A novel solution to a combinatorial optimization problem in bicycle
sharing systems
Scientists propose a novel approach for finding the best routing paths
for vehicles in charge of bicycle rebalancing

Date:
October 27, 2021
Source:
Tokyo University of Science
Summary:
Bicycle sharing systems have become an attractive option to
alleviate traffic in congested cities. However, rebalancing
the number of bikes at each port as time passes is essential,
and finding the optimal routing paths for the vehicles in
charge of rebalancing constitutes a combinatorial optimization
problem. Now, scientists propose an innovative algorithm that can
find near-optimal solutions more quickly even for a large number
of ports, paving the way for more efficient bicycle sharing systems.



FULL STORY ========================================================================== Traffic congestion has been worsening since the 1950s in large cities
thanks to the exorbitant number of cars sold each year. Unfortunately,
the figurative price tag attached to excessive traffic includes higher
carbon dioxide emissions, more collectively wasted time, and exacerbated
health problems. Many municipalities have tackled the problem of traffic
by implementing bicycle sharing systems, in which people can borrow
bikes from strategically placed ports and ride wherever they want,
as long as they eventually return the bikes to a port, although not
necessarily the one from where the bike was originally obtained.


==========================================================================
As one may or may not immediately notice, this last permission creates a
new problem by itself. Whenever someone borrows a bike and does not make
a round trip with it, an additional bike crops up at the destination port
just as there's a loss of one bike at the origin port. As time passes,
the distribution of bikes across ports becomes unbalanced, causing both
an excessive accumulation of bikes at certain ports and a dearth of bikes
in others. This issue is generally addressed by periodically sending out
a fleet of vehicles capable of transporting multiple bikes in order to
restore ports to their 'ideal' number of bikes.

Much research has been dedicated to the bicycle rebalancing problem using
a fleet of vehicles. Finding the optimal routing paths for the vehicles
is in and of itself a highly complex mathematical problem in the field
of combinatorial optimization. One must make sure that the optimization algorithms used can reach a good-enough solution in a reasonable time
for a realistically large number of ports and vehicles. Many methods,
however, fail to find feasible solutions when multiple constrains are considered simultaneously, such as time, capacity, and loading/unloading constraints for the vehicles.

But what if we allowed the optimization strategy to change the strategies
a little bit to make the best out of difficult situations? In a recent
study published in MDPI's Applied Sciences, a team of scientists suggested
an innovative twist to the routing problem of bicycle sharing systems
using this concept. Led by Professor Tohru Ikeguchi of Tokyo University
of Science, the team comprising PhD student Honami Tsushima from Tokyo University of Science and Associate Professor Takafumi Matsuura from
Nippon Institute of Technology, Japan, proposed a new formulation of the routing problem in which the constraints imposed on the routings can be violated. This enabled using the optimization algorithm for exploring
what is known as the space of "infeasible solutions." Prof. Ikeguchi
explains their reasoning, "In real life, if a work can be completed
through overtime within a few minutes, we would work beyond the time
limit. Similarly, if we are only carrying four bikes and need to supply
five, we would still supply the four we have." Following this line
of thought, the researchers formulated the "soft constraints" variant
of the routing problem in bicycle rebalancing. Using this approach,
instead of outright excluding solutions that violate constraints, these
can be considered valid paths that incur dynamically adjusted penalties
and taken into consideration when assessing possible routings. This
approach enabled the team to devise an algorithm that can make use of
the space of infeasible solutions to speed up the search for optimal or near-optimal solutions.

The researchers evaluated the performance of their method through
numerical experiments with benchmark problems including up to 50 ports and three vehicles. The results show that their strategy could find optimal
or near- optimal solutions in all cases, and that the algorithm could
search both the feasible and infeasible solution spaces efficiently. This paints a brighter future for people in cities with congested traffic in
which bicycle sharing systems could become an attractive solution. As
Prof. Ikeguchi remarks, "It is likely that bike sharing systems will
spread worldwide in the future, and we believe that the routing problem
in bicycle rebalancing is an important issue to be solved in modern
societies." Hopefully, further efforts to improve bicycle sharing systems
will alleviate traffic congestion and make people's lives in big cities healthier and more enjoyable.

========================================================================== Story Source: Materials provided by Tokyo_University_of_Science. Note:
Content may be edited for style and length.


========================================================================== Journal Reference:
1. Honami Tsushima, Takafumi Matsuura, Tohru Ikeguchi. Strategy for
Exploring Feasible and Infeasible Solution Spaces to Solve a
Multiple- Vehicle Bike Sharing System Routing Problem. Applied
Sciences, 2021; 11 (16): 7749 DOI: 10.3390/app11167749 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2021/10/211027122102.htm

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