Formulation of Green Metro Train Service Plan Considering Passenger Travel Costs, Operational Costs, and Carbon Emissions

Abstract

Grounded in the core principle of green transportation, this paper proposes a metro train service planning approach aimed at enhancing efficiency and reducing carbon emissions. The approach integrates environmental, passenger, and operator benefits, employing multiple train formations under full-length and short-turning route operations. Considering the high dimensionality of model variables and the complexity of the solution process, improvements are made to the neighborhood search strategy in the Adaptive Large-scale Neighborhood Search (ALNS) algorithm, and the improved algorithm is applied to the model solving process. Comprehensive data experiments are conducted to calibrate the algorithm parameters. Using Jinan Metro as a case study, the approach is empirically validated. The results demonstrate that, compared to the single-route and single-formation train service plans, the multi-route and multi-formation plan delivers superior performance in terms of carbon emissions, enterprise operating costs, and passenger travel time costs. Additionally, the Improved Adaptive Large-scale Neighborhood Search (IALNS) algorithm significantly outperforms the ALNS algorithm in both computational efficiency and solution quality. The main contribution of this paper is to balance the interests of both enterprises and passengers while effectively reducing carbon emissions. It also contributes to providing decision support for the green operation and sustainable development of metro systems.

1. Introduction

The metro system, characterized by high capacity, exceptional punctuality, and low energy consumption, delivers significant practical implications for promoting urban rail modernization, improving traffic environments, guiding spatial structure optimization, and fostering urban innovative development. As of the end of 2024, 58 cities in mainland China had operational urban rail transit systems comprising 361 lines spanning 12,160.77 km. Metro systems accounted for 9306.09 km, representing 76.53 percent of the total network length, while registering a net annual expansion of 936.23 km.

According to incomplete statistics, the total electricity consumption of urban rail transit in China reached 27.023 billion kWh in 2024, representing a year-on-year increase of 6.83%. Among this, traction energy consumption accounted for 14.150 billion kWh, with a year-on-year growth of 8.26%. Traction energy consumption constituted 52.36% of the total electricity consumption. With the persistent growth of newly commissioned lines, aggregate energy consumption metrics continue to rise, driving both total electricity consumption and traction energy usage to record highs. Based on total electricity consumption data and the grid CO₂ emission factors, the corresponding relationship between total electricity consumption and CO₂ emissions for urban rail transit in China from 2023 to 2024 is shown in

Table 1. Correspondence between total electricity consumption and CO₂ emissions of urban rail transit in 2023–2024.

Indicator	Year		YoY Change
	2023	2024
Total Electricity Consumption (MWh)	2,529,406.09	2,702,252.06	6.83%
Electricity Consumption per Vehicle-kilometer (kWh/veh·km)	3.56	3.54	−0.42%
Electricity Consumption per Passenger-kilometer (kWh/pax·km)	0.104	0.102	−1.34%
Total CO2 Emissions (tCO2)	13,572,793.10	14,500,284.57	6.83%
CO2 Emissions per 10,000 Vehicle-kilometers (tCO2/10,000 veh·km)	19.10	19.02	−0.42%
CO2 Emissions per 10,000 Passenger-kilometers (tCO2/10,000 pax·km)	0.556	0.549	−1.34%

. Table 1 reveals that in 2024, total CO₂ emissions increased by 6.83% year-on-year, while CO₂ emissions per vehicle-kilometer decreased by 0.42% and per passenger-kilometer emissions declined by 1.34% compared to the previous year.

A comparison of carbon emissions between the metro and other transportation modes reveals that the metro’s per capita energy consumption is only 5% of that of a gasoline-powered car. Meanwhile, high-speed rail emits merely 30.48 g of carbon per kilometer, which is only one-ninth of gasoline vehicles. Additionally, bus systems generate only one-third of the carbon emissions per 10 km compared to private cars. These findings collectively indicate that rail transit constitutes a green, low-carbon, and environmentally friendly transportation mode, excelling in carbon emission reduction compared to trams, buses, and private transportation.

Carbon emission characteristics and pathways to enhance emission efficiency exhibit significant heterogeneity across transportation systems of divergent types and varying network scales [1]. Current research primarily focuses on the calculation and forecasting of carbon emissions [2,3,4], analysis of emission-influencing factors [5,6,7], and emission mitigation methodologies [8,9,10]. Da Fonseca-Soares et al. utilized life cycle assessment methodology to quantify greenhouse gas emissions and highlighted the need for strategies to mitigate air pollution in urban transport systems [11]. Wang et al. used a difference-in-difference model to analyze the impact of the 21st Century Maritime Silk Road policy on SO2 emissions from coastal and inland ports in China [12]. Additional studies have explored pathways for energy conservation through utilization of redundant capacity [13], optimization of inter-station train operations [14], and multimodal route planning [15]. Lin et al. developed a bi-level programming model for railway network design that, unlike classical models, incorporates the opportunity cost and carbon emissions of infeasible flows in its objective function to balance investment and carbon emissions, while also addressing passenger flow, empty car flow, and corridor link relationships as per railway planning practices [16]. Wen et al. employed a system dynamics model to simulate carbon emissions in China’s freight transport system under 13 scenarios, identifying the key internal drivers [17].

Several scholars have also investigated the impact of metro operations on urban green development, demonstrating their intrinsic low-carbon, environmentally friendly, and sustainable attributes [18]. Jia et al. assessed the environmental impact of Beijing Metro by projecting carbon emissions and traffic congestion under scenarios where rail passengers switch to buses or taxis during morning and evening peaks, highlighting the significant role of the metro in alleviating traffic congestion and reducing carbon emissions [19]. Yang et al. demonstrated that subway openings significantly enhance green productivity, with stronger effects observed in larger cities and areas with higher digital infrastructure or regional competition [20].

It is evident that the metro, functioning as the backbone and core framework of urban public transportation, represents a pioneer of green mobility. Consequently, it should proactively respond to the Dual Carbon strategy and achieve carbon emission control through optimized transport organization planning. Train service plans constitute the core of transport organization, and their scientific formulation facilitates efficient passenger turnover, rational allocation of transportation resources, and enhanced utilization efficiency of equipment and facilities [21]. Specifically, the preparation process aims to determine the optimal routes, types of trains, service frequencies, train formations, and stopping patterns [22,23]. Xu et al. set the train operation ratio for different routes while considering passenger travel choice behavior to formulate the urban rail train service plan [24]. Shi et al. employed a two-stage approximation algorithm to conduct computational analysis on the express/local train plan problem [25]. Chen et al. developed a line plan model by regarding the imbalance in the spatiotemporal distribution of passengers, on the basis of passenger departure time choice behavior under uncertain conditions [26]. Yang et al. integrated virtual coupling technology with full-length and short-turning route operations, which facilitates better alignment of transport capacity with passenger demand [27]. Ding et al. developed a peak-period short-turning route strategy to mitigate congestion, demonstrating its efficacy through a Shanghai Metro case study [28]. Li et al. addressed the train planning problem involving multiple lines and diverse train configurations, determining turn-back stations, train consists, and service intervals for each line [29]. Lin et al. developed a multi-objective model with an improved harmony search algorithm for formulating train plans under multimodal rail integration conditions in metropolitan areas, generating train plans that effectively balance demand–supply and optimize existing infrastructure utilization [30]. Dai et al. developed a refined passenger flow classification using forecasted ridership data from Xi’an Metro Line 6, constructing low-carbon and eco-efficient full-length and short-turning route operation schemes [31]. Huang et al. optimized train timetables with energy conservation objectives using the Xi’an Metro network as a case study [32].

Through analysis of the existing literature, it is observed that current research on metro train service plans predominantly focuses on optimal routes, passenger flow allocation, and service frequency. In most studies, the objective of train service plan models is to minimize the costs for transport enterprises and passengers. Few scholars, however, have considered carbon emissions as an objective, let alone integrated this with the scheduling problems of multi-type urban rail trains.

To conserve resources and reduce carbon emissions, this paper develops a metro train service plan model integrating full-length and short-turning routes and variable train consists from the perspectives of enterprises, passengers, and environmental sustainability. The aim is to deliver more eco-efficient transport services while enhancing resource integration.

The key contributions of this paper are outlined below.

(1)

Investigating energy conservation and emission reduction from a transportation organization perspective, we propose a novel green metro train service plan model that optimizes service frequency, route strategies, and train formation configurations.

(2)

An Improved Adaptive Large-scale Neighborhood Search (IALNS) algorithm is proposed to solve the train service plan problem, which represents an innovation in algorithm design and application.

(3)

The proposed methodology maximizes rolling stock turnover efficiency while fulfilling passenger demand, concurrently reducing operator costs and carbon emissions, thereby fostering sustainable metro operations through green innovation.

The remainder of this paper is organized as follows. Section 2 mathematically formulates the problem and constructs the eco-efficient metro train service plan model. Section 3 designs an IALNS algorithm and presents the calculation steps for the train service plan model in Section 2. Section 4 verifies the effectiveness of the proposed method through a computational analysis based on a real case of Jinan Metro. Section 5 draws conclusions and suggests potential avenues for future research.

2. Train Service Plan Model

2.1. Assumptions

The construction of the train service plan model relies on the following simplified assumptions: (1) Passengers always prefer direct services. Transfer behavior occurs if and only if no direct train connects the origin and destination stations. Moreover, during their journey, passengers are allowed to transfer at most twice. (2) The various equipment and facilities at the turnaround stations, depots, and stabling yards, as well as the station platform lengths, all meet the requirements for operating a multi-formation train. (3) In the multi-formation operation mode, the speed of the long-formation train, the speed of the short-formation train, as well as their turnaround time and turnaround interval, are all the same. The train stopping plan is fixed, adopting the mode of stopping at every station. (4) According to the first-come, first-served principle, passengers always choose the first arriving train.

2.2. Mathematical Notation

The mathematical notation for the train service plan model is listed in

Table 2. The notations used in the model.

Notations	Description	Role
$W_1$	Total travel costs for passengers	Sub-objective
$W_2$	Operating costs for enterprise	Sub-objective
$W_3$	Carbon emissions from metro trains	Sub-objective
$T_{ij,k}^h$	Total travel time for passengers from station i to station j via travel path k during time period h	Intermediate variable
$T_{ij,k}^{h,wait}$	Waiting time for passengers from station i to station j via travel path k during time period h	Intermediate variable
$T_{ij,k}^{h,run}$	Onboard travel time for passengers from station i to station j via travel path k during time period h	Intermediate variable
$T_{ij,k}^{h,stop}$	Onboard dwell waiting time incurred by passengers traveling from station i to station j via travel path k during time period h at intermediate stations	Intermediate variable
$T_{ij,k}^{h,trans}$	Transfer time for passengers from station i to station j via travel path k during time period h	Intermediate variable
$P_{ij,k}^{h,crowd}$	The crowding-induced disutility cost for passengers traveling from station i to station j via travel path k during period h	Intermediate variable
$R$	Total power consumption over the study period	Intermediate variable
$R_{trac}$	Traction power consumption of metro trains	Intermediate variable
$R_{ligh}$	Power consumption of the lighting system in metro trains	Intermediate variable
$R_{sig}$	Power consumption of the signaling system in metro trains	Intermediate variable
$R_{air}$	Power consumption of the air conditioning system in metro trains	Intermediate variable
$f_{e,m}^h$	Service frequency of trains with m formations on train route e during period h	Decision variable
$x_{i,k}^e$	It takes a value of 1 if routing e services station i and aligns directionally with passenger path choice k, otherwise 0	0–1 variable
${\lambda }_{ij,k}$	It takes the value 1 if station j is directly accessible from station i on passenger path choice k without intermediate stops, otherwise 0	0–1 variable
${\delta }_{ij,k}$	It takes the value 1 if passengers traveling from station i to station j via path choice k incurs exactly one transfer along the entire path, otherwise 0	0–1 variable
$x_{u_1{u}_2,k}^{e^{\prime }}$	It takes the value 1 if routing $e^{\prime }$ services both transfer station $u_1$ and transfer station $u_2$ while aligning directionally with passenger path choice $k$, otherwise 0	0–1 variable
$H$	Set of research periods. Each research period h has a fixed duration of one hour	Set
$K$	Set of feasible passenger travel paths. k is an arbitrary route in the set	Set
$S$	Set of stations	Set
$E$	Set of train routes, where $e$ and $e^{\prime }$ are arbitrary routes in the set	Set
$m^{\prime }$	Short-formation train	Symbol
$m^{″}$	Long-formation train	Symbol
$q_{ij,k}^h$	Passenger flow from station i to station j via path k during time period h	Parameter
$c_{time}$	Monetary conversion coefficient for value of time	Parameter
$d_{ij,k}$	Distance from station i to station j traversing path k	Parameter
$v_{ij,k}^h$	Average running speed via path k from station i to station j during time period h	Parameter
$t_{stop}^h$	Average per-stop dwell time during period h, comprising boarding/alighting time and start–stop additional time	Parameter
$t_{walk}$	Transfer walking time	Parameter
$A_m$	Rated passenger capacity of an m-formation train	Parameter
$c_{vehi}$	Operating cost per vehicle-kilometer	Parameter
$b_m$	Total number of vehicles in an m-formation train	Parameter
$L_e$	The operating mileage of trains on route e	Parameter
$\xi$	Share of fossil fuel-fired power generation	Parameter
$F_{\mu ,m}$	Adhesive traction force of an m-formation train	Parameter
$N_{\mu ,m}$	Adhesive mass of an m-formation train	Parameter
$\mu$	Adhesion coefficient	Parameter
$v_e$	Average operating speed of trains on route e	Parameter
${\psi }_0$	Specific basic resistance	Parameter
$\theta$	Number of lighting fixtures per carriage	Parameter
$u$	Internal surface area of the carriage	Parameter
$\Delta t$	Indoor–outdoor temperature difference of the carriage	Parameter
$f_{\min }$	Minimum service frequency	Parameter
$f_{\max }$	The maximum capacity of lines and stations	Parameter
$q_n^h$	Cross-sectional passenger volume in section n during period h	Parameter
$N$	The total number of sections	Parameter
${\chi }_{\max }$	Maximum load factor	Parameter
$B$	The number of available vehicles per unit time period	Parameter

.

2.3. Objective Function

• Minimizing Total Passenger Travel Costs

Fundamentally, metro systems exist to serve passengers; consequently, enhancing service quality and minimizing full-cycle travel costs stand as paramount imperatives. In this paper, the total passenger travel costs are divided into three components: fare expenditure, time costs, and discomfort penalties. For metro systems, fares between specific origin–destination pairs are fixed constants unaffected by train service plan adjustments. Passenger comfort is predominantly influenced by train operational stability, onboard environmental conditions, and crowding levels. The first two factors primarily depend on hardware parameters, including track alignment geometry, infrastructure quality, and rolling stock configurations, while also being subject to human factors like operator proficiency. However, their linkage to train service plans demonstrates negligible correlation. In summary, the travel cost objective function in this paper is formulated primarily based on travel time and crowding level. Travel time consists of waiting time, in-vehicle time, dwell time at stations, and transfer time. We quantify time and crowding into a cost measure through the time value coefficient and the crowding perception penalty coefficient.

$$\min W_1={\displaystyle \sum _{i,j\in S}{\displaystyle \sum _{k\in K}{\displaystyle \sum _{h\in H}{q}_{ij,k}^h\cdot (c_{time}\cdot T_{ij,k}^h+P_{ij,k}^{h,crowd}}}})$$

(1)

$$T_{ij,k}^h=T_{ij,k}^{h,wait}+T_{ij,k}^{h,run}+T_{ij,k}^{h,stop}+T_{ij,k}^{h,trans}$$

(2)

Since the headways between metro trains are usually short, passenger arrivals can be considered a random normal distribution independent of the train timetable. In this case, the passenger mean waiting time at origin stations exhibits proportionality to half of the train headway [30,31].

$$T_{ij,k}^{h,wait}={\displaystyle \frac{1}{2{\displaystyle \sum _{e\in E}{\displaystyle \sum _{m\in \{m^{\prime },m^{″}\}}{f}_{e,m}^h\cdot x_{i,k}^e}}}}$$

(3)

The time passengers spend within a section consists of two components: in-train travel time while the train is in motion, and aggregate dwell time at intermediate stations. Transfer time comprises both walking time between platforms and waiting time for the connecting train.

$$T_{ij,k}^{h,run}+T_{ij,k}^{h,stop}={\displaystyle \frac{d_{ij,k}}{v_{ij,k}^h}}+(j-i-1)\cdot {\displaystyle \frac{t_{stop}^h}{60}}$$

(4)

$$T_{ij,k}^{h,trans}=(1-{\lambda }_{ij,k})\cdot [(2-{\delta }_{ij,k})\cdot {\displaystyle \frac{t_{walk}}{60}}+{\displaystyle \sum _{e,e^{\prime }\in E}{\displaystyle \sum _{m\in \{m^{\prime },m^{″}\}}\frac{1}{2}}}({\displaystyle \frac{1}{f_{e,m}^h\cdot x_{j,k}^e}}+{\displaystyle \frac{1-{\delta }_{ij,k}}{f_{e^{\prime },m}^h\cdot x_{u_1{u}_2,k}^{e^{\prime }}}})]$$

(5)

The crowding penalty can be determined based on the level of crowding along different paths. When passengers from station i to station j via path k during period h exceeds the rated capacity of the train, a crowding penalty is incurred.

$$P_{ij,k}^{h,crowd}=\left\{\begin{array}{l}0,q_{ij,k}^h\le {\displaystyle \sum _{m\in \{m^{\prime },m^{″}\}}{f}_{e,m}^h\cdot x_{\left|S_e\cap S_k\right|\ge 2}\cdot A_m\forall e\in \mathrm{E}}\\ 0.15\cdot {\displaystyle \frac{d_{ij,k}}{v_{ij,k}^h}}\cdot {({\displaystyle \frac{q_{ij,k}^h}{{\displaystyle \sum _{e\in E}{\displaystyle \sum _{m\in \{m^{\prime },m^{″}\}}{f}_{e,m}^h\cdot x_{\left|S_e\cap S_k\right|\ge 2}\cdot A_m}}}})}^4, \\ q_{ij,k}^h>f_{e,m}^h\cdot x_{\left|S_e\cap S_k\right|\ge 2}\cdot A_m\forall e\in \mathrm{E}\end{array}\right.$$

(6)

In the equation, 0.15 and 4 are dimensionless empirical coefficients for the disutility penalty [33]. It converts the discomfort penalty caused by crowding into monetary metrics. Let ${\mathrm{S}}_e$ and ${\mathrm{S}}_k$ represent the station sequence sets for train routing e and travel path k, respectively. $x_{\left|S_e\cap S_k\right|\ge 2}$ is a binary variable that takes the value of 1 if the intersection of ${\mathrm{S}}_e$ and ${\mathrm{S}}_k$ is a non-empty subset with more than one element; otherwise, $x_{\left|S_e\cap S_k\right|\ge 2}$ takes the value of 0.

2.

Minimizing Total Enterprise Operating Costs

The operating cost of enterprises consists of two components: fixed costs and variable costs. Given the limited correlation between fixed costs and train service plan formulation, this paper focuses exclusively on variable costs. The magnitude of variable costs depends on the number of vehicles, operating mileage, and the unit cost per vehicle-kilometer.

$$\min W_2=c_{vehi}\cdot {\displaystyle \sum _{e\in E}{\displaystyle \sum _{h\in H}{\displaystyle \sum _{m\in \{m^{\prime },m^{″}\}}{f}_{e,m}^h\cdot b_m\cdot L_e}}}$$

(7)

3.

Minimizing Carbon Emissions

In response to the carbon emission reduction objectives of green metro initiatives, this paper sets the minimization of carbon emissions during train operation as the objective function. Carbon emissions from the metro system primarily originate from train movements and station operations. The electricity consumption of these two components constitutes 82% of the total system carbon emissions [31]. Among them, the electricity consumed by station operation is primarily used for escalators, lighting, ventilation, and air conditioning. This consumption is relatively constant and is not directly related to the operation plan. Consequently, this paper exclusively considers carbon emissions from train movements.

According to national energy statistical reports, generating 1 kW·h of electricity consumes approximately 295 g of standard coal. The conversion coefficient from raw coal to standard coal is 0.7143 kg-ce/kg, with the CO₂ emission factor for raw coal being 1.9003 kg-CO₂/kg. Therefore, the calculation formula for carbon emissions from train operation during the study period is as follows:

$$\min W_3=R\cdot \xi \times 0.295\times 0.7143\times 1.9003$$

(8)

$$R=R_{trac}+R_{ligh}+R_{sig}+R_{air}$$

(9)

Electrical energy consumption during train movement is primarily consumed by the traction system, air conditioning systems, lighting equipment, and signaling systems. Traction energy consumption is calculated using kinematic methods, where the work performed during train operation is represented as the product of adhesive traction force, base resistance, and travel distance. The computational formula is as follows:

$$R_{trac}={\displaystyle \sum _{m\in \{m^{\prime },m^{″}\}}(F_{\mu ,m}+{\psi }_0\cdot N_{\mu ,m}\cdot g)\cdot {\displaystyle \sum _{h\in H}{\displaystyle \sum _{e\in E}{L}_e}\cdot f_{e,m}^h/3600}}$$

(10)

$$F_{\mu ,m}=N_{\mu ,m}\cdot g\cdot \mu$$

(11)

$$\mu =0.24+{\displaystyle \frac{12}{100+8v_e}}$$

(12)

$${\psi }_0=A+B\cdot v_e+C\cdot v_e^2$$

(13)

$g$ denotes the gravitational acceleration, $g=9.8 {\mathrm{m}/\mathrm{s}}^2$, while A, B, and C are empirical coefficients for base resistance (which are set to 2.4, 0.014, and 0.001,293, respectively, in this study).

Metro vehicle lighting fixtures are typically rated at 40 W per unit, while onboard signaling systems consume 230 W. The referenced 40 W value represents the power consumption of an individual luminaire, not the entire lighting system. For instance, Jinan Metro employs 40 W Philips F36-33 fluorescent lamps, though variations may exist across different cities. The air conditioning energy consumption is jointly determined by per-vehicle surface area, temperature differential between interior and exterior environments, and the number of vehicles. Consequently, power consumption for lighting, signaling, and air conditioning systems can be calculated separately using the following equations:

$$R_{ligh}={\displaystyle \sum _{h\in H}{\displaystyle \sum _{e\in E}{\displaystyle \sum _{m\in \{m^{\prime },m^{″}\}}{f}_{e,m}^h\cdot b_m\cdot \theta \times 40}}}/1000$$

(14)

$$R_{sig}={\displaystyle \sum _{h\in H}{\displaystyle \sum _{e\in E}{\displaystyle \sum _{m\in \{m^{\prime },m^{″}\}}2f_{e,m}^h\cdot b_m\times 230}}}/1000$$

(15)

$$R_{air}={\displaystyle \sum _{h\in H}{\displaystyle \sum _{e\in E}{\displaystyle \sum _{m\in \{m^{\prime },m^{″}\}}2u\cdot \Delta t\cdot f_{e,m}^h\cdot 3b_m}}}/1000$$

(16)

4.

Multi-Objective Function Integration and Optimization

Due to dimensional inconsistency and disparate orders of magnitude among the three objective functions, along with the inherent complexity in solving multi-objective problems directly, we first determine the maximum and minimum values for each single objective. Subsequently, the following normalization procedure is applied. Since the constraints in this paper directly define the feasible solution space, the maximum and minimum values can only be determined at or near these boundaries. Specifically, passenger travel costs increase with reduced service frequency and smaller train formations due to extended headways and heightened carriage crowding levels, whereas operator costs and carbon emissions rise with higher service frequencies, larger train formations, and longer routing distances.

$$U_i={\displaystyle \frac{W_i-W_i^{\min }}{W_i^{\max }-W_i^{\min }}},i=1,2,3$$

(17)

Finally, the objective functions are combined using the linear weighted sum method.

$$\min U={\sigma }_1\cdot U_1+{\sigma }_2\cdot U_2+{\sigma }_3\cdot U_3$$

(18)

where ${\sigma }_1$, ${\sigma }_2$, and ${\sigma }_3$ are the weight coefficients of different objective functions, and ${\sigma }_1+{\sigma }_2+{\sigma }_3=1$.

2.4. Constraints

• Minimum Departure Frequency and Maximum Capacity Constraints

Since train departure frequency must meet passenger travel demand while not exceeding station and line capacity constraints, it must be bounded by both a lower limit and an upper limit.

$$f_{\min }\le {\displaystyle \sum _{e\in E}{\displaystyle \sum _{m\in \{m^{\prime },m^{″}\}}{f}_{e,m}^h}}\le f_{\max },\forall h\in H$$

(19)

2.

Maximum Load Factor Constraint

During peak hours, allowing train overloading on specific sections can effectively enhance capacity utilization and operational efficiency. However, when the load factor reaches a critical threshold, passenger comfort rapidly deteriorates. Paradoxically, this undermines the operator’s ability to attract ridership. Therefore, the maximum load factor constraint is formulated as follows.

$${\displaystyle \frac{\max \left\{q_n^h\left|n=1,2,\dots ,N\right.\right\}}{{\displaystyle \sum _{e\in E}{\displaystyle \sum _{m\in \{m^{\prime },m^{″}\}}{A}_m\cdot f_{e,m}^h}}}}\le {\chi }_{\max },\forall h\in H$$

(20)

3.

Available Rolling Stock Constraint

Per-period rolling stock utilization remains bounded by contemporaneous fleet capacity.

$${\displaystyle \sum _{e\in E}{\displaystyle \sum _{m\in \{m^{\prime },m^{″}\}}{b}_m\cdot f_{e,m}^h}}\le B,\forall h\in H$$

(21)

4.

Train Frequency Range Constraint

The train service frequency in each time period must be a positive integer.

$$f_{e,m}^h\in {{\rm Z}}^{+},\forall e\in E,m\in M,h\in H$$

(22)

3. Algorithm Design

The train service plan problem has been proven NP-hard [34]. As the problem size increases, commercial optimization solvers fail to yield feasible solutions within a reasonable time. The ALNS algorithm incorporates a performance evaluation mechanism for operators. During each iteration, it preferentially selects operators demonstrating superior improvement effects, thereby enhancing the probability of obtaining satisfactory solutions within computationally acceptable time. This algorithm exhibits promising performance in solving train planning problems [35,36]. Considering the characteristics of the studied problem, this paper designs an IALNS algorithm. The algorithmic improvements primarily involve the initial solution construction method and the neighborhood search strategy.

3.1. Construction of the Initial Solution

In the initial solution, both the operating frequency of each rolling stock circulation and the train formation types are randomly generated while satisfying all constraints. To accelerate solution efficiency, this paper adopts the passenger flow sequencing strategy proposed by Binder et al. [37] and Li et al. [38], assigning passenger flows sequentially based on the ascending order of theoretical shortest-path costs across all OD pairs under the current solution.

3.2. Adaptive Large Neighborhood Search

Drawing on Reference [36], this paper constructs the neighborhood in each iteration using either a destroy operator or a repair operator. The operator for each iteration is selected via a roulette-wheel strategy. If the operator perturbation yields a feasible solution, the Metropolis criterion (Equation (23)) is employed as the acceptance condition for the neighborhood solution. If the optimal solution fails to update after $A_{\max }$ consecutive iterations at the same temperature, the inner loop is terminated. After executing the cooling strategy, it is necessary to check whether the convergence condition is met. The optimal solution is output when the temperature decays to the designated value $Te{p}_{end}$; otherwise, the iteration process continues.

$$p=\left\{\begin{array}{ll}1,& U<U^{\ast }\\ \exp [{\displaystyle \frac{-(U^{\ast }-U)}{Tep}}],& U>U^{\ast }\end{array}\right.$$

(23)

where $p$ denotes the acceptance probability of the new solution, $Tep$ represents the current temperature. The temperature is updated in each iteration according to the formula $Tep=\gamma \cdot Tep$, where $\gamma$ is the cooling factor. $U$ denotes the new solution, and $U^{\ast }$ represents the current solution.

This paper selects three destruction operators: reduction in train frequency, reduction in train formation number, and skipping of station stops. To avoid the algorithm getting trapped in local optima and to accelerate convergence, a random selection strategy (for destruction operators 1, 3, and 5) and a priority selection strategy (for destruction operators 2, 4, and 6) are designed based on the characteristics of the operators. The specific execution methods are as follows.

(1) Train frequency reduction operators: Reduce the train frequency of an operating train route by 1 or cancel the route. Destruction operator 1 uses a random selection mode, while destruction operator 2 selects a route with a lower load factor preferentially based on the roulette-wheel selection rule.

(2) Train formation reduction operators: Select a route with long-formation trains and convert these trains into short-formation trains. Destruction operator 3 adopts a random selection mode, whereas destruction operator 4 preferentially selects a route with a lower load factor.

(3) Stop-skipping operators: Select a station eligible for train stop-skipping, then randomly select a train service to implement stop-skipping at that station. Destruction operator 5 employs a random selection mode, whereas destruction operator 6 preferentially selects stations with lower passenger boarding and alighting volumes.

This paper designs three repair operators for neighborhood solution construction and the repair of infeasible solutions. Repair operator 1 randomly selects a route from the operating trains and increases its service frequency by 1, or selects a route that is not currently operated and sets its service frequency to $f_{\min }$. Repair operator 2 randomly selects a route with a short-formation train and changes it to a long-formation train. Repair operator 3 randomly selects a station currently skipped by trains, then randomly selects a route and changes the station from a skipped stop to a scheduled stop for that route.

At the beginning of each iteration, the category of the operator to be selected is determined based on its current weights. These weights are initialized before the iteration starts and updated according to their performance in previous iterations. The probability of each operator being selected is determined by its weight relative to other operators of the same type. The weight update formula is as follows:

$${\upsilon }_j^{i+1}=\tau \cdot {\upsilon }_j^i+(1-\tau )\cdot {\pi }_j^i$$

(24)

where ${\upsilon }_j^i$ represents the weight of operator j used in the i-th iteration, and ${\pi }_j^i$ denotes the score of operator j after the i-th iteration, quantifying the operator’s role in augmenting the objective function across iterations. The update formula is provided in Equation (25). $\tau$ is a control coefficient satisfying $0<\tau <1$.

$${\pi }_j^{i+1}=\left\{\begin{array}{l}{\pi }_j^i+\iota ,U<U^{\ast }\\ {\pi }_j^i-\iota ,U\ge U\end{array}\right.$$

(25)

where $\iota$ denotes the step size for operator score updating. All operators are assigned initial scores before the first iteration begins.

The occurrence of infeasible solutions during the iteration process is due to the inability to fully satisfy the constraint conditions. Therefore, the generated new solution must be verified, and if the solution is infeasible, the corresponding repair operator must be applied to transform it into a feasible solution. Repair operator 1 corresponds to destruction operators 1 and 2, repair operator 2 corresponds to destruction operators 3 and 4, and repair operator 3 corresponds to destruction operators 5 and 6.

3.3. Algorithm Solution Procedure

The procedure of the IALNS algorithm proposed in this paper is outlined below, with its corresponding flowchart illustrated in Figure 1.

Step 1: Import the basic data and configure algorithm parameters, including the initial temperature $Te{p}_0$, cooling coefficient $\gamma$, the count of iterations at each temperature $A_{\max }$, the current search count $trail(a)$, the termination temperature of the algorithm $Te{p}_{end}$, etc. Let $trail(a)=1$.

Step 2: Based on the initial solution construction strategy, randomly generate train routes that satisfy the constraint conditions, along with the corresponding service frequencies, train formation.

Step 3: Use the neighborhood search strategy, introduce destruction and repair operators to perturb the solution, and check whether the solution is feasible. If the solution is infeasible, apply the repair operators to restore feasibility.

Step 4: Evaluate the objective function, then apply the Metropolis criterion to decide if the current solution should be accepted. Update and record the current solution, then set $trail(a)=trail(a)+1$. Check whether the maximum iteration count at this temperature has been reached. If $trail(a)\ge A_{\max }$, proceed to Step 5; otherwise, return to Step 3.

Step 5: Check whether the algorithm has reached the termination temperature $Te{p}_{end}$. If the termination temperature is reached, output the optimal solution; otherwise, set $Tep=\gamma \cdot Tep$, $trail(a)=1$, generate a new solution by perturbing the current best solution, then proceed to Step 3.

4. Computation Case and Results Analysis

4.1. Basic Parameter Settings

This paper takes Jinan Metro as a case study, and the dataset is based on actual operational data. It should be emphasized that the proposed model is not specifically designed for Jinan Metro. The algorithmic improvements, such as the initial solution construction method and the neighborhood search strategy, are designed to address the general problem of train service plan optimization, independent of any particular route configuration. The real-world data from Jinan is selected solely for specifying model parameters in the case study. Replacing these parameters with data from any other urban rail system would yield optimal train service plans for that system.

The schematic diagram of the metro lines is shown in Figure 2. The average operating speeds of trains on Lines 1, 2, and 3 are 46 km/h, 45 km/h, and 42 km/h, respectively. Passenger flow data from a typical workday are selected, with its full-day passenger flow coefficients shown in Figure 3. As observed in Figure 3, Jinan Metro exhibits distinct morning and evening peak periods, with passenger flows typically more concentrated during the morning peak. The service frequency and train formation of urban rail transit are largely determined by passenger demand during peak hours. Consequently, this paper adopts the one-hour origin–destination (OD) passenger flow data from Jinan Metro’s morning peak period as the demand input. The corresponding peak-hour passenger demand is shown in Figure 4.

Field investigations revealed that the section mileages and train dwell times (including additional time for acceleration and deceleration) are listed in

Table 3. Section mileages of Jinan Metro lines.

Section	Distance (m)	Section	Distance (m)
Fangte–Jinanxi	1545	Beiyuan–Lishanlu	814
Jinanxi–Dayang	1994	Lishanlu–Qilipu	2377
Dayang–Wangfuzhuang	3953	Qilipu–Zhudian	1500
Wangfuzhuang–Yufuhe	2961	Zhudian–Bajianpu	2174
Yufuhe–Zhaoying	3136	Bajianpu–Jiangjiazhuang	2086
Zhaoying–Ziweilu	3424	Jiangjiazhuang–Fenghuanglu	1682
Ziweilu–Daxuecheng	1903	Fenghuanglu–Baoshan	3771
Daxuecheng–Yuanboyuan	1841	Baoshan–Pengjiazhuang	3755
Yuanboyuan–Chuangxingu	3003	Tantou–Jinandong	2524
Chuangxingu–Gongyanyuan	1975	Jinandong–Wangsheren	3145
Wangfuzhuang–Lashannan	1836	Wangsheren–Zhangmatun	2112
Lashannan–Lashan	3703	Zhangmatun–Bajianpu	2228
Lashan–Erhuanxilu	2055	Bajianpu–Huayuandonglu	1532
Erhuanxilu–Laotun	2040	Huayuandonglu–Dingjiazhuang	1619
Laotun–Baliqiao	836	Dingjiazhuang–Ligenglu	1050
Baliqiao–Yikanglu	987	Ligenglu–Aotizhongxin	888
Yikanglu–Jinanzhanbei	1175	Aotizhongxin–Longaodasha	1151
Jinanzhanbei–Jiluolu	1310	Longaodasha–Mengjiazhuang	2002
Jiluolu–Shengchanlu	1985	Mengjiazhuang–Longdong	1713
Shengchanlu–Beiyuan	1604

and

Table 4. Dwell times of Jinan Metro.

Station	Dwell Time (s)	Station	Dwell Time (s)	Station	Dwell Time (s)
Fangte	200	Laotun	80	Pengjiazhuang	110
Jinanxi	100	Baliqiao	85	Tantou	115
Dayang	80	Yikanglu	80	Jinandong	100
Wangfuzhuang	95	Jinanzhanbei	95	Wangsheren	85
Yufuhe	80	Jiluolu	100	Zhangmatun	85
Zhaoying	80	Shengchanlu	90	Huayuandonglu	95
Ziweilu	90	Beiyuan	90	Dingjiazhuang	90
Daxuecheng	85	Lishanlu	90	Ligenglu	90
Yuanboyuan	80	Qilipu	95	Aotizhongxin	95
Chuangxingu	80	Zhudian	85	Longaodasha	85
Gongyanyuan	110	Bajianpu	105	Mengjiazhuang	80
Lashannan	85	Jiangjiazhuang	80	Longdong	110
Lashan	80	Fenghuanglu	85
Erhuanxilu	90	Baoshan	90

.

Table 5. Parameter settings of the model.

Parameter	Value	Measurement Unit
$c_{time}$	25	CNY/h
$\left|H\right|$	17	h
$b_{m^{\prime }}$	4	Vehicle
$b_{m^{″}}$	6	Vehicle
$t_{walk}$	4.8	min
$c_{vehi}$	60	CNY/(Vehicle·km)
$\xi$	80	%
$N_{\mu ,m^{\prime }}$	146.2	t
$N_{\mu ,m^{″}}$	222.2	t
$\theta$	10	Count
$u$	322	m2
$\Delta t$	10	°C
$f_{\min }$	6	Train pairs/hour
$f_{\max }$	40	Train pairs/hour
${\chi }_{\max }$	120	%
$B$	210	Vehicle

presents the parameters associated with the model. To balance the interests of both passengers and operators while prioritizing the green urban rail objectives of improving efficiency and reducing carbon emissions, this paper adopts the expert scoring method to scientifically assign weights. We engage 22 experts to conduct the expert scoring for weight assignment. Ten experts are from Jinan Metro, including six train dispatchers (two representing each of Lines 1, 2, and 3), three duty supervisors (one representing each of Lines 1, 2, and 3), and three designers. The remaining 12 experts are from universities, all with extensive research experience in the field of transportation planning and management.

The expert scoring method is a widely adopted approach in multi-objective optimization, designed to determine the relative weights of objective functions through expert judgment. Each expert rates the importance of each objective function, with scores assigned based on its relative significance in practical decision-making. Following the collection of all expert ratings, the scores are aggregated and averaged across all experts. Since the weights of all objective functions must sum to unity, the expert ratings undergo normalization. This is achieved by dividing the rating for each objective function by the sum of all ratings, thereby ensuring the weights collectively sum to 1. By aggregating expert opinions and applying normalization, the final weights of the objective functions are determined as ${\sigma }_1=0.3$, ${\sigma }_2=0.3$, and ${\sigma }_3=0.4$.

4.2. Analysis of Solution Results

All cases in this paper are implemented using C# 12.0 programming on a computer with an Intel Core i7-12700H, 2.30 GHz, and 16 GB of RAM. After extensive repeated experiments, the algorithm parameters were determined as $Te{p}_0={10}^3$, $Te{p}_{end}={10}^{-3}$, $\gamma =0.96$, $A_{\max }=10$. This paper applies the IALNS algorithm to obtain a solution for the train service plan model. After 358 iterations, the total objective value converged to a minimum of 0.522. The optimal train service plan for the direction illustrated in the diagram is depicted in Figure 5. Since metro trains typically operate in pairs for upward and downward directions, the train frequency for the opposite direction is the same as that shown in the figure. For analytical clarity, the train frequencies mentioned in the following sections refer to the frequency for a single running direction.

4.2.1. Comparative Analysis of Models

Fixed objective weights are used to analyze the results across different models. To ensure a fair representation of multiple stakeholders’ interests, the weights assigned to the objective functions are kept unchanged. A comparison is conducted between the proposed model and the optimal solutions under single-route and single-marshaling patterns, as shown in

Table 6. Comparative analysis of different models.

Model	Line 1	Line 2	Line 3
This model	Long routing: 8 trains/h, 4 formation Short routing: 5 trains/h, 4 formation	Long routing: 10 trains/h, 6 formation + 5 trains/h, 4 formation Short routing: 6 trains/h, 6 formation	Long routing: 6 trains/h, 6 formation + 4 trains/h, 4 formation Short routing: 11 trains/h, 6 formation
Long routing model	13 trains/h, 4 formation	16 trains/h, 6 formation 5 trains/h, 4 formation	12 trains/h, 6 formation 12 trains/h, 4 formation
Long-formation model	9 trains/h, 6 formation	Long routing: 14 trains/h, 6 formation Short routing: 6 trains/h, 6 formation	Long routing: 9 trains/h, 6 formation Short routing: 11 trains/h, 6 formation
Short-formation model	13 trains/h, 4 formation	Long routing: 21 trains/h, 4 formation Short routing: 8 trains/h, 4 formation	Long routing: 13 trains/h, 4 formation Short routing: 17 trains/h, 4 formation
The currently implemented timetable	13 trains/h, 4 formation	20 trains/h, 6 formation	20 trains/h, 6 formation

. The variations in the values of each objective function under different schemes are illustrated in Figure 6 and Figure 7. From Figure 6 and Figure 7, it can be seen that compared with the single-routing model, the proposed model (mixed routing) better adapts to the spatial heterogeneity of passenger flow distribution and improves the utilization efficiency of transportation resources. Under the operation mode featuring a mix of full-length and short-turning routes and multiple train formations, the operator’s cost is reduced by CNY 203,496.72, representing a 21.54% decrease, while carbon emissions are reduced by 565,595.67 kg, corresponding to a 21.29% reduction. Meanwhile, passenger travel costs are reduced by CNY 60,138.45, a decline of 6.28%. Compared with the single large-marshaling model, the proposed model (multiple marshaling) reduces passenger travel costs by CNY 176,774.27, representing a 16.47% decrease; operator costs by CNY 52,958.16, a reduction of 6.67%; and carbon emissions by 161,301.02 kg, corresponding to a 7.16% decrease. Compared with the two aforementioned models (single-routing, single large-marshaling), the proposed model clearly demonstrates superior performance in terms of passenger travel time, operator cost, and carbon emissions.

Compared with the single small-marshaling model, the proposed model (multiple marshaling) reduces operator costs by CNY 37,167.60, representing a 4.77% decrease, and carbon emissions by 88,427.89 kg, corresponding to a 4.06% reduction. Although the proposed model results in an increase of CNY 39,705.75 in passenger travel costs, the number of train services under the single small-marshaling mode has already reached its capacity limit. In the event of a sudden surge in passenger demand, multiple marshaling modes would be insufficient to respond effectively. In contrast, the proposed model retains considerable capacity redundancy, allowing additional trains to be scheduled to accommodate fluctuations in passenger flow. Therefore, compared with the single small-marshaling model, the proposed model not only balances corporate interests and low-carbon environmental goals but also better serves diversified, high-flexibility, and high-capacity passenger transport demands.

Furthermore, we provide a comparative analysis against the currently implemented timetable of Jinan Metro. It should be noted that Lines 4–8 have not yet commenced operations, and the existing network operates exclusively in a single-route, fixed-formation mode. Full-length and short-turning routes with flexible train formations are planned for future implementation. From the comparative analysis shown in Table 4 and Figure 6 and Figure 7, it can be seen that the proposed model achieves a carbon emission reduction of 622,269.27 kg, decreases operator costs by CNY 220,627.92, and reduces passenger travel costs by CNY 132,889.92. These results confirm the validity of the proposed model. The operation mode featuring a combination of multiple routes with flexible train formations can better align with transportation demands, reduce operational costs, decrease carbon emissions, and advance green initiatives in practical applications.

4.2.2. Comparative Analysis of Algorithms

Since the performance of an algorithm is highly dependent on the selection of parameter values, horizontal comparisons among different algorithms may introduce bias. This occurs when one algorithm is assigned suboptimal parameter settings while another benefits from well-tuned parameters. Consequently, it is difficult to ensure that the observed differences in solution quality are entirely caused by the inherent differences in algorithm performance. Therefore, to ensure a fair comparison, the IALNS algorithm proposed in this paper is evaluated against the baseline ALNS algorithm (prior to improvements) under identical parameter configurations. As an example, the comparison is conducted using objective function weights set to ${\sigma }_1=0.3$, ${\sigma }_2=0.3$, and ${\sigma }_3=0.4$, and both algorithms are coded in C# and executed on identical hardware.

The optimal train service plan obtained by the ALNS algorithm is shown in Figure 8. As can be seen from Figure 8, the optimal solution obtained by the IALNS algorithm features shorter short-turn routes and a reduced total number of operating trains. As a result, train turnaround times are faster, fewer rolling stock units are required, and overall, the enterprise operating costs are reduced by CNY 109,973.52, while carbon emissions decrease by 304,991.04 kg. A comparison of the sub-objective function values obtained by the two algorithms is presented in Figure 9.

Additionally, Figure 10, illustrating the algorithm iteration process, visually demonstrates that the IALNS algorithm achieves both superior solution efficiency and higher solution quality. The ALNS algorithm converged to a minimum total objective value of 0.536 after 396 iterations. Compared to the ALNS algorithm, the IALNS algorithm resulted in a 2.61% decrease in the total objective value and improved the convergence speed by 9.6%. Overall, these results validate the efficacy of the algorithmic enhancements introduced in this paper.

5. Conclusions

This paper focuses on the development of a low-carbon and green metro train service plan in the context of sustainable development. Incorporating carbon emissions, passenger travel costs, enterprise operating costs, and various practical operational constraints, we establish a train service plan model featuring short-turn and full-length routing with flexible marshaling. In accordance with the characteristics of the model, the IALNS algorithm is selected to address the problem. Destruction and repair operators are introduced, along with the design of corresponding random selection and priority selection strategies. A detailed analysis is conducted using Jinan Metro as a case study. The results show that, in comparison with the single-route and single-formation operation mode, the combined operation mode of short-turn and full-length routes with multiple train formations can effectively reduce transportation costs and lower carbon emissions. Through the improved algorithmic design, both the number of iterations and the objective value are reduced, indicating a significant enhancement in the algorithm’s performance and a better adaptation to the characteristics of the model.

The proposed method balances the expectations of enterprises, passengers, and environmental protection, promoting the deep integration of energy conservation, emission reduction, and green development concepts with the development of the rail transit industry. It also enriches and advances the theory of transportation organization, providing a valuable reference for formulating more scientific and rational train service plans. In practical implementation, the proposed method may face challenges including heightened operational and scheduling complexity, as well as physical constraints such as limited turn-back station capacity and platform length. Moreover, it is prone to incidents where passengers bound for the terminal station of the long route mistakenly board short-turn trains, necessitating transfer at the turn-back station. Therefore, a more sophisticated passenger information system and higher-quality transportation service are required to effectively support its operation.

This paper only considers scenarios with fixed passenger demand and paired bidirectional train operations. The above analysis is confined to passenger flow equilibrium states, without accounting for variations during peak-to-off-peak transitions. In estimating carbon emissions, the train traction energy consumption is calculated using a kinematic approach, which accounts only for the basic running resistance while neglecting various additional resistances. Future research should consider various additional resistances and calculate carbon emissions using three operational models: traction, coasting, and braking. Additionally, the analysis of elastic passenger flow and the non-equilibrium state of passenger flow should be incorporated to address the limitations of this paper. Further directions should also consider how the multi-formation strategy affects the flexibility of train scheduling and identify major contributing factors to carbon emission reduction.