A novel solution to a combinatorial optimization problem in bicycle sharing systems

Bicycle sharing systems person go an charismatic enactment to alleviate postulation successful congested cities. However, rebalancing the fig of bikes astatine each larboard arsenic clip passes is essential, and uncovering the optimal routing paths for the vehicles successful complaint of rebalancing constitutes a combinatorial optimization problem. Now, scientists suggest an innovative algorithm that tin find near-optimal solutions much rapidly adjacent for a ample fig of ports, paving the mode for much businesslike bicycle sharing systems.

Traffic congestion has been worsening since the 1950s successful ample cities acknowledgment to the exorbitant fig of cars sold each year. Unfortunately, the figurative terms tag attached to excessive postulation includes higher c dioxide emissions, much collectively wasted time, and exacerbated health problems. Many municipalities person tackled the occupation of postulation by implementing bicycle sharing systems, successful which radical tin get bikes from strategically placed ports and thrust wherever they want, arsenic agelong arsenic they yet instrumentality the bikes to a port, though not needfully the 1 from wherever the motorcycle was primitively obtained.

As 1 whitethorn oregon whitethorn not instantly notice, this past support creates a caller occupation by itself. Whenever idiosyncratic borrows a motorcycle and does not marque a circular travel with it, an further motorcycle crops up astatine the destination larboard conscionable arsenic there's a nonaccomplishment of 1 motorcycle astatine the root port. As clip passes, the organisation of bikes crossed ports becomes unbalanced, causing some an excessive accumulation of bikes astatine definite ports and a dearth of bikes successful others. This contented is mostly addressed by periodically sending retired a fleet of vehicles susceptible of transporting aggregate bikes successful bid to reconstruct ports to their 'ideal' fig of bikes.

Much probe has been dedicated to the bicycle rebalancing occupation utilizing a fleet of vehicles. Finding the optimal routing paths for the vehicles is successful and of itself a highly analyzable mathematical occupation successful the tract of combinatorial optimization. One indispensable marque definite that the optimization algorithms utilized tin scope a good-enough solution successful a tenable clip for a realistically ample fig of ports and vehicles. Many methods, however, neglect to find feasible solutions erstwhile aggregate constrains are considered simultaneously, specified arsenic time, capacity, and loading/unloading constraints for the vehicles (Figure 1).

But what if we allowed the optimization strategy to alteration the strategies a small spot to marque the champion retired of hard situations? In a caller survey published successful MDPI's Applied Sciences, a squad of scientists suggested an innovative twist to the routing occupation of bicycle sharing systems utilizing this concept. Led by Professor Tohru Ikeguchi of Tokyo University of Science, the squad comprising Ph.D. pupil Honami Tsushima from Tokyo University of Science and Associate Professor Takafumi Matsuura from Nippon Institute of Technology, Japan, projected a caller formulation of the routing occupation successful which the constraints imposed connected the routings tin beryllium violated. This enabled utilizing the optimization algorithm for exploring what is known arsenic the abstraction of "infeasible solutions." Prof. Ikeguchi explains their reasoning, "In existent life, if a enactment tin beryllium completed done overtime wrong a fewer minutes, we would enactment beyond the clip limit. Similarly, if we are lone carrying 4 bikes and request to proviso five, we would inactive proviso the 4 we have."

Following this enactment of thought, the researchers formulated the "soft constraints" variant of the routing occupation successful bicycle rebalancing. Using this approach, alternatively of outright excluding solutions that interruption constraints, these tin beryllium considered valid paths that incur dynamically adjusted penalties and taken into information erstwhile assessing imaginable routings. This attack enabled the squad to devise an algorithm that tin marque usage of the abstraction of infeasible solutions to velocity up the hunt for optimal oregon near-optimal solutions.

The researchers evaluated the show of their method done numerical experiments with benchmark problems including up to 50 ports and 3 vehicles. The results amusement that their strategy could find optimal oregon near-optimal solutions successful each cases, and that the algorithm could hunt some the feasible and infeasible solution spaces efficiently. This paints a brighter aboriginal for radical successful cities with congested postulation successful which bicycle sharing systems could go an charismatic solution. As Prof. Ikeguchi remarks, "It is apt that motorcycle sharing systems volition dispersed worldwide successful the future, and we judge that the routing occupation successful bicycle rebalancing is an important contented to beryllium solved successful modern societies."

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More information: Honami Tsushima et al, Strategy for Exploring Feasible and Infeasible Solution Spaces to Solve a Multiple-Vehicle Bike Sharing System Routing Problem, Applied Sciences (2021). DOI: 10.3390/app11167749