Digitizing Highways: Unleashing Potential Through Data Element Circulation for Safety, Cost Efficiency, and Environmental Impact Optimization

Yanyan JIA; Wen LONG; Yingjie TIAN

doi:10.21078/JSSI-2024-0095

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Journal of Systems Science and Information ›› 2025, Vol. 13 ›› Issue (1) : 23-60. DOI: 10.21078/JSSI-2024-0095

Digitizing Highways: Unleashing Potential Through Data Element Circulation for Safety, Cost Efficiency, and Environmental Impact Optimization

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Abstract

As the era of large-scale highway maintenance arrives, the maintenance strategies have transitioned to a holistic approach that prioritizes safety, economic feasibility, and environmental sustainability. This research introduces a multi-objective optimization model for highway maintenance that incorporates the interplay of decision-maker preferences across three key objectives: Highway safety performance, maintenance engineering cost, and carbon emissions. This study employs a large-sample data analysis on a subset of the Lianhuo Highway network, which includes 2,842 pavement sections. This approach mitigates the impact of outliers, ensuring a substantial data buffer that fortifies the model's capacity for generalization and bolsters its robustness. The findings reveal a Pareto-optimal relationship among the three scrutinized variables. A particularly noteworthy observation is the M-shaped trajectory of carbon emissions, which initially rise, then decline, and ultimately rebound, contingent upon the selected maintenance strategy. Furthermore, an examination of the relationship between maintenance costs and safety performance discloses a trend of diminishing marginal returns, illustrating that the incremental gains in safety performance attenuate as maintenance investment escalates.

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data element / circulation / highway maintenance / multi-objective optimization

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Yanyan JIA , Wen LONG , Yingjie TIAN. Digitizing Highways: Unleashing Potential Through Data Element Circulation for Safety, Cost Efficiency, and Environmental Impact Optimization. Journal of Systems Science and Information, 2025, 13(1): 23-60 https://doi.org/10.21078/JSSI-2024-0095

1 Introduction

Data has emerged as an indispensable fifth factor of production, complementing the traditional factors of land, labor, capital, and technology. Data integration has become a pivotal catalyst in the development of novel productivity paradigms. It facilitates innovative allocations of existing production factors, reshapes traditional development paradigms, and spearheads the internal drive for innovation across diverse industries and sectors. Intensified digitization magnifies the "multiplier effect" of data elements, expanding its applications beyond critical sectors like finance, transportation, healthcare, energy, industry, and telecommunications to pervade the entire national economy. This expansion is instrumental in underpinning the modern economic system, providing critical support for both current and medium-to-long term strategies. With the swift progression of transportation information technology, the convergence of building information modeling (BIM) and geographic information system (GIS) technologies has achieved integrated transportation information management. The highway electronic map has achieved 100% coverage of the entire highway network, as has the highway video monitoring system. The utilization rate of the electronic toll collection (ETC) systems on highways has surpassed 70%, and the construction of the national infrastructure and vehicle transportation information platform has been completed, thereby solidifying the foundation for digital transportation development. The social and economic value of transportation data is being increasingly unlocked through the impetus of digital technology and data elements, fostering the emergence and application of innovative business models. These include the transportation "data brain", intelligent digital highways, digital travel networks, intelligent logistics networks, and management information networks. These advancements have injected significant momentum into the high-quality development of highways. Building upon this foundation, the digitization of highways is continuously advancing. The widespread application of new digital technologies such as the electronic non-stop toll collection system and the highway video cloud networking system have led to the generation of massive traffic data, including traffic flow, vehicle trajectories, and vehicle types. This data deluge accelerates the transformation of highways into data-intensive industries. Digitally enabled maintenance algorithms are increasingly deployed for intelligent highway maintenance and digital management.

Highways are critical elements of logistics systems vital for the modern economy by facilitating efficient resource allocation and seamless movement of production factors. Maintenance management stands as a pivotal strategy to ensure the ongoing safety and smooth operation of highways. The timeliness and efficacy of maintenance are paramount in securing the highway network's performance, ensuring it remains safe, convenient, and efficient^[1]. Data has emerged as a key driver for the advancement of intelligent and digital highway maintenance, with multi-objective optimization serving as a vital technique for reducing maintenance costs and increasing value^[2]. The harnessing of traffic data holds significant potential in supporting the multi-objective optimization of highway maintenance. The real-time collection processing analysis and application of traffic data encompassing numerical text images and video from new sources significantly enhance the scientific basis of decision-making processes within highway maintenance. This approach ensures the harmonization of economic and environmental benefits, providing a safeguard for the integrated optimization of maintenance efforts. The creation of a data-driven dynamic allocation system for highway maintenance resources has become a demand stemming from the current trajectory of high-quality development in transportation. However, in current highway maintenance practices, the utilization of traffic data is suboptimal, and the depth and breadth of its integration with scientific decision-making are limited, restricting its exploratory application in highway services^[3]. Thus, the amalgamation of new production factors with innovative modeling methods is essential to generate fresh impetus for development. The pursuit of high-quality development in highway maintenance necessitates not only the infusion of novel paradigms but, more critically, the integration of data elements. This integration is vital for propelling digital transformation and intelligent upgrading within the maintenance sector. The innovation of allocation mechanisms for highway maintenance resources and the construction of a circular system within the multi-objective optimization model are both essential for enhancing the efficiency and sustainability of maintenance operations. This system facilitates efficient resource allocation and elevates economic and environmental benefits of maintenance, ensuring the enhancement of overall value in the maintenance process.

This study leverages multi-source heterogeneous traffic data to delve into the optimization of highway maintenance objectives across three critical dimensions: Social, economic, and environmental. Initially, the research categorizes diverse traffic data, identifies independent variables through correlation analysis, and refines them to enhance the accuracy and reliability of subsequent data analytics. This foundational work lays the groundwork for crafting multi-objective optimization models and devising algorithmic solutions that are both robust and contextually relevant. Building upon the conventional framework of multi-objective optimization, which typically encompasses cost and environmental impact, this study introduces safety as an additional parameter, thereby enriching the optimization paradigm. A new multi-objective optimization model for highway maintenance incorporates decision-maker preferences and focuses on three main objectives: The maximization of safety, the minimization of costs, and the reduction of environmental impact. The study culminates in the application of multi-objective particle swarm optimization (MOPSO) algorithm to identify the optimal solution that reconciles these three objectives, in quest of a strategy conducive to the sustainable evolution of highway maintenance practices. This paper makes three distinct contributions that address the gaps in the existing research. First, this paper presents an innovative approach to applying data, effectively utilizing information from highway maintenance and traffic monitoring systems. It ventures into new realms such as safety enhancement and environmental sustainability, broadening the scope of traditional maintenance applications. This extension into innovative areas not only diversifies the range of data applications but also sets new standards for multi-objective optimization within highway maintenance, thereby fully realizing the intrinsic value of data assets. Second, integrating multi-source traffic data offers a holistic perspective for assessing highway maintenance. This approach facilitates a multi-indicator and multi-dimensional quantitative analysis, enabling a nuanced prioritization of maintenance objectives that include safety, economic viability, and environmental impacts. By capitalizing on the distinct insights gleaned from diverse datasets, this study deepens the comprehension of maintenance dynamics, thereby laying the groundwork for developing well-informed and targeted maintenance strategies. Third, focusing on highways with extensive networks and significant mileage, this paper utilizes a vast array of empirical traffic data to uncover intricate relationships between safety, cost, and carbon emissions. This approach counters the limitations and biases often associated with small-sample studies, enhancing the accuracy of predictive models. Consequently, it provides a robust data-driven foundation for making strategic decisions in highway maintenance and management.

The subsequent sections of this paper are organized as follows: Section 2 reviews the empirical literature on digital transportation applications and the domain of conservation multi-objective optimization. Section 3 delineates the research methodology and conducts a thorough data analysis. Section 4 formulates the highway maintenance multi-objective optimization model, meticulously constructs the objective functions and describes solution algorithm. The penultimate section, Section 5, engages in empirical analysis and presents a social-economy-environmental discussion of the results. Conclusively, the final section encapsulates the findings and synthesizes the overall content of the paper, providing a cohesive summary that encapsulates the study's contributions to the field.

2 Literature Review

2.1 Data Elements Circulation

Digital technology serves as a pivotal catalyst for the advancement of modern economies and acts as a key driver for propelling society towards high-caliber and high-efficiency development. The widespread proliferation of data elements has significantly broadened across diverse domains such as agriculture, manufacturing, finance, education, healthcare, transportation, and energy. These elements offer robust informational backing for stakeholders to delineate strategic growth plans and to make informed, data-driven business decisions. Effective data leverage enhances business decision-making, boosting economic value and optimizing industry performance through quality, cost reduction, and efficiency. In Table 1, accelerated digital infrastructure construction has significantly expanded the richness of highway data elements. The circulation of data resources has become more seamless, and the manifestation of data value has become increasingly pronounced. In the swiftly evolving digital landscape, data plays a crucial role in safeguarding the operations and strategic planning of highways^[4]. The fluidity of data element circulation hastens the integration of highways into the information age. Moreover, the circulation of data elements, the realization of data value, and the application of digital technologies foster an integrated approach to economic, social, and environmental development^[5], thereby optimizing the overall benefits.

Table 1 Classification of highway data

Highway data	Data attribute	Data type	Data format
Maintenance analysis and decision-making	Dynamic	Unstructured	Text
Maintenance project plan	Dynamic	Structured and unstructured	Text and number
Maintenance investment	Dynamic	Structured and unstructured	Text and number
Highway technical condition	Dynamic	Structured	Number
Highway assets	Static	Structured and unstructured	Text, number, and image
Average annual daily traffic	Dynamic	Structured	Number
Traffic conditions	Dynamic	Structured and unstructured	Number and image
Mileage	Static	Structured	Number
Route	Static	Structured	Number
Service facilities	Static	Structured	Number
Supply reserves and mechanical equipment	Static	Structured	Number

2.2 Data Applications in Highways

Specifications of pavement condition data, traffic volume data, and maintenance engineering data is essential for accurately depicting the operational status of highways throughout their lifecycle. The efficacy and utilization of this data are instrumental in aiding highway management entities in decision-making^{[1, 5–7]}, optimizing resource allocation, prolonging the lifespan of the highways, enhancing the economic returns of maintenance efforts, curtailing maintenance costs, and bolstering highway safety^{[8, 9]}. Li, et al.^[10] developed the rain 365 and sun 520 pavement databases, leveraging a lightweight convolutional neural network. By enriching the dataset and refining the pavement crack database, the detection performance and efficiency of pavement cracks have been significantly enhanced, offering vital support for pavement maintenance decision-making. Wu, et al.^[11] amalgamated various traffic data sources for lifecycle predictions of transportation infrastructure. Through the analysis of both historical and real-time data, a novel pavement maintenance system was devised. This system incorporates algorithmic models to establish an intelligent transportation framework that optimizes objectives involving people, vehicles, and highways. It improves the efficiency of highway network accessibility, mitigates highway safety risks and hazards, and diminishes environmental pollution. In the era of big data, the cyclical momentum of data elements and the extensive application of digital technologies offer a potent solution to the increasingly intricate challenges in transportation^[3]. This approach not only addresses these complexities but also generates substantial societal value^[12].

2.3 Multi-Objective Optimization of Maintenance

Multi-objective decision-making is a prevalent approach in realms such as economic planning, resource allocation, and engineering optimization. The maintenance of highways epitomizes a multi-objective optimization challenge, often encompassing a variety of considerations^[13] as illustrated in Figure 1. Traditionally, maintenance optimization has predominantly centered on cost minimization. However, in recent years, the optimization of high-dimensional objective decision models and variables has emerged as a focal point in highway maintenance research^[14]. Concurrently, social, economic, and environmental factors have increasingly been integrated into the multi-objective optimization framework of highway maintenance^[15–20]. Economic efficiency in maintenance is a crucial metric for evaluating highway performance, with the reduction of agency and user costs being the primary objectives of multi-objective optimization^[21]. As the public's expectations for the quality of highway travel escalate, the condition of highways has become a pivotal aspect of performance evaluation^[22]. With the transition from a phase of large-scale construction to one of extensive maintenance, the consumption of materials such as asphalt in highway maintenance is intricately linked to greenhouse gas emissions^[23]. Nonetheless, some decision-makers in highway maintenance have been observed to overlook environmental considerations^{[24, 25]}. In 2021, the State Council of the People's Republic of China promulgated the "Action Program for Carbon Peak by 2030", which underscores the imperative of industry development founded on resource-efficient utilization and green, low-carbon principles. It advocates for the advancement of green transportation to meet carbon peaking goals. Consequently, the significance of environmental factors in highway maintenance has been thrust into the spotlight^{[5, 26]}, with the potential to significantly curtail greenhouse gas emissions through the strategic scheduling of maintenance activities^[27]. Furthermore, while some studies on highway maintenance take into account the technical condition and associated costs, the safety aspect of highways is frequently neglected^{[28, 29]}. This oversight is critical, given the profound implications for both the economy and society^[29]. It is imperative that highway maintenance strategies not only prioritize cost-efficiency and environmental impact but also ensure the safety and longevity of the transportation infrastructure.

Figure 1 Distribution map of criteria in multi-objective optimization for highway maintenance

Full size|PPT slide

2.4 Optimization Techniques and Models

Pareto-optimality characterizes the interplay between safety performance, maintenance costs, and greenhouse gas emissions^[30], representing a delicate balance where improvements in one aspect can lead to trade-offs in another. The field of multi-objective optimization is replete with a variety of techniques, as enumerated in Table 2. These include but are not limited to linear programming^[22], integer programming^{[31, 32]}, dynamic programming^{[19, 32]}, constraint programming^[33], multi-objective differential evolutionary algorithms^[26], Lagrangian relaxation^[34], the Analytic Hierarchy Process^[14], genetic algorithms^{[28, 35–38]}, coyote optimization algorithms^[16], and particle swarm optimization algorithms^{[39, 40]}. The development and refinement of multi-objective optimization models have been tailored to address diverse conservation decision-making objectives, both at the network-level and project-level. These models include budget allocation models^[41], nonlinear mathematical models^[42], bi-objective genetic algorithm optimization models^[35], high-dimensional objective decision-making optimization models^[43], network optimization models^[44], semi-Markov international roughness exponential degradation models^[28], and cloud decision tree models^[45]. In the quest for the Pareto optimal solution of the multi-objective optimization function, it is essential to consider economic, safety, environmental, and sustainability array of factors and to harness the full potential of data elements. By doing so, decision-makers can navigate the complex interplay between safety performance, maintenance costs, and environmental impact, striving for outcomes that are not only economically viable but also sustainable and safe.

Table 2 Main features of multi-objective optimization for highway maintenance

Multi-objectives			Applied data	Techniques applied for multi-objective optimization	Reference
Economic	Society	Environ-mental	Applied data	Techniques applied for multi-objective optimization	Reference
AC+UC+SC			AADT + IRI	Genetic algorithm	Lu, et al.^[28]
AC	PP	CE	PCI + W + L	MODE algorithm	Li, et al.^[26]
AC+EC	PP		PCI + RDI + SRI + RQI	Genetic algorithm	Chen, et al.^[38]
	PP	CE	IRI	Coyote optimization algorithm	Naseri, et al.^[16]
AC+UC		CE	AADT+CS	NSGA II	Guan, et al.^[49]
AC+UC	PP		AADT + W + L + MC	Integer Programming	Sun, et al.^[32]
AC	PP		PCI + W + L + AADT	Particle swarm optimization algorithm	Ahmed, et al.^[39]
AC		GHGE	MB + W + L	Dynamic programming	Lee and Madanat^[19]

Note: AC = agent cost; UC = user cost; SC = safety cost; EC = emissions cost; PP = pavement performance; CE = carbon emissions; GHGE= greenhouse gas emissions; AADT = average annual daily traffc; CS = car speed; IRI = international roughness index; PCI = pavement surface condition index; RDI = pavement rutting depth index; SRI = pavement skidding resistance index; RQI = pavement riding quality index; W = width; L = length; MC = maintenance cost; MB = maintenance budget; NSGA = non-dominated sorting genetic algorithm; MODE = multi-objective differential evolution.

Data elements are assuming an increasingly significant role in the realm of resource planning and decision-making^[8]. Within the context of multi-objective optimization for highway maintenance, the safety performance of highways stands out as a paramount consideration. The prominence of the maintenance decision-making process is escalating. In upcoming highway maintenance practices, bolstering traffic data sub-analysis and expanding multi-objective decision-making utilization is imperative. This strategic enhancement aims to refine the scientific basis and precision of decision-making, ensuring informed strategies that address the dynamic complexities of highway maintenance effectively.

This study distinguishes itself from prior research by offering a robust multi-source data framework to enhance multi-objective optimization in highway maintenance. First, this paper innovatively attempts cross-domain data empowerment, exploring the application of data resources generated by highway maintenance systems and traffic operation monitoring systems to fields beyond maintenance, such as safety and environmental conservation. This cross-disciplinary application of data not only extends the purview of data usage but also diversifies the application scenarios, setting new precedents for highway maintenance multi-objective optimization and further unlocking its latent data value. Second, the synthesis of multi-source traffic data is instrumental in forging a more holistic multi-objective research perspective for highway maintenance. This approach facilitates a more nuanced quantification and dimensionality reduction of maintenance objectives, including highway safety, cost, and carbon emissions. By harnessing the complementary strengths of diverse data sources, the study enhances the researchers' capacity to adapt to and comprehend the dynamics of the maintenance environment, thereby bolstering the development of more scientifically grounded and targeted highway maintenance strategies. Third, this paper focuses on highways with extensive scales and mileages as the subject of investigation, leveraging a wealth of empirical traffic data to delve into the underlying patterns and correlations among safety, cost, and carbon emissions. This methodology mitigates the biases inherent in small-sample research and elevates the precision of model predictions, thereby offering more robust data support for highway maintenance decision-making.

3 Theory and Methodology

3.1 Multi-Objective Decision Theory

Multi-objective decision-making theory constitutes a vital theoretical framework within the domains of operations research, economics, psychology, and other disciplines across both the social and natural sciences. Multi-objective optimization employs mathematical programming and genetic models to improve decision-making. Algorithms balance conflicting objectives to achieve an optimal and balanced decision-making strategy. Such balanced decision-making programs have found extensive application across various industries and sectors within society. Multi-objective decision-making techniques include non-fractal generation, continuous methods with preferences, discrete evaluation with preference accounting, and interactive methods that aggregate preferences. Multi-objective decision-making problems are typically encapsulated by models such as multi-attribute decision-making, multi-objective planning, multi-objective hierarchical planning, and multi-indicator planning. The fundamental components of these models include decision-making entities, objectives and attributes, conditions and constraints, the preferences of decision-makers, information and its associated uncertainties, and the methodologies employed for decision-making. These elements collectively contribute to the formulation and resolution of multi-objective decision-making problems, ensuring an economical, safe, environmentally friendly, and sustainable approach to achieving balanced outcomes.

3.2 Multi-Objective Optimization Framework

Highway maintenance decision-making is inherently multi-objective and multi-attribute in nature^[43]. The aim of this study is to integrate three critical elements (highway safety performance, maintenance engineering costs, and carbon emissions) into a safety-economic-environmental multi-objective optimization model. This model is constructed by considering the interplay of decision-makers' preferences, with the goal of incorporating a broader array of data and indicators into the highway maintenance optimization function. The study seeks to analyze and balance these three objectives through a trade-off analysis, with the objective of identifying a set of optimal solutions that enhance social, economic, and environmental benefits.

The problem of highway maintenance decision-making is defined as follows: Within a highway network, individual sections are categorized based on the five-tiered assessment of highway technical condition, ranging from excellent to good, average, poor, and bad. Maintenance engineering is targeted at sections classified as average, poor, and bad, as well as those with latent safety hazards. Given the constraints of the maintenance engineering budget, highway maintenance quality indicators, and carbon emissions, the multi-objective optimization problem in highway maintenance is to simultaneously satisfy three objective functions. The aim is to derive a set of optimal solutions that maximize the collective benefits to society, the economy, and the environment. This approach balances safety, cost, and environmental impact for a holistic highway maintenance strategy.

3.3 Data

Highway data is bifurcated into two primary categories based on its inherent attributes: Dynamic and static. Static highway data changes little and infrequently over time, such as total highway mileage, while dynamic highway data varies with time and external condition, such as average daily traffic volume. Data is further classified into structured and unstructured types. Structured data encompasses elements like the highway's technical condition, which includes pavement index, pavement surface index, subgrade condition index, and index related to facilities along the highway. This data possesses fixed fields and types and is stored and managed in a standardized format as stipulated by the "Highway Maintenance Statistical Survey System". Unstructured data is integral to maintenance analysis and decision-making, and it comprises a variety of data forms and free-form text. Lacking a fixed structure and format, this data is more intricately organized. Data is also categorized by form into text-based data (e.g., for maintenance analysis and decision-making), numerical data (such as traffic volume), and video-based data (from highway network monitoring systems). As data continues to evolve, the emergence of hybrid data is on the rise, characterized by its increasing diversity and multi-source nature. Data is no longer confined to a singular type or origin but exhibits a complex and mutable state. To address the intricate and dynamic attributes of data, a suite of agile technologies and strategies is essential. This includes data cleaning to ensure quality, integration to amalgamate diverse datasets, visualization to represent data graphically, and modeling to analyze and predict trends and outcomes. These methodologies are crucial for effectively managing and leveraging the rich tapestry of highway data.

3.4 Objective Function

3.4.1 Definition of Safety Objective Function

The principal goal is to enhance safety, a pivotal factor underscored by studies linking the incidence of highway traffic accidents to the condition of the highway^[46]. Presently, a significant body of research employs the international roughness index (IRI) as a metric for enhancing highway performance^{[47, 48]}. However, this measure is somewhat limited, as it predominantly reflects the pavement's smoothness and does not encapsulate the cracking, rut-depth, and sensor measured texture depth safety performance of highways. The technical condition of highways typically encompasses a more holistic evaluation, including the subgrade, pavement, bridge structures, and the condition of facilities along the highway. This approach is essential for a thorough assessment of the safety performance of highways. To reflect the systemic safety of highways in a more integrated manner, this paper adopts four key indices: SCI (subgrade condition index), PQI (pavement quality index), BCI (bridge, tunnel, and culvert condition index), and TCI (traffic facility condition index). The aim is to ensure that these indices reach an optimal state following the execution of maintenance engineering. Drawing from the objective function for improving pavement condition scores^[38], the overarching objective of maximizing highway safety is formulated as follows:

\begin{aligned} max F_{1} = \sum_{s = 1}^{S} \sum_{k = 1}^{K} \sum_{t = 1}^{T} {M Q I}_{s k t} \times x_{s k t}, \end{aligned}

(1)

\begin{aligned} {M Q I}_{s k t} = w_{S C I} \times {S C I}_{s k t} + w_{P Q I} \times {P Q I}_{s k t} + w_{B C I} \times {B C I}_{s k t} + w_{T C I} \times {T C I}_{s k t} . \end{aligned}

(2)

In Eqs. (1) and (2), MQI denotes the Highway Maintenance Quality Index. The coefficients

w_{S C I}

w_{S I C}

w_{P Q I}

, and

w_{B C I}

signify the weights allocated to the respective indices within the technical condition assessment of highways, as prescribed by the Highway Performance Assessment Standard (JTG 5210–2018). These weights play a crucial role in the evaluation process. The variables

w_{S C I}

w_{S I C}

w_{P Q I}

, and

w_{B C I}

correspond to the aggregate safety performance indices for the highway segment unit

s

under maintenance approach

k

over the time horizon

t

, The binary decision variable

x_{s k t}

takes the value of 1 to indicate that maintenance is conducted on the highway segment unit

s

using the maintenance approach

k

within the time period

t

, and 0 if no maintenance is performed. Variables

S

K

, and

T

represent the sets of highway segment units, maintenance approaches, and time periods, respectively. The maintenance approaches include preventive maintenance engineering (PME), rehabilitative maintenance engineering (RME), emergency maintenance engineering (EME), and special maintenance engineering (SME). Considering the minimal impact of routine maintenance on enhancing the technical conditions of highways, this study excludes its influence from the analysis to focus on more substantial interventions.

3.4.2 Definition of Cost Objective Function

The secondary objective is to minimize maintenance engineering costs. Agency costs primarily pertain to enterprise costs, which are the funds utilized by the highway operation and management entity to sustain the highway at a given technical condition, thereby ensuring public access services. In this study, the term "maintenance engineering cost" (agency cost) specifically refers to the expenses incurred during the execution of maintenance activities. Considering the brief duration of maintenance engineering and the measures implemented to maintain the continuity and flow of the highway network, the disruption costs to highway users are deemed negligible. From the vantage point of highway management, this paper aims to establish a rational strategy for the allocation of maintenance funds through the optimization of strategic investments. Drawing on the objective function for minimizing maintenance engineering costs (MEC)^[26], the objective function for minimizing maintenance engineering costs is formulated as follows:

\begin{aligned} min F_{2} = \sum_{s = 1}^{S} \sum_{k = 1}^{K} \sum_{t = 1}^{T} {M E C}_{k} \times L_{s k} \times W_{s k} \times x_{s k t} . \end{aligned}

(3)

In Eq. (3),

{M E C}_{k}

signifies the per-unit cost associated with the application of maintenance method

k

per unit area for the highway. It is assumed within the scope of this study that the cost per unit area remains constant throughout the maintenance life cycle

t

. The variable

L_{s k}

represents the linear extent of the maintenance intervention applied via method

k

to the segment unit

s

of the highway.

W_{s k}

characterizes the width of the maintenance application within the same segment unit

s

under the purview of maintenance method

k

. The binary decision variable

x_{s k t}

is introduced to denote the implementation status of maintenance on a segment unit

s

with dimensions

L

and

W

, where

L

and

W

correspond to the length and width of the pavement area, respectively. This variable assumes the value of 1 to indicate that maintenance has been executed on the segment unit

s

using method

k

over the specified area, and 0 to signify the absence of such maintenance activities.

3.4.3 Definition of Cost Objective Function

The tertiary objective of this research is the minimization of carbon emissions, a critical endeavor for attaining carbon peaking and neutrality within the transportation sector. This study integrates environmental goals into the optimization objectives of highway maintenance, specifically targeting the reduction of carbon emissions. The environmental impact is primarily measured in terms of carbon emissions, which encompass emissions generated during maintenance activities and those resulting from construction vehicles traveling under suboptimal highway conditions, leading to increased fuel consumption. During the maintenance work period, traffic diversion measures are typically implemented, thereby circumventing the traffic interruptions associated with temporary traffic controls. Consequently, the greenhouse gas emissions resulting from such scenarios are not factored into the analysis. Expanding upon foundational research^[30], a refined objective function has been formulated to minimize environmental impact, taking into account a more granular classification of vehicle types.

\begin{aligned} min F_{3} = C E M + C E H R, \end{aligned}

(4)

\begin{aligned} C E M = \sum_{s = 1}^{S} \sum_{k = 1}^{K} \sum_{t = 1}^{T} g m_{k} \times x_{s k t}, \end{aligned}

(5)

\begin{aligned} C E H R = \sum_{s = 1}^{S} \sum_{t = 1}^{T} (g r_{1} \times {A A D T}_{1} + g r_{2} \times {A A D T}_{2}) \times S_{A T D} \times N_{l a n e} \times [α \times ({R Q I}_{max} - {R Q I}_{s t})] . \end{aligned}

(6)

In Eq. (4), the total carbon emissions are comprised of two components:

C E M

and

C E H R

, which represent carbon emissions from highway maintenance engineering and those caused by the roughness of the highway pavement, respectively.

Eq. (5) introduces

g m_{k}

denoting the average carbon emissions associated with the adoption of maintenance method

k

in highway maintenance engineering. The binary decision variable

x_{s k t}

is also defined, where a value of 1 signifies that carbon emissions are released when maintenance method

k

is applied to a unit highway segment

s

, and

x_{s k t} = 0

otherwise, indicating no emissions are released.

Eq. (6) delineates

g r_{1}

and

g r_{2}

as the average carbon emissions from passenger vehicles (encompassing small and medium-sized passenger cars, large coaches) and freight vehicles (including categories such as small trucks, medium trucks, large trucks, extra-large trucks, and container trucks), respectively. These emissions are a consequence of the disparity between ideal and actual highway pavement conditions at a given unit of annual average daily traffic volume.

{A A D T}_{1}

signifies the annual average daily traffic for cars, and

{A A D T}_{2}

represents the same metric for trucks.

S_{A T D}

refers to the average travel distance per vehicle.

N_{l a n e}

is the total number of lanes on the highway. The parameter

α

captures the highway ride quality factor, while

{R Q I}_{max}

and

{R Q I}_{s t}

symbolize the ideal and actual state highway pavement riding quality indices, respectively.

3.4.4 Definition of Cost Objective Function

This study incorporates technical performance, budgetary limitations, and environmental considerations constraints, including technical performance, budgetary limitations, and environmental considerations. In Eqs. (7), (8), (9) and (10),

{M Q I}_{s k t}

signifies the maximum safety performance attainable by the highway segment unit

s

through the application of maintenance method

k

over the service life

t

. The indices

{S C I}_{s k t}

{B C I}_{s k t}

and

{T C I}_{s k t}

evaluate the technical conditions at levels ranging from excellent to poor and bad, reflecting the states achieved by employing maintenance method

k

on a unit area over a specific duration

t

. These indices are crucial for assessing the overall safety and serviceability of the highway segments. The maintenance engineering costs (MEC) are constrained to be within the bounds of the allocated maintenance budget (MB), yet they must also exceed the costs associated with preventive maintenance (

C_{p m}

), ensuring that the expenditures are both economical and sufficient to achieve the desired outcomes.

{C E}_{i d e a l}

represents the

C E

under ideal conditions, and

{C E}_{n m}

represents the

C E

under ideal conditions.

\begin{aligned} w_{S C I} \times {S C I}_{s k t} + w_{P Q I} \times {P Q I}_{s k t} + w_{B C I} \times {B C I}_{s k t} + w_{T C I} \times {T C I}_{s k t} \leq {M Q I}_{s k t}, \end{aligned}

(7)

Could not find closing ']' for argument to \\

(8)

\begin{aligned} C_{p m} \leq \sum_{s = 1}^{S} \sum_{k = 1}^{K} \sum_{t = 1}^{T} {M E C}_{s k t} \times L_{s k} \times W_{s k} \leq {M B}_{s k t}, \end{aligned}

(9)

\begin{aligned} {C E}_{i d e a l} \leq C E M + C E H R \leq {C E}_{n m} . \end{aligned}

(10)

3.5 Normalization

This study confronts a multifaceted optimization challenge by simultaneously striving to maximize safety, minimize maintenance costs, and reduce carbon emissions. Considering the diverse units and scales of these objectives, which leads to a lack of standardization, the study sets specific minimum and maximum values based on the characteristics of the data to better display the trends and features of the data. Building on foundational research^[32], the study constructs objective functions for safety, cost, and carbon emissions, as articulated in Eq. (12). The study then hones the maximization of the safety objective, as shown in Eq. (13). This refinement culminates in the development of an extreme value normalization composite objective function, presented in Eq. (14). This composite function offers a balancing safety, maintenance cost and carbon emission methodology for addressing the optimization challenge, adeptly reconciling the multiple and sometimes competing priorities into a unified decision-making framework. To reflect the preferences of decision-makers, the study strategically integrates weight factors to determine the priority weighting of each optimization criterion in Eq. (15).

\begin{aligned} F_{i} = a + \frac{f_{i} - f_{min}}{f_{max} - f_{min}} \times (b - a), \end{aligned}

(11)

\begin{aligned} z = F_{1} (x) + F_{2} (x) + F_{3} (x), \end{aligned}

(12)

\begin{aligned} max {F (x)} \leftrightarrow min {- F (x)}, \end{aligned}

(13)

\begin{aligned} min z = w_{1} {- F_{1} (x)} + w_{2} F_{2} {x} + w_{3} F_{3} {x}, \end{aligned}

(14)

\begin{aligned} w_{1} + w_{2} + w_{3} = 1. \end{aligned}

(15)

3.6 MOPSO Algorithm

Multi-objective optimization solution methods mainly include traditional algorithms and evolutionary algorithms. Traditional algorithms primarily consist of the constraint method (CM), goal programming (GP), ideal point method (IPM), and mini-max method (MMM). Evolutionary algorithms mainly include genetic algorithm (GA), non-dominated sorting genetic algorithm (NSGA), differential evolution (DE), simulated annealing (SA), and multi-objective particle swarm optimization (MOPSO) algorithm. Compared to traditional algorithms, evolutionary algorithms have the advantages of strong global search capabilities, good robustness, strong adaptability, and proficiency in handling multi-objective optimization problems. Among algorithms in Table 3, MOPSO stands out for its ability to quickly converge, require fewer parameters, exhibit strong adaptability, and maintain diversity, especially when balancing the quality and diversity of optimization solution objectives in complex, multi-modal, and high-dimensional multi-objective optimization problems. Its potential in solving combinatorial optimization problems has garnered significant attention and provides effective solutions for a variety of complex optimization issues.

Table 3 Comparison analysis of strengths and weaknesses for multi-objective optimization algorithms

No.	Technique	Strengths	Weaknesses
1	CM	Transforming a multi-objective problem into a single-objective one simplifies the issue complexity.	Overemphasis on the constraints of certain objectives can result in the degradation of performance for other objectives.
2	GP	Allocating weights to different objectives ensures that decision-makers can optimize based on the importance of each objective.	The process of determining objective weights involves numerous factors that are often difficult to quantify.
3	IPM	Decision-makers can directly observe the distance between each solution and the ideal solution.	The accuracy of the ideal point setting is crucial; imprecise definitions can lead to biased outcomes.
4	MMM	Performs effectively when the interests of the two parties are diametrically opposed.	An excessive emphasis on worst-case scenarios may lead to the neglect of other significant optimization goals.
5	GA	Possesses robust global search capabilities. Exhibits great adaptability to various optimization scenarios.	The algorithm converges too quickly and requires intricate parameter settings for optimal performance.
6	NSGA	Well-suited for complex problems that require consideration of multiple objectives and constraints.	Algorithm performance is significantly influenced by parameter settings.
7	DE	Possesses an effective capability for searching the global solution space.	The selection of parameters significantly impacts the algorithm's effectiveness, necessitating iterative experimentation and adjustment.
8	SA	The algorithm's strategy to avoid getting stuck in local optima by accepting less optimal solutions during an initial exploratory phase.	The performance of the algorithm is highly sensitive to parameters such as initial temperature and cooling rate, requiring careful adjustment for optimal performance.
9	MOPSO	MOPSO is adaptable to complex multi-objective problems, unaffected by scale, dimension, or complexity changes, and it requires few parameters that are easy to adjust. The algorithm approximates the Pareto front while maintaining solution diversity.	When reaching the Pareto optimal front, the convergence speed is relatively slow.

3.6.1 The Fundamental Principle of PSO

PSO is a heuristic global optimization algorithm that emulates the foraging behavior of natural animal groups, proposed by Kennedy and Eberhart in 1995. The algorithm's foundational principle is the harnessing of swarm intelligence to address complex optimization challenges by mimicking the social dynamics observed within animal collectives. MOPSO is an extension of PSO, which introduces additional mechanisms to handle multi-objective problems and can find trade-off solutions among multiple objectives. In PSO, potential solutions to optimization problems are conceptualized as "particles" within the search space, each representing a candidate solution that navigates through a multidimensional landscape. These particles dynamically adjust their velocities and positions informed by both personal experience (Personal best, Pbest) and collective experience (Global best, Gbest), encapsulated by the global best position attained by the swarm. The individual best position denotes the most favorable solution a particle has discovered to date, whereas the global best position is the optimal solution identified across the entire particle ensemble. Central to the efficacy of the PSO algorithm is the intricate interplay of cooperation and information sharing among particles. As they traverse the search space, particles leverage not only their own historical data but also the collective insights of swarm particles, thereby achieving a harmonious blend of global exploration and local exploitation. This collaborative framework is instrumental in steering the PSO algorithm away from the pitfalls of local optima, thereby bolstering its capacity for comprehensive search across the solution domain.

3.6.2 Process of the Basic PSO Algorithm

Step 1 Initialization

a. Randomly initialize the position

x_{i}

and velocity

v_{i}

b. Determine the size of the particle swarm, max iterations, the dimensions, and the boundaries of the search space

Step 2 Estimation

a. Calculate the fitness of each particle (Object function value)

Step 3 Initialize Pbest and Gbest

a. For each particle, find and record the personal best position

b. For all particles, find and record the global position

Step 4 Iterative process

a. Update the velocity and position of particle according to the following Eq. (16) and (17):

\begin{aligned} v_{i, n + 1}^{j} = ω v_{i, n}^{j} + c_{1} r_{1} (P_{i, n}^{j} - x_{i, n}^{j}) + c_{2} r_{2} (G_{i, n}^{j} - x_{i, n}^{j}), \end{aligned}

(16)

\begin{aligned} x_{i, n + 1}^{j} = x_{i, n}^{j} + v_{i, n + 1}^{j} . \end{aligned}

(17)

v_{i, n + 1}^{j}

represents the velocity of the particle

i

in the

j

-th dimension in the next iteration

(n + 1)

;

x_{i, n + 1}^{j}

represents the position of the particles

i

in the

j

-th dimension in the next iteration;

ω

is inertia weight;

c_{1}

and

c_{2}

are cognitive coefficient and social coefficient respectively;

r_{1}

and

r_{2}

are random numbers.

For each particle, if the fitness of the new position is better than its personal best, then update the personal best

Among all particles, if any particle's personal best is better than the current global best, then update the global best

Step 5 Check the termination conditions

a. If the maximum number of iterations is reached, the fitness requirement is met, or other termination conditions are satisfied, then terminate the algorithm

b. Otherwise, return to step 4 to continue iterating

Step 6 Output the results

a. Output the found optimal solution or set of solutions

In PSO, the key parameters that influence the algorithm's performance include: Population size, dimensions, inertia weight, max iterations, cognitive coefficient and social coefficient.

3.6.3 MOPSO Algorithm

In the domain of highway maintenance, MOPSO serves as an effective optimization tool for decision-makers by concurrently considering multiple objectives such as safety, cost-effectiveness, and environmental impact. The algorithm's capability to dynamically update the Pareto optimal set allows it to flexibly adapt to variations in traffic volumes and the level of road technical conditions, ensuring the timeliness and adaptability of maintenance plans. By employing mechanisms like crowding distance, MOPSO maintains a diverse set of highway maintenance solutions, offering decision-makers a range of maintenance strategies to navigate the complex trade-offs among objectives. The simplicity of parameter adjustment enables the algorithm to swiftly respond to diverse maintenance requirements. Furthermore, MOPSO algorithm's insensitivity to problem size enables it to easily address maintenance challenges in large networks. Its swift convergence facilitates outstanding performance in handling maintenance issues that demand immediate response. By balancing global and local search, the algorithm can effectively identify satisfactory solutions within a minimal number of iterations, which is particularly crucial for the optimization of extensive road networks. Overall, MOPSO algorithm provides robust decision support for developing efficient, economical, and environmentally friendly maintenance plans.

In the context of highway maintenance multi-objective optimization, MOPSO algorithm is chosen primarily for the following reasons: First, its iterative process utilizes an external archive to record, update, and dynamically adjust the set of non-dominated solutions, ensuring a diversity and comprehensiveness of maintenance strategies. Second, mechanisms such as crowding distance help maintain the diversity of particle swarm, leading to a uniformly distributed Pareto front and offering a range of solutions that consider multiple objectives like safety, economy, and environmental impact, as well as various constraints including budget and environmental considerations. Third, the algorithm involves a minimal set of parameters, including the particle swarm size, inertia weight, individual learning factor, and social learning factor, which are intuitive to adjust and have clear impacts, enabling rapid adaptation to different highway maintenance optimization scenarios.

4 Case Study

This paper utilizes the Lianhuo Highway as a case study to explore the multi-objective optimization of highway maintenance under budgetary constraints, incorporating social, economic, and environmental impacts. The aim is to balance the competing objectives during the maintenance process, seeking the optimal equilibrium among safety, cost, and carbon emission reduction, thereby maximizing the overall maintenance benefits. The selected section of the highway, spanning from K2825 to K4245, is predominantly situated in a plain area and extends for 1,421 kilometers, as detailed in Table 4. This section of the highway varies in the number of lanes, offering 4, 6, and 8 lanes in both directions. The widths of the pavements range from 18 to 42 meters, with each lane measuring 3.75 meters in width, and the pavement surfaces are composed of asphalt concrete. The traffic volume along this section varies significantly, from 5,177 to 489,045 passenger car units (PCU). The composition of vehicles is diverse, encompassing small, medium, and large trucks, extra-large trucks, container trucks, passenger cars, and large buses. In this study, the highway section has been segmented into 15 distinct pavement units based on traffic survey stations. Traffic volume and speed data for these units were collected through highway data gathered at each traffic survey station. The predominant vehicle types within these units include minivans, medium-sized trucks, large trucks, extra-large trucks, container trucks, minibuses, and buses. This detailed analysis ensures a thorough understanding of the traffic dynamics and pavement conditions along the Lianhuo Highway, providing a solid foundation for the development of an effective and balanced multi-objective optimization strategy for highway maintenance.

Table 4 Key information data of highway maintenance unit

Highway Unit	Length (km)	Width (m)	Lane	Traffic Volume	Average Vehicle Speed (km/h)	Current MQI
PU2825	132	24.5	4	48945	111.5	91.21
PU2957	39	24.5	4	15230	110.5	90.53
PU2996	19	24.5	4	47129	116	90.50
PU3015	40	24.5	4	20835	107.3	90.10
PU3055	170	24.5	4	30101	110.4	91.00
PU3225	55	24.5	4	16858	102.1	93.70
PU3279	48	24.5	4	23943	78.2	92.11
PU3371	34	24.5	4	10862	85.3	92.82
PU3587	34	24.5/33/40.5	4/6/8	38676	102.2	90.39
PU3852	56	30/37.5/40.5/42	6/8	15049	116.5	91.13
PU3908	26	37.5	8	21798	99	91.36
PU3934	75	37.5	8	19254	99.5	94.20
PU4082	30	18	4	14712	101	95.41
PU4111	48	18	4	15401	100.5	92.96
PU4159	39	22	4	5218	95.5	89.57

The technical inspection of the Lianhuo highway includes four parts: Sub-grade, pavement, bridge, tunnel, and culvert, and traffic facilities. The basic inspection unit is a 1000-meter section length, and the inspection is carried out in both the upstream (increasing direction of the milestone) and downstream (decreasing direction of the milestone). As shown in Table 5, the technical condition inspection results of the Lianhuo highway for the year 2023 are divided into 28 sections. Each section includes MQI and the sub-item values of the highway technical condition index, namely PQI, SCI, BCI, and TCI, with PCI being the main sub-item indicator value of PQI. Upon reviewing the inspection results, the detection value ranges for PCI, SCI, BCI, and TCI are 75.28

\sim

96.27, 90.71

\sim

100, 78.42

\sim

96.44, and 98.32

\sim

100, respectively, with mean values of 83.01, 97.45, 87.22, and 99.91, and standard deviations of 4.34, 2.97, 4.85, and 0.35, respectively. The data fluctuation of PCI and SCI is relatively large, with data points distributed in the "Good" (80

\sim

90) highway technical condition rating level, which requires improvement in highway performance. The data fluctuation of BCI and TCI is relatively small, with data points distributed in the "Excellent" (90

\sim

100) highway technical condition rating level, indicating that the highway performance is maintained at a high level, and it is necessary to continue to sustain it.

Table 5 Multi-objective optimization for highway technical condition index

Pavement unit	Detection indicator values							Improved indicator values
	Div (MQI)	Div (PQI)	Div (PCI)	Div (SCI)	Div (BCI)	Div (TCI)		Iiv (PQI)	Iiv (PCI)	Iiv (BCI)
	PU1	91.30	89.83	81.06	100.00	86.83	100.00	0.17		8.94	3.17
PU2	90.98	89.50	79.93	100.00	86.04	100.00	0.50		10.07	3.96
PU3	91.16	89.87	81.82	100.00	85.45	100.00	0.13		8.18	4.55
PU4	90.64	89.04	80.76	97.66	87.43	100.00	0.96		9.24	2.57
PU5	90.37	89.54	80.42	90.72	86.93	100.00	0.46		9.58	3.07
PU6	90.52	89.93	80.59	90.71	85.94	100.00	0.07		9.41	4.06
PU7	90.74	90.39	82.34	91.01	84.85	100.00	-		7.66	5.15
PU8	91.84	90.78	82.90	92.05	91.09	100.00	-		7.10	-
PU9	93.59	92.19	86.31	99.46	92.52	100.00	-		3.69	-
PU10	91.87	89.91	80.98	98.44	92.08	100.00	-		9.02	-
PU11	92.38	91.71	84.87	99.29	85.35	100.00	-		5.13	4.65
PU12	91.56	91.74	83.17	99.20	78.42	100.00	-		6.83	11.58
PU13	93.03	92.32	86.42	99.94	86.73	100.00	-		3.58	3.27
PU14	93.03	91.62	85.30	99.73	90.99	100.00	-		4.70	-
PU15	93.85	91.90	83.92	99.95	96.04	100.00	-		6.08	-
PU16	89.68	88.44	77.49	98.05	83.38	99.22	1.56		12.51	6.62
PU17	90.23	88.30	75.28	98.52	87.82	100.00	1.70		14.72	2.18
PU18	91.03	90.72	82.97	98.00	80.69	100.00	-		7.03	9.31
PU19	89.56	88.37	76.12	96.83	82.97	100.00	1.63		13.88	7.03
PU20	91.53	90.91	82.38	97.71	83.96	100.00	-		7.62	6.04
PU21	90.97	89.64	79.35	97.62	86.73	100.00	0.36		10.65	3.27
PU22	91.37	91.54	85.96	95.42	80.50	100.00	-		4.04	9.50
PU23	92.67	91.50	85.54	97.42	90.20	100.00	-		4.46	-
PU24	94.27	92.96	89.69	99.53	93.66	100.00	-		0.31	-
PU25	96.54	95.69	96.27	99.80	96.44	100.00	-		-	-
PU26	92.70	92.02	86.89	99.92	85.74	100.00	-		3.11	4.26
PU27	90.57	90.65	87.09	96.28	79.20	100.00	-		2.91	10.80
PU28	90.48	88.17	78.57	95.25	94.26	98.32	1.83		11.43	-

As depicted in Figure 2, the correlation between the highway maintenance quality level and traffic volume and speed is not pronounced. In the Table 6, the MQI peaks at 95.41, coinciding with a traffic volume of 14,712 pcu and a vehicle speed of 101 km/h. At its minimum, the MQI is 89.57, with corresponding traffic volume and speed of 5,218 pcu and 95.5 km/h, respectively. The principal rationale for this phenomenon is that highway with lower traffic volumes is subject to maintenance less often than those with higher volumes, which enables them to sustain a higher MQI. Furthermore, due to speed restrictions within certain highway sections, vehicle speeds do not escalate with an increase in MQI values but are instead capped at the predefined speed limit. This observation underscores the influence of traffic volume on maintenance frequency and the regulatory impact of speed limits on vehicle velocities, irrespective of the highway condition index.

Figure 2 Comparison of the relationship among traffic volume, average vehicle speed, current speed and width

Full size|PPT slide

Table 6 Lianhuo highway traffc volume and speed observation data

Div (MQI)	Div (PQI)	Div (PCI)	Current MQI	Width (m)
TDOS1	48945	111.5	91.21	24.5
TDOS2	15230	110.5	90.53	24.5
TDOS3	47129	116	90.5	24.5
TDOS4	20835	107.3	90.1	24.5
TDOS5	30101	110.4	91	24.5
TDOS6	16858	102.1	93.7	24.5
TDOS7	23943	78.2	92.11	24.5
TDOS8	10862	85.3	92.82	24.5
TDOS9	38676	102.2	90.39	33
TDOS10	15049	116.5	91.13	37.5
TDOS11	21798	99	91.36	37.5
TDOS12	19254	99.5	94.2	37.5
TDOS13	14712	101	95.41	18
TDOS14	15401	100.5	92.96	18
TDOS15	5218	95.5	89.57	22

In accordance with the highway technical condition evaluation standard, the assessment is conducted with a 1000-meter section length serving as the fundamental evaluation unit. This evaluation encompasses the pavement technical condition, subgrade technical condition, bridge and tunnel structure technical condition, and the technical condition of the facilities along the highway. The entire section is then segmented into a total of 15 units for a detailed assessment. This methodology offers a systematic and segmented approach to assess the highway's condition. It allows for precise identification of areas needing maintenance or enhancement.

Highway technical condition serves as a pivotal indicator of safety performance, as illustrated in Figures 3, 4, 5, and Table 7. The TCI curve exhibits a stable trend, indicating that the highway consistently maintains an excellent state, thereby exerting minimal impact on safety performance. In contrast, the PQI, SCI, and BCI curves display greater fluctuations, suggesting a more substantial influence on safety performance. The overall trajectories of the PQI and SCI are observed to be congruent, primarily due to the synchronized maintenance cycles of the pavement throughout the highway's lifecycle. This synchronization results in a consistent technical condition trend for both indices. Budgetary constraints have delayed maintenance, causing the trend to deviate. This deviation leads to a divergence in the SCI curve.

Table 7 Lianhuo highway maintenance quality indicator inspection values

Measured Pavement Unit	PQI	SCI	BCI	TCI
MPU1	89.82	100.00	85.83	100.00
MPU2	89.51	93.95	87.60	100.00
MPU3	90.69	92.54	87.70	100.00
MPU4	91.11	99.00	88.99	100.00
MPU5	91.85	99.60	85.83	100.00
MPU6	89.69	98.85	89.05	99.72
MPU7	89.70	97.49	83.22	100.00
MPU8	90.75	96.92	83.39	100.00
MPU9	93.75	99.19	95.09	100.00
MPU10	89.94	96.90	85.58	99.31

Adhering to the Highway Maintenance Technical Specifications and the Highway Maintenance Engineering Management Regulations, and considering the distinctive maintenance characteristics of this region, extensive consultations with highway maintenance management experts were conducted. Subsequently, a tailored set of maintenance methodologies has been formulated for this case study. These methodologies include preventive maintenance engineering (PME), rehabilitative maintenance engineering (RME), emergency maintenance engineering (EME), and special maintenance engineering (SME). Notably, the RME specifically addresses the maintenance requirements of pavements, bridges, and tunnels, ensuring a restoring the maintenance quality of highway infrastructure approach to highway upkeep.

As shown in Figure 6, the commencement of maintenance strategies is based on a quintile classification system for highway conditions, delineating them into five distinct categories: Excellent, good, average, poor, and bad. This stratification provides a clear framework for the targeted initiation of appropriate maintenance actions in response to the varying conditions of the highway.

Figure 6 Highway maintenance condition indicator level

Full size|PPT slide

In the quest for a detailed assessment of individual pavement units, a precise subdivision is meticulously implemented, following the established methodologies for maintenance unit segmentation. This categorization takes into account the variability in indices observed across different pavement units, enabling a more refined evaluation process in Table 8.

Table 8 Method of classification for maintenance types of evaluation units

Interval range of highway technical condition indicators				Maintenance type
PCI	RQI	RDI	SRI	Maintenance type
$\geq A_{1}$	$\geq B_{1}$	$\geq C$	< D	PM
	$\geq B_{1}$	< D	-	RM
	$B_{2} - B_{1}$			PM
	< $B_{2}$			RM
$A_{2} - A_{1}$	$\geq B_{2}$			PM
$A_{2} - A_{1}$	< $B_{2}$			RM
< $A_{2}$				RM

Note: A₁ = 92, A₂ = 85, B₁ = 90, B₂ = 85, C = 80, D = 75.

Utilizing historical highway maintenance data and relevant research^{[26, 27, 30]}, the financial implications of highway maintenance engineering are detailed in Table 9. Moreover, the carbon emissions for preventive maintenance engineering (PME) and rehabilitative maintenance engineering (RME) are delineated, with PME

g m_{1}

emitting 3551.1363 kg CO

_{2}

equivalent per lane-kilometer and RME

g m_{2}

emitting 10653.4091 kg CO

_{2}

equivalent per lane-kilometer. Furthermore, the carbon emissions generated by different vehicle types are specified: Cars

g r_{1}

contribute 0.5275 kg CO

_{2}

equivalent per RS-lane-kilometer, while trucks

g r_{2}

contribute 1.3776 kg CO

_{2}

equivalent per RS-lane-kilometer. These data offer a clear perspective on the environmental footprint of both maintenance operations and vehicular traffic, highlighting the ecological aspects integrated into the strategic management of highway maintenance.

Table 9 Types of highway maintenance method

Serial no.	Maintenance treatment option	Unit agency Cost
M1	PME	18.05 (¥/m $^{2}$ )
M2	RME (Pavement)	36.63 (¥/m $^{2}$ )
M3	RME (Bridge)	2434.56 (¥/m)
M4	RME (Tunnel)	3001.13 (¥/m)
M5	EME	24.20 (million ¥/year)
M6	SME	22.69 (million ¥/year)

Note: Agency cost was obtained from annual report on highway maintenance statistics from 2019 to 2023.

Examining the historical data from 2019 to 2023, as illustrated in Figure 7 and Table 10, a pronounced positive correlation is observed among maintenance budgets, highway maintenance quality index, and carbon emissions. Throughout this five-year period, the financial outlay for maintenance oscillated between 141.21 million and 334.64 million Yuan, against a backdrop of improving highway technical condition indicators, which rose from 89.63 to 91.73. Strikingly, between 2020 and 2021, an unexpected trend was noted: Technical indicators reached their zenith at 92.51 despite a decrease in maintenance funding, and it demonstrates a discernible marginal increment effect. However, from 2022 onwards, the relationship between maintenance investment and technical indicators reversed, with indicators falling rather than rising in tandem with increased or sustained financial support, and it displays a marginal diminishing effect. Additionally, maintenance funding and carbon emissions were found to have a positive correlation, with carbon emissions mirroring the financial investment's trajectory from 2019 to 2023. The variability in the rate of increase or decrease in carbon emissions corresponds to the different maintenance strategies employed annually, namely preventive maintenance engineering (PME) and rehabilitative maintenance engineering (RME). In 2021, the implementation of a preventive maintenance strategy yielded significant outcomes. Characterized by reduced financial demands and carbon emissions in comparison to corrective approaches, this strategy led to a notable decrease in both maintenance engineering costs and carbon emissions for the year. This observation underscores the pivotal role of strategic maintenance planning in achieving a delicate balance between economic efficiency and environmental sustainability in the realm of highway management. By prioritizing preemptive actions, the strategy not only curtailed immediate expenses but also contributed to long-term ecological stewardship.

Figure 7 MQI changes as CE varies for different MB from 2019 to 2023

Full size|PPT slide

Table 10 Lianhuo highway MB, MQI, and CE from 2019 to 2023

Year	Maintenance budget (¥)	Maintenance quality index	Carbon emissions (t)
2019	334641006	90.66	7824.141608
2020	37749377	91.83	13866.95537
2021	241195414	92.51	10514.31925
2022	386819046	92.36	16476.2957
2023	141219081	91.73	6089.726841

As depicted in Figure 8 and Table 11, the majority of carbon emissions from highways stem from emissions associated with maintenance activities and those induced by highway surface irregularities. Rehabilitative maintenance is a significant contributor to the carbon footprint of highways, accounting for 99.86%, 99.91%, 73.40%, 80.95%, and 96.83% of total emissions across different periods. The trend of these two sources of emissions is largely congruent. The contribution of preventive maintenance and highway surface irregularities to overall carbon emissions is comparatively minor, with a proportion ranging from 0.09% to 26.60%, exerting a negligible impact on the carbon emissions profile of highways. Between 2019 and 2023, the trajectory of carbon emissions followed an M-shaped curve. This pattern primarily resulted from the decision-makers' preference for maintenance strategies aimed at reducing costs. Initially, corrective maintenance was favored over a combination of preventive and rehabilitative approaches, leading to a secondary peak in carbon emissions of 13,867 tons in 2020. Subsequently, as the highway's technical condition improved, there was a shift in maintenance strategy. A combination of preventive and rehabilitative maintenance was adopted, coupled with a reduction in the intensity of rehabilitative maintenance works, which corresponded with a decline in carbon emissions. The performance of the highway degraded over the three years of service, yet it was sustained at an acceptable technical level through increased investment in preventive and rehabilitative maintenance. Consequently, carbon emissions peaked at 16,476 tons. By 2023, despite continuing with a combined approach of preventive and rehabilitative maintenance, there was a substantial reduction in maintenance investment, leading to a swift decrease in carbon emissions for that year.

Figure 8 Carbon emissions varies for CEPM, CERM and CEHR from 2019 to 2023

Full size|PPT slide

Table 11 Lianhuo highway CE from 2019 to 2023

Year	CEPM (ton)	CERM (ton)	CEHR (ton)	Total (ton)
2019	0	7813	11	7824
2020	0	13854	12	13867
2021	2787	7717	11	10514
2022	3127	13338	12	16476
2023	173	5897	20	6090

To sustain a high level of safety and enhance user comfort on highways, the expenses associated with maintenance engineering are observed to rise in tandem with improvements in safety performance. Highways exhibiting lower safety performance necessitate a more substantial investment in maintenance engineering resources. The Pareto Boundary encapsulates the intricate trade-offs among safety performance, maintenance costs, and carbon emissions. It reflects the anticipated increase in both maintenance costs and carbon emissions in conjunction with the desired elevation in safety performance. This study explores how the Lianhuo Highway's maintenance strategy changes with safety, cost, and carbon emission fluctuations. For analysis, various highway maintenance strategies informed by unique preference criteria have been implemented.

Within the safety preference framework, the weightings are allocated as follows:

w_{1} =

w_{2} =

w_{3} =

0, signifying that the optimization of safety performance is the paramount objective, with maintenance costs and carbon emissions being secondary considerations. In line with this preference, the study targets highway segments with PCI, BCI, and TCI scores beneath 90, aiming to elevate these to a minimum standard of 90. This targeted enhancement is visually represented in Figure 9, which illustrates the strategic focus on improving those segments that fall below the established safety thresholds.

Figure 9 Maximization of safety for Lian-Huo line sections

Full size|PPT slide

Under the cost preference framework, where weights are allocated as

w_{1} =

w_{2} =

1, and

w_{3} =

0, the strategy is singularly focused on minimizing financial outlays. In this scenario, safety performance and carbon emissions are not the primary concerns. The approach acknowledges the practical realities of maintenance, allowing the highway's technical condition to decline to a specified minimum threshold of 75. Should conditions fall below this level, proactive corrective measures are engaged to restore the highway's integrity (as illustrated in Figure 10). This framework emphasizes economic efficiency while ensuring that the highway remains operational, albeit at a potentially reduced service level, until the need for intervention arises.

Figure 10 Minimization of maintenance costs for Lian-Huo line sections

Full size|PPT slide

Within the carbon emission preference approach, designated by weights

w_{1} =

w_{2} =

0, and

w_{3} =

1, the overarching priority is the minimization of carbon emissions, with safety performance and maintenance engineering costs taking a secondary role. This strategy advocates for an enhanced focus on preventive maintenance to reduce the frequency and intensity of rehabilitative maintenance activities, thereby curtailing carbon emissions more effectively. The approach is designed to achieve a lower carbon emission in highway maintenance operations, as depicted in Figure 11, which illustrates the targeted reduction in carbon emissions through a strategic shift towards more sustainable maintenance practices.

Figure 11 Minimization of carbon emission for Lian-Huo line sections

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As the landscape of highway maintenance evolves in complexity and the preferences of decision-makers increasingly interact, the strategies for highway maintenance correspondingly become more intricate. There is a necessity to uphold the safety of highways while favoring periodic preventive maintenance to sustain performance indicators in a "good" or "excellent" state. Concurrently, these strategies must address the significant objective of substantially reducing carbon emissions. This multifaceted approach ensures that the highway system remains secure and efficient, without compromising on environmental sustainability.

Traffic volume is intimately linked to the deterioration of highway performance. However, there are three specific scenarios in which the impact of traffic volume on the MQI is minimal. First, the overall MQI is above 90. Second, there is a significant fluctuation in traffic volume. Third, the traffic volume is below the designed value. As illustrated in Figure 12 and Table 12, the traffic volume experiences a substantial variation, ranging from 5,218 pcu to 48,945 pcu, marking an 838% change within the unit highway section. In contrast, the MQI value is less affected, with a modest change from 95.41 to 89.57, representing a 6.52% fluctuation. This indicates that on sections of the highway with a higher MQI, the increase in traffic volume does not significantly detract from the MQI, nor does it substantially impair safety performance. This observation indicates that on highway sections with superior MQI ratings, escalated traffic volumes do not lead to a sharp decline in MQI, nor do they significantly compromise safety performance. Consequently, it precludes the need for a substantial augmentation in maintenance costs associated with the implementation of further preventive maintenance measures. This insight is pivotal for the strategic optimization of maintenance approaches and the targeted allocation of resources in accordance with traffic-induced alterations in highway integrity.

Figure 12 Relationship between traffic volume and MQI

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Table 12 Traffc volume and MQI measurements

Traffc data observation station	Design traffic volume (PCU)	Traffc volume measurements (PCU)	TVM/DTV (%)	Currentn MQI	C(MQI)/90 (%)
TDOS1	15000	48945	326.30%	91.21	101.34%
TDOS2	15000	15230	101.53%	90.53	99.48%
TDOS3	15000	47129	314.19%	90.5	98.37%
TDOS4	15000	20835	138.90%	90.1	96.88%
TDOS5	15000	30101	200.67%	91	96.81%
TDOS6	15000	16859	112.39%	93.7	98.63%
TDOS7	15000	23943	159.62%	92.11	95.95%
TDOS8	15000	10862	72.41%	92.82	95.69%
TDOS9	25000	38676	154.70%	90.39	92.23%
TDOS10	25000	15049	60.20%	91.13	92.05%
TDOS11	37000	21798	58.91%	91.36	91.36%
TDOS12	37000	19254	52.04%	94.2	93.27%
TDOS13	15000	14712	98.08%	95.41	93.54%
TDOS14	15000	15401	102.67%	92.96	90.25%
TDOS15	15000	5218	34.79%	89.57	86.13%

In the realm of multi-objective optimization analysis, this study examines the trade-off dynamics between maintenance engineering costs and carbon emissions. Contrary to prevailing research outcomes that suggest a linear escalation of carbon emissions alongside increased maintenance inputs or a pattern of initial decrease followed by an increase^{[25, 49]}, the findings of this study reveal a more complex trend: An initial surge, subsequent decline, and eventual resurgence in total carbon emissions. This fluctuation primarily attributes to several key factors. Firstly, the highway section in question maintains an overall superior technical condition, with an MQI exceeding 90, leading to minimal variance in pavement smoothness and consequently low carbon emissions at 0.5275 kg CO

_{2}

eq/RS-lane-km. In comparison to the emissions associated with maintenance activities, which range from 3551 kg CO

_{2}

eq/lane-km to 10653 kg CO

_{2}

eq/lane-km, the carbon footprint stemming from pavement irregularities is relatively insignificant. Despite the dynamic interplay between maintenance operations and highway condition levels, the carbon emissions attributable to highway surface unevenness remain limited. Secondly, the selection of the Lianhuo highway section, characterized by its extensive length, provides a more highway operation and maintenance quality performance reflection of the entire highway's technical condition and vehicular traffic patterns. This approach effectively mitigates the impact of singular outliers on the overall analysis, thereby enhancing the model's predictive accuracy and generalization capacity. In contrast, an analysis confined to a subsection of the highway may lead to variations in carbon emissions that correspond with maintenance costs, potentially diminishing the model's forecasting precision and versatility. Lastly, the selection of maintenance modalities is intrinsically connected to carbon emissions. This paper takes into account the interplay between preventive and corrective maintenance strategies. Initially, preventive maintenance is prioritized as the highway section commences maintenance projects. With advancements in highway condition technical levels and concurrent improvements in safety performance, the strategy shifts towards a predominately preventive maintenance approach, complemented by corrective measures. The carbon emissions resulting from preventive maintenance are a mere 33.33% of those associated with corrective maintenance, leading to a reduction in overall emissions. Preventive maintenance's effect on highway conditions is temporary. As a result, highways return to rehabilitative maintenance phases, leading to increased carbon emissions.

The objective of devising an optimal highway maintenance strategy is to enhance the of overall benefits to the greatest extent possible within the constraints of limited resources. This paper utilizes five years of historical highway data to assess selected highway sections. The maintenance actions undertaken for each segment are denoted by integers ranging from 0 to 5, symbolizing the varying degrees of intervention. The sustainability indices for these highway segments are computed, yielding 56 sets of viable maintenance plan combinations for decision-makers to consider. Each set represents a non-dominated solution within the multi-objective optimization framework of highway maintenance, where no combination outperforms another across all objectives. Moreover, frequent maintenance activities may have detrimental environmental impacts. Each point within the analysis represents a potential non-dominated solution to the multi-objective optimization challenge. For instance, as depicted in Figure 13, the point (0, 1, 2) signifies the optimal maintenance combination for highway sections 1, 2, and 3, with corresponding outcomes

F_{1} =

274.833,

F_{2} =

825.440 million Yuan, and

F_{3} =

31,209.746 tons of carbon emissions. The Pareto frontiers delineate the optimal trade-offs between individual objectives, allowing decision-makers to select the final strategy based on a composite of safety performance, budgetary constraints, and carbon emissions. By addressing the multi-objective optimization problem and considering diverse objective attributes alongside the preferences of decision-makers, a multitude of optimal maintenance solutions can be generated. When prioritizing safety performance, strategies such as (0, 1, 2, 4, 5), (0, 2, 3, 4, 5), and (1, 2, 3, 4, 5) can be adopted, achieving optimal safety scores of 459.504, 458.727, and 459.476, respectively. In scenarios where the minimization of maintenance costs is the primary preference, strategies like (0, 5), (1, 5), and (4, 5) can be implemented, with the optimal conservation costs calculated at 491.043 million Yuan, 464.384 million Yuan, and 436.611 million Yuan, respectively. When the minimization of carbon emissions is the central focus, strategies including (2, 4), (2, 5), and (4, 5) can be considered, with carbon emissions at these junctures being 18070.090 tons, 16686.831 tons, and 17085.317 tons, respectively.

Figure 13 Integrated maintenance optimization strategies

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The interplay between safety performance and maintenance engineering costs is characterized by a trade-off relationship: As maintenance costs escalate, the level of highway safety performance correspondingly increases. In the initial phase, there is a marked surge in safety performance with the initial influx of capital. Additional maintenance funds lead to a slower rate of improvement in safety performance. This reflects a scenario where returns on investment are diminishing. The apex of safety performance is achieved when the maintenance outlay is allocated according to the combination (0, 1, 2, 3, 5), peaking at a cost of 1,262.05 million Yuan. As depicted in Figure 14, with incremental increases in conservation investment — representing various maintenance strategies — the performance of highway conservation exhibits a stepped progression. Yet, within combinations of maintenance plans of equivalent scale, the trajectory of safety performance stabilizes, while the costs and carbon emissions exhibit fluctuations, predominantly in a positive correlation. Specifically, carbon emissions surge in tandem with increased conservation investment and recede as investment diminishes. This pattern is exemplified when the maintenance expenditure reaches 1,262.05 million yuan, at which point the safety performance metric culminates at a value of 460. Conversely, when the investment is upped to 1,381.49 million Yuan, the safety performance slightly declines to 458. These outcomes align with the principle of diminishing marginal utility, indicating that within a certain timeframe, once the highway's safety performance has attained an "excellent" status, further increments in maintenance investment yield progressively smaller benefits to the highway's technical condition. Once the highway's safety performance has reached an "excellent" state, the positive influence on the technical condition wanes with each additional investment. When the extra investment does not exceed the threshold needed to enhance or sustain an index value, the value of the safety performance index for each additional unit of investment tends to decline. This underscores the importance of strategic allocation of resources to optimize both safety performance and economic efficiency within highway maintenance operations.

Figure 14 Trade-off relationship between safety performance and maintenance costs

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The trade-off relationship between maintenance engineering costs and carbon emissions, as illustrated in Figure 15, delineates a significant inverse relationship. Within a set of maintenance plans of equivalent scale, carbon emissions are observed to escalate (or diminish) in correspondence with an upsurge (or reduction) in maintenance investment. The carbon emissions culminate at a peak of 53,507 tons upon an investment of 1,381.49 million Yuan in maintenance. Conversely, the nadir of carbon emissions, amounting to 170, 85 tons, is achieved at a comparatively lower maintenance outlay of 436.61 million Yuan. This dynamic underscores the intricate balance that must be struck between financial expenditure and environmental impact within highway maintenance strategies.

Figure 15 Trade-off relationship between maintenance costs and carbon emissions

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The relationship between safety performance and carbon emissions is characterized by a positive correlation: As safety performance escalates, so too does the volume of carbon emissions (as illustrated in Figure 16). This dynamic is influenced by two opposing factors. Firstly, improvements in safety performance boost the driving quality index, lessening the highway surface's effect on vehicle travel and potentially reducing carbon emissions. Secondly, the enhancement of safety performance requires the execution of maintenance projects aimed at improving various indicators. Both preventive and corrective maintenance activities significantly contribute to carbon emissions, leading to an overall increase. It is particularly important to note that when the technical indicators of highway conditions surpass an average value of 91, the selection of different combinations from the same set of maintenance projects can lead to a reduction in carbon emissions as safety performance improves. This reduction is primarily attributed to a strategic shift in maintenance practices from corrective to preventive approaches. Preventive maintenance is associated with significantly lower carbon emissions, highlighting the environmental benefits of proactive highway maintenance strategies.

Figure 16 Trade-off relationship between safety performance and carbon emissions

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5 Conclusion and Discussion

Maintenance engineering research increasingly focuses on ensuring highway safety, achieving comprehensive maintenance benefits, and advocating low-carbon practices within a complex, interrelated process involving safety, benefits, and environmental impacts. These interactions shape the strategic approaches to safety, maintenance, and environmental considerations across various scenarios. In response to the expanding highway network and persistent demand for maintenance, compounded by the need for social progression, economic return, and environmental stewardship, this paper introduces a multi-objective optimization model. The model addresses the intricate balance between safe access, maintenance benefits, and environmental impacts within the context of highway maintenance management. The paper further advocates for the quantification and optimization of these multi-objectives through the utilization of extensive, accurate, and continuous data from multiple highway sources. This approach aims to analyze the trade-offs in maintenance portfolios due to decision-making interactions and provides a balanced social-economy-environmental framework for informed strategic planning in highway maintenance.

The theoretical and practical implications of this work are as follows: Firstly, on a theoretical level, this paper provides empirical data support for multi-objective studies related to highway maintenance, refines the index system for measuring multiple maintenance objectives, and enriches the quantitative research on safety, cost, and carbon emissions. It explores the interplay and the intrinsic relationships among these factors, thereby validating the potential for achieving a Pareto-optimal state in terms of safety, cost, and carbon emissions within the context of highway maintenance. Secondly, on a practical level, this study aids governments in scientifically assessing the sustainable development of highway maintenance, fostering a safe, economical, and environmentally friendly approach. It promotes a virtuous cycle and sustainable development in highway maintenance and holds significant value for informing the development of highway maintenance strategies.

In multi-objective optimization, assigning weight values to objectives is standard practice to prioritize their importance. This approach allows decision-makers to tailor the weighting of objectives according to the prevailing societal, economic, and environmental conditions of each phase, facilitating the adoption of distinct conservation strategies. Each unique weighting configuration generates a different set of solutions, reflecting the absence of a singular optimal solution in a multi-objective context. A variety of optimal solutions arises, providing options for strategic maintenance planning and implementation. This flexibility is crucial for aligning maintenance actions with the dynamic priorities of decision-makers and the evolving needs of the system being managed.

In the sphere of multi-objective optimization, the practice of assigning relative weight values to a spectrum of objectives is essential for delineating their relative significance. Decision-makers are empowered to adjust these weights in response to the specific social, economic, and environmental dynamics of each phase, thus enabling the formulation of customized conservation strategies. Each distinct set of weights engenders a unique array of solutions. This ensemble of solutions offers a diverse toolkit for the deliberate orchestration and execution of conservation initiatives, and the approach is aligned with the multi-dimensional criteria that shape the decision-making environment.

Inside the multi-objective optimization framework, the proposed multi-objective model adeptly reconciles three potentially conflicting objectives: Enhancing safety performance, managing maintenance engineering costs, and mitigating environmental impact. This integration is pivotal in crafting a safety-economy-environment maintenance strategy that yields an optimal project library for highway maintenance over the planning horizon. Armed with this library, decision-makers are equipped to select a maintenance plan that is not only financially viable but also aligned with the specific target tasks of different maintenance stages. This approach allows for the achievement of maintenance management objectives within the parameters of budgetary constraints, ensuring that resources are allocated efficiently and effectively to meet the multifaceted demands of highway maintenance.

The case study elucidates the dynamics within a multi-objective model that accounts for the interplay of decision-makers' preferences. Initially, it observes that as maintenance expenditures rise, the efficiency of capital utilization begins to diminish once the MQI reaches 93. Beyond this threshold, further investments in maintenance do not yield improvements in the highway's safety performance, adhering to the principle of diminishing marginal returns. Subsequently, the study indicates that the influence of fluctuating traffic volumes on maintenance strategy is rather constrained. Although the highway is engineered to handle a daily traffic volume of 66,418 vehicles, the actual average daily traffic volume stands at 25,914 vehicles. Despite the actual volume being substantially lower than the highway's designed safety performance capacity, its overall impact on the maintenance strategy remains minimal. Additionally, maintenance is carried out during off-peak hours to minimize disruption. Systematic and rational traffic management ensures that normal vehicle traffic is not impeded. Consequently, at low operational traffic levels, the influence on greenhouse gas emissions attributable to congestion is marginal. Furthermore, the study posits that increasing maintenance investments can optimize the reduction of greenhouse gas emissions from vehicles to the fullest extent possible. The case study shows that greenhouse gas emissions from vehicles are significantly lower on highways with high safety performance. These emissions are much lower than those from maintenance and construction activities. The aggregate minimum emissions resulting from both maintenance operations and vehicle traffic hinge on the sensitivity and selection of the maintenance approach. It is also noteworthy that practical maintenance strategies continue to confront challenges stemming from policy shifts and fiscal limitations, particularly given the annual variability in operational phases.

This study performs in-depth research and analysis on Lianhuo highway data within a comprehensive scale perspective. It employs a micro division of measurement units at 1-kilometer intervals and a meso division into six distinct highway sections. Through the analysis at both the unit and highway section levels, the study aims to enhance the efficiency of data utilization. Additionally, it refines the selection and adjustment of the scale division for highway section maintenance, as well as the focal points of maintenance efforts. This approach is conducive to devising a balanced safety-economy-environment maintenance strategy. One of the study's limitations is its omission of the impact of emergencies on highway safety performance and maintenance. In emergency maintenance projects, the strategy tends to prioritize safety performance. This aspect will be a focal point for future research on the "combination of peacetime and emergency" in highway maintenance, ensuring a more integrated approach to addressing both routine and emergency maintenance scenarios.

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Funding

the National Natural Science Foundation of China(72471223)

the National Natural Science Foundation of China(72231010)

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Abstract
Key words
Cite this article
1 Introduction
2 Literature Review
2.1 Data Elements Circulation
Table 1 Classification of highway data
2.2 Data Applications in Highways
2.3 Multi-Objective Optimization of Maintenance
Figure 1 Distribution map of criteria in multi-objective optimization for highway maintenance
2.4 Optimization Techniques and Models
Table 2 Main features of multi-objective optimization for highway maintenance
3 Theory and Methodology
3.1 Multi-Objective Decision Theory
3.2 Multi-Objective Optimization Framework
3.3 Data
3.4 Objective Function
3.4.1 Definition of Safety Objective Function
3.4.2 Definition of Cost Objective Function
3.4.3 Definition of Cost Objective Function
3.4.4 Definition of Cost Objective Function
3.5 Normalization
3.6 MOPSO Algorithm
Table 3 Comparison analysis of strengths and weaknesses for multi-objective optimization algorithms
3.6.1 The Fundamental Principle of PSO
3.6.2 Process of the Basic PSO Algorithm
3.6.3 MOPSO Algorithm
4 Case Study
Table 4 Key information data of highway maintenance unit
Table 5 Multi-objective optimization for highway technical condition index
Figure 2 Comparison of the relationship among traffic volume, average vehicle speed, current speed and width
Table 6 Lianhuo highway traffc volume and speed observation data
Figure 3 PQI and SCI changes on the selected section of Lianhuo line in 2023
Figure 4 BCI and TCI changes on the selected section of Lianhuo line in 2023
Figure 5 Index values in 2023 on the 10 units of Lianhuo line
Table 7 Lianhuo highway maintenance quality indicator inspection values
Figure 6 Highway maintenance condition indicator level
Table 8 Method of classification for maintenance types of evaluation units
Table 9 Types of highway maintenance method
Figure 7 MQI changes as CE varies for different MB from 2019 to 2023
Table 10 Lianhuo highway MB, MQI, and CE from 2019 to 2023
Figure 8 Carbon emissions varies for CEPM, CERM and CEHR from 2019 to 2023
Table 11 Lianhuo highway CE from 2019 to 2023
Figure 9 Maximization of safety for Lian-Huo line sections
Figure 10 Minimization of maintenance costs for Lian-Huo line sections
Figure 11 Minimization of carbon emission for Lian-Huo line sections
Figure 12 Relationship between traffic volume and MQI
Table 12 Traffc volume and MQI measurements
Figure 13 Integrated maintenance optimization strategies
Figure 14 Trade-off relationship between safety performance and maintenance costs
Figure 15 Trade-off relationship between maintenance costs and carbon emissions
Figure 16 Trade-off relationship between safety performance and carbon emissions
5 Conclusion and Discussion
References
Funding

Received	Accepted	Published
2024-07-21	2024-12-10	2025-02-25
Issue Date
2025-02-25

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1 Introduction

2 Literature Review

2.1 Data Elements Circulation

Table 1 Classification of highway data

2.2 Data Applications in Highways

2.3 Multi-Objective Optimization of Maintenance

Figure 1 Distribution map of criteria in multi-objective optimization for highway maintenance

2.4 Optimization Techniques and Models

Table 2 Main features of multi-objective optimization for highway maintenance

3 Theory and Methodology

3.1 Multi-Objective Decision Theory

3.2 Multi-Objective Optimization Framework

3.3 Data

3.4 Objective Function

3.4.1 Definition of Safety Objective Function

3.4.2 Definition of Cost Objective Function

3.4.3 Definition of Cost Objective Function

3.4.4 Definition of Cost Objective Function

3.5 Normalization

3.6 MOPSO Algorithm

Table 3 Comparison analysis of strengths and weaknesses for multi-objective optimization algorithms

3.6.1 The Fundamental Principle of PSO

3.6.2 Process of the Basic PSO Algorithm

3.6.3 MOPSO Algorithm

4 Case Study

Table 4 Key information data of highway maintenance unit

Table 5 Multi-objective optimization for highway technical condition index

Figure 2 Comparison of the relationship among traffic volume, average vehicle speed, current speed and width

Table 6 Lianhuo highway traffc volume and speed observation data

Figure 3 PQI and SCI changes on the selected section of Lianhuo line in 2023

Figure 4 BCI and TCI changes on the selected section of Lianhuo line in 2023

Figure 5 Index values in 2023 on the 10 units of Lianhuo line

Table 7 Lianhuo highway maintenance quality indicator inspection values

Figure 6 Highway maintenance condition indicator level

Table 8 Method of classification for maintenance types of evaluation units

Table 9 Types of highway maintenance method

Figure 7 MQI changes as CE varies for different MB from 2019 to 2023

Table 10 Lianhuo highway MB, MQI, and CE from 2019 to 2023

Figure 8 Carbon emissions varies for CEPM, CERM and CEHR from 2019 to 2023

Table 11 Lianhuo highway CE from 2019 to 2023

Figure 9 Maximization of safety for Lian-Huo line sections

Figure 10 Minimization of maintenance costs for Lian-Huo line sections

Figure 11 Minimization of carbon emission for Lian-Huo line sections

Figure 12 Relationship between traffic volume and MQI

Table 12 Traffc volume and MQI measurements

Figure 13 Integrated maintenance optimization strategies

Figure 14 Trade-off relationship between safety performance and maintenance costs

Figure 15 Trade-off relationship between maintenance costs and carbon emissions

Figure 16 Trade-off relationship between safety performance and carbon emissions

5 Conclusion and Discussion

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References

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Footnotes

Funding