Multi-Objective Planning of Commuter Carpooling under Time-Varying Road Network

Abstract

Aiming at the problem of urban traffic congestion in morning and evening rush hours, taking commuter carpool path planning as the research object, the spatial correlation of traffic flow at adjacent intersections is mined using convolutional neural networks (CNN), and the temporal features of traffic flow are mined using long short-term memory (LSTM) model. The extracted temporal and spatial features are fused to achieve short-term prediction. Considering the travel willingness of drivers and passengers, a multi-objective optimization model with minimum driver and passenger loss time and total travel time is established under the constraints of vehicle capacity, time windows and detour distances. An Improved Non-dominated Sorted Genetic Algorithm-II (INSGA-II) is proposed to solve it. The open-loop saving algorithm is used to generate an initial population with better quality, and the 2-opt local search strategy is adopted in the mutation operation to improve search efficiency. The influence of vehicle speed on the matching scheme is analyzed. The research results show that under the same demand conditions, the total travel distance of the carpool scheme is reduced by about 56.19% and total travel time is reduced by about 65.52% compared with the non-carpool scheme. Research on carpool matching under time-varying road networks will help with urban commuting efficiency and environmental quality, and play a positive role in alleviating traffic congestion and promoting carpool services.

1. Introduction

With the rapid development of new urbanization and motorization, the high-density agglomeration of the urban population and the blowout growth of car ownership have led to increasingly significant supply-demand contradictions in urban transportation. Especially in the morning and evening rush hour of urban commuting, the sudden gathering of people exceeds the road carrying capacity, which is bound to cause congestion. Nowadays, traffic congestion has become a persistent problem that troubles the development of big cities.

Currently, there are frequent extreme weather events worldwide, and addressing climate change has become a global consensus. Countries that account for 75% of the world’s GDP and 65% of carbon emissions have proposed their own vision of carbon neutrality. France, Sweden and others have incorporated it into their laws. China, Japan and others have made target commitments, and some countries have reached joint agreements or are under discussion [1].

With the popularity of cars and the Internet, the sharing economy and platform economy are developing rapidly. In 1973, California built the world’s first High-occupancy Vehicle Lane (HOV) [2], which optimized vehicle traffic efficiency and effectively promoted the development of carpooling. Finland established a personal traffic management system (PTM) in 2002 to provide real-time dynamic matching services for vehicles and passengers. In 2012, China’s local government issued policies to encourage and regulate the development of carpools [3]. Carpooling has gradually entered people’s daily life. However, some car-hailing drivers have defaulted on their operations, infringing on the legitimate rights and interests of consumers.

Private carpooling meets the needs of people’s all-round development and social sustainable development at the same time. Compared with operational passenger transport services such as taxis and online car hailing, private carpooling is not for profit. It is a voluntary civil act of all participants. Drivers and passengers have the same status and should pay full attention to the balance of interests.

Based on the existing literature, the shortcomings are as follows: (1) there are few papers on the practical application scenario of private carpooling. (2) Some studies usually assume that vehicles run at a constant speed, which leads to limitations in application, and results are prone to deviation. (3) Most studies only consider objective factors such as distance or cost. A few studies involving satisfaction, only from the perspective of passengers, rarely consider the travel preferences of drivers. (4) In the existing papers that consider the time varying of road networks, the changing trend of vehicle speed is mostly expressed by a step function, which can not reflect the real vehicle driving process. (5) With the increase in data size and complexity, it is necessary to improve the standard heuristic algorithm to enhance its solving performance.

In view of the above problems, this paper fully considers the interests of both owners and passengers, describes the continuous changes in road traffic flow based on deep learning, establishes a multi-objective optimization model, and uses multiple strategies to optimize the performance of the NSGA-II algorithm to achieve the optimal matching of commuter carpooling.

The rest of this article is structured as follows. Section 2 reviews the relevant literature. Section 3 introduces the methodology. Section 4 presents the findings and discussions. Finally, Section 5 is the conclusions and implications.

2. Literature Review

In recent years, in the context of green and sustainable development, carpooling has gradually been valued by people due to its many advantages, and more and more researchers have conducted in-depth and multi-angle research on carpooling, and a relatively mature theoretical system has been formed. Through the literature review, it is found that research mainly focuses on path optimization and algorithm improvement. In the following, the relevant literature is presented separately.

2.1. Research on Path Optimization

The Vehicle Routing Problem (VRP) is a key focus of carpooling, and the significance of path optimization research lies in how to plan the optimal driving route for passengers with different travel needs at different locations. The existing VRP has been preliminarily matured through extensive research by scholars. According to the different combinations of attribute relationships and conditions of each core element of the vehicle path, VRP has generated many different extension forms. References [4,5,6] studied the dynamic vehicle routing problem with time windows and capacity constraints. References [7,8,9] studied the multi-vehicle routing problem under dynamic road networks.

Depending on the actual problem, the constraint conditions and objective function will be different. Mansoureh and Mahdi established an open time-dependent vehicle path optimization model considering carbon dioxide and nitrogen oxide emissions [10]. Xiao and He proposed a taxi-pooling scheme based on multi-objective models and optimization algorithms, aiming to minimize boarding and alighting distance, carpooling waiting time, and reach the destination [11]. He and Zhao constructed a taxi-pooling scheduling model with the goal of minimizing vehicle operation time and passenger travel time and solved it using a hybrid ant colony genetic algorithm [12]. Yan and Luo et al. used the shareable network method to calculate the optimal carpooling scheme with the maximum reduction in total vehicle travel [13]. Hu and Yuan et al. comprehensively considered the optimal meeting location and multiple vehicle types to optimize the carpooling scheduling of services [14]. Zhu and Ye et al. proposed a time-optimal and privacy-preserving carpooling path planning system based on deep reinforcement learning [15]. Yuan and Chen et al. constructed a robust optimization model for carpooling paths with the objective of minimizing the total mileage and number of vehicles, considering the uncertainty of travel time [16]. Lotfi and Sepide et al. used a hybrid heuristic algorithm to achieve on-demand dynamic carpool matching with the goal of total enterprise profit and passenger transfer frequency [17].

2.2. Research on Algorithm Design

Under the background of new environments and technologies, the vehicle routing problem and the solution methods have been continuously studied in depth. The most common algorithms are accurate algorithm and heuristic algorithm.

Li combined the greedy algorithm and k-d tree method to solve the dynamic vehicle routing problem and verified the effectiveness of the algorithm by using a case [18]. Filcek and ŻAK used the dynamic programming method and the Dijkstra algorithm to generate a carpool matching scheme [19]. Wu used the bilateral matching algorithm to limit road grid spacing and improved the A* algorithm to solve the dynamic path planning problem [20]. Coindreau and Gallay et al. proposed a dedicated variable neighborhood search for solving vehicle routing problems with transferable resources, which can save both total travel distance and the number of vehicles in tight time windows [21]. Ding and Zhang et al. designed a fusion of a genetic algorithm and a gray wolf algorithm to solve multi-vehicle carpooling problems with soft time windows, which improved the global search ability and population diversity of the algorithm [22]. Lu and Luca et al. developed a polynomial-time solution method based on optimal pair matching among participants, improved by a construction insertion-based heuristic [23]. Gong and Zhang proposed a carpool matching algorithm combining genetic algorithm and artificial neural network to improve the efficiency of carpool matching [24].

3. Methodology

3.1. Scenario Description

The research object of this paper is the employees of a company who are willing to carpool and commute by car. The company builds a scheduling platform and supervises the whole carpool process. Participants choose to become drivers or passengers and release travel information in advance. Drivers start from their own places and pick up matching passengers in turn to the common destination. The service is completed when the vehicle arrives at the company without returning to their respective departures, which is an open vehicle routing problem.

The assumptions in this paper are as follows:

(1)

Each passenger can only be served by one vehicle;

(2)

The geographic location, time window and other information of the ride participants are known;

(3)

Considering the comfort, the maximum driver–passenger capacity of the shared vehicle is set as 4 persons;

(4)

Passengers shall wait at the boarding point in advance as agreed, and the passengers can be picked up when the vehicle arrives, ignoring the parking start time of the vehicle and the boarding and alighting time of passengers;

(5)

The performance of carpool vehicles is similar, and the driving speed changes with time.

The schematic diagram of carpool service mode is shown in Figure 1.

The variables and parameters in the model are shown in

Table 1. Variable and parameter definitions.

Types	Symbols	Explanation
sets	K = {2, …, k}	Vehicles’ departure nodes set in the area
	G = {2, …, g}	Passengers boarding nodes set in the area
	H = K∪G = {2, …, k + g}	Drivers’ and passengers’ departure nodes set
	N = {1}∪H = {1, 2, …, k + g}	Drivers’ and passengers’ departure and destination nodes set
	K = {2, …, k}	Vehicles’ departure nodes set in the area
parameters	ak	Number of passengers in the k-th vehicle
	i, j, p, g ∈ N	Nodes at any position in the area
	M	Time interval
	dij	Actual distance between node i and j (km)
	tij	Travel time of vehicle from node i to j (h)
	vij	Vehicle travel speed from node i to j (km/h)
	tik	The moment when the k-th vehicle leaves the i-th node
	OTh	Departure time when the h-th participant does not carpool
	STk	Departure time of the k-th vehicle
	ATk	Arrival time of the k-th vehicle
	Lhc	Ride distance of the h-th carpool participant
	Lh	Ride distance of the h-th participant who does not carpool
	θ	Elasticity coefficient of acceptable detour distance for all participants
	LT	Latest arrival time at the company, this paper is set to 8:20
decision variables	Xijk	$X_{ij}^k=\{\begin{array}{l}1,thek-thvehiclefromnodeitoj\\ 0,otherwise\end{array}$
	Yik	$Y_i^k=\{\begin{array}{l}1,\mathrm{t}hepassengeratthei-thnodeispickedupbythek-thvehicle\\ 0,otherwise\end{array}$

.

3.2. Related Terms

In this section, the indistinguishable terms related to this paper will be explained.

(1)

Carpool

It is a term used to describe a group of people who share a vehicle to a common destination, usually for work or school. Carpooling can be a cost-effective and environmentally friendly alternative to driving alone, as it allows individuals to share the cost of gas and reduce their carbon footprint. This is consistent with the scenario in this paper.

(2)

Rideshare

It typically refers to using a mobile application to request a ride and are matched with a driver who is available to take them to their destination for a fee.

(3)

Ride-hailing

Something is accomplished by hailing a taxi from the street, calling up a car service on the phone, or virtually hailing a car from an app. Ride-hailing works simply for one traveler. No stranger can join.

3.3. Model Building

3.3.1. Dynamic Travel Time Determination

In the real road network, road traffic flow and vehicle speed are random and dynamic, which are influenced by various uncertain factors. In order to describe the continuous changes in vehicle driving, this paper combines convolutional neural networks (CNN) [25] and long short-term memory networks (LSTM) [26] to predict traffic speed. Based on the prediction results, the entire process is divided into several time periods, and the different functional relationship between vehicle speed and time in each period is obtained. Then, according to whether the vehicle is traveling across time periods, the expressions of time-varying travel time are as follows:

The driving process is divided into $M$ time intervals, expressed as $T^1,T^2,\dots ,T^M$. Corresponding speed $v^m\ge 0$ of traffic flow in any time period $T^m$. Assuming that the time when the vehicle leaves node $i$ is at the $m-th$ time interval, there are:

(1)

If $d_{ij}\le {\displaystyle {\int }_{T^m}^{T^{m+1}}v(t)dt}$, the vehicle k arrives at the node $j$ before $T^{m+1}$ without crossing the time period, and the travel time $t_{ij}$ can be obtained by calculating the upper limit of the integral according to $d_{ij}$ and the speed function relation in the period of $\left[T^m,T^{m+1}\right]$;

(2)

If $d_{ij}\ge {\displaystyle {\int }_{T^m}^{T^{m+1}}v(t)dt}$, it means that the vehicle k runs across time periods between node $i$ and node $j$. Assuming that the distance traveled across $w$ time periods in each period is $d_{ij}^m,d_{ij}^{m+1},\dots ,d_{ij}^{m+w}$, the travel time between two nodes is expressed as $t_{ij}=\left(T^{m+w}-T^m\right)+t_{ij}^{m+w}$. $t_{ij}^{m+w}$ is the travel time of vehicle k in the $(m+w)-th$ period, which can be obtained by calculating the upper limit of the integral according to $d_{ij}^{m+w}$ and the speed function relation in the period of $\left[T^{m+w},T^{m+w+1}\right]$.

3.3.2. Objective Function

In the commuter carpooling problem, commuter time is an optimization objective that cannot be ignored, so the total travel time is taken as one of the objective functions. The relationship between drivers and passengers is friendly and mutual aid, carpooling cannot affect the travel demand of drivers. In order to ensure the interests of both drivers and passengers, this paper comprehensively considers the travel willingness of vehicle owners and passengers, so the loss time of drivers and passengers is taken as the second objective function. The loss of time for drivers and passengers refers to the sum of the time for all drivers and passengers in the system to depart early due to participating in carpooling. The specific function expression and constraint condition are as follows:

$$\min F_1={\displaystyle {\sum }_{k\in K}{\displaystyle {\sum }_{i,j\in N}{t}_{ij}^k{X}_{ij}^k}}$$

(1)

$$\min F_2={\displaystyle {\sum }_{k\in K}{\displaystyle {\sum }_{i\in H}(t_i^k-O{T}_i})Y_i^k}$$

(2)

$${\displaystyle {\sum }_{i\in N(i\ne j)}{X}_{ij}^k}\le 1,\forall j\in N,k\in K$$

(3)

$${\displaystyle {\sum }_{j\in N(j\ne i)}{X}_{ij}^k}\le 1,\forall i\in N,k\in K$$

(4)

$${\displaystyle {\sum }_{i\in N}{Y}_i^k}=1,\forall k\in K$$

(5)

$$1\le {\displaystyle {\sum }_{i\in N}{Y}_i^k\cdot a_k}\le 4,\forall k\in K$$

(6)

$${\displaystyle {\sum }_{p\in N}{X}_{pj}^k}-{\displaystyle {\sum }_{q\in N}{X}_{jq}^k}=0,\forall j\in N,k\in K$$

(7)

$$t_i^k\le t_{i+j}^k,\forall i,j\in N,k\in K$$

(8)

$$A{T}_k\le LT,\forall k\in K$$

(9)

$$S{T}_k\le 1.2·O{T}_k,\forall k\in K$$

(10)

$$L_h^C\le (1+\theta )L_h,\forall h\in H$$

(11)

Formulas (3)–(5) are travel path constraints to ensure that passengers at each demand point have and only have the same vehicle for service; Formula (6) is the vehicle capacity constraint, indicating that the maximum number of drivers and passengers per vehicle is 4; Formulas (7) and (8) are the constraints of the ride in sequence, and the vehicle must travel in the sequence of passing through the passenger demand point from its starting point and then to the destination. Formula (9) specifies the latest arrival time of the carpool. Formula (10) indicates that the driver’s departure time in advance is at most 1.2 times the usual departure time, so as to balance the loss of interests of both drivers and passengers and maintain the fairness of the carpool. Formula (11) represents the maximum driving distance acceptable to the driver and passengers participating in the ride.

3.4. INSGA-II Algorithm

For multi-objective optimization problems, many excellent algorithms have emerged, among which the most classic is Non-dominated Sorted Genetic Algorithm-II (NSGA-II) proposed by Deb in 2002 [27]. Compared with basic genetic algorithms, it improves accuracy and efficiency by introducing non-dominated sorting, elite strategy and crowding. However, NSGA-II has weak local search ability, which easily causes premature convergence, poor distribution and local optimization. For the above problems, this paper initializes the population by an open-loop saving algorithm, and 2-opt is adopted for mutation operation. The Improved NSGA-II (INSGA-II) flow is shown in Figure 2.

3.4.1. Open-Loop Saving Algorithm

The quality of the initial population has a great impact on the global convergence speed and the quality of the solution of the swarm intelligence optimization algorithm [28]. The original algorithm usually initializes the population randomly, which affects the diversity of the population.

The saving algorithm is the most famous heuristic algorithm used to solve the problem of an uncertain number of vehicles [29]. By merging loops of the problem in turn, the optimal scheme with the minimum time, the shortest distance and the lowest cost is obtained. The principle of the traditional saving algorithm is shown in Figure 3 as a closed-loop system. P is the destination, and A and B are passengers. The distance between P and A and B is a and b, respectively, and the distance between A and B is c. The original path is option 1, and the path by closed-loop saving algorithm is option 2.

Carpooling ends with vehicles arriving at the company, and vehicles need not be back to their own departures. It is an open-ended vehicle routing problem. Therefore, this paper uses the open-loop saving algorithm to generate the initial population. By carpool matching, multiple separate open-loop routes are merged into an open-loop route with the driver as the starting point. The basic principle is shown in Figure 4. P is the destination, A is the driver, B and C are the passengers, and the distances from P to A, B and C are a, b and c, respectively. The distance from A to B is d, and the distance from B to C is e. The original path is option 3, and the path after using the open-loop saving algorithm is option 4.

The specific process is as follows:

Step 1: generate the initial demand points, destination and driver points;

Step 2: obtain the OD matrix of the shortest path distance between points;

Step 3: generate a mileage saving table for each driver, and arrange them in descending order according to the mileage savings;

Step 4: calculate the sum of mileage savings for each driver and the top three passengers;

Step 5: the driver with the largest mileage saved shall be matched for carpool, and remove the matched driver and passengers from the system;

Step 6: return to Step 3 until all drivers are matched.

3.4.2. 2-Opt Local Search

In order to eliminate the path-crossing phenomenon in VRP, a 2-opt local search strategy is adopted in the mutation operation. The basic idea is to randomly select two nodes on a randomly initialized path and flip the middle path including both nodes [30]. If the improved path distance decreases, keep it; otherwise, return to the original situation.

This method effectively solves the path-crossing problem and can obtain higher-quality solutions. Considering the time consumption, a 2-opt local search was performed on individuals with fitness values from small to large and 20% of the population size. The operation process is shown in Figure 5. Suppose a driver departs from node 2, node 1 is the destination, nodes 3, 12, 16, and 18 are all passenger demand points, and (a) indicates that the original path is (2,12,3,18,16,1), and after a 2-opt search, the path is (2,16,18,3,12,1) as shown in (b).

By introducing a 2-opt strategy, the passenger node sequence corresponding to the shorter path distance is selected, so that the algorithm searches towards global optimum.

4. Experimental Studies

4.1. Experimental Setting

In order to verify the effectiveness of the model and algorithm, this paper designs an example with 29 drivers and 70 passengers. As the only destination for carpooling, the company’s node number is marked as 1. The starting places of all participants are evenly and randomly distributed in the road network. The actual distance and location information between nodes is obtained through a map API tool. The nodes distribution and related data are shown in Figure 6 and

Table 2. Node distance matrix (partial) km.

D	1	2	3	4	5	6	7	8	9	10	$\cdots$	91	92	93	94	95	96	97	98	99	100
O
1	0	11.9	11.0	9.8	9.1	11.2	5.7	7.3	6.3	4.3	$\cdots$	9.7	15.6	3.6	9.0	12.5	14.5	12.9	9.3	9.1	4.1
2	11.2	0	7.5	10.1	20.5	12.8	21.8	14.7	16.0	7.7	$\cdots$	3.9	10.6	11.6	4.5	4.3	11.9	2.2	8.3	13.6	14.4
3	10.8	8.3	0	2.8	13.0	5.5	10.8	7.7	10.2	7.8	$\cdots$	4.3	4.7	12.8	8.7	6.8	5.7	9.1	1.8	6.1	12.2
4	9.0	10.7	3.2	0	10.0	4.1	7.8	5.0	7.2	6.6	$\cdots$	7.3	7.0	12.1	10.2	9.6	6.0	12	2.2	3.1	10.5
5	8.8	20.5	12.9	10.6	0	9.9	4.1	5.5	4.4	13.4	$\cdots$	16.9	15.5	11.8	19.9	18.7	13.8	21.7	11.7	8.2	7.6
6	11.6	14.7	5.5	3.4	9.7	0	9.7	7.1	9.3	9.2	$\cdots$	9.5	4.9	14.7	12.7	10.7	3.3	14.1	4.3	3.9	12.8
7	5.4	17.1	10.2	8.5	4.1	10.6	0	3.0	1.0	8.2	$\cdots$	12.3	14.3	8.5	16.7	14.5	13.8	19.0	8.5	7.5	3.9
8	7.1	15.7	7.6	5.5	5.4	7.6	3.3	0	2.7	8.0	$\cdots$	10.9	11.3	10.2	14.7	14.1	10.1	18.3	6.5	4.6	6.0
9	6.0	16.8	9.9	7.9	4.4	9.8	1.0	2.5	0	7.9	$\cdots$	11.9	13.7	9.3	16.4	14.2	13.4	16.5	8.2	6.9	4.9
10	4.1	8.2	8.2	7.3	11.8	10	8.1	6.9	7.6	0	$\cdots$	6.0	13.6	5.5	6.7	8.7	12.2	9.1	6.4	7.0	7.1
$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$\ddots$		$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$	$⋮$
91	9.7	4.0	4.2	6.7	16.5	9.5	12.6	11.1	12.1	5.9	$\cdots$	0	7.4	10.9	5.5	3.1	8.7	4.5	5.0	9.6	12.7
92	15.4	11.1	4.4	6.4	15.4	4.7	14.2	11.3	13.6	13.2	$\cdots$	7.0	0	19.2	11.9	8.0	2.4	10.3	6.2	8.4	17.3
93	2.8	11.7	15.9	12.2	11.1	16.6	8.4	9.4	8.5	4.9	$\cdots$	10.7	21.1	0	9.3	13.4	19.5	14.1	14.2	11.7	4.9
94	9.3	5.1	8.7	9.4	19.7	12.4	16.3	13.4	15.5	6.2	$\cdots$	6.2	13.4	8.6	0	9.1	12.5	6.9	7.8	11.9	14.8
95	11.9	3.6	6.4	8.9	18.6	10.5	15.6	13.7	15.0	8.1	$\cdots$	3.8	8.4	13.1	7.7	0	10.0	3.0	7.4	11.6	14.9
96	15.5	12.6	5.1	5.1	13.3	3.2	13.1	10.2	12.6	11.7	$\cdots$	9.2	4.2	18.7	12	11.2	0	13.5	5.0	6.9	15.8
97	13.5	2.2	9.0	11.5	21.1	13.0	18.7	16.7	18.1	9.0	$\cdots$	4.7	11.1	14.2	6.1	3.5	12.4	0	10.4	14.1	18.4
98	9.0	8.8	1.7	1.7	11.7	4.6	8.8	6.6	8.3	6.0	$\cdots$	5.1	6.6	11	8.1	7.5	6.1	9.8	0	5.0	10.4
99	9.8	14.4	6.7	4.5	9.8	3.0	7.8	4.9	7.3	8.0	$\cdots$	10.4	7.4	13.0	13.7	12.6	5.8	15.6	5.6	0	10.5
100	3.7	14.9	12.1	11.0	7.4	12.9	4.0	5.5	4.7	7.5	$\cdots$	12.3	17.3	5.2	12.6	15.1	15.7	15.4	10.4	10.1	0

.

The travel information of 99 participants is filled in

Table 3. Passenger demand point information.

Passenger Number	Starting Coordinate (Longitude and Latitude)	Node Number	Departure Time without Ridesharing
1	(125.4113, 43.8975)	2	7:30
2	(125.3872, 43.8465)	3	7:35
3	(125.2477, 43.8255)	5	7:45
4	(125.3555, 43.8209)	6	7:35
5	(125.2712, 43.8481)	7	8:00
6	(125.2985, 43.8428)	8	7:50
7	(125.3205, 43.8560)	9	8:00
8	(125.3355, 43.8817)	10	8:05
9	(125.2884, 43.9156)	11	7:40
10	(125.3718, 43.9253)	12	7:55
11	(125.2588, 43.8980)	13	8:05
12	(125.3143, 43.9202)	14	7:50
13	(125.3389, 43.9010)	15	7:55
14	(125.2895, 43.8596)	16	7:45
15	(125.3508, 43.8484)	17	7:35
16	(125.3458, 43.8904)	18	8:00
17	(125.3179, 43.8254)	19	7:45
18	(125.4025, 43.8575)	21	7:55
19	(125.3241, 43.8773)	22	7:40
20	(125.3755, 43.8617)	23	8:05
21	(125.2961, 43.8986)	24	8:05
22	(125.2834, 43.8357)	25	7:55
23	(125.3702, 43.8834)	27	7:40
24	(125.2748, 43.8954)	29	7:55
25	(125.3064, 43.8750)	30	7:35
26	(125.2359, 43.8478)	33	8:00
27	(125.3879, 43.8948)	36	7:40
28	(125.2371, 43.8656)	38	7:45
29	(125.3739, 43.8247)	40	7:45
30	(125.2462, 43.8712)	41	7:50
31	(125.3947, 43.9198)	42	7:30
32	(125.3534, 43.9104)	43	7:55
33	(125.2843, 43.8078)	44	8:00
34	(125.3510, 43.8669)	45	7:55
35	(125.2659, 43.8004)	46	8:05
36	(125.2402, 43.8866)	48	7:40
37	(125.4065, 43.8847)	49	7:35
38	(125.2387, 43.9010)	50	7:50
39	(125.2756, 43.9134)	51	7:45
40	(125.3181, 43.8910)	52	7:40
41	(125.3397, 43.8419)	53	7:55
42	(125.2978, 43.8121)	54	7:35
43	(125.3394, 43.8599)	55	7:35
44	(125.3366, 43.9143)	56	8:05
45	(125.4124, 43.8417)	61	7:30
46	(125.3065, 43.9540)	62	7:55
47	(125.2989, 43.8598)	64	7:50
48	(125.2511, 43.9137)	68	8:00
49	(125.3352, 43.8522)	69	7:35
50	(125.3239, 43.8443)	71	7:45
51	(125.3707, 43.9534)	72	7:20
52	(125.2564, 43.9499)	73	7:50
53	(125.3924, 43.9578)	74	7:50
54	(125.2749, 43.9392)	77	7:45
55	(125.2236, 43.8410)	78	7:55
56	(125.3191, 43.9347)	79	7:55
57	(125.3076, 43.8374)	80	7:40
58	(125.2761, 43.8257)	82	7:50
59	(125.4063, 43.9216)	83	8:05
60	(125.3604, 43.8875)	84	7:50
61	(125.2767, 43.8626)	85	7:30
62	(125.2629, 43.8564)	88	7:40
63	(125.4180, 43.9532)	90	7:30
64	(125.3984, 43.8791)	91	7:30
65	(125.2877, 43.9021)	93	8:05
66	(125.3800, 43.9136)	94	7:40
67	(125.4245, 43.8764)	95	7:30
68	(125.3712, 43.8491)	98	7:35
69	(125.3407, 43.8274)	99	7:45
70	(125.2689, 43.8729)	100	8:05

and

Table 4. Vehicle travel information.

Vehicle Number	Starting Coordinate (Longitude and Latitude)	Node Number	Departure Time without Ridesharing
1	(125.3607, 43.8417)	4	7:45
2	(125.2138, 43.8663)	20	7:45
3	(125.3568, 43.8035)	26	7:35
4	(125.2600, 43.9262)	28	7:50
5	(125.3841, 43.8806)	31	7:30
6	(125.2316, 43.8236)	32	7:35
7	(125.2431, 43.8362)	34	7:55
8	(125.3958, 43.8262)	35	7:30
9	(125.3673, 43.9054)	37	7:40
10	(125.2621,43.8129)	39	7:40
11	(125.2532, 43.8408)	47	7:55
12	(125.3276, 43.8118)	57	7:45
13	(125.3282, 43.7975)	58	7:40
14	(125.2951, 43.9411)	59	7:55
15	(125.3806, 43.7975)	60	7:20
16	(125.2368, 43.7983)	63	7:35
17	(125.4216, 43.8623)	65	7:30
18	(125.2212, 43.8872)	66	7:55
19	(125.3035, 43.7953)	67	7:35
20	(125.3537, 43.9390)	70	7:30
21	(125.2368, 43.9287)	75	7:45
22	(125.3821, 43.9416)	76	7:40
23	(125.334, 43.9439)	81	7:40
24	(125.3614, 43.8659)	86	7:50
25	(125.4202, 43.9187)	87	7:30
26	(125.4028, 43.9360)	89	7:40
27	(125.4094, 43.8187)	92	7:15
28	(125.3867, 43.8168)	96	7:25
29	(125.4314, 43.8938)	97	7:35

according to the identity of the passenger or driver, respectively.

The parameter settings in the model are shown in

Table 5. Parameter settings.

Parameter Names	Settings
Maximum carrying capacity	4
Initial population	40
Maximum iterations	500
Crossover probability	0.90
Mutation probability	0.08
Latest arrival time of employees	8:20

.

Relying on a traffic data platform, 7 main roads in the region are selected for speed prediction. The real-time traffic speed of each road is recorded at 10 min intervals from 6:30 to 8:30 every day for 30 days. The simulation experiment software environment is based on Windows 10, MATLAB R2021b.

4.2. Analysis of Results

The continuous variation trend of vehicle travel speed on each road is shown in Figure 7.

Based on the prediction results of different roads, different carpool matching results are generated. This paper takes road 1 as an example to discuss in detail. Assuming that the free flow speed is 45 km/h, four Pareto optimal solutions are finally obtained, and the distribution is shown in Figure 8.

The specific matching scheme is shown in

Table 6. Specific matching scheme.

Section	Multiplicative Path	Total Travel Time/h	Total Lost Time/h
1	75-73-77-1; 28-68-51-93-1 59-11-24-1; 81-79-14-1 70-56-52-1; 76-43-1 89-12-1; 87-83-42-94-1 37-15-1; 97-49-2-36-1 31-27-84-18-1; 65-95-91-1 86-45-10-1; 92-61-21-23-1 35-3-98-1; 4-22-1; 66-50-13-1 96-40-17-1; 60-6-55-1 26-99-53-69-1; 58-71-9-30-1 57-19-80-64-1; 67-54-82-25-1 39-46-44-8-1; 63-5-7-16-1 47-88-85-1; 34-33-100-1 32-78-38-41-1; 20-48-29-1	18.78	1.87
2	97-2-36-84-1; 65-95-49-91-1 86-45-55-30-1; 31-27-10-22-1 76-12-43-15-1; 37-18-52-1 70-56-1; 81-79-14-24-1 87-83-42-1; 89-42-94-1 92-61-21-23-1; 35-3-98-1 4-17-69-9-1; 96-40-53-1 60-6-1; 26-99-71-1; 59-11-93-1 57-19-80-64-1; 58-8-16-1 67-54-44-1; 63-46-82-25-1 39-7-85-1; 20-38-41-1 32-78-33-1; 47-88-100-1 34-5-1; 28-73-77-51-1 75-68-29-1; 66-48-50-1	19.33	1.78
3	81-79-14-24-1; 70-56-52-1 31-27-84-1; 97-91-30-1 76-12-43-15-1; 39-46-82-1 86-45-55-1; 4-17-69-9-1 37-18-10-22-1; 59-11-93-1 65-95-49-1; 35-3-23-1 92-61-21-1; 96-40-98-1 60-6-53-1; 26-99-71-1 57-19-80-64-1; 58-8-16-1 63-5-7-1; 89-42-83-94-1 67-44-54-25-1; 20-41-38-1 32-78-33-1; 66-50-48-13-1 34-88-100-1; 75-68-51-29-1 28-73-77-1; 47-85-1; 87-2-36-1	19.84	1.72
4	32-5-7-85-1; 63-46-44-1 39-82-25-16-1; 67-54-8-64-1 26-99-1; 58-80-1; 35-98-55-1 4-17-69-30-1; 60-6-1 92-61-3-1; 65-21-23-1 97-95-91-49-1; 20-41-38-78-1 34-33-48-29-1; 59-24-1 81-79-14-1; 66-50-13-93-1 75-73-77-11-1; 28-68-51-1 96-40-53-1; 31-27-84-18-1 87-2-36-1; 89-42-83-94-1 76-12-43-1; 86-45-10-22-1 37-15-52-1; 70-56-1 47-88-100-1; 57-19-71-9-1	18.91	1.82

. As shown, 29 drivers were matched with suitable passengers, 99 participants’ travel needs were met, and a good result was achieved in carpooling.

When the total travel time reaches the optimal value, which is $F_1^{*}=18.78\mathrm{h}$, the corresponding driver and passenger loss time is $F_2=1.88\mathrm{h}$, which is increased by $\left(1.88-1.72\right)/1.72=8.74\%$ compared with the optimal value. When the loss time of drivers and passengers reaches the optimal value, which is $F_2^{*}=1.72\mathrm{h}$, the corresponding total travel time is $F_1=19.83\mathrm{h}$, which increases by $\left(19.83-18.78\right)/18.78=5.59\%$ compared with the optimal value.

To sum up, the dual objective matching model constructed in this paper does not have two objectives to achieve the optimal solution at the same time. When the decision-maker prefers to minimize the total travel time, in order to avoid congestion, drivers and passengers will depart earlier, which increases lost time. When priority is given to drivers and passengers with lost time, the departure time is easy to fall into a period of severe congestion, resulting in slower vehicle speed and more travel time. Decision-makers can choose the appropriate matching scheme according to their actual needs and preferences.

In light of

Table 7. Carpooling effect analysis.

Section	Total Travel Distance/km		Reduced Distance/km	Total Travel Time/h		Reduced Time/h
	Non-Carpooling	Carpooling		Non-Carpooling	Carpooling
1	926.7	396.6	530.1	55.75	18.78	36.97
2	926.7	409.1	517.6	55.75	19.33	36.42
3	926.7	417.8	508.9	55.75	19.84	35.91
4	926.7	400.4	526.3	55.75	18.91	36.84

, carpooling requires less travel time and distance under the same demand. By averaging the results of the four schemes, it can be concluded that total travel distance has decreased by about 56.19% and total travel time has decreased by about 65.52%. This indicates the effectiveness of the carpool matching model and algorithm in this paper, as well as the advantages and development potential of private carpooling.

4.3. Speed Sensitivity Analysis

This section compares the differences in the effectiveness of optimal matching schemes for seven roads with different speeds. It can be seen from

Table 8. Influence analysis of vehicle speed.

Road Name	Number of Pareto Solutions	Optimal Value of Total Lost Time/h	Optimal Value of Total Travel Time/h
Road 1	5	1.83	19.22
Road 2	4	1.79	19.56
Road 3	4	1.72	18.78
Road 4	3	1.82	18.66
Road 5	4	1.67	17.54
Road 6	4	1.61	17.89
Road 7	5	1.78	19.45

.

Under different road conditions, Pareto optimal solution and objective function values are different, and the time-varying road network has an unignored impact on commuting carpool matching. Therefore, considering the continuous variation of vehicle speed has strong practical significance.

5. Conclusions

In response to the current situation of urban congestion and the concept of green and sustainable development in various countries, this paper studies the problem of commuter carpool matching under time-varying road networks. Based on deep learning, the continuous variation of vehicle speed is described, and a multi-objective model that fully considers the needs and interests of drivers and passengers is constructed according to the characteristics of private carpooling. INSGA-II is designed for solution. Finally, the effectiveness of the algorithm and model is verified through experiments. It has been proven that constructing a multi-objective optimization model that emphasizes the fairness of the status of commuter carpooling participants can generate paths with higher matching degrees better optimization effects, and have positive significance for the implementation of carpooling. Also, compared with a static road network, carpool matching under a time-varying road network is more in line with the actual situation. According to the analysis of carpooling schemes under different roads, the speed has a greater impact on the matching results, so it is more practical to not set the speed as a constant value during simulation. Moreover, this paper combines an open-loop saving algorithm and a 2-opt local search strategy because of poor search efficiency in traditional genetic algorithms and improves the accuracy and speed of the algorithm.

Although this paper has made some achievements in commuter carpooling, there are many shortcomings in this paper due to the limited level. Therefore, in subsequent research, some of the ignored uncertainties, such as accidents, weather, sudden changes in road traffic environment, and dynamic changes of customer points on carpool matching, will be deepened. Also, the scenario discussed in this paper is only for appointments within a company, and multi-destination and dynamic matching can be carried out. Furthermore, limited by resources and conditions, the scale of road and carpooling demand studied is relatively small. To be more effective, a larger dataset is needed, which will continue to be improved in subsequent research.