Using an Airport Pavement Management System to Optimize the Influence of Maintenance Alternatives on Operating Conditions

Abstract

In the airport pavement management systems (APMSs), a focus point is the decision-making process. It enables finding the optimal strategy for maintaining a flight infrastructure in adequate condition over a given period, while considering the operating conditions of the airside. In this context, the present study analyzes the factors involved in the optimization processes by investigating how much they influence the solutions. Using the analysis processes connected to the APMS, the present study also includes the identification of specific intervention areas through clustering algorithms, minimizing the fixed operating costs. More specifically, the use of K-means clustering and the heuristic algorithms connected to the choices of the maintenance activities, allow possible scenarios replicating the different needs of managers to be investigated. In this way, the research work analyzes the influence of the alternatives in terms of pavement quality and total activities duration. Through this study it is shown that there is not a unique optimal strategy, but several possible solutions that can be undertaken by the airport managers according to their needs. However, the comparison of the results obtained in this study could become a useful tool for airport managers for better planning and management of the flight infrastructures.

1. Introduction

In the airport field, the need to offer an efficient transport system is leading to a constant increase in the quality and safety of the service offered. In view of the growing demand for air transport in recent years, more attention should be paid to the qualitative conditions of the pavement, as it often involves the planning of repairs and restorations. Furthermore, various expansions and adaptations to the flight infrastructures are requested, to adapt them to the passage of higher category aircrafts [1]. In this context, the development of the airport pavement management system (APMS) is strategic, as it helps airport stakeholders to better manage all the airport infrastructures. In fact, applying an effective maintenance plan, a reduction of the life cycle cost, an increase in the service life and a maintenance of a high level of serviceability over the years is possible [2].

To function properly, the APMS has to be able to perform a series of operations [3] including the following macro-components: (I) the database, to collect and storage the data relating to the infrastructures under study; (II) the models, to allow the evaluation of the pavement condition; and (III) the analysis tools, to estimate the future pavement condition and select the optimal maintenance and rehabilitation (M&R) activities to be applied to the critical areas according to the adopted strategy.

Since most of the studies relating to the pavement management system concern the road sector, various similarities have been exploited and appropriately calibrated in the research on the airport field. Usually, the optimization processes of the road pavement maintenance programs focus on factors such as limited resources, local climate, type of road classification and political considerations [4,5,6,7]. In the airport field, further factors are analyzed, namely the high operational impacts caused by the implementation of M&R activities. Hence, the APMS helps the airport managers to identify the most appropriate cost-effective activities, also evaluating the operational impact in a simple and intuitive way [8]. Obviously, every possible strategy has to comply with the requirements and rules of the current national and international legislation [9].

Usually, the strategies adopted could refer to routine, periodic or emergency maintenance [10]. In an emergency scenario, the pavement reaches the point of collapse, risking the stop of airport operations. The preventive activities, instead, are planned, so they allow maintenance of adequate conditions of the pavement with less invasive activities, minimizing the impact of airport operations. In any case, according to the strategy applied, possible factors triggering the activation of the different pavement repair type change, such as overall condition level, type of distress present, and rate of deterioration [11].

Based on the assumption that even small distresses to parts of the airport infrastructures can seriously compromise the functionality of their operations [12], correctly predicting the performance of the pavement through an accurate and efficient pavement deterioration model is the key element for the correct use of an APMS [13]. In fact, the selection and use of technical parameters and performance indicators lead to an accurate evaluation of pavement condition [14] and this choice has to be made carefully as it could influence subsequent M&R activities that are conducted.

In this framework, the present research aims at analyzing how the strategies applied by airport managers influence the maintenance activities to be applied. In detail, the present approach includes both a clustering process, to minimize the fixed operating costs of the activities, and an optimization method or the choice of activities. Based on the previous knowledge submitted in the previous study by Ragusa et al. [15], this work focuses on the influence factors that clustering and optimization processes have on APMS problems.

To the best of our knowledge, this paper represents the first attempt to use properly calibrated clustering and optimization algorithms for an analysis of influencing factors in an airport context, through application on a real case study. Focusing on the runway layout related to one of the most important airports in Southern Italy, the study demonstrates that there is not an optimal cluster combination or a strategy, but different possible solutions depending on the needs of airport managers. Consequently, an analysis of the results, deriving from the application of the different scenarios, is conducted, focusing on costs, duration and quality of the pavement.

The remainder of this paper is organized as follows. Section 2 analyzes the state of the art of optimization processes for the definition of multi-year pavement maintenance problems, presenting several studies present in the literature over the years. Section 3 discusses the methodological framework used for this study. Section 4 illustrates the application of a case study according to the hypothesized parameters and assumptions. In Section 5, there is a discussion of the obtained results. Finally, conclusions and guidelines for future works are drawn in Section 6.

2. State of the Art

As early as 1991, transport agencies recognized the pavement management system as a tool for optimizing the use of the available funds [16], for its ability to choose the M&R activities, among the various possible optimal alternatives [17,18,19,20].

Maintaining pavement efficiency and functionality over the years requires the conduction of M&R activities that need budgets [21] which is identifiable through optimization processes aimed at defining multi-year pavement maintenance problems. The pavement M&R optimization problem is an integer, discrete type [22], whose objectives may even contradict each other. For example, a reduction in costs could lead to a deterioration in the quality of the pavement.

Several mathematical optimization methods have been used for optimal pavement management, including the optimal control theory, the linear and nonlinear programming, the dynamic programming and the integer programming [23,24]. However, the dynamic structure of the proposed APMS problem, due to the interaction between decay functions and maintenance activities during the planning horizon, requires complex forms of mathematical formulations with consequent difficulties in solving the problem in a short time. Hence, this issue is solved by the development of artificial intelligence that allows road engineers to use non-deterministic polynomial-time (NP-hard) [25], including applications of expert systems, artificial neural networks, fuzzy logic, genetic algorithms, and hybrid systems [26].

Focusing on heuristics and meta-heuristic algorithms, since the early 1990s there has been a worldwide improvement in the use of the genetic algorithms by many civil engineering researchers [27]. These algorithms allow general-purpose stochastic optimization techniques capable of generating accurate solutions in large size networks and in reasonable time [28].

Most of the literature studies include the analysis of road infrastructure pavements, whose logic is the also the same in the airfield. In the road field, Mathew and Isaac [29] used a constraint-based genetic algorithm to minimize the total maintenance costs and maximize the performance of the road network in terms of Pavement Condition Index (PCI). Moreira et al. [30] first conducted an optimization methodology to maximize the pavement quality and minimize the agency costs at the pavement section level. Subsequently, they minimize agency and user costs at the network level. In this study, the pavement condition was evaluated through performance, combined and global performance indicators. Hafez et al. [31], used a multi-objective approach converted to a single-objective approach by dividing cost by the network’s condition objective function. The pavement performance was determined by an indicator based on a trend analysis of different normalized distresses. Gerami Matin et al. [32] demonstrated that non-domination sorting genetic algorithm II (NSGAII) performed better than multi-objective particle swarm optimization (MOPSO) in costs and pavement performance in terms of PCI. However, recent studies have also evaluated the performance of the pavement through other indicators, such as PSI and IRI [33,34].

From the above it can be deduced that several variables can be considered during the optimization processes. The evaluation of the pavement condition could refer to distress type, distress amount, distress severity, smoothness, structural adequacy, and, of course, initial cost and life cycle cost [35].

Focusing on the airfield, there are few research works, and this is due to the complex managerial implications related to the multi-year pavement maintenance. For instance, Ansarilari and Golroo [36] applied NSGA-II for planning M&R activities in an airport pavement network based on both monetary resources and pavement conditions and assessed the pavement condition through the use of PCI indicator. Moayedfar et al. [37] relied on an APMS software, PAVER 7, to determinate the best restoration method based on the type of damage and, therefore, they used PCI to evaluate the pavement condition.

However, the decision-making aspects in the airport context cannot ignore the time variable, as maintenance activities in the flight infrastructures could compromise airport operations. Huge investments are made annually for M&R activities related to the airport infrastructures, which is why the stakeholders are always looking for ways to reach the best solutions that also take into account operational effectiveness [38]. For this reason, Zou and Madanat [39] developed a finite-horizon dynamic program to investigate the interplays among maintenance and repair M&R action time, functional interdependence between runways and traffic growth. Results from computational studies reveal the tradeoff between the M&R actions, the delay cost and long-term benefits of significantly improving pavement conditions through reconstructing runways and confirm that if an infrastructure is not properly and timely repaired, repair costs could increase exponentially. Zaki et al. [40] integrated life-cycle cost analysis (LCCA) and life cycle assessment (LCA) to develop a method for assessing pavement sustainability. In relation to the indirect/user costs, they considered the airport revenue reduction cost and the airline delay cost as, depending on the duration of each pavement event construction, it is necessary to estimate reduction in airplane operations and loss of daily operating revenue.

In this paper, the authors illustrate different M&R optimization strategies, already implemented in a previous study by Ragusa et al. [15], to apply them to a real case study in an updated version. The proposed approach considers the project level of several sections and investigates different scenarios because, especially in the airport sector, there is no optimal strategy, but several possible solutions that can be undertaken by the operator based on the needs of the airport, aiming to minimize the total maintenance cost ensuring the optimum quality level for each performance measure. In this context, the clustering function provided in the present model helps to optimize the areas in which to predict activities thanks to the identification of work-zones. Using the clustering model is a common practice in the pavement management context. For instance, to reliably build network-level pavement performance prediction models, Rejani et al. [41] performed homogeneous clusters using k-means clustering, which is a nonhierarchical clustering algorithm, based on PCI, IRI, age, and traffic volume of the pavement sections. In this paper, clustering is used to identify homogeneous zones in which to perform M&R activities.

For the evaluation of the pavement condition, the indicators relating to RL, IRI and PCI are used [42], allowing their performance to be evaluated both from a structural and a functional point of view. The three performance indicators reflect those usually used to investigate the air infrastructures through periodic instrumented surveys, but the same approach could be used regardless of any other performance indicator. The optimization model used for this study is detailed below.

3. Methodology

3.1. Methodological Framework

The present section provides a brief description of the methodological framework used in this study. The model is formulated in accordance with the relevant international and national legislation, focusing on the flight infrastructure at the project level. By analyzing strategies consistent with possible airport management needs, the study aims to minimize the total maintenance cost, ensuring adequate structural and functional conditions of the pavement. To facilitate the understanding of the model, the work refers to an airport runway with flexible pavement, but it is useful to highlight that the same approach could be generalized for any flight infrastructures.

3.1.1. Problem Statement

The present study focuses on the runway infrastructure which, in accordance with ASTM D-5340-20, could represent a single branch, divided into S homogeneous sections and N = Ks∙S sample units, whose extension has to be equal to 450 ± 180 m² [43]. The S homogeneous sections consider the differentiation of the pavement deterioration and the dissimilar stresses depending on the load given by the passage of the aircraft landing gear.

Let Q be the number of the performance indicators q used for evaluating the pavement condition. In this regard, let p_k^q (0) the performance indicator value of the k-th sample unit at time zero. Hence, the approach of this study involves the identification of specific work-zones. Specifically, they consist in the grouping of sample units belonging to the same section and featured by a similar pavement deterioration condition at time zero. To this end, on the basis of pre-established performance indicators, q and J cluster levels, in this paper, a well-established K-means method is used, adequately adapted to ensure the grouping of only adjacent sample units, as detailed further in Section 3.2.

Figure 1 illustrates the airport pavement schematization, including sample units and work-zone limits, explained above.

At time zero, each performance indicator q of the w-th work-zone is equal to the worst value among those evaluated in the U_w sample units u_w (u_w = 1, …, U_w) belonging to it:

$$p_w^q\left(0\right)=\underset{u_w=1,..,U_w}{\min }{p}_{u_w}^q\left(0\right)$$

(1)

Each performance indicator q is strictly connected to a deterioration rate from which to estimate the future pavement conditions, i.e., time-dependent [43]. In this regard, this study fixes a planning period, hereinafter denoted as T, as the number of years t in which to conduct the M&R activities in the work-zones subject to performance deterioration. Consequently, assuming a limit threshold Th(q) for each performance indicator q, the W critical work-zones are defined as those characterized by at least one indicator q below the respective threshold at time t ∈ T. Therefore, the W critical work-zones need at least one M&R activity within the planning period T, to ensure the quality requirements of the pavement.

Moreover, to ensure that the pavement maintenance problem has effects on the execution of the M&R activities carried out even in the last year of T, the approach used in this research work considers a control time horizon. It is equal to T + 2 years and indicates the number of years t in which the work-zones have to be the performance indicators q above the relative thresholds Th_q.

However, the solution of the proposed problem is a matrix where W is the set of critical work-zones, $T$ is the planning time horizon and $x_{wt}\in I$ is the activity at time t on the critical work-zone w, being $I=\left\{0,1,\dots ,N\right\}$ the set of available M&R actions. Specifically, it can be configured as follows:

$$X=\left[\begin{array}{ccc}{x}_{11}& \dots & x_{1\mathrm{T}}\\ \dots & x_{wt}& \dots \\ x_{W1}& \dots & x_{W\mathrm{T}}\end{array}\right]$$

(2)

If $x_{wt}=0$, no action is conducted for the critical work-zone $w$ at time $t$ and the related cost is zero. Let $C\left(x_{wt}\right)$ be the maintenance cost associated with maintenance action $x_{wt}$ on work-zone w at time t, then the optimization problem can be formulated as follows:

$$\min C_t$$

(3)

s.t.

$$P^q\left(x_{wt}\right)\ge T{h}_q, \forall q\in 1,\dots ,Q; w=1,\dots ,W; t=1,\dots ,T$$

(4)

$$C_t={\displaystyle \sum }_{w=1}^W{\displaystyle \sum }_{t=1}^{T}C\left(x_{wt}\right)$$

(5)

with:

$C_t$ total maintenance costs [€].

$C\left(x_{wt}\right)$ maintenance cost associated to the activity $x_{wt}$ on work-zone w at time t [€].

$P^q\left(x_{wt}\right)$ the q-th performance measure of work-zone w at time t after the maintenance intervention $x_{w,t}$.

$q=1,\dots ,Q$ index of performance indicator.

$T{h}_q$ critical threshold for performance measure q.

$t=0,\dots ,T$ index of the time period.

$w=1,2,\dots , W$ index of critical work-zones.

$x_{wt}\in I$ solution variable: M&R activity assigned to critical work-zone w at time t.

Below, a brief description of the applied methodology.

3.1.2. Methodology

The methodology proposed has already been developed and presented in a previous study [15], in which its robustness, in terms of effectiveness and the computational efficiency, has already been demonstrated through a benchmark of randomly generated test-cases. It is comprised of three stages, i.e., input data, clustering and heuristic algorithm, described briefly below. The algorithms developed for this study have involved the use of Matlab^®.

3.2. Input Data

The length and the width of the runway, as well as its subdivision into $S$ sections and sample units, provide information on the layout of the infrastructure under study. Other input data are those relating to possible $I$ M&R activities, in which the type of treatment, costs, effects and expected duration are specified. Furthermore, the runway deterioration conditions $p_k^q\left(0\right)$ related to the $Q$ performance indicators and the relative critical thresholds ($T{h}_q$) are input data which, linked to the number of years established for the planning period $T$, allow the subsequent stages to be proceeded. For this research work, the pavement conditions are estimated starting from the results provided during the planned investigations, but with some modifications to guarantee the confidentiality of the real pavement conditions. In this way, we have guaranteed pavement conditions consistent with the real ones, i.e., more deteriorated in the areas most stressed by the loads.

3.3. Clustering

By identifying the $K_s$ sample-units within each homogenous section and assigning them the performance measures $p_k^q\left(0\right)$, a clustering method is provided. As already mentioned in the previous paragraph, it consists of a grouping of sample units featured by similar initial conditions of the pavement deterioration. A well-established K-means method is used, that is a hard clustering technique used to group similar items of dataset based on their attributes [44]. More specifically, once the number of centroids J have been fixed, every sample unit is assigned to one of them, in order to minimize the intra-cluster variance. The objective function of the K-means can therefore be summarized with the following relationship:

$${\displaystyle \sum }_{n=1}^N{\displaystyle \sum }_{j=1}^J{r}_{nk}{\Vert x_n-m_n\Vert }^2$$

(6)

where N is to total number of sample units, J is the number of clusters, x_n the vector of measurement n, m_j is the mean for cluster j, and r_nj is an indicator variable that indicates whether to assign x_n to j. The best number of clusters J leading to the greatest separation (distance) is not known as a priori, so it has to be computed from the data. For this work, the number of clusters has been set to three on the basis of what was experienced by Rejani et al. [40] for an urban road context.

However, K-means does not consider the placement of objects. Consequently, once the cluster classes have been identified, the approach used in this study involves the grouping of adjacent sample units belonging to the same cluster, leading to the identification of the work-zones.

Once the work-zones have been identified, they assume each performance indicator q is equal to the worst value among those evaluated in the U_w sample units u_w belonging to it. Hence, the deterioration rate of the indicators q over the years is assessed. Consequently, any M&R activities conducted in each work-zone w are carried out as soon as the sample unit u_w having the worst indicator value reaches the predetermined threshold Th_q. Generally, the choice of adopting the clustering method based on the characteristics of the pavement allows reduction of the variables of the problem. From a managerial point of view, since the implementation of the M&R actions on the runway could compromise airport activities, the clustering avoids the M&R activities that are carried out on small areas i.e., the individual sample units. Specifically, treating the work-zones instead of sample units guarantees an operational optimization, a further reduction in fixed costs (i.e., construction equipment, etc.), and a minimization of the time required to comply with the operational constraints.

3.4. Heuristic Algorithms

For this study, the optimization with heuristic algorithms aims at minimizing the total maintenance cost while keeping the pavement performance level above certain limits. Once the heuristic algorithms is implemented, it is possible to find the near-optimal solution relating to the multi-year maintenance problem.

It is believed that this type of algorithms is ad hoc for the M&R optimization problem. Having to identify the type of activity to conduct in the W critical work-zones at time $t$, the problem can be configured as a combinatorial one, whose complexity increases exponentially with the problem size and, therefore, also with the number of decision variables.

In this study, the developed heuristic algorithms generate an effective solution through a constructive criterion in a reasonable time, even for large-sized issues.

Once the critical work-zones and the relative values of the performance indicators at year zero have been identified, the implementation of the decay functions allows identification of the trend of the performance conditions over the years. Therefore, having fixed the number of years t of the planning period T, different possible M&R activities have to be implemented in the model. In this way, it is possible to hypothesize the most suitable activities to be carried out in the critical work-zones according to the decay of the performance indicators. By way of example, possible types of feasible M&R activities could be deep structural, intermediate structural, surface structural and functional.

For each critical work-zone, the algorithm identifies the year t in which at least one performance indicator q is below the critical thresholds Th_q. Therefore, the model hypothesizes the most suitable intervention to be carried out in order to eliminate any violation at the minimum cost. However, if no type of M&R activity is able to set at zero the constraint violation, the algorithm selects the one capable of minimizing such violation, at minimum cost.

Depending on the strategy adopted, one or more activities can be carried out for each critical work-zone w. For this work, five strategies are constructed reflecting different possible airport managerial rationale, as illustrated in

Table 1. Strategies used in the heuristic algorithms implemented for this study.

Strategy 1 (H1)	For each critical work-zone w, application of a single M&R activity during the planning period T
Strategy 2 (H2)	For the critical work-zones w requiring rehabilitation activities, merging of them at the same year t, identified as the minimum one among all those found
Strategy 3 (H3)	For all critical work-zone w, merging of all the M&R activities in the year t in which there are the greatest number of interventions.
Strategy 4 (H4)	For each critical work-zone w, implementation of a single M&R activity or, if it is considered more convenient, of two less invasive activities
Strategy 5 (H5)	For each critical work-zone w, implementation of only superficial M&R activities to mitigate any risk of interruption of the airport operations

.

4. Results: Model Application and Experiments

To verify its applicability and provide a better understanding on how the model operates, this research proposed its application to a real case study. Specifically, it refers to one of the most relevant airports in Southern Italy, namely Catania airport.

Catania airport has only one runway, 2666.01 m long and 45 m wide, with 2 × 7.50 m wide shoulders. The Aerodrome Reference Code for Catania Airport is 4D [9]; therefore, the flight infrastructures are subject to high loads due to the types of aircraft that can transit. Focusing on the pavement of the runway, it has a flexible pavement type, with a Pavement Classification Number (PCN) 97/F/A/W/T, between the progressive 200.00 and 2545.93 m. Having a single runway and constantly growing traffic at Catania airport, it is essential to optimize a pavement maintenance program, and also take into account the duration of the activities, to manage any operational restrictions.

The following sub-section details the parameters and the assumptions setting for the clustering and heuristic methods.

Parameters and Assumptions

In this study, the runway sections with flexible pavement are considered. Each sample unit is assumed to have a width of 7.5 m and a length of 50 m, for a total area 375 m².

This research works focuses on the $Q=3$ performance indicator, namely the Residual Life (RL), the International Roughness Index (IRI) and the Pavement Condition Index (PCI).

In accordance with the literature [43,45,46], the performance indicator values related to the best condition and the critical thresholds are, respectively, assumed to be equal to 20 and 0 years for RL, 0.7 and 3.60 m/km for IRI, and 95 e 25 for PCI. Note that the higher both the RL and PCI, the better the residual life and surface condition of the pavement under study. To make IRI consistent with the trend of the previous performance indicators, the reciprocal IRI indicator, hereinafter referred to as IRRI, is adopted for the subsequent analysis.

Actually, all these indicators are connected to specific decay functions [47] and, since predictive degradation models are not easily transferable from one airport to another and considering that this study does not want to be specific for a single airport, theoretical time-dependent decay models are used. Specifically, the deterioration models of $RL$ and $IRRI$ are linear, while a non-linear relationship is assumed for PCI [42], as follows [15]:

$$RL\left(t\right)=RL\left(t-1\right)-1|0\le RL\left(t\right)\le R{L}_{opt}=20 years \forall t$$

(7)

$$IRI\left(t\right)=IRI\left(0\right)+0.4\times t$$

(8)

$$IRRI\left(t\right)=1/IRI\left(t\right)$$

(9)

$$PCI\left(t_0+t\right)=-0.14{\left(t_0+t\right)}^3+2.28{\left(t_0+t\right)}^2-15(t_0+t)+100|PCI\left(t\right)\ge 0 \forall t$$

(10)

where $t_0$ is a time reference value necessary to assess the PCI indicator at time zero. The relations described in (9) and (10) evaluate the functional conditions of the pavement in terms of longitudinal roughness and general distress conditions. For this study, their correlation is not in depth but, certainly, they are determined by the detected distresses. Referring to the M&R activities, in this research five types of M&R activities (I = {0, 1, 2, 3, 4}) have been taken into account [15]. It is assumed that it is possible to do only one intervention for each work-zone per year. Note that the so-called do-nothing activity (I = 0) means that no M&R action is conducted in the critical work-zone at year $t$ (x_wt = 0). Below are the M&R activities hypothesized for this study (Figure 2).

For all types of intervention, their definition and related effects are based on some laboratory studies on the materials used for the pavement in question. Regarding the residual life reported in the manuscript, it is the parameter related to the moduli of the existing and requalified pavement courses.

Table 2. Costs and effects of the M&R activities.

M&R Activities	$\mathit{C}\left(\mathit{x}\right)$ [€/m2]	Effects
		ΔRL [Year] $\mathit{T}{\mathit{h}}_{\mathit{R}\mathit{L}}$ = 0-Year	IRI [m/km] $\mathit{T}{\mathit{h}}_{\mathit{I}\mathit{R}\mathit{I}}$ = 3.60 m/km	PCI $\mathit{T}{\mathit{h}}_{\mathit{P}\mathit{C}\mathit{I}} = 25$
0. Do-nothing (xwr = 0)	–	Do nothing
1. Deep structural (xwr = 1)	168.89	20	0.7	95
2. Intermediate structural (xwr = 2)	102.04	5	0.7	95
3. Surface structural (xwr = 3)	46.94	2	0.7	95
4. Functional (xwr = 4)	18.05	0	0.7	95

indicates the costs and effects of M&R activities. According to the Federal Aviation Administration [46], they depend on the materials used during the activities and the composition of the hypothesized pavement package.

In the end, in accordance with the common airport practice, this study sets a short-term time horizon. More specifically, T is assumed to be equal to six years. Instead, the constraint of maintaining the performance indicators above the critical thresholds for a control time equal to (T + 2) years is considered in all the strategies described in Section 3.2. The only exception is in Strategy 5, due to the impossibility of eliminating the violations given the limited effects of possible actionable activities.

5. Discussion

Using the methodology and assumptions illustrated above, the present Section aims to demonstrate the potential of using an APMS in providing flexible solutions to the needs of airport managers.

Referring to the parameters and assumptions of Section 3, the study aims to analyze the results obtained by applying the five heuristic algorithms to the case study of the Catania airport in terms of pavement quality and total duration of the activities at the end of the planning period T. In addition, the impact of the clustering model on the solutions obtained is verified.

The present study considers that in Catania airport the presence of a single runway determines the total absence of operation in the case of maintenance activities on it. For this reason, surface requalification maintenance activities often take place within a few hours, at night, reducing the inconvenience to a minimum. Hence the results obtained from this work, with maintenance activities in consecutive years. In any case, the threshold values defined in the airport context are clearly defined to guarantee constant safety of flight operations without any derogation. The strategy adopted is to always carry out the work before the total breakdown of the infrastructure in question.

Figure 3 shows a Pareto diagram in which the y-axis represents the total cost in kEUR, and the x-axis is the reciprocal of the residual life (1/RL) at the end of the planning time (T = 6 years). In this way, it is possible to verify the trend of the structural pavement conditions over the years for the different heuristics. This study confirms that H1, H2 and H4 represent the Pareto-font of the non-dominates heuristics. H4 is the best heuristic method in terms of costs for solving the APMS problem for a better RL condition at minimum cost. However, this study confirms that there is not a unique optimal strategy, but several possible solutions that can be undertaken by the airport managers according to their needs. From Figure 3 it has emerged that H5 could be considered an inconvenient strategy as it is associated with high costs and low RL value.

Focusing on the cluster impacts on optimizing the problem, the subsequent analyses are based on H4. In fact, the authors have verified, except for H5, H4 is the heuristic that tends to have a shorter total duration of interventions than the other algorithms. Since H5 is built considering only functional activities not always resolutive, H4 is therefore the optimal strategy for solving pavement problems in the shortest possible time. In fact, H4 tends to choose less invasive maintenance treatments that allows for reduced impact on airport operations.

In this regard, Figure 4 illustrates the total duration of the M&R activities in the y-axis, and the number of work-zones in the x-axis. First of all, it is noted that the clustering in which the three indicators are included allows a reduction in the number of work-zones. The grouping of the areas into work-zones is conducted using a K-means method based on three well-known performance indicators, which in turns considers adjacency among the pavement portions as a further clustering constraint [15].

With regard to the duration of the interventions, this is calculated according to the type of intervention and the area to be treated. The more invasive the treatment, the longer the duration. The larger the area to be treated, the shorter the intervention duration. From Figure 4 it emerged that, when tending to treat more extensive areas, the clustering with the three indicators leads to a longer duration of the activities. However, from the figure it is clear that a strategy of airport managers could be to calibrate the clustering factors according to the pavement conditions. By way of example, in the hypothesis of a pavement in which there are mostly structural problems, one could consider clustering according to the RL factor.

Analyzing more in-depth Strategy 4, Figure 5a summarizes the number of the different types of pavement treatments over the years with and without clustering. It can be noted that the use of clustering leads to a decrease in the number of M&R activities.

Figure 5b–d, instead, represent the trend of performance indicators over the years with and without clustering. In Figure 5b, the effectiveness of the clustering method in terms of deterioration rate of structural pavement performance is marked. With regard to the IRI and PCI indicators, since the effect of each possible activity is not incremental but restorative, the functional conditions of the pavement improve as the number of treatments increases. In any case, in the three graphs the average trend of the performance indicators is better when using clustering.

It might then be interesting to pay attention to the effects of the pavement maintenance program by implementing Strategy 4 with the use of clustering. In this regard, Figure 6 illustrates a runway schematization with the comparison between the current state plan and the prevision at the end of the maintenance program in terms of the three performance indicators RL, IRI and PCI. It emerges that the use of heuristic algorithms in the optimization process of the APMS problems leads to generating accurate solutions for the maintenance and resolution of the critical issues present in the pavement.

6. Conclusions

This paper illustrates the potential of using an APMS in providing flexible solutions to the needs of airport managers. For this purpose, this study investigates the impact of clustering and optimization factors in the decision-making context aimed at identifying the appropriate decision-making criteria.

Using models already tested on a benchmark of randomly generated test cases, this study verifies the effectiveness of the method through the application to a real case study, to provide a better understanding of the functioning of the model and identify how much the factors influence the results obtained.

Starting from the identification of the runway layout and the relative sample units and work-zones, the definition of the pavement conditions allowed testing of the model. In this framework, different strategies have been considered: (H1) during the planning period, application of a single M&R activity for each critical work-zone; (H2) merging of the activities in the critical work-zones requiring the most invasive activities at the same year; (H3) application of all the activities in all the critical work-zones in year t in which there are the greatest number of interventions; (H4) implementation of a single M&R activity or, if more convenient, of two less invasive activities for each critical work-zone; and (H5) implementation of only superficial M&R activities for each critical work-zone.

The different algorithms have been tested revealing that H4 is the best heuristic method in terms of costs for solving the APMS problem for a better RL condition at minimum cost. However, the obtained numerical results revealed that no single heuristic can be selected as the most performing one. In fact, based on the Pareto-font representing the total cost in kEUR in the y-axis, the reciprocal of the residual life (1/RL) in the x-axis, it emerged that H1, H2 and H4 represent the Pareto-font of the non-dominates heuristics. Consequently, this study confirms that there is not a unique optimal strategy, but several possible solutions that can be undertaken by the airport managers according to their needs. Also, since H5 application leads to high costs and low RL value, implementing a temporary scenario could be considered, pending a more invasive intervention planning.

Analyzing H4 and focusing on the cluster impacts on optimizing the problem, it is noted that the clustering in which the three indicators are included allows a reduction in the number of work-zones. Tending to treat more extensive areas, the clustering with the three indicators leads to a longer duration of the activities. However, it is clear that a strategy of airport managers could be to calibrate the clustering factors according to the pavement conditions. Comparing the results with and without clustering, the results reveal that the use of clustering leads to a decrease in the number of M&R activities. The use of the clustering method leads to a reduction of the deterioration rate of the structural pavement performance. Furthermore, the average trend of the performance indicators is better when using clustering.

From this study, several actions can be pursued for future research works. For instance, other clustering methods could be analyzed in order to verify how much these affect the obtainable results. Referring to the optimization methods relative to the definition of multi-year pavement maintenance problems, it might be interesting to understand if the influence factors vary when additional objectives are included in the optimization. Furthermore, the results obtained from heuristics could be compared with mathematical models. In this way, the effectiveness and the reliability of the models obtained with the heuristic algorithms could be demonstrated.