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Article

A Simulated Annealing for Optimizing Assignment of E-Scooters to Freelance Chargers

1
Centre for Accident Research and Road Safety, Queensland University of Technology, Brisbane 4059, Australia
2
School of Economics and Management, Fuzhou University, Fuzhou 350105, China
3
Department of Civil Engineering, College of Engineering, King Saud University, P.O. Box 2454, Riyadh 11451, Saudi Arabia
4
Qatar Transportation and Traffic Safety Center, College of Engineering, Qatar University, Doha P.O. Box 2713, Qatar
5
Department of Civil and Architectural Engineering, College of Engineering, Qatar University, Doha P.O. Box 2713, Qatar
*
Author to whom correspondence should be addressed.
Sustainability 2023, 15(3), 1869; https://doi.org/10.3390/su15031869
Submission received: 18 November 2022 / Revised: 9 January 2023 / Accepted: 17 January 2023 / Published: 18 January 2023
(This article belongs to the Section Sustainable Transportation)

Abstract

:
First- and last-mile trips are becoming increasingly expensive and detrimental to the environment, especially within dense cities. Thus, new micro-mobility transportation modes such as e-scooter sharing systems have been introduced to fill the gaps in the transportation network. Furthermore, some recent studies examined e-scooters as a green option from the standpoint of environmental sustainability. Currently, e-scooter charging is conducted by competitive freelancers who do not consider the negative environmental impact resulting from not optimizing the fuel efficiency of their charging trips. Several disputes have been recorded among freelance chargers, especially when simultaneously arriving at an e-scooters location. The paper aims to find the optimal tours for all chargers to pick up e-scooters in the form of routes, such that each route contains one charger, and each e-scooter is visited only once by the set of routes, which are typically called an E-Scooter-Chargers Allocation (ESCA) solution. This study develops a mathematical model for the assignment of e-scooters to freelance chargers and adapts a simulated annealing metaheuristic to determine a near-optimal solution. We evaluated the proposed approach using real-world instances and a benchmark-simulated dataset. Moreover, we compare the proposed model benchmark dataset to the baseline (i.e., state-of-practice). The results show a reduction of approximately 61–79% in the total distance traveled, leading to shorter charging trips.

1. Introduction

Micro-mobility modes, such as dockless e-scooter systems, have recently emerged as an alternative mode of transportation, filling the gap in transportation systems. This modern transport mode gained momentum in 2018 because e-scooters are energy-efficient, environmentally friendly, easy to handle, and compact. There are many advantages to e-scooter use, including lower costs, environment friendliness, exercise and fitness, and improved accessibility to other transport systems. According to the National Association of City Transportation Officials, more than 38.5 million rides were taken with e-scooters in 2018 in the U.S. Furthermore, e-scooters are now operational in over 65 major U.S. cities [1].
Micro-mobility, such as an e-scooter, is a useful means of transportation that provides sustainability in the face of the current hazards presented by an over-growing population, traffic congestion, and greenhouse gas impacts [2]. Environmental pollution and carbon dioxide emissions can be significantly minimized by utilizing micro-mobility rather than regular motor vehicles [3,4]. Furthermore, replacing private vehicle trips with micro-mobility promotes sustainability by lowering gas emissions and traffic accidents [5]. In [6], the relation between the E-scooters and characteristics of sustainable urban development was examined, such as land use type and walkability. Recently, research has examined e-scooters as a green choice in terms of environmental sustainability [7,8].
Brisbane, Australia, recorded more than one 50,000 trips commuted by e-scooters within the first two weeks of launching the service; after four months, in mid-November 2018, the number of trips increased to one million. This highly significant rise in demand is backed by a vast, un-noticed infrastructure network designed to sustain charged and available scooters at all times. Currently, e-scooter charging primarily depends on freelancers who compete without considering the negative environmental impact resulting from not optimizing their charging-trip fuel-efficiency. Freelance chargers spend significant time searching for e-scooters because of the competitive nature of the profession and the inaccuracy of the location-finders of some e-scooters [9]. The charger’s task is to locate e-scooters that need to be charged via the app and drive them home for charging. Although simple, there are two significant problems with this approach. First, the current practice is focused on a first-come-first-serve basis and can only be verified when a charger arrives at the scooter’s location and has been unlocked with the app. This aspect of app usage results in rivalry and causes the chargers to travel long distances without first verifying the availability of the e-scooter in order to upgrade the online application. Many disputes between freelance chargers have been reported when they have simultaneously arrived at an e-scooter [10]. The rivalry between chargers can result in physical violence and threatens the safety of the operation [11]. Second, due to the nature of their tasks, freelance chargers are considered independent contractors, as defined by the “gig” economy. While this gig economy provides the chargers with flexibility and independence, it also does not guarantee a minimum wage or maximum hours [12].
We hypothesized that matching chargers with an optimal assignment of e-scooters could eliminate competition and possibly avert physical violence. It could also reduce the charging and rental costs of e-scooters that could be converted into increased income for the chargers. E-scooter assignment has been widely discussed, and potential models have been implemented in various other operations, such as e-bike and electric vehicle sharing systems. Ref. [13] proposed two approaches to solving the problem of charging shared e-bikes. Ref. [14] explored electric vehicle charging methods at the lowest possible cost for a practical vehicle sharing system. They developed a queuing network model using a nonlinear optimization system with fractional quadratic constraints. Ref. [15] suggested a model that would fit battery locations with electric taxis. Ref. [16] created a model for assigning vehicle blocks to busses in public transit, considering various temporal and spatial constraints. Ref. [17] developed a two-stage heuristic algorithm to solve the school bus routing problem. Ref. [18] investigated the optimal locations for e-scooter sharing stations and developed a mathematical model formulated as a multi-objective topic with maximum utility at minimum cost. However, they did not study the assignment of freelance chargers to e-scooter locations.
To the best of our knowledge, there have been few studies on e-scooter planning and scheduling problems in the literature, and none of these studies have addressed the problem of integrating e-scooter locations and charger-assignment. In consultation with E-Scooter-Chargers Allocation (ESCA), an e-scooter sharing company in Brisbane, Australia, we found that the allocation problem can be static or dynamic, and chargers use their private vehicles to collect e-scooters for both. The static ESCA activity assumes the e-scooter and charger positions are either the same or are slightly apart. In the dynamic ESCA activity, the positions of the e-scooters and chargers are constantly changing, significantly influencing the model and affecting the potential solution. This study formulates the static ESCA activity as a mixed-integer linear programming (MILP) model. To overcome the time computation of MILP, we adapted the simulated annealing (SA) algorithm to find an effective solution to the assignment problem.

2. Problem Statement and Formulation

In this study, a real-world assignment problem with a large number of variables was formulated as an MILP model [19], which is a combinatorial optimization problem that makes use of exact solution techniques or commercial optimization software packages (e.g., IBM ILOG-CPLEX), intractable due to unacceptably long CPU (Central Processing Unit) time and memory requirements [20]. For this reason, we developed a specific SA metaheuristic algorithm to solve the ESCA problem, where the SA approximates the optimal global solutions in the large search space of the optimization problem. The problem of assigning e-scooters to chargers was adapted as a “real-world assignment situation”, as generally known in operations research. It is a trade-off between finding an effective solution and converging in a short time. This problem is formulated using an objective function and constraints, considering both computational time and the quality of the solution, targeting a near-optimal solution while assigning jobs ( n ) to the number of individuals ( m ).
In this study, we adopt the SA algorithm to solve the assignment problem between freelance chargers and e-scooters, in which each e-scooter is assigned to only one charging freelancer at a time, considering predefined constraints.
Consider the complete graph   G = V , E , where V is the set of nodes with two subsets S and   R ; S V and   R V , and E is the edge set of graph G. G is adapted to be the route network, and V is the number of locations. The ESCA activity is defined on a set of e-scooters S in the system and R is the set of chargers, where |S| = s, and |R| = r and assume that s ≥ 1 and r ≥ 1, unless otherwise stated, select a subset of chargers s S based on their location. The key purpose of this suggested solution is to evaluate the e-scooter location based on obtaining a successful assignment for the location to develop an efficient e-scooter assignment to a charger. The objective function consists of two types of costs, the chargers’ travel distance to collect the e-scooter and the cost of adding new freelance chargers. The cost of recruiting new chargers is included to penalize the selection of more chargers than needed to charge the e-scooters.
The ESCA aims to find the optimal tours for all chargers to pick up e-scooters in the form of routes, such that each route contains one charger, and each e-scooter is visited only once by the set of routes, which are typically called an ESCA solution. Additionally, there is only one charger located at charger location i, and each charger must return to their original location. The potential tours occur within a predetermined interval to minimize the total cost of all tours. In addition, constraints are imposed on the number of e-scooters in a tour, where the upper and lower boundaries for the number are denoted by U and L , respectively. In this study, based on the current state-of-practice for all scenarios, we set the maximum number of e-scooters collected by each charger to six (based on the number of charging adapters received from the e-scooter operator). For each charger,   o i is the number of nodes (e-scooters) visited on the charger’s path from the origin to node i; 1 o i U for all i 2 and if x i k k = 1 then L o i U must be satisfied. For each   i , j     E , we define one binary variable x i j k which takes the value 1 if one charger departs from the kth node (location) and travels through the arc (edge) i j , and 0 if otherwise. In the ESCA solution approach, the six charged e-scooters are returned to a single position, and hence, the solution does not achieve the redistribution of the charged e-scooters.
Figure 1 depicts an illustrative example of the ESCA, with seven chargers and twenty-four e-scooters. In this example, there is only one e-scooter at each location, and each charger collected a maximum of six e-scooters. From Figure 1, we can find four chargers have collected the twenty-four e-scooters, and the three chargers are not selected. The solution does not consider the redistribution of the charged e-scooters.

2.1. Notation

The mathematical notation of the ESCA problem formulation is presented below, including the objective function and constraints.
s : number of e-scooters
r : number of chargers
R : set of charger vertices, R = 1 , . ,   r
S : set of e-scooter pickup vertices, S =   r + 1 , r + 2 , ,   n
V : set of all vertices, V = R S ; V = 1. ,   n
E : set of all arcs i j , E = V × V
c i j : transportation costs traveling from i to j ; i = 1 V and j = 1 V
U : highest number of e-scooters allocated to a charger within a sub-tour.
L : lowest number of e-scooters allocated to a charger within a sub-tour.
o i : number of nodes (e-scooters) visited on the charger’s path from origin to node i.
x i j k : a binary variable that equals 1 if arc i j is used and belongs to the k th charger; 0, if otherwise.

2.2. Objective Function

Equation (1) is specified to minimize relevant e-scooter charging costs. Two expense words are used in the objective function; the expense of distances between the positions of e-scooters and freelancers, and the cost of adding a new freelancer. The first term shows the traveling costs in the two directions ( c k j , c j k ) (pick up and deliver the e-scooters), while the second term shows the costs of adding a new freelancer ( c i j ).
x k j k : a binary variable that equals 1 if arc k j is used and belongs to the k th charger; otherwise, it equals zero.
x j k k : a binary variable that equals 1 if arc j k is used and belongs to the k th charger; otherwise, it equals zero.
f = M i n k = 1 r j = r + 1 n c k j x k j k + c j k x j k k + k = 1 r i = r + 1 n j = r + 1 n c i j   x i j k

2.3. Constraints

Equation (2) constraints that only one charger departs from each charger location; k  R .
j = r + 1 n x k j k = 1   k R  
Equation (3) constraints that each e-scooter can only be visited once
k = 1 r x k j k + k = 1 r i = r + 1 n x i j k = 1   j S
Equation (4) ensures that the number of chargers in the inbound direction equals the outbound direction. This means that, at each location, the number of chargers who deliver and send e-scooters must be the same at each location. In this case, using Equation (2), the number of chargers in each direction is one.
x k j k + i = r + 1 n x i j k x j k k i = r + 1 n x j i k = 0 ,   k R , j S  
Equation (5) requires that the charger location nodes respect that the number of chargers in the outbound direction at the origin (charger start point) equals the number of chargers in the inbound direction at the same origin. In this case, based on Equation (2), the number of chargers in both directions is one.
j = r + 1 n x k j k j = r + 1 n x j k k = 0   k R
Equation (6) indicates the limitations on the maximum number,   U , of e-scooters picked up in each tour; where, if i is the first node on the tour, then the initial value of nodes (e-scooters) visited on the charger’s path from the origin to node i, O i is 1.
O i + U 2 k = 1 r x k i k k = 1 r x i k k U 1   i S
Equation (7) displays the limitations on the minimum number, L , of e-scooters picked up in each tour; where, if i is the first node on the tour, then the initial value of nodes (e-scooters) visited on the charger’s path from the origin to node i,  O i is 1.
O i + k = 1 r x k i k + 2 L k = 1 r x i k k 2   i S .
Equation (8) prevents each charger from picking up only one e-scooter during the whole tour; therefore, tours with only one e-scooter picked up are not allowed.
k = 1 r x k i k + k = 1 r x i k k 1   i S .
Equations (9) and (10) are sub-tour elimination constraints that break all sub-tours of e-scooter nodes in which closed sub-tours are made for each charger.
O i O j + U k = 1 r x i j k U 2 k = 1 r x j i k U 1 ; i j , i ,   j S .  
x i j k 0 , 1 , i ,   j V   a n d   k R  

3. The SA-Based Assignment Algorithm

Finding the optimal solution for most complex optimization problems is a highly challenging task, and, in many cases, impossible. As a problem increases in complexity, the search space for the optimal solution of the problem exponentially increases with the increase in the space of the states. Even with modern computing capabilities, large computation times are still needed to search the entire space for possible solutions. Metaheuristic techniques tend to overcome this problem by providing heuristics to guide the search process, thereby improving its efficiency in reaching near-optimal solutions within a reasonable time. Metaheuristic approaches have proven their value in solving many complex problems, such as scheduling [21,22,23]. According to [24], four aspects should be considered when comparing metaheuristic techniques:
  • the solution representation
  • the neighborhood structure
  • the local search method within the neighborhood
  • acceptance-reject criteria
These algorithms adapt the iterative improvement mechanisms, in which each iterate moves toward the solution by progressive approximation. This iterative process stops if there is no improvement in the objective function (reaching either the local minimum or maximum value). SA is among the most successful metaheuristic, and local search techniques are used to solve combinatorial optimization problems using mathematical techniques to obtain an optimal solution for complex problems by exhaustive search methods [25]. SA is a probabilistic method to obtain the approximated global optimum for a given minimum or maximum objective function, and is extensively used, with positive results. SA searches the solution space and avoids being trapped in the local optimum [26]. It starts with an annealing temperature T associated with a proposed preliminary solution as the current solution. Then, it updates the solution by searching in the neighborhood of the preliminary solution and moving toward the solution one step at a time by progressive approximation. This is accomplished by calculating the difference (∆) between the value of the objective function of the preliminary solution, f(current solution), and the value of the new solution, f(new solution), and deciding if the new step (i.e., new solution) is acceptable or not; ∆ = f(new solution)f(current solution). If ∆ is less than zero, then the new solution is acceptable (for minimization problems); otherwise, the SA accepts the new solution with the probability of 1 1 + exp Δ / T where T is the temperature to be reduced through iterations using the cooling (decreasing) factor α.
The environment of the ESCA problem is dynamic, where the number of e-scooters that need to be charged is changeable with time, especially in the peak hours. Furthermore, charger availability is changeable from time to time. Hence, we need a good and fast solution which can fit into this dynamic and does not require large computational resources. Based on these reasons, SA was selected to solve the proposed problem under these criteria. SA is one of the most common metaheuristic approaches and has been successfully used to solve the traditional capacitated vehicle routing problem (VRP) with multi-depots and its variants [27,28,29,30], where the ESCA problem is highly related to the capacitated VRP with multi-depots.
Encoding the ESCA problem in a suitable form for the SA is the most important step in the implementation process. We established two lists, one of all the chargers and another of all the e-scooters. The first charger in the chargers list was assigned the first six e-scooters in the e-scooters list. In other words, the mth charger in the chargers list was assigned the e-scooters with positions from 6 m 1 + 1 to 6 m in the e-scooters list.
At the beginning of the SA, we randomly initialized two lists of e-scooters and chargers, as shown in Figure 2. Each charger was assigned a maximum of six e-scooters (based on the number of charging adapters received from the e-scooter operator). The objective was to minimize the number of freelance chargers used. The number of chargers needed was calculated as n u m b e r   o f   e s c o o t e r s   n e e d   c h a r g i n g 6 , where ⌈ ⌉ is the ceiling function. For example, for eight e-scooters and three chargers, we need 8 6 = 2 chargers out of the three. As shown in Figure 3, the third charger was not assigned to an e-scooter.
In the implementation, the charger and e-scooter lists were set up with the proposed objective function. We searched the solution space in the proposed SA by repeatedly swapping chargers within the charger list and e-scooters within the e-scooter list, and re-evaluating the objective function. The swapping procedure is termed non-adjacent pairwise interchange (NAPI). As shown in Figure 4, NAPI was used to swap two non-adjacent elements, i   and   j , within the given list.
As presented in Algorithm 1, the SA guided the above search to find a near-optimal solution.
Algorithm 1. Procedure of the proposed SA for E-Scooter-Charger Allocation
  • Create an initial solution
    1.1
    Randomly set the chargers in the charger list
    1.2
    Randomly set the e-scooters in the e-scooter list
    1.3
    Evaluate the objective function using the initial solution (initial assignment)
  • Set the algorithm parameters
    2.1
    Set the initial temperature, T
    2.2
    Set the cooling (decreasing) parameter, α
    2.3
    Set the maximum number of the inner loop iterations (M_ILC)
    2.4
    Set the maximum number of the outer loop iterations (M_OLC)
  • Set the outer loop counter O.L.C. = 1
  • While OLC < M_OLC
    4.1
    Set the inner loop counter I.L.C. = 1
    4.2
    While ILC < M_ILC
    4.2.1
    Swap the chargers within the charger list using non-adjacent pairwise interchange (NAPI).
    4.2.2
    Swap the e-scooters within the e-scooter list using NAPI
    4.2.3
    Evaluate the objective function using the new lists
    4.2.4
    Metropolis-Hastings
    4.2.4.1
    If the current solution is better than the previous, increment the I.L.C. and go to Step 4.2
    4.2.4.2
    Accepting the new solution if the prior solution is greater than the current solution with probability 1 1 + e x p Δ T increment I.L.C. and go to step 4.2.
    4.2.4.3
    Otherwise, reverse the charger list swap, reverse the e-scooter list swap, increment I.L.C., and go to Step 4.2.
    4.3
    Reduce the temperature
    4.4
    Increment O.L.C. and go to step 4.
As shown in the above table, the adapted SA algorithm consists of an outer and inner loop. The number of iterations in the outer loop is larger in than the inner loop. The outer loop is responsible for reducing the temperature (T) at the end of each outer iteration number (k) using Equation (11).
T k + 1 = α T k
where T k is the temperature during outer iteration number k and T k + 1 is the temperature for the next outer iteration.
Simulated annealing is a way of searching for a solution to a problem that is modeled after the physical process of annealing. Annealing is a slow process that happens when a thermal system starts melting at high temperatures, and then slowly cools down until it reaches a stable state. In this process, the system’s energy is lowered until it is at its lowest possible level [31].
The SA algorithm is able to escape local optima by using a mechanism that allows deterioration in the objective function value (OFV). This is because, in the early stages of the algorithm, when the temperature parameter T is relatively high, the search for the solution space is widely “explored”, and often “bad” solutions are accepted with high probability. As the temperature parameter T decreases, the probability of accepting solutions that lead to worse objective function values gradually decreases. This allows for controlled “uphill” movements, which eventually lead to higher quality solutions [31].

4. Computational Experiments

The validation of the developed SA algorithm was performed in two stages, first using simulation data and later using real-world data. The simulation dataset was used to evaluate the solution provided by the SA algorithm only against the state-of-practice (baseline), since this was a new application and there were no other approaches in the literature to compare. In the simulation data, we generated and randomly placed the e-scooters and chargers within a 5 km2 area. This placement was based on uniform distribution and Euclidean distances. The proposed approach was evaluated using real-world instances of different sizes ([14,18]). The goal of the second dataset was to evaluate the variances of the solutions and the means and variances of the running time.

4.1. Simulated Instances

We developed an agent-based simulator in MATLAB to simulate four scenarios. In the first scenario, 120 e-scooters were to be charged by 20 chargers. In the other three scenarios, the number of chargers was increased while maintaining the number of e-scooters. The simulation assumed that each charger could collect six e-scooters during the simulation time and the chargers had a competitive approach to e-scooter collection. At the start of the simulation, each charger checked the locations of their available e-scooters, went to the nearest one, unlocked it, and picked it up. Then, the chargers referred to the app to choose their next nearest e-scooter. Each charger continued the collection process until all of their six e-scooters had been collected, and returned home to charge them. The simulation ended when all e-scooters had been collected by their respective chargers. To statistically compare the total distance traveled in the proposed approach to the baseline, 100 runs were performed for each scenario and the total distance traveled for each run was estimated. It was noted that previous studies have not considered pre-reservation of an e-scooter; thus, it could have been possible for a charger to arrive to find that another charger had already collected the e-scooter. Therefore, this proposed approach was designed to overcome this limitation and assumed the following:
(i)
Chargers can collect a maximum of six e-scooters; thereby, no competition can occur.
(ii)
This proposed algorithm heuristically minimizes the objective function, leading to a reduction in the distance traveled by the chargers.
The total distance traveled in this proposed approach and the state-of-practice was calculated for each scenario using 100 randomly generated locations for e-scooters and chargers. The distances traveled by chargers for each scenario for both the baseline and proposed algorithms are presented in Figure 5. The results indicate that assigning e-scooters to chargers saves time by reducing the total distance traveled by the chargers. Moreover, it is worth mentioning that, due to competition, the total distance traveled by the chargers in the baseline model increased as the number of chargers increased. Figure 5 shows the simulated cases that were used as a proof of concept to show the reduction in the travelled distance to collect the e-scooters. Moreover, using simulations, we were able to generate a large number of instances and statistically compare the quality of the state-of-practice and simulated annealing.
Table 1 compares the proposed approach to the state-of-practice in terms of the mean of the total distance traveled and the standard deviation for the solutions of the different simulated instances. In the state-of-practice, the increase in the number of chargers is always accompanied by an increase in the mean of the total distance traveled due to higher competition between chargers. On the other hand, the proposed SA approach uses resources more efficiently, and an increase in the number of chargers leads to a decrease in the mean total distance traveled. The Wilcoxon rank-sum test results are summarized in Table 1. This test examines the null hypothesis that the total distance traveled in the state-of-practice and the proposed approaches are samples of continuous distributions with equal medians, against the alternative that they are not.

4.2. Real-World Benchmark Instances

For validation purposes, 18 benchmark instances ranging from 13 to 410, were tested by the proposed algorithm; the data is available in [32,33]. Table A1 and Table A2 show the mean and standard deviation of the travel distance and running time. The parameter tuning of the proposed algorithm was prepared using a grid search approach to find the best combination of parameters. The grid search approach is considered a straightforward approach; however, it requires high computational time. Therefore, the hyper-parameters of the algorithm were set to 1000, 20,000, 200, and 0.95 for the initial temperature, the outer loop maximum number of iterations, the inner loop number of iterations, and the cooling parameter, respectively. Table A1 and Table A2 show a similar trend in that the quality of the solution improves as the number of available chargers increases, because increasing the available e-scooters raises chances for better assignments between freelancers and e-scooters.

5. Discussion

The e-scooter/charger assignment is a dynamic problem in nature. Furthermore, operators need to monitor the status of their vehicles and run an efficient and accurate e-scooters /chargers assignment algorithm more than once a day. Hence, as shown in the paper, the SA has been proposed to provide good solutions in a reasonable time, where, from Table 1, in all cases, the SA found good solutions compared to the baseline for small and medium cases. From Table A1 and Table A2, the SA quickly found a good solution with the increasing number of rechargers, because increasing the available e-scooters raises chances for better assignments between freelancers and e-scooters. Therefore, the proposed algorithm is more suitable in the case of solving large-scale problems. The key point here is finding a good solution to the e-scooters /chargers assignment problem in a short time, considering that the SA is easy for the operator to run it.
To further discuss the proposed approach performance, we examined simulated annealing as a practical heuristic approach to solve the ESCA problem by comparing the SA to our previous work [12]. In [12], the college admission algorithm (ACA) and the black hole optimizer (BHO) algorithm were used to solve the ESCA problem, where the performance of these algorithms was compared to the results of a mixed-integer linear programming (MILP) model for small and medium cases. As ESCA is an NP-complete combinatorial optimization problem, the MILP is inapplicable to finding the exact solution for large-scale real cases.
In the current work, the SA was proposed to improve the solution of the ESCA problem compared to ACA and BHO, as shown in Table 2, and how far from the optimal solution using MILP.
The successful implementation of this technique can assist e-scooter firms in meeting client demand while considering rental costs and increasing the hourly fee of chargers. Further considerations should be made when developing the commercial software for the ESCA as follows:
  • How to extend the model in such a way that it is generally applicable based on real data acquired from a large number of places in Australia, including Queensland.
  • How to discover a decent (near optimum) solution for major e-scooter operators who may have to address this problem for thousands of e-scooters.

6. Conclusions

The public’s interest in micro-mobility modes has recently grown at a rapid rate, altering many cities’ transportation infrastructure. Micro-mobility provides an economical and quick way to commute, relieving consumers from interminable waiting and time wasted in congested locations.
Recently, the usage of dockless electric e-scooters for first- and last-mile trips has gained momentum as a micro-mobility mode. This new model has been introduced to fill the gaps in the current transportation network and mitigate traffic congestion in dense cities. The significant rise in demand for e-scooter sharing systems has been accompanied by an expanding network of freelancers to maintain the e-scooters in charged and accessible conditions. The current scenario is that freelancers compete for the charging of the e-scooters to maximize their income at the cost of the environment. In this study, we developed a mathematical model for the ESCA. Specifically, we adapted an SA algorithm that solves the ESCA problem while overcoming the common shortcomings of the existing state-of-practice approach. The performance of the SA algorithm was evaluated in two stages, using both simulation and real-world data. First, the simulated dataset was used to compare the SA algorithm approach’s solution to the state-of-practice (baseline), and the results indicated a 61% to 79% reduction in the total distance traveled. Then, the SA algorithm was evaluated using 18 instances of real-world data, and, in most cases, the results showed a near-optimal solution in less than three minutes.
Overall, this pioneering study implemented an SA algorithm to solve the ESCA problem and provided significantly better and reliable solutions than the baseline (existing state-of-practice) method. It provided the model needed for assigning e-scooters to chargers to minimize the chargers’ average distance traveled and eradicated direct competition between chargers. This could eliminate the physical violence and disputes that have been reported by chargers due to simultaneously arriving at the same e-scooter. Moreover, implementing the proposed SA model solution could help guarantee a minimum wage for chargers. Because the proposed SA algorithm uses the available resources (chargers) more efficiently and eliminates duplication of effort; it provides opportunities for maximizing e-scooter rental time, leading to a higher income for e-scooter sharing system operators.
The limitations of this study are:
  • We used a static ESCA approach that does not account for time-variations in the location of e-scooters or chargers.
  • Our method assumes that the chargers would accept the assignment solution, which may or may not be the case
Hence, future studies should extend the model as a fuzzy dynamic ESCA problem. Fuzzy Dynamic Programming (FDP) is a mathematical tool based on fuzzy numbers or logic that can solve many complex and multivariable problems. In FDP, the best solution of the Dynamic ESCA is obtained by decomposing the sub-problem of a single variable. Furthermore, future directions should be considered, such as the battery swapping problem, constructing charging stations, and incentivizing the users to visit the charge stations and deliver the e-scooters to recharge or swap the batteries and gain credits.

Author Contributions

Conceptualization, M.M. and M.E.; methodology, M.M. and M.E.; software, M.M. and M.E.; validation, M.M., M.E. and S.Q.L.; formal analysis, M.A.; investigation, M.M., M.E., S.Q.L. and S.G.; resources, W.A.; data curation, S.G.; writing—original draft preparation, M.M., M.E. and M.A.; writing—review and editing, S.G. and W.A.; visualization, M.A. and S.G.; supervision, S.G.; project administration, M.A. and S.G.; funding acquisition, S.G. and M.A. All authors have read and agreed to the published version of the manuscript.

Funding

This research received no external funding.

Institutional Review Board Statement

The study did not require ethical approval.

Informed Consent Statement

Not applicable.

Data Availability Statement

The data available here at [32,33].

Acknowledgments

The authors would like to acknowledge the financial and in-kind support from the Centre for Accident Research and Road Safety at the Queensland University of Technology, Brisbane, Australia.

Conflicts of Interest

The authors declare no conflict of interest.

Appendix A

Table A1. Evaluation of proposed approach using different sizes of benchmark instances (small and medium).
Table A1. Evaluation of proposed approach using different sizes of benchmark instances (small and medium).
CitySRNo. of Selected ChargersMean Total Dist. (km)Std. of Total Dist.Average Dist. per Charger (km)Mean (s)Std.
(s)
Bari133317.420.69255.8124.28250.6536
4316.480.45905.4926.68022.8873
5316.040.23665.3526.41210.9359
6315.890.21325.3025.88820.2477
Denver5110993.774.299210.437.66490.0925
15984.855.68369.437.66420.0688
20983.164.81029.247.75220.1255
25977.194.12368.577.74650.0920
Rio De Janeiro551010156.034.280915.607.86840.1018
1510130.514.068813.058.44860.5078
2010126.635.854212.668.43890.1110
2510118.216.974811.829.06330.1438
Boston591010149.531.810414.957.97690.1624
1510118.663.780111.878.18540.1057
2010107.243.441010.728.71850.2075
251097.593.11609.769.05400.2089
Torino75151382.492.69826.359.33050.5826
201376.463.66235.889.18470.1975
251371.201.75415.489.20490.1094
301370.671.77145.449.83590.3867
Toronto80151485.461.68116.1010.05700.3215
201480.923.10125.7810.55670.5761
251477.063.03545.5011.30080.6557
301474.274.75035.3010.67100.4708
Miami821514225.595.434316.1126.46891.5830
2014159.784.915911.4126.24280.7857
2514112.975.39438.0723.92921.2262
301489.824.79626.4119.53316.9275
Ciudad De Mexico902015116.932.97147.8026.17733.1219
2515101.661.99046.7826.57321.9891
301593.973.03226.2626.95001.1487
351586.372.13995.7627.50160.5540
Minneapolis1162520265.374.850713.2716.04120.4177
3020247.418.136412.3716.17410.3450
3520239.358.911911.9716.29440.2845
4020230.905.202411.5416.20570.2166
Table A2. Evaluation of the proposed approach using large-size benchmark instances.
Table A2. Evaluation of the proposed approach using large-size benchmark instances.
CitySRNo. of Selected ChargersMean Total Distance (km)Std. of Total DistanceAverage Dist. per Charger (km)Mean
(s)
Std.
(s)
Brisbane1503025157.265.56746.2970.69940.7181
3525156.906.59326.2871.19030.5602
4025155.558.34226.2271.15790.2525
4525150.214.55196.0172.24310.1981
Milano1844031170.243.70025.4978.66490.6661
5031168.735.33495.4478.90160.2877
6031166.535.03475.3779.20270.3343
7031167.874.26115.4279.36850.5798
Lille2004034404.6312.109211.9082.16380.3132
5034397.1819.025811.6882.47240.4127
6034334.0619.71149.8382.88990.2982
7034280.1720.64078.2483.83844.2350
Toulouse2404040320.268.35258.0166.92410.6171
5040300.728.61947.5269.53750.5668
6040291.3410.28897.2878.24930.4577
7040279.788.82026.9970.21050.8201
Sevilla2585043360.488.57478.3872.42982.7409
6043324.7612.11067.5574.18081.3228
7043312.8911.33187.2874.09121.0718
8043307.9810.43387.1673.17070.3482
Valencia2765046485.5410.194610.5575.26975.1969
6046439.799.97109.5679.28743.0556
7046402.617.95948.7579.31391.5698
8046396.408.89158.6281.55181.4524
Bruxelles3046051486.9016.29579.5582.00233.2712
7051448.1716.95978.7984.64691.9173
8051439.3814.44318.6282.41341.1279
9051428.269.72408.40184.421655.3400
Lyon3366056589.3712.542610.5293.42954.3040
7056538.877.54019.6297.10096.8603
8056508.9110.78599.0988.61712.0332
9056492.4211.82518.7991.01581.5686
Barcelona4107069610.016.06568.84101.20632.7764
8069548.789.64747.95102.56392.8394
9069510.668.13147.40103.16101.9283
10069491.6312.95227.13103.75721.4365

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Figure 1. An illustrative example of the ESCA problem.
Figure 1. An illustrative example of the ESCA problem.
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Figure 2. Illustration of E-Scooter-Charger Allocation encoded by the SA.
Figure 2. Illustration of E-Scooter-Charger Allocation encoded by the SA.
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Figure 3. Example of a small-size E-Scooter-Charger Allocation, encoded with more chargers than required for e-scooters.
Figure 3. Example of a small-size E-Scooter-Charger Allocation, encoded with more chargers than required for e-scooters.
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Figure 4. Illustration of NAPI technique for ten elements, where i = 4   and   j = 8 .
Figure 4. Illustration of NAPI technique for ten elements, where i = 4   and   j = 8 .
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Figure 5. Comparison of the proposed approach and state-of-practice.
Figure 5. Comparison of the proposed approach and state-of-practice.
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Table 1. Comparison of proposed and baseline approaches using simulated instances.
Table 1. Comparison of proposed and baseline approaches using simulated instances.
The BaselineSA
No. of ChargersMean (km)Std (km)Mean (km)Std
(km)
m e a n b a s e l i n e m e a n S A m e a n b a s e l i n e p-Value
20213.5866.0882.684.510.61 0.0001
30307.68115.9769.204.150.78 0.0001
40301.0486.0668.033.850.77 0.0001
50322.01110.8567.174.450.79 0.0001
Table 2. Comparison of the proposed SA, MILP, ACA, BHO, and baseline approaches using simulated instances. The SA (highlighted with colors) minimized the total distances compared to other algorithms in difference cases.
Table 2. Comparison of the proposed SA, MILP, ACA, BHO, and baseline approaches using simulated instances. The SA (highlighted with colors) minimized the total distances compared to other algorithms in difference cases.
The BaselineMILP (Optimal)ACABHOSA
# of ChargersTotal Dis.Total Dis.Total Dis.Total DistanceTotal Distance
20213.5876.798.2131.982.68
30307.6865.685.9122.669.20
40301.0461.481.0129.768.03
50322.0160.479.3130.167.17
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MDPI and ACS Style

Masoud, M.; Elhenawy, M.; Liu, S.Q.; Almannaa, M.; Glaser, S.; Alhajyaseen, W. A Simulated Annealing for Optimizing Assignment of E-Scooters to Freelance Chargers. Sustainability 2023, 15, 1869. https://doi.org/10.3390/su15031869

AMA Style

Masoud M, Elhenawy M, Liu SQ, Almannaa M, Glaser S, Alhajyaseen W. A Simulated Annealing for Optimizing Assignment of E-Scooters to Freelance Chargers. Sustainability. 2023; 15(3):1869. https://doi.org/10.3390/su15031869

Chicago/Turabian Style

Masoud, Mahmoud, Mohammed Elhenawy, Shi Qiang Liu, Mohammed Almannaa, Sebastien Glaser, and Wael Alhajyaseen. 2023. "A Simulated Annealing for Optimizing Assignment of E-Scooters to Freelance Chargers" Sustainability 15, no. 3: 1869. https://doi.org/10.3390/su15031869

APA Style

Masoud, M., Elhenawy, M., Liu, S. Q., Almannaa, M., Glaser, S., & Alhajyaseen, W. (2023). A Simulated Annealing for Optimizing Assignment of E-Scooters to Freelance Chargers. Sustainability, 15(3), 1869. https://doi.org/10.3390/su15031869

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