
addresses these issues by optimizing meeting points computation for
car-pooling, emphasizing equitable travel time distribution. The study
introduces a variant of Optimal Meeting Point (OMP) problem,
exploring multimodal networks for efficient solutions.
INTRODUCTION
EXACT SOLUTION ALGORITHM
The main idea behind the algorithm 3 is to reduce the search space of
the OMP. To achieve this, we apply the following pre-processing:
(1) First, we take the node located at the 1/k of the way along the
shortest path between the two users a and b on the side of the
walker, we name this intermediate node x.
(2) Then, we take the node located at the 1/k of the way along the
shortest path between this node xand the destination don the
side of node x, and name this node y.
(3) Then, using the getNodesWithinNNeighbors function, we retrieve
all nodes that are within Nsteps from the node y.
(4) Finally, we give this set of nodes to the Exact Algorithm 2, which
searches for the OMP in this set rather than in the entire graph.
FUTURE WORKS
In future research, we would like to extend the scope of this study by
including more users and other modes of transport, to better reflect
real-world carpooling conditions.
Worst case complexity: Ototal = 3 OD(V logV)
Multi-modal: A road network for pedestrians and a road network for car users. Each of the
networks has different characteristics in terms of topology but also speeds associated with the
edges linking the road intersections.
Optimal Meeting Point (OMP): Meeting point in the combined network for which the two users
take the same time to reach. From this point, the two users can start the carpooling process.
Result: The heuristic algorithm manages to find the OMP 5.01 times faster than the exact solution
algorithm, while having an average relative error close to 1.5 in terms of road intersections.
Julien Baudru & Hugues Bersini
IRIDIA, Université Libre de Bruxelles (ULB), Brussels, Belgium
FARI, AI for the Common Good Institute, Brussels, Belgium
Heuristic Optimal Meeting Point
Algorithm for Car-Sharing in Large
Multimodal Road Networks.
HEURISTIC SOLUTION ALGORITHM
We define two directed weighted graphs, Gw = {V,E} the walking
graph and Gd = {V,E} the driving graph representing the road
networks for each user u.
Let a be the starting point of the walking user uw, b the starting point
of the user ud and d the shared destination point of uw and ud.
The goal is to find the point m (OMP) that minimises the objective
function f in the graph pruned G built thanks to Gw and Gd.
PROBLEM FORMULATION Worst case complexity: Ototal = [2 OD(V logV)] + [3 OD(M logM)]
NetSci Conference, 2024, Québec City, Canada
julien.baudru@ulb.be
Networks data
Average run time over 100
random iterations
Average percent of correct
solutions depending on N
value over 100 random
iterations
RESULTS
The algorithm is particularly effective for road networks with large
numbers of nodes |G| > 10 000.
Video
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