Optimal Scheduling of Electric Bus Fleets Considering Battery Degradation Effects

Abstract

During routine operation, the power batteries of electric buses (EBs) gradually age due to the combined effects of numerous factors, including charging/discharging cycles, load fluctuations, and ambient temperature. This paper focuses specifically on the problem of battery aging in the context of actual urban electric bus system operations. It explores how to comprehensively incorporate the battery degradation effect into optimization schemes for EB fleet scheduling. This paper proposes an integrated optimization methodology that combines a capacity degradation model, a scheduling optimization model, and a genetic algorithm. A comprehensive scheduling optimization model is constructed, incorporating vehicle procurement costs, operational charging costs, off-peak charging costs, and battery capacity degradation costs, subject to rigorously defined constraints. Subsequently, an improved genetic algorithm framework is developed. Finally, the constructed model is validated using operational data from the Chongqing bus system. An analysis of the optimization mechanisms is provided, and a sensitivity analysis is conducted on vehicle procurement costs and battery capacity degradation costs. Based on the results, the model can reduce the total cost to 92% of the original level, proving that it is effective to a certain extent in reducing the operating costs of electric buses.

1. Introduction

1.1. Background

The escalating global environmental crisis has prompted national governments to intensify their environmental protection efforts, with particular emphasis on mitigating localized ecological degradation. Among these measures, the electrification of public transit systems has gained international prominence, as electric buses demonstrate superior environmental performance compared with conventional diesel buses by reducing carbon emissions and lowering noise pollution [1]. As a pivotal component of China’s ecological civilization construction, electric bus networks have been extensively deployed nationwide and continue to expand across regions. Since their initial introduction in China in the 2010s, electric buses have undergone rapid proliferation alongside infrastructure development, characterized by three principal trends: systematic municipal policy support, exponential growth in fleet size, and large-scale deployment of charging piles and battery swapping stations [2]. This transition has contributed significantly to national carbon-reduction targets and environmental governance [1].

However, as the industry enters a phase of profound restructuring, the sustainable operation of electric bus systems faces numerous practical challenges. In terms of financial support, the gradual phasing out of subsidies has made the full lifecycle cost of vehicles increasingly prominent, while the replacement cost of power battery systems and residual value management have become critical factors affecting operational economics. Regarding market demand, profound changes in urban travel patterns have led to a persistent decline in traditional bus ridership. The rapid expansion of shared mobility, the continuous growth of rail transit networks, and shifts in commuting habits post-pandemic have collectively driven a long-term decline in demand for bus services [3]. The bus systems of some small and medium-sized cities have become trapped in a vicious cycle characterized by declining ridership, reduced services, and diminished appeal, directly threatening the sustainability of large-scale electric bus deployment.

To tackle these systemic challenges, building a resilient electric bus operation system requires breakthroughs across multiple areas. Technological progress should focus on developing high-durability battery materials, systematically improving vehicle economics by extending battery cycle life, reducing charging times, and lowering energy consumption per mile. AI can further boost system efficiency and flexibility through optimized energy management, vehicle control, and infrastructure design. In the future, AI is expected to become the “intelligent hub” of electric transport systems, which will depend on it to create a smart ecosystem integrating energy, transportation, and information [4]. In operations management, electrifying vehicles not only cuts carbon emissions and noise but also reshapes urban transit networks and energy system architectures. This calls for a multi-departmental policy framework to handle issues like grid pressure [5]. Exploring dynamic scheduling models based on big data analytics integrates real-time passenger flow, battery health, time-of-use electricity prices, and other data into decision-making. This enables the combined optimization of vehicle deployment and energy replenishment strategies. In terms of business model innovation, electric bus charging systems have advanced from slow charging to dynamic charging technologies. Future bus charging infrastructure might move toward distributed, intelligent, and dynamic setups, forming an energy-interactive system with the grid to improve overall efficiency [6]. Combining infrastructure layouts such as charging stations, energy storage facilities, and distributed energy centers can improve asset utilization and expand secondary applications of retired vehicle batteries. This promotes a circular economy involving energy storage, backup power, and low-speed vehicle propulsion. Such innovations address current cost barriers in electric bus operations and are transforming the value-creation mechanism of urban transport. They provide a solution framework for global urban green transitions that balance environmental and economic benefits.

1.2. Motivation and Literature Review

In this study, the battery parameter that demands primary attention is the State of Health (SOH), which represents the current level of health of the battery, usually expressed as a percentage. Generally, SOH denotes the decline in the battery’s maximum capacity. During the operation of electrical devices, various types of batteries, such as lithium batteries, experience gradual capacity loss as a result of a series of chemical reactions, and the complex operating conditions of electric vehicles inevitably accelerate this process. For electric buses, a reduction in battery capacity translates directly into decreased driving range, potentially leading to operational issues. Therefore, carefully monitoring the onboard battery SOH is of critical importance. Liu et al. [7] employed systematic review and meta-analysis methodologies to quantitatively assess key factors influencing electric vehicle performance. Findings indicate that environmental conditions and operational behavior significantly impact range and energy consumption performance, underscoring the need for enhanced multi-factor experimentation and data modeling within real-world operational scenarios.

However, to integrate battery health into an electric bus scheduling framework, it is insufficient merely to measure and record SOH; accurate forecasting is also required. To predict battery health, one must build an appropriate mathematical model based on existing data to estimate the rate of capacity degradation under varying conditions, such as different temperatures and operating intensities. This topic has long featured prominently in the field of electric vehicles, with numerous domestic and international researchers proposing diverse predictive approaches. Deng [8] presented an SOH estimation method for lithium-ion traction batteries by selecting a second-order Thevenin equivalent circuit model. The author analyzed the relationship between model parameters and state of charge (SoC), then employed a Kalman filter algorithm to estimate parameters under different operating conditions, achieving a high degree of accuracy. Yan [9] compared various models and ultimately selected a second-order RC equivalent circuit model for his analysis. Li [10] utilized data-mining techniques, constructing a neural network based on battery log data and driving records collected from the vehicle’s onboard computer. This approach enabled an in-depth study and accurate prediction of SOH without dismantling the battery. Xie [11] combined data mining with a recursive least squares (RLS) algorithm to predict the remaining useful life (RUL) of automotive batteries. Lin [12] applied a LightGBM model, addressing data sparsity issues and proposing specific handling strategies. Huang [13] compared electrochemical, equivalent circuit, and empirical models, concluding that artificial neural networks offered the best balance of simplicity and accuracy; thus, an LMBP neural network was constructed for SOH prediction. Shen et al. [14] also developed a neural-network-based predictive model for the SOH of new energy bus batteries. They analyzed extensive operational data, considered various driving conditions, and selected ten key features—voltage differential, operational day type, weather, start time, ambient temperature at start, etc.—to build their model. Zhang [15] proposed a gray-model–Markov chain method for SOH estimation. Wang et al. [16] introduced a joint estimation approach for SOH and RUL of lithium-ion batteries, extracting multiple health features and constructing a Gaussian Process Regression (GPR) model. Hu [17] employed a PSO-GPR model for SOH estimation and an improved Elman neural network (ENN) for RUL prediction. Cheng [18] approached SOH estimation from a mechanistic perspective, thoroughly analyzing the electrochemical processes, structural composition, and chemical transformations during charge-discharge cycles, and emphasizing capacity and internal resistance as evaluation metrics. Kang [19], noting the difficulty of direct measurement of pack internal resistance, utilized a Kalman filter algorithm to predict this parameter. Gao et al. [20] focused on using charging current as a proxy for remaining capacity estimation, arguing that internal parameters are difficult to measure directly and selecting charging current—less influenced by environmental factors—after Box–Cox transformation for model construction. Tang et al. [21] investigated battery characteristics under electric bus operating conditions, collecting and analyzing data to assess how real-world usage affects battery properties. Qi [22] studied the impact of different operating scenarios on bus battery health by examining charge–discharge attributes, driving conditions, and operational states. Using ampere-hour integral methods for SOH estimation and factor analysis to identify the most influential factors, the researchers then applied cluster analysis to categorize batteries by degradation rate. Wang et al. [23] designed an optimization method for wireless charging infrastructure layout that accounts for battery health. By estimating the aging rate through SoC variation intervals and employing a Tabu Search (TS) algorithm, they developed a layout optimization model.

In previous studies, both domestic and international researchers have extensively investigated the dispatching problem of electric buses. Similarly to other public-transport modes, electric-bus dispatching seeks to meet transport demand under resource constraints—fleet size, vehicle capacity and range, depot and charging-station locations—so as to maximize operational efficiency and minimize costs. Generally, when formulating an electric-bus dispatch strategy, scholars consider energy-replenishment methods and charging-station layout, charging strategies, and scheduling policies that accommodate operational uncertainties.

Sui et al. [24] summarized optimization research in public transport systems across timetables, routes, charging infrastructure and facilities, emphasizing the interdependence and importance of synergistic optimization among these elements. They noted that future research is shifting from localized optimization towards comprehensive optimization that integrates multi-dimensional objectives and element coupling. Zhang et al. [25] systematically reviewed research progress in electric bus vehicle scheduling and charging scheduling, encompassing optimization models, constraints, and algorithms. The authors noted that research is evolving from static planning towards dynamic, real-time, and multi-objective optimization, emphasizing that future efforts should focus on vehicle-to-grid (V2G) interaction and artificial-intelligence-assisted intelligent scheduling systems. The battery is the energy-storage device of an electric bus, and among its state parameters, SoC directly reflects remaining driving range and cannot be ignored. Jin [26] systematically reviewed SoC-aware dispatch methods—especially time-constrained models—summarized base formulations and solution algorithms, analyzed battery behaviors during operation, proposed a residual-range estimator, and finally embedded these into a genetic-algorithm-based dispatch model. Li et al. [27] studied the impact of a “shallow-charge/shallow-discharge” policy, incorporating departure constraints and in-service state dynamics, and developed an optimization algorithm validated numerically. Yang [28] compared slow-charging versus fast-charging/swapping, modeled each via network-compact and 0–1 integer program, and proposed an exact branch-and-price solution for dispatch.

Recent work has explored ultracapacitors alongside batteries. Song et al. [29] modeled a dual-system (battery + ultracapacitor) energy-decay dynamic, then solved the optimal energy-allocation via dynamic programming. Fusco et al. [30] considered mixed fleets of diesel, CNG, hybrid, and electric buses, constructing a comprehensive model that accounts for daily energy production, distribution, consumption, and charging to optimize fleet-wide dispatch.

It can be observed from

Table 1. Comparison of literature research contents.

Research	Research Direction
	Battery Capacity Degradation Model	Electric Bus Dispatching Model	Integration Model	Lexicographic Optimization
[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23]	√	×	×	×
[24,25,26,27,28,29,30]	×	√	×	×
[31,32,33]	√	√	√	×
This paper	√	√	√	√

that in the aforementioned studies, when conducting lifecycle economic assessments of electric buses and formulating scheduling strategies, most research focuses solely on energy consumption and electricity costs, prioritizing the maintenance of individual electric buses’ battery health. Incorporating the economic costs of battery degradation into the objective function remains relatively uncommon. When optimizing the full lifecycle costs of electric buses, efforts should focus on two fronts: leveraging technological iteration to reduce energy consumption and thoroughly exploring cost control potential within operational processes. This particularly addresses the challenge of managing degradation in the power battery system, a core component whose cost contribution throughout the vehicle’s lifecycle cannot be overlooked. Consequently, this study should prioritize developing optimized scheduling schemes for electric bus fleets that account for battery capacity degradation, fully considering its implications to construct a reasonable optimization model.

Power battery capacity degradation exhibits non-linear characteristics, with its deterioration process influenced by the interplay of multiple factors such as depth of charge and discharge. This degradation directly reduces the vehicle’s operational range and triggers a series of other adverse effects. Against this backdrop, intelligent algorithm-based scheduling optimization techniques demonstrate unique value. By constructing multi-objective decision models that deeply integrate battery degradation mechanisms into scheduling strategy formulation, synergistic optimization across multiple dimensions can be achieved.

The cost savings from scheduling optimization yield compound effects: extending battery replacement cycles directly reduces capital expenditure; optimized charging strategies enable more rational allocation of charging time; and enhanced vehicle usability reduces the need for spare vehicle provisioning. The distinctive advantage of this cost-reduction pathway lies in its avoidance of substantial hardware investments. Instead, it leverages data-driven management innovation to unlock latent asset potential, holding particular significance for public transport systems in smaller cities facing fiscal constraints. At this pivotal juncture of industry transformation, establishing an intelligent scheduling system that accounts for battery degradation constraints represents an effective approach to ensuring the sustainable development of public transport services.

After achieving effective battery SOH estimation, researchers have begun embedding SOH into dispatch optimization. Bie et al. [31] represented the dispatch problem as a directed network, defined objectives and constraints, and solved it using a simulated annealing algorithm with Gurobi-based charging plans. Duan [32] included SOH in a multi-route linear programming model, revealing how dispatch strategies influence SOH and its correlation with capacity. Zheng et al. [33] formulated battery degradation cost in a linear program and applied an immune optimization algorithm with greedy heuristics to solve the proposed dispatch problem.

1.3. Contributions

This paper first outlines the current status and challenges faced by domestic electric bus fleets. It then identifies feasible approaches to reduce operational costs at this stage, specifically through optimized scheduling to cut daytime operational expenses—particularly losses stemming from battery capacity degradation. Subsequently, it analyses and summarizes existing research on battery health state prediction and bus fleet scheduling optimization. Subsequently, a specific problem scenario is constructed. The operational costs of electric buses are divided into four distinct components and quantified. Constraints are imposed on the parameter ranges within the model, establishing a fundamental scheduling optimization framework. Subsequently, this paper proposes utilizing the lexicographic optimization method to enhance the original model. Through this refinement, the model can further reduce the cost associated with battery capacity degradation. Finally, a genetic algorithm is selected to solve for the optimal solution, forming a relatively standard genetic algorithm model.

Subsequently, Chongqing Bus Route 579 was selected as the study subject. Using test data from a specific model of BAIC Foton pure electric bus as a reference, the relevant data were input into the model. This yielded both an initial solution and an optimal solution, including the route chain, residual battery charge at the end of daytime operations, total cost, and detailed costs for each component. The results demonstrate a cost reduction in the optimal solution compared with the initial solution. Subsequently, the operational mechanism of the scheduling optimization model was analyzed by examining changes in component costs. A sensitivity analysis was then conducted on vehicle acquisition costs and battery acquisition costs by progressively increasing the proportion of battery acquisition costs in the total cost and evaluating the corresponding impacts. Finally, this paper presents a comparison of the output results before and after the algorithmic improvements, thereby validating the effectiveness of the enhancements.

Compared with previous studies, the uniqueness of this paper lies in integrating battery capacity degradation as an important factor into the scheduling optimization model for electric buses. Previous scheduling optimization models focused more on battery state of charge, mainly tracking the battery charge status of electric buses during operation and optimizing consumption rates to ensure that the entire bus fleet can operate reasonably with lower energy consumption via more efficient scheduling. However, current research on battery aging is limited to analyzing aging rates in experimental environments and has not been widely applied to practical scenarios. Unlike existing studies that combine the two aspects, this research adopts distinct research methods and modeling approaches, thereby demonstrating certain unique advantages.

2. Optimal Scheduling Model Formulation

2.1. Battery SoH Estimation Model

In the domain of lithium-ion battery health assessment, existing research has primarily constructed capacity-fade models driven by intrinsic battery parameters, relying on continuous monitoring of micro-scale variables such as electrode phase-transition characteristics and interfacial film evolution. In practical engineering applications—especially for commercial platforms like electric buses—real-time acquisition of these internal parameters is significantly constrained by onboard sensor precision and cost considerations. Core metrics such as electrode structural evolution require offline laboratory-grade instrumentation, and dynamic electrochemical impedance responses cannot be directly measured by conventional vehicle equipment. These technical bottlenecks limit the applicability of parameter-driven evaluation methods in real-world environments.

To overcome these limitations, current research is gradually shifting toward alternative assessment strategies based on vehicle operation data. In actual operating scenarios of electric buses, macro-scale parameters continuously recorded by the vehicle control system exhibit intrinsic correlations with battery aging. Cumulative driving mileage indirectly reflects cycle stress accumulation; charge–discharge depth and energy throughput directly correlate with active material loss; and ambient temperature fluctuations influence side-reaction kinetics. Compared with micro-electrochemical indicators such as voltage, these macro-operational parameters offer clear engineering advantages: their acquisition systems are fully integrated into standard vehicle configurations, requiring no additional hardware for full-cycle data capture; their sampling frequencies cover the dynamic features of battery usage; and their standardized data structures facilitate the development of platform-agnostic evaluation frameworks.

This data-driven innovation holds dual engineering value: it transcends the dependence of traditional detection methods on physical sensors, enabling indirect quantification of battery health; and it lays the groundwork for vehicle-to-cloud collaborative management systems, in which real-time data can be dynamically matched with historical aging profiles to continuously track battery lifecycle degradation trajectories.

Lam et al. [34] proposed a method for estimating battery capacity degradation:

$$\delta \xi =k_{s1}\cdot {SoC}_{dev}\cdot e^{\left(k_{s2}\cdot {SoC}_{avg}\right)}+k_{s3}\cdot e^{\left(k_{s4}\cdot {SoC}_{dev}\right)}$$

(1)

In this method, ${SoC}_{avg}$ represents the average SoC, defined as the average value of the SoC over a predefined period (such as a complete driving cycle), with respect to the amount of charge processed. ${SoC}_{dev}$ denotes the deviation of the state of charge, defined as the normalized standard deviation of the SoC relative to the average value over the cycle, used to quantify the fluctuations in SoC. $k_{s1}$, $k_{s2}$, $k_{s3}$, and $k_{s4}$ are fitting parameters, which depend on battery parameters and environmental conditions. This model is a prediction model for battery health based on the cycle amount of battery charging and discharging. The authors specifically studied the differences in the changes in battery health under different battery charge–discharge state ranges, different charging–discharging rates, different temperatures, and different intensities of regeneration systems, as well as under different total charging-discharging amounts. In this study, the authors found that for the battery charge–discharge state and temperature, the decline in battery health reaches the optimal value at a certain level; within a certain range, the higher the temperature and the stronger the regenerative braking, the higher the rate of decline in battery health. In this paper, the research on the changes in the battery’s state of charge and the relationship between the battery’s state of charge change range and the battery’s health condition is mainly referred to. By controlling other variables, the relationship between the total charge and discharge of the battery and the battery’s health condition can be obtained, and the ability to predict the battery’s health condition can be established.

In the original study, the calculations for ${SoC}_{avg}$ and ${SoC}_{dev}$ were relatively complex. In a separate investigation, Zhang et al. [35] proposed a streamlined computational framework for the aforementioned variables:

$${SoC}_{avg}={\displaystyle \frac{{SoC}_{max}+{SoC}_{min}}{2}}$$

(2)

$${SoC}_{dev}={\displaystyle \frac{{SoC}_{max}-{SoC}_{min}}{2}}$$

(3)

where ${SoC}_{max}$ is the maximum state of charge observed during a single predefined cycle, and ${SoC}_{min}$ is the minimum state of charge in that same cycle. Because each charge–discharge cycle induces some capacity fade, the battery’s lifetime may be expressed in terms of the total energy throughput over its service life. This establishes a quantitative relationship between the cumulative charge-discharge throughput of an electric bus and its battery-capacity loss, thereby enabling one to estimate capacity fade by recording the bus’s total charge–discharge energy. The principal advantage of this modeling approach lies in its elimination of the need for real-time monitoring of internal microscopic battery parameters (e.g., SEI-film thickness, changes in electrode porosity, etc.); instead, capacity fade can be evaluated online solely from the macroscopic energy-flow data recorded by the vehicle’s BMS, thereby greatly reducing the complexity of the data-acquisition system. However, the accuracy of this method hinges on the proper calibration of the SoC thresholds: if the actual operating SoC frequently falls outside the preset range, dynamic compensation factors must be introduced to correct the model’s outputs.

2.2. Problem Description

When conducting research on the optimization of electric bus scheduling, constructing a mathematical model with engineering guidance value requires the systematic integration of multi-dimensional operational factors. At the fleet resource allocation level, it is essential to conduct an in-depth analysis of transport capacity demand characteristics across different traffic scenarios. At the vehicle technical parameter level, the focus should be on examining technical heterogeneity within the fleet. Differences exist in the performance of power battery systems between buses of different batches or models. Specifically, key metrics such as nominal battery pack capacity, charging rate, energy density, and cycle life exhibit technical variability. These discrepancies directly impact individual vehicle range per charge, required charging time windows, and full-lifecycle operational costs. Regarding operational load dimensions, a multi-scale evaluation framework must be established. At the micro level, daily mileage correlates with battery cycle counts; at the macro level, time constraints define charging facility utilization windows, while service intervals influence vehicle turnaround efficiency. Charging window limitations constrain the formulation of energy replenishment strategies. These operational parameters interact through complex non-linear mechanisms to shape the feasible boundaries of vehicle scheduling solutions.

Within this framework, a scheduling model is constructed. Each decision moment corresponds to a time node when the vehicle completes its trip and returns to the depot. The system state is defined by the remaining battery charge of each vehicle and the queue of pending trips. The objective function is to minimize the sum of vehicle acquisition cost, total charging cost, and battery degradation cost while ensuring the completion of all scheduled trips. By using a genetic algorithm, the optimal charging strategy sequence is determined to achieve coordinated optimization between operational economics and battery life. This baseline model provides an expandable platform for future research, and the model’s practical relevance can be gradually improved by relaxing assumptions such as homogeneity or introducing factors such as stochastic traffic delays.

The core decision-making mechanism in this study is designed such that after each bus completes its current trip and returns to the depot, it triggers a charging decision process based on the real-time battery charge status. Several constraints are defined: when the vehicle’s remaining charge falls below a predefined safety threshold, if the next task is carried out, the system will force the charging process to prevent deep discharge of the battery. The choice of charging strategy will directly affect the subsequent trip’s range and the charging facility’s utilization efficiency, thus requiring the optimization of the charging decision sequence under the premise of meeting operational demands.

In various scheduling optimization studies, researchers often create different research environments for their studies. In this research, in order to focus as much as possible on the scheduling optimization, some details and micro-level factors will be simplified. To build the baseline analysis model, the following key assumptions are made:

(1)

All buses in the fleet use identical powertrain configurations, and their initial states are the same.

(2)

The route operational parameters are fixed, and the depot is equipped with a sufficient number of dedicated charging stations with stable and non-fluctuating output power.

(3)

Vehicles will operate according to the planned timetable at a constant speed, ignoring time deviations due to road congestion.

(4)

Daily capacity degradation is minimal, and its impact on the capacity of power batteries can be neglected within the 24 h operational cycle.

(5)

Battery cycle life is only related to the accumulated equivalent full charge cycles, with calendar aging effects excluded.

2.3. Model Formulation

In order to construct the scheduling model, the relevant parameters and variables need to be introduced, as detailed in

Table 2. Parameters.

Parameter Name	Parameter Symbol	Parameter Unit
Vehicle purchase cost	$C^{buy}$	yuan
Battery purchase cost	$C^{batt}$	yuan
Vehicle charging power	$P_{chg}$	kW
Unit energy consumption of vehicles	$\rho$	Wh/km
Power battery capacity	$E_{max}$	kWh
Vehicle service life	$L$	years
Total length	$d$	km
Single operation time	$t_{au}$	min
Daytime electricity price	$p_1$	yuan/kWh
Nighttime electricity price	$p_2$	yuan/kWh
Charging specified time	${\mathit{\Delta }}_{max}$	min

and

Table 3. Variables.

Variable Name	Meaning
$U_k$	$\mathrm{whether} \mathrm{bus} k$ has undertaken any scheduled trip tasks
$X_{ij}$	$\mathrm{whether} \mathrm{the} \mathrm{logical} \mathrm{relationship} \mathrm{where} \mathrm{a} \mathrm{bus} \mathrm{performs} \mathrm{trip} i$$\mathrm{followed} \mathrm{immediately} \mathrm{by} \mathrm{trip} j$ is hold
$Y_{ij}$	$\mathrm{whether} \mathrm{a} \mathrm{bus} \mathrm{undergoes} \mathrm{a} \mathrm{charging} \mathrm{operation} \mathrm{prior} \mathrm{to} \mathrm{performing} \mathrm{trip} j$
$e_{k,t_j^{-}}$	$\mathrm{the} \mathrm{energy} \mathrm{level} \mathrm{of} \mathrm{vehicle} k$$\mathrm{before} \mathrm{completing} \mathrm{shift} j$
$e_{k,t_j^{+}}$	$\mathrm{the} \mathrm{energy} \mathrm{level} \mathrm{of} \mathrm{vehicle} k$$\mathrm{after} \mathrm{completing} \mathrm{shift} j$
$e_{k,t_{last}^{+}}$	$\mathrm{the} \mathrm{energy} \mathrm{level} \mathrm{of} \mathrm{vehicle} k$ at the moment when the last shift is completed
$e_{k,l}^{lost}$	the capacity loss experienced by vehicle k in the l-th cycle
$M_k$	the total energy cycles of vehicle k
$w_{k,l}$	the total charge/discharge amount for vehicle k during the l-th cycle
${{SoC}_{avg}}_{k,\mathcal{l}}$	the average SoC of vehicle k in the l-th cycle
${S{oC}_{dev}}_{k,\mathcal{l}}$	the standardized standard deviation of the SoC for vehicle k in the l-th cycle
$t_i^{end}$	$\mathrm{the} \mathrm{time} \mathrm{when} \mathrm{the} \mathrm{vehicle} \mathrm{completes} \mathrm{executing} \mathrm{shift} i$
$t_j^{start}$	$\mathrm{the} \mathrm{departure} \mathrm{time} \mathrm{for} \mathrm{shift} j$
$\mathit{\Delta }{e}_{k,i\to j}$	$\mathrm{the} \mathrm{amount} \mathrm{of} \mathrm{energy} \mathrm{the} \mathrm{vehicle} \mathrm{charges} \mathrm{between} \mathrm{shifts} i$$\mathrm{and} j$

, respectively.

In this paper, we study the entire fleet of buses serving a single route. Let K represent the set of all buses in the fleet, with $k\in K$ representing each bus in the fleet. The process in which a bus departs from the origin station, runs to the destination, and returns is defined as a “trip.” Let T represent the set of all trips that need to be executed on a given day, with $i,j\in T=\{0,1,2,\dots ,N\}$ being specific trips within the set.

In the operation of electric buses, the charge–discharge range of the traction battery is specified as $[{SoC}_{min},{SoC}_{max}]$. Here, ${SoC}_{max}$ denotes the upper bound of the prescribed energy cycling range, while ${SoC}_{min}$ represents the lower bound. Both ${SoC}_{max}$ and ${SoC}_{min}$ take values within the interval $(0,1]$, with the constraint that ${SoC}_{max}>{SoC}_{min}$ must be satisfied.

The model introduces three decision variables: $U_k$, $X_{ij}$ and $Y_{ij}$. Specifically, $U_k$ is a binary variable used to indicate whether the bus $k$ has undertaken any scheduled trip tasks. If it has executed at least one trip, $U_k$ = 1; otherwise, $U_k$ = 0. $X_{ij}$ represents the logical relationship where a bus performs trip $i$ followed immediately by trip $j$. If this condition holds, then $X_{ij}$ = 1; if not, $X_{ij}$ = 0. $Y_{ij}$ denotes whether a bus undergoes a charging operation prior to performing trip $j$, given that it has previously completed trip $i$. If charging occurs, then $Y_{ij}$ = 1; otherwise, $Y_{ij}$ = 0.

In this study, the core of scheduling optimization lies in minimizing the total lifecycle operating costs of electric buses. To achieve this, we define the objective function as the total cost incurred during the operation of the vehicles, and in the subsequent optimization process, we aim to minimize this function’s value. In alignment with the research context, the objective function needs to comprehensively reflect four major cost elements: first, the capital expenditure related to vehicle acquisition; second, the electricity costs incurred from multiple charging sessions during daily operations; third, the electricity costs and related expenses during centralized overnight charging; and fourth, the capacity degradation costs arising from the repeated charge and discharge cycles of the battery.

2.4. Main Formulation

Based on these considerations, the objective function of this scheduling optimization model is composed of the sum of these costs, which will guide the evolution and optimization of the scheduling strategy.

$$minZ=Z_1+Z_2+Z_3+Z_4$$

(4)

The capital expenditure related to vehicle acquisition $Z_1$ is

$$Z_1=\sum _{k\in K}{U}_k·{\displaystyle \frac{C^{buy}}{L·365}}$$

(5)

The electricity costs incurred from multiple charging sessions during daily operations $Z_2$ is

$$Z_2=\sum _k\sum _{j=1}^N\left[Y_{k,j}·P_{chg}·{\Delta }_{max}\right]·p_1$$

(6)

The electricity costs and related expenses during centralized overnight charging $Z_3$ is

$$Z_3=\sum _k{U}_k·\left[{SoC}_{max}·E_{max}-e_{k,t_{last}^{+}}\right]·p_2$$

(7)

The capacity degradation costs arising from the repeated charge and discharge cycles of the battery $Z_4$ is

$$Z_4=C^{batt}·{\displaystyle \frac{{\sum }_k{\sum }_{l=1}^{M_k}{e}_{k,l}^{lost}}{1.0-{SoC}_{min}}}$$

(8)

where $e_{k,l}^{lost}$ is

$$e_{k,l}^{lost}={\delta \xi }_{k,l}·{\displaystyle \frac{w_{k,l}}{E_{max}}}$$

(9)

and ${\delta \xi }_{k,l}$ is

$$\begin{array}{c}{\delta \xi }_{k,l}=k_1·{SoC}_{{dev}_{k,\mathcal{l}}} ·\exp \left(k_2·{SoC}_{{avg}_{k,\mathcal{l}}}\right)+k_3·\exp \left(k_4·{SoC}_{{dev}_{k,\mathcal{l}}}\right)\end{array}$$

(10)

where $k_1$ to $k_4$ are model parameters, where $k_1=-4.09\times {10}^{-4}$, $k_2=-2.167$, $k_3=1.418\times {10}^{-5}$, $k_4=6.13$ [35].

In the operational phase,

$${SoC}_{avg}={\displaystyle \frac{e_{pre}+e_{post}}{{2E}_{max}}} {SoC}_{dev}={\displaystyle \frac{e_{pre}-e_{post}}{{2E}_{max}}}$$

(11)

At this point, $e_{pre}$ represents the state of charge of the vehicle before the shift is executed, and $e_{post}$ represents the state of charge of the vehicle after the shift is completed.

In the charging phase,

$${SoC}_{avg}={\displaystyle \frac{e_{post}+e_{pre}}{{2E}_{max}}} {SoC}_{dev}={\displaystyle \frac{e_{post}-e_{pre}}{{2E}_{max}}}$$

(12)

At this point, $e_{pre}$ represents the state of charge of the vehicle before charging, and $e_{post}$ represents the state of charge of the vehicle after charging [23].

To ensure that the data remains within realistic bounds during the optimization process, a series of constraint conditions must be established.

$$\sum _k{X}_{k,i}=1 \forall i=1,\dots ,N$$

(13)

$$t_i^{end}+\left\{\begin{array}{cc}\hfill t_{au},& \mathrm{i}\mathrm{f} {\mathrm{Y}}_{\mathrm{k},\mathrm{j}}=0,\\ t_{au}+{\Delta }_{max},& \mathrm{i}\mathrm{f} {\mathrm{Y}}_{\mathrm{k},\mathrm{j}}=1\end{array}\right.\le t_j^{start} \forall k,X_{k,i,j}=1$$

(14)

$$e_{k,t_i^{-}}-\rho d\ge {SoC}_{min}·E_{max} \forall k,i$$

(15)

$${SoC}_{min}{E}_{max}\le e_{k,t}\le {SoC}_{min}{E}_{max} \forall k,t$$

(16)

where Equation (13) means full coverage and unique assignment of shifts: Each shift must be executed, and each shift can only be assigned to one vehicle. Equation (14) ensures time feasibility: The time interval between consecutive shifts must be sufficient for a smooth transition. Equation (15) means the vehicle’s battery energy must always be above the minimum allowable charge level. Equation (16) means the battery charge level of the electric bus must always remain within the specified cycling range.

2.5. Model Enhancement

In the previous algorithm, the battery capacity degradation cost could be effectively reduced. However, based on the sensitivity analysis results, it is evident that under typical conditions, battery cost accounts for only a limited proportion of the total vehicle procurement cost. In most cases, the weight of vehicle procurement cost outweighs that of battery degradation cost. To enhance the relative importance of battery degradation cost within the optimization process, the original algorithm can be modified so that this cost component becomes a more prominent optimization objective.

To achieve this, the lexicographic optimization method can be employed. Lexicographic optimization is a hierarchical multi-objective optimization strategy. Its core idea is to rank multiple objective functions by priority and optimize them sequentially. Each objective is optimized only after a higher-priority objective has reached its optimum, and the optimization of a lower-priority objective must not compromise the optimality of any higher-level objective. Unlike commonly used methods such as linear weighting or penalty functions, the lexicographic approach does not aggregate multiple objectives into a single scalar function. Instead, it preserves the hierarchical structure among objectives, providing a more structured and principled optimization framework.

To apply the lexicographic method, the original objective function needs to be decomposed into two parts: a primary objective $Z_{main}$, which consists of other cost components, and a secondary objective $Z_4$, which represents the battery capacity degradation cost that is the focus of this study.

$$Z_{main}=Z_1+Z_2+Z_3$$

(17)

After applying the lexicographic method, the optimization process is divided into two stages. The objective of the first stage is to minimize the primary objective. In this stage, a genetic algorithm is employed to search over the entire feasible solution space to obtain the optimal value $Z_{main}^{🞶}$.

In the second stage, the goal is to minimize the secondary objective while remaining within an acceptable range of the primary objective. To achieve this, a relaxation parameter $\epsilon$ (e.g., 2%) is defined, and a threshold is set as $THRESH=Z_{main}^{🞶}\cdot (1+\epsilon )$.

Then, the battery capacity degradation cost is further optimized among the feasible solutions that satisfy the following condition:

$$Z_1+Z_2+Z_3\le THRESH$$

(18)

The final output is the scheduling solution that achieves the lowest battery degradation cost under the condition that the primary objective remains “nearly optimal”.

2.6. Genetic Algorithm

This paper selects the genetic algorithm (GA) to solve the optimization problem of electric bus scheduling. The genetic algorithm is an intelligent optimization algorithm that simulates biological evolution. By mimicking mechanisms such as natural selection, crossover, and mutation, it searches for the optimal solution in the solution space. The selection of the genetic algorithm in this study is based on the following considerations:

As a metaheuristic approach based on population search, the GA can be applied to large-scale combinatorial optimization problems. It can explore multiple solution paths simultaneously and is suitable for NP-hard problems such as flight scheduling and vehicle dispatching. Compared with single-point search, the GA maintains solution diversity through crossover and mutation and is less likely to become trapped in local optima in the solution space. The parallel population search of the GA enables more efficient global sampling for the bus scheduling problem, which involves the assignment of multiple buses, multiple shifts, and charging decisions. The fitness function, the core component of the GA, can effectively integrate these multiple objectives. Using weighting or penalty mechanisms, it can handle both hard and soft constraints. This programmable fitness evaluation allows rapid adjustment of the weights of each cost component, satisfying scheduling optimization requirements under different operational strategies or electricity price policies.

In bus scheduling work, it is necessary to comply with various complex constraints such as time alignment, voltage threshold, and charging time limit. The GA has strong constraint handling capabilities. It can perform feasibility screening on the initial population, perform local repair after crossover or mutation, and set penalty functions to impose high-cost penalties on individuals that do not meet hard constraints.

The detailed implementation process of the genetic algorithm in this study is shown in Figure 1, and the specific process settings are as follows:

Each individual is represented by a vector $C=(c_1,c_2,\dots ,c_N)$, where $c_j=k$ indicates that trip $j$ is assigned to vehicle k in the fleet. During vehicle assignment, trips are allocated sequentially according to their departure times. Specifically, the strategy assigns the first trip to the first vehicle, and then assigns the next trip to the next vehicle in order. During each allocation, there is a probability of $\epsilon =0.5$ that a random selection is made, thereby generating an initial candidate solution. During vehicle assignment, trips are allocated sequentially according to their departure times. Specifically, the strategy assigns the first trip to the first vehicle, and then assigns the next trip to the next vehicle in order. During the initial generation, crossover operation and mutation operation, each individual undergoes a “time–energy feasibility” check: if there exists a pair of consecutive trips with insufficient connection time or the assigned vehicle lacks the required battery energy to complete the trip, the chromosome is discarded and resampled. This ensures that all individuals in the population always satisfy the fundamental constraints. For chromosomes with time conflicts or violations of the minimum SoC threshold caused by random assignments, a local reallocation strategy is applied—conflicting trips are reassigned to available vehicles randomly. The population size is fixed at $P=30$.

To reflect the goal of minimizing total cost, the fitness value $f$ of an individual is defined as the reciprocal of the objective cost $Z$ in Equation (19).

$$f\left(C\right)={\displaystyle \frac{1}{1+Z\left(C\right)}}$$

(19)

To address the potential issue of the objective function $Z$ taking a value of zero—which would result in a mathematical indeterminacy when taking its reciprocal—a positive constant is introduced into the denominator to shift the cost function appropriately.

In the selection operation phase, the roulette wheel selection strategy can be employed. In this process, the total fitness of the population is defined as $F=\sum f_i$, and the selection probability for individual i is set as $f_i/F$. During the individual evolution process within the GA, a crossover genetic operation strategy is employed to fully explore the solution space and promote beneficial recombination. This operation entails selecting two parent chromosomes from the current population and subsequently performing a random exchange of segments at identical positions between them, thereby generating two offspring chromosomes exhibiting a hybridized structure. After that, to enhance solution diversity and facilitate the discovery of superior scheduling configurations during the optimization process, an improved local perturbation-based mutation strategy is employed. The fundamental operation of this strategy involves randomly selecting a chromosome from the current solution and subsequently swapping the vehicles assigned to two specific shifts within it, thereby generating a new solution. The relevant references provide a more detailed description of the operation methods mentioned in this article [36].

In this study, considering the balance between problem scale and computational resources, a fixed iteration count is used as the termination criterion. Specifically, the algorithm will stop once the preset maximum number of iterations $G_{max}$ is reached, regardless of whether the optimal solution continues to improve. The algorithm will then terminate and output the best scheduling solution found in the final generation.

3. Case Study and Analysis

3.1. Case Study

In this study, vehicle parameters are based on the pure electric bus model of BAIC Foton, as listed in

Table 4. Vehicle parameters.

Parameters	Value
Battery capacity	215 kWh
Unit driving energy consumption	549 Wh per km
Charging power	197.64 kW
Purchase cost of a single vehicle	1.2 million yuan
Battery replacement cost	258,000 yuan
Battery design lifespan	10 years

.

To construct a realistically representative scheduling scenario, the study selects the 579 bus route in Chongqing as a typical case for modeling and analysis. The route is shown in Figure 2, and the corresponding route parameters are listed in

Table 5. Route parameters.

Parameters	Value
Total route distance	58 km
Time required for a single trip	85 min
Bus departure interval	20 min
Size of bus fleet	10 buses

.

Regarding the schedule arrangement, the vehicle operates daily from 6:00 AM to 9:00 PM. Additionally, considering local policies and market electricity prices, the electricity pricing in Chongqing is set as follows: During daytime hours, the rate is ¥0.52 per kWh, while the nighttime electricity price is ¥0.36 per kWh.

For battery energy management, the charge and discharge control range is set between 20% and 100% to ensure the safety and longevity of the battery. At the same time, the fixed time for charging is set at 35 min to reflect the actual charging equipment efficiency and the coordination demands of operational scheduling.

Next, based on the aforementioned actual data, we will perform the solution process. First, an initial feasible solution will be generated using the initialization strategy. This solution reflects the basic operational state of the vehicle scheduling and charging arrangement under the current parameter conditions before any optimization algorithm iterations and improvements. The specific trip chain corresponding to the initial solution is detailed in

Table 6. Trip Chain of Initial Solution.

Bus ID	Assigned Trip Chain	End-of-Daytime Remaining SoC
1	0, 22, 29, 43	40.8%
2	1, 10, 17, 27, 33, charge, 39	64.8%
3	2, 11, 23, 37	40.8%
4	3, 16, 28, 36, 42	25.9%
5	4, 9, 25, 34, 45	25.9%
6	5, 12, 19, 24, 32, charge, 44	64.8%
7	6, 14, 35	55.6%
8	7, 15, 21, 30, 38	25.9%
9	8, 13, 18, 26, 40	25.9%
10	20, 31, 41	55.6%

, and the key indicators of the initial solution are summarized in

Table 7. Initial Solution.

Z	Z1	Z2	Z3	Z4
4032.11	3287.67	111.90	444.29	180.24

. Meanwhile, the operational process of the initial solution, including trip assignments and charging intervals, is visually presented in Figure 3.

On this basis, we will further use the genetic algorithm to perform multi-generation evolution and optimization of the initial solution, ultimately obtaining the optimal solution within the current model framework. The trip chain of the optimized solution is shown in

Table 8. Trip Chain of Optional Solution.

Bus ID	Assigned Trip Chain	End-of-Daytime Remaining SoC
1	0, 6, 14, 20, 41	25.9%
2	14, 18, 24, 42	64.8%
3	1, 10, 17, 27, 33, charge, 39	50.0%
4	2, 7, 13, 22, 29, charge, 35, 43	50.0%
5	4, 18, 25, 45	40.8%
6	5, 12, 19, 24, 32, charge, 44	64.8%
7	8, 26, 34, 40	40.8%
8	11, 28, 37	55.6%
9	15, 21, 31, 38	40.8%

, and its core performance indicators are listed in

Table 9. Optional Solution.

Z	Z1	Z2	Z3	Z4
3703.84	2958.90	239.80	361.29	143.84

. The Gantt chart of the optimal solution, which clearly illustrates the optimized scheduling and charging sequence, is presented in Figure 4.

A comprehensive comparison of key indicators between the initial solution and the optimal solution is visualized in Figure 5, which intuitively reflects the optimization effect of the proposed genetic algorithm.

When the fleet size is set to 50 vehicles, the convergence behavior of the algorithm is shown in the Figure 6. As observed from the figure, the total cost decreases rapidly within the first 200 generations, after which the rate of decline slows down, and it stabilizes around the 1700th generation.

Through data analysis of the optimization results, it was found that the total cost associated with the optimal solution obtained via the genetic algorithm was 3703.84 yuan. Compared to the initial solution’s cost of 4032.11 yuan, it has decreased by 328.27 yuan, representing a reduction of 8.86%, indicating that the model is effective in cost control. A detailed breakdown reveals distinct trends among the various cost components.

First, an analysis will be conducted from the perspective of vehicle purchase cost. The cost of vehicle purchase decreased from 3287.67 yuan to 2958.90 yuan, representing a reduction of 10%. The unit purchase cost of vehicles is relatively high, accounting for 81.5% of the total cost. Therefore, this change has a direct impact on the allocation of fixed costs and is the main reason for the decrease in the total cost. During the optimization process, the optimization model adjusted the shift chain and vehicle assignment reasonably, reducing the minimum number of vehicles required by the fleet and lowering the total purchase cost of vehicles.

As for the cost related to charging, the optimized results show that during the operation period, the overall charging cost increased from 556.19 yuan to 601.09 yuan. Specifically, the cost for charging at night decreased by 83 yuan, while the charging cost during the operation period increased by 129.7 yuan. This outcome is partially attributable to the generation strategy of the initial solution. The initial solution was derived using a randomized greedy algorithm, which tends to allocate more vehicles for task execution. As a result, fewer vehicles required daytime charging, and most charging activities were concentrated at night. In contrast, the optimized solution emphasized reducing procurement costs by minimizing fleet size, leading to fewer vehicles executing trips and higher daytime energy demands. Consequently, vehicles needed to charge more frequently during the day, which led to an increase in daytime charging costs. From the perspective of optimization logic, reducing procurement costs relies on minimizing the overall fleet size and increasing vehicle utilization to reduce capital investment. This results in significantly higher operational intensity for individual vehicles, as reflected by increased daily mileage and shortened time intervals between trips. These operational shifts directly impact charging behavior: with reduced energy reserves, vehicles require more frequent interim charging during the day, thereby raising operational-period charging costs. Given that daytime charging is generally more expensive than nighttime charging, this leads to a moderate increase in the total charging cost.

Finally, by analyzing the cost of battery capacity decline, it can be found that in the optimal solution, the cost of battery capacity decline has decreased from 180.24 yuan to 143.84 yuan. This indicates that the battery capacity decline situation of the electric bus fleet has been alleviated to some extent after the model optimization. This may be attributed to more frequent daytime charging, which narrows the energy cycling range for each vehicle and thus mitigates the overall rate of capacity fade.

In conclusion, the optimized scheduling plan improves resource allocation efficiency and effectively reduces daily operational costs, thereby verifying the practical feasibility and application value of the proposed model and algorithm.

3.2. Sensitivity Analysis

To test the validity of the model proposed in this paper, a sensitivity analysis will be conducted next. First, the model will be modified so that the objective function during the process of scheduling optimization does not include the cost of battery capacity degradation, but the battery capacity degradation cost will still be included in the calculation results. The results before and after the modification are listed in

Table 10. Comparison of the Optimal Solutions before and after the Modification.

	Z	Z1	Z2	Z3	Z4
Before	3703.84	2958.90	239.8	361.29	143.84
After	4444.05	3616.44	179.85	460.11	187.65

.

As can be seen from the table and Figure 7, compared with the original model, the optimal solution obtained by the modified model has higher total costs and battery capacity degradation costs than the optimal solution obtained by the original model. This indicates that the electric bus scheduling optimization model in this study, by taking into account the degradation of battery health conditions, successfully reduces the battery health degradation losses during the bus operation and further helps to lower the overall operating cost of the fleet.

In the entire cost structure, vehicle acquisition costs and battery acquisition costs belong to the fixed costs that are made in the early stage and do not change with the specific operation scheduling plan. However, to more accurately reflect their role in the daily operational economy, such fixed expenditures should be reasonably allocated to the daily operational costs based on the vehicle usage cycle and included in the evaluation index system of scheduling optimization. This paper chooses to increase the vehicle acquisition cost by 20% and decrease the battery acquisition cost by 20% and compares the total cost in the obtained results with the total cost in the original results to obtain a percentage. The impact of these price fluctuations on the total cost is illustrated in Figure 8. By observing the obtained results, it is possible to determine the impact of both on the costs generated during the vehicle operation.

It can be seen that when the vehicle acquisition cost increases or decreases by 20%, the total cost becomes 123.64% or 91.90% of the original. When the battery acquisition cost increases or decreases by 20%, the total cost becomes 107.99% or 99.19% of the original. That is to say, compared with the battery acquisition cost, the increase or decrease in vehicle acquisition cost has a greater impact on the total cost. This is in line with the strategy of reducing the fleet size in the scheduling optimization process.

3.3. Model Enhancement Effect Verification

When the fleet size is set to 25 vehicles, the headway is reduced to 18 min, $\epsilon =2\%$, and the population size and total number of generations are set to 30 and 600. Respectively, the optimal solutions obtained by the original algorithm and the modified algorithm using the lexicographic method are presented in

Table 11. Optimal Cost of the Original Algorithm.

Z	Z1	Z2	Z3	Z4
4756.94	3945.21	119.90	501.61	190.22

and

Table 12. Optimal Cost of the New Algorithm.

Z	Z1	Z2	Z3	Z4
4750.17	3945.21	299.75	377.10	130.66

, respectively.

The results indicate that, after optimization, the total costs obtained by the original and the new algorithms are relatively similar. However, the battery capacity degradation cost in the new algorithm is significantly lower. Additionally, the daytime charging cost is higher, while the nighttime charging cost is lower—consistent with the conclusions drawn earlier in this chapter. These findings confirm that the new algorithm has indeed increased the weight of battery degradation cost within the optimization process.

The vehicle procurement cost remains unchanged, likely due to its still-dominant weight in the overall cost structure. Nonetheless, the adjustment introduced by the new objective function has sufficiently increased the importance of the battery degradation cost.

4. Conclusions and Future Work

This paper initially examines the degradation mechanisms of electric bus power batteries, selecting unit energy consumption as the degradation estimation variable. A scheduling optimization model incorporating battery capacity degradation costs was constructed. This model employs an empirical battery capacity degradation model, converting capacity loss during each charge–discharge cycle into financial costs, thereby supplementing previous domestic and international research on electric bus scheduling. The study considers multiple scheduling decision points, integrating daytime peak electricity prices and nighttime off-peak rates into the cost model. Billing is conducted separately for the operational period and nighttime phase, which better reflects practical conditions while refining the impact of battery capacity degradation costs. Subsequently, a genetic algorithm specifically tailored for bus scheduling optimization is developed. This algorithm integrates constraints related to both the temporal sequence of bus scheduling and energy consumption, embedding local feasibility repair mechanisms following both crossover and mutation operations. Furthermore, following a detailed analysis of vehicle acquisition costs and battery capacity degradation costs, the paper proposes employing lexicographic optimization to increase the weighting of battery capacity degradation costs in the optimization process. This method implements hierarchical processing, focusing specifically on the critical factor of battery capacity degradation costs. The results obtained align with expectations, demonstrating the effectiveness of this improved approach. Following the results, the paper also analyzes its applicability. Finally, the study employs data from Chongqing Bus Route 579 and test data from a specific model of the BAIC Foton pure electric bus for case analysis. The findings confirm that the algorithm can tangibly reduce the overall operational costs of bus fleets. Through detailed examination, the paper elucidates the practical operational mechanism of this scheduling optimization model. Utilizing sensitivity analysis, it further explores the potential impact of battery acquisition costs within this optimization framework. Subsequently, based on the analysis findings, the original genetic algorithm was refined, with its enhanced effectiveness subsequently verified.

The findings of this study offer the following policy implications:

Firstly, the optimization results indicate that daytime charging requirements for the electric bus fleet increase following optimization. This places greater demands on charging infrastructure, necessitating enhanced capacity to accommodate daytime charging tasks. Relevant authorities may consider expanding electric bus depot facilities, installing additional charging points, or refining depot charging procedures to improve the fleet’s charging efficiency.

Secondly, sensitivity analysis indicates that when total costs are fixed, a higher proportion of battery costs leads to lower final optimized total costs. Therefore, when procuring electric buses, relevant authorities should prioritize evaluating vehicle battery models, ultimately selecting those where battery costs account for a larger share of the total vehicle acquisition cost.

The present study retains certain limitations and warrants more in-depth investigation in future research. This study is confined to a single route with a fixed fleet size, assuming constant journey times and distances throughout. It does not account for traffic congestion, fluctuations in dynamic travel times, or uneven distances between stops. Consequently, the model is overly idealized and cannot fully replicate all practical factors. Future work could extend this model to multi-route urban networks, incorporating vehicle sharing between routes and collaborative scheduling decisions to enhance overall network capacity utilization. Additionally, the genetic algorithm employed in this study may exhibit premature convergence when solving multi-peak complex functions. Subsequent work could incorporate local optimization operators within the genetic algorithm, such as 2-opt or simulated annealing, to refine local structures following crossover or mutation. Dynamic adjustment of crossover and mutation rates based on population diversity metrics or iteration progress could improve convergence speed and solution quality. This approach would strengthen exploration in the early stages and focus on exploitation later, balancing global and local search capabilities to avoid premature convergence.