Integrated Hybrid Framework for Urban Traffic Signal Optimization Based on Metaheuristic Algorithm and Fuzzy Multi-Criteria Decision-Making

Abstract

Traffic signal control at urban intersections is one of the key determinants of the overall efficiency of the transportation system, given its direct impact on travel time, congestion levels, and emissions of exhaust fumes. This study proposes an integrated hybrid model that combines a metaheuristic Genetic Algorithm for generating potential signal timing plans with fuzzy multi-criteria decision-making (MCDM) for their evaluation and selection of the optimal solution. In order to determine the relative importance of criteria, the fuzzy methods F-AHP, F-FUCOM, and F-PIPRECIA were employed, thus providing stable assessments of criteria importance under conditions of uncertainty and expert subjectivity. The ranking of generated alternatives was performed by employing the F-TOPSIS, F-WASPAS, and F-ARAS methods, while the robust decision-making rule approach was employed to develop a robust decision-making rule by integrating multiple MCDM methods. The proposed model was tested using data collected from a real urban intersection. The results show that the integrated hybrid approach enables a significantly more reliable selection of the optimal signal timing plan and achieves higher traffic management efficiency compared to traditional methods. The proposed model provides a flexible and scalable framework that can be adapted to different types of intersections and traffic demand conditions, thereby significantly contributing to the development of modern intelligent traffic management systems.

1. Introduction

Traffic management is one of the key and most challenging issues contemporary urban environments are facing. Almost all major cities worldwide are confronted with various forms of traffic-related problems, with a particularly prominent factor being the continuous growth of the population in urban areas, while the development of transportation infrastructure generally does not follow this trend, thus resulting in an imbalance between the number of vehicles and the capacity of the road network. This, consequently, results in frequent traffic congestion and prolonged travel times for road users.

At-grade intersections play a central role in the operation of the traffic network, serving as points where traffic flows converge and conflict. Ensuring safe and efficient movement for all users at these locations requires minimizing conflicts and delays. A key instrument in achieving this is traffic control devices, which serves as the primary means of communication between road authorities and road users. Traffic control devices include traffic signs, pavement markings, traffic signals, and other supporting equipment. Traffic signals are of particular importance, as they enable the right-of-way allocation, i.e., allocating priority in traffic, among conflicting flows, in accordance with predefined control criteria.

The improvement of traffic flow conditions requires reducing total vehicle delays, the number of stops, and queue lengths, as well as mitigating negative environmental impacts. The achievement of the aforementioned goals requires a detailed analysis of signal timing plans, including the determination of optimal cycle length and the appropriate allocation of green time within individual phases.

Intelligent Transportation Systems have been developed with the aim of ensuring more efficient management of the factors that cause traffic congestion, thereby contributing to an overall improvement in the quality of life. Modern technological advancements have enabled transportation systems to collect and process vast amounts of real-time data, thus significantly accelerating the evolution and application of ITSs. These systems are based on the integration of various technologies, including electronics, computer data processing, and wireless communication networks, thereby enhancing safety, reliability, and efficiency of the transportation infrastructure. In this regard, an ITS constitutes an integrated framework that enables the collection, exchange, and analysis of information, communication coordination, and the management of different elements within a transportation network, with the primary goals of increasing safety, reducing traffic congestion, and lowering carbon dioxide (CO₂) emissions.

One of the most significant ITS applications is the smart traffic signal, as presented in [1,2]. A smart traffic signal essentially constitutes the optimization of traffic signal operation based on the application of advanced ICT [3,4], the IoT [5], and AI [6]. In particular, artificial intelligence is recognized as one of the most advanced fields of contemporary computer science, focused on developing methods and algorithms that enable computers to imitate human-like intelligent behavior, solve complex optimization and prediction problems, and make decisions based on logic and data-driven analysis.

Since the optimization of traffic signal control at intersections is an extremely important and publicly relevant issue, numerous researchers have devoted significant attention to its modeling and improvement over the past decades. In this context, a wide range of algorithms and decision-making methods have been used. Traditional traffic signal control methods are based on fixed-time cycles configured based on historical traffic volume data. However, this approach has limited capability to adapt to changing real-time conditions, which is why modern systems incorporate intelligent control methods, including adaptive algorithms and sensor-based technologies which enable dynamic optimization of signal timing plans [7].

One practical illustration of mitigating congestion at intersections can be found in the role of a traffic police officer, who makes real-time decisions based on direct observation, personal experience, and knowledge of local traffic patterns, thereby substantially reducing or eliminating congestion. The application of artificial intelligence in the domain of smart traffic signals aims to replace this form of human intervention, which is costly, limited in availability, and often unsustainable, by enabling sensors and surveillance devices to continuously collect traffic data. Based on the data collected in this manner, signal timing plans optimization can be performed using metaheuristic methods such as a GA [8] and Particle Swarm Optimization [9], as well as through the application of hybrid metaheuristic approaches that integrate multiple models and algorithms [10,11]. Alternatively, the signal control system itself can be trained using machine learning methods [12], deep learning techniques [13,14], reinforcement learning [5,15,16], and deep reinforcement learning [17,18], enabling it to acquire behavioral patterns comparable to human reasoning and to adaptively regulate traffic signals in interaction with the environment. Nevertheless, in most cases, only a single criterion is considered when determining the cycle length and green time durations, whereas only a limited number of studies simultaneously analyze multiple criteria. Depending on the proposed traffic signal control model, the following criteria can be identified as dominant in the selection of cycle length or green time duration: minimization of delay [19], minimization of total travel time [20], minimization of queue length and number of vehicles [21,22], maximization of the residual intersection capacity [23], minimization of efficiency losses in traffic flow [24], maximization of average vehicle speed [25], maximization of pedestrian safety [26], minimization of fuel consumption [27], and minimization of exhaust fumes emissions [28], among others.

Recent research has expanded intersection analysis toward simulation-based infrastructure assessment and control selection [29,30], network-level delay estimation using passive sensing technologies [31,32,33], and safety-oriented deep learning analysis of red-light violation behavior [34,35]. However, these studies predominantly address isolated operational or safety aspects, while integrated optimization and multi-criteria decision-making frameworks remain comparatively underexplored [36,37]. In contrast, limited attention has been devoted to integrated frameworks that simultaneously combine optimization techniques with multi-criteria decision-making for robust selection of optimal signal timing plans under varying traffic conditions. The proposed hybrid framework aims to address this research gap by integrating metaheuristic optimization with fuzzy MCDM methods within a unified decision-support environment.

The introduction of MCDM into the process of selecting the optimal signal timing plan arises from the need to simultaneously consider multiple, often mutually conflicting criteria, as well as to determine their relative importance within the overall performance assessment. The determination of criteria weight coefficients plays a crucial role in the quality of the final solution, as it directly affects the accuracy and stability of the optimization results. Involving a group of traffic engineering experts, whose assessments are based on professional knowledge and experience in analyzing and managing traffic flows, allows for a more objective determination of a weight set, thereby yielding more reliable signal timing plans optimization outcomes.

The earliest attempts to integrate MCDM into traffic signal control involved the application of the AHP methods to assess the performance of different signal timing plans using criteria such as queue length, average delay, and number of stops [38]. These methods provide a systematic framework for ranking alternatives and determining the relative importance of criteria based on expert evaluation.

Furthermore, methods such as VIKOR and ELECTRE, combined with Data Envelopment Analysis, have proven useful in scenarios involving several alternative signal timing plans, where it is necessary to balance efficiency, safety, and environmental aspects [39]. These methods enable the identification of compromise solutions, especially in urban networks with a large number of intersections and variable traffic conditions.

Later, hybrid and fuzzy-based approaches have been developed, combining MCDM with uncertainty modeling. For instance, F-AHP and F-TOPSIS methods have been applied to optimize green time allocation under real traffic conditions, taking into consideration the uncertainties in expert assessments and fluctuating traffic flows [40]. Taking into account the inherent uncertainty in traffic data, fuzzy TOPSIS frameworks have been developed, enabling the ranking of traffic signal control methods based on their similarity to the ideal solution by integrating both fixed and adjustable criteria, thereby achieving transparent and systematic decision-making process [41].

The most recent studies focus on integrating MCDM with ITS and adaptive traffic signal control. Hybrid models that combine fuzzy logic with MCDM techniques provide adaptable and robust real-time control, effectively reducing average delay and enhancing traffic throughput in critical urban areas [42].

The optimization of traffic signal operations constitutes a complex research problem, involving numerous mutually conflicting criteria, from the minimization of delays, number of stops, and travel time along corridors to the reduction in total user’s costs, as well as the maximization of intersection capacity and the control of queue lengths. Taking all of the factors into account, it can be concluded that the problem is obviously an MCDM task, wherein a single alternative solution is selected that best meets the conflicting performance criteria.

Based on the identified research gap, the main contributions and innovative aspects of this study can be summarized as follows:

• Development of an integrated hybrid framework combining metaheuristic optimization and fuzzy MCDM methods for traffic signal timing optimization;
• Generation of feasible signal timing plan alternatives using a GA based on real traffic data collected from an operational intersection;
• Implementation of a structured group decision-making approach with aggregation-based weighting to reduce expert subjectivity;
• Application of multiple fuzzy ranking methods followed by the RDMR to ensure stable final decision selection;
• Validation of the proposed framework under multiple traffic demand scenarios derived from a seven-day field data collection period.

Accordingly, the proposed framework represents a generalized decision-support methodology rather than a case-specific solution.

Compared with conventional traffic signal optimization approaches based solely on single optimization or decision-making techniques, the proposed hybrid framework enables simultaneous generation, evaluation, and robust selection of signal timing plans using multiple performance criteria. The integration of metaheuristic optimization with fuzzy MCDM methods and aggregation-based decision rules improves solution stability and reduces sensitivity to subjective parameter selection, providing a more reliable basis for traffic signal control decision-making under varying traffic conditions.

In this study, a hybrid framework integrating metaheuristic optimization and fuzzy MCDM methods is proposed for traffic signal timing optimization at signalized intersections. The novelty of the study lies in the integration of metaheuristics and multiple fuzzy MCDM methods within a robust decision-making framework to enable a comprehensive optimization of traffic signal timing in order to achieve higher traffic management efficiency compared to traditional methods. The model is structured as a two-level architecture separating solution generation from multi-criteria sustainability-oriented decision-making.

Accordingly, this study investigates whether the integration of metaheuristic optimization and fuzzy MCDM can provide a more robust and sustainable traffic signal timing plan compared to conventional approaches. It is hypothesized that the proposed hybrid GA–fuzzy MCDM framework enables the identification of signal timing plans that improve overall intersection performance by simultaneously considering operational, environmental, and public transport related criteria.

The paper is structured as follows: Section 2 provides a review of the relevant literature, with the focus on the application of the MCDM methods in the process of traffic signal control at intersections, with special emphasis on the integration of fuzzy logic-based models for determining the criteria weighting coefficients. Section 3 provides on overview of the employed methods and describes the proposed methodology. Within this section, a model for designing the optimal signal timing plan is presented, based on a hybrid approach which requires the participation of a group of experts and the application of a metaheuristic algorithm for generating alternative solutions. Section 4 presents the case study carried out based on data collected from a real urban intersection, along with a comparative evaluation of criteria provided by a group of experts. Section 5 focuses on the experimental validation, along with the analysis, and discussion of the obtained results. Finally, Section 6 provides concluding remarks, summarizes the main findings and scientific contributions of the research, and outlines potential directions for future research in this field.

2. Materials and Methods

The proposed model for determining the optimal signal timing plan at a signalized intersection represents an integrated hybrid framework combining a GA and MCDM methods. The GA is used to generate potential signal timing plan alternatives based on collected traffic data, while the MCDM framework is applied for the evaluation and selection of the optimal signal timing plan. The proposed methodology consists of two main stages:

• Generation of feasible signal timing plan alternatives using a GA;
• Multi-criteria evaluation and selection of the optimal solution using fuzzy MCDM methods.

In the first stage, a GA is applied to explore the feasible search space of signal timing parameters and generate a diversified set of candidate signal timing plans under predefined operational constraints. In the second stage, the generated alternatives are evaluated using fuzzy MCDM methods, enabling the simultaneous consideration of operational, environmental, and public transport performance criteria.

The Genetic Algorithm was selected due to its well-established capability to efficiently explore nonlinear and constrained search spaces typical of traffic signal timing optimization problems. Unlike gradient-based or deterministic optimization techniques, a GA does not require problem linearization or differentiable objective functions, making it particularly suitable for multi-criteria traffic control problems involving conflicting performance indicators and discrete decision variables. Furthermore, a GA enables generation of multiple feasible signal timing alternatives, which is consistent with the subsequent multi-criteria evaluation stage of the proposed hybrid decision-making framework. The complete conceptual framework of the proposed model is shown in Figure 1.

The model utilizes detailed traffic data collected at the individual intersection, including traffic volumes, queue lengths, vehicle delays, and other relevant parameters that directly affect signal timing plan performance. Based on these data, a GA generates candidate signal timing plans used as alternatives in the subsequent MCDM evaluation stage. Each generated alternative is subsequently evaluated through an MCDM framework, where fuzzy-based methods are applied for determining the criteria weight coefficients and ranking the alternatives.

A Genetic Algorithm was employed to generate a set of potential signal timing plans. In the multi-criteria decision-making process, F-AHP, F-FUCOM, and F-PIPRECIA methods were applied to determine criteria weight coefficients. Since the assessments of criteria importance were obtained from a group of experts, the results of individual methods were aggregated using a mathematical aggregation operator, thereby forming a unified set of weight coefficients. In the subsequent stage, the generated signal timing plan alternatives were ranked using F-TOPSIS, F-WASPAS, and F-ARAS methods, while the RDMR approach was applied to establish a robust decision-making rule. This procedure enabled a multidimensional evaluation of traffic control performance and facilitated the selection of the optimal signal timing plan under conditions of uncertainty.

The integration of these steps enables comprehensive multi-criteria evaluation of the generated signal timing plans, taking into account operational indicators (delay, queue length, number of stops), as well as environmental and energy-related aspects. The process ultimately yields the optimal signal timing plan that meets the defined goals and constraints, providing efficient, stable, and adaptive traffic signal control.

2.1. Integration of GA and MCDM in Traffic Signal Optimization

For the purposes of the mathematical formulation of the problem, the following variables are introduced:

• $i$—index of traffic lane, $i=\mathrm{1,\; 2},\dots ,n$;
• $j$—index of signal phase, $j=\mathrm{1,\; 2},\dots ,m$;
• $q_i$—traffic flow in lane $i$ (veh/h);
• $s_i$—saturation flow in lane $i$ (veh/h);
• $X_i$—degree of saturation of lane $i$;
• $c_i$—capacity of lane $i$ (veh/h);
• $T$—duration of the analysis period (h);
• $t_i$—duration of oversaturation (unserved demand) during T in lane $i$ or lane $i$ group;
• $u_i$—delay parameter in lane $i$ or lane $i$ group;
• $C$—cycle length (s);
• $C_{min}$—minimum cycle length (s);
• $C_{max}$—maximum cycle length (s);
• $L$—delay time per cycle (s);
• $g_i$—green time allocated to lane $i$ (s);
• $g_j$—green time allocated to phase $j$ (s);
• $g_{min}$—minimum allowable green time (s);
• $g_{max}$—maximum allowable green time (s);
• $g_{ef}$—effective green time (s);
• $g_{efped}$—effective green time of the pedestrian signal group (s);
• $r_{ef}$—effective red time (s);
• $D$—total average delay of all vehicles passing through the intersection during the analysis period (s/veh);
• $d_i$—average delay per vehicle in lane $i$ (s/veh);
• $d_{1i}$—uniform delay per vehicle in lane $i$ (s/veh);
• $d_{2i}$—incremental delay per vehicle in lane $i$(s/veh);
• $d_{3i}$—delay caused by the initial queue per vehicle in lane $i$ (s/veh);
• $d_{1i}^{*}$—uniform delay per vehicle in lane $i$ when an initial queue of unserved vehicles exists (s/veh);
• $d_{ped}$—average delay of the pedestrian signal group (s/ped);
• $h$—average number of stops (VS/h);
• $y$—degree of utilization of ideal capacity;
• $N$—number of vehicles in queue (veh);
• $N_0$—number of unserved vehicles (veh);
• $q$—flow rate (veh/s);
• $U$—green time utilization coefficient;
• $Q$—traffic flow (veh/h);
• $Lq$—queue length (m);
• $l$—average vehicle length (m);
• $p_{fuel}$—average fuel consumption per vehicle (L/veh);
• $\alpha$—average idle fuel consumption (L/veh);
• $\beta$—average fuel consumption during deceleration–acceleration cycles (L/veh);
• $d$—average delay (h/veh);
• $d_{ad}$—average delay during deceleration and acceleration (h/veh).

The determination of alternatives, i.e., potential cycle lengths and the green time allocation across phases, was performed through optimization using a GA, whereby the optimization was performed via minimization of the total delay of all vehicles (D). This objective function has previously been applied in traffic management using the Artificial Bee Colony optimization algorithm [43]. The mathematical form of the objective function is expressed as follows:

$$D={\displaystyle \frac{\sum _{i=1}^{\left|K\right|}{q}_i·d_i}{\sum _{i=1}^{\left|K\right|}{q}_i}}$$

(1)

In order to determine the optimal signal timing plan that corresponds to the minimum total delay time of all the vehicles passing through the intersection during the analysis period, it is first necessary to calculate the average delay per vehicle in the i traffic lane. For undersaturated traffic flow, the following applies:

$$d_i=d_{1i}+d_{2i}$$

(2)

$d_{1i}$ is calculated as follows:

$$d_{1i}={\displaystyle \frac{0.5·C ·{\left(1-\frac{g_i}{C}\right)}^2}{1-\left[\mathrm{m}\mathrm{i}\mathrm{n}(1,X_i)·\frac{g_i}{C}\right]}}$$

(3)

$d_{2i}$ is calculated as follows:

$$d_{2i}=900T\left[\left(X_i-1\right)+\sqrt{{(X_i-1)}^2+{\displaystyle \frac{4·X_i}{c_i·T}}}\right]$$

(4)

To ensure consistency and computational tractability within the iterative optimization process, the above analytical formulations were adopted for performance estimation. The analytical evaluation approach was intentionally selected to ensure computational efficiency within the Genetic Algorithm framework. Since a large number of candidate signal timing plans are generated and repeatedly evaluated, the integration of a microsimulation model would result in substantial computational burden and reduced practical applicability. The objective of this study is to support multi-criteria sustainability-oriented decision-making at the strategic level rather than to replicate detailed microscopic vehicle interactions.

For oversaturated traffic flow, additional delay caused by the presence of an initial queue is introduced, and the following applies:

$$d_i={d_{1i}^{*}+d}_{2i}+d_{3i}$$

(5)

$$d_{1i}^{*}=d_{si}·{\displaystyle \frac{t_i}{T}}+d_{ui}·{\displaystyle \frac{(T-t_i)}{T}}$$

(6)

$$d_{ui}=d_{1i}$$

(7)

$$d_{3i}={\displaystyle \frac{1800·Q_{bi}·(1+u_i)·t_i}{c_i·T}}$$

(8)

The optimization constraints are as follows:

$$C_{min}\le C\le C_{max}$$

(9)

$$g_{min}\le g_j\le g_{max}, \forall j\in F$$

(10)

$$\sum _{j=1}^{\left|F\right|}{g}_j=C-L$$

(11)

Equation (9) constitutes the range of the cycle length, while Equation (10) defines the range of green times allocated to every phase. The relationship between the cycle length, green time, and the delay within the cycle is defined by Equation (11).

The proposed minimum cycle length is $C_{min}=30 \mathrm{s}$ [27], while the maximum cycle length is adopted as $C_{max}=120 \mathrm{s}$ [44]. The minimum green time is set to ${ g}_{min}=7 \mathrm{s}$ and the maximum green time to $g_{max}=80 \mathrm{s}$ [43]. The delay per cycle $L$ depends on the selected number of phases. The adopted value of the delay in the case of using “The two-way crossing signal timing plan” [44] for the assumed two-phase regime is 10 s. For the optimization process, the following GA parameters were used:

• Crossover probability: 30%;
• Mutation probability: 4%;
• Convergence threshold: 0.01%;
• Population size: 10;
• Maximum number of generations: 10, 20, and 30.

The selected GA population size and number of generations were adopted considering the limited dimensionality of the signal timing optimization problem and previous validated applications in traffic signal optimization studies [33]. Since a GA is primarily used for generating feasible alternative signal timing plans rather than direct single-solution convergence, the adopted parameter configuration provides sufficient exploration while maintaining computational efficiency. Preliminary experimental runs confirmed that increasing population size beyond the adopted values did not produce significant improvements in solution quality but considerably increased computational time.

The result of the optimization is the cycle length and the allocation of green time to the phases, whose mathematical formulation is given as follows:

$$A_i=\left(C_i,g_{i1},g_{i2},\dots ,g_{ij}\right)$$

(12)

where $i=1,\dots ,n$ stands for a potential cycle, while $j=1,\dots ,m$ denotes the number of green phases within the cycle.

In order to determine the optimal signal timing plan, considering both traffic-related and non-traffic-related parameters through the application of MCDM, a set of nine criteria ($C_i,i=1,\dots , 9$) are evaluated: minimization of vehicle delay, number of stops, queue length, pedestrian delay, exhaust fumes emissions, and fuel consumption, as well as maximization of intersection capacity, green time utilization, and public transport vehicle throughput. The selection of criteria was based on the authors’ previous experience, a comprehensive review of the literature related to traffic signal control at intersections, and the feasibility of applying these criteria to isolated intersections.

Criterion C₁: Intersection capacity [veh/h] is defined as the maximum number of vehicles that can pass through the intersection per unit of time. By maximizing the intersection capacity, overall traffic throughput is increased, congestion is reduced particularly during peak periods and traffic efficiency on arterial roads is improved. The value of the intersection capacity is obtained using the following equation [45,46]:

$$K={\displaystyle \frac{s_i·g_{ef}}{C}}$$

(13)

Criterion C₂: Vehicle delay or waiting time [s/veh] is defined as the time a vehicle spends idling or moving at reduced speed at an intersection. The objective of minimization of vehicle delay is to reduce the average time that vehicles spend waiting at the intersection, which contributes to faster traffic flow, and improved travel comfort. The value of vehicle delay is obtained using Equation (1).

Criterion C₃: The number of stops is intended to minimize the frequency with which vehicles are forced to stop at a red signal at the intersection. Applying this criterion improves traffic flow, enables vehicles to maintain a higher average travel speed, reduces total travel time, enhances driving comfort, and increases safety, since fewer stops reduce the likelihood of traffic accidents caused by sudden braking.

The average number of vehicle stops is obtained using the following Equation (14) in accordance with ref. [47]:

$$h=0.9·\left({\displaystyle \frac{1-\frac{g_{ef}}{C}}{1-y}}+{\displaystyle \frac{N_0}{q·C}}\right)$$

(14)

Criterion C₄: Queue length [m] is defined as a constraint used in determining the signal timing plan to ensure that the vehicle queue length on the intersection adjacent roadways does not exceed a predefined acceptable threshold. During the optimization of the signal timing plan, special emphasis is placed on preventing the queue from becoming long enough to block the intersection or adjacent streets. By applying this criterion, intersection blocking is avoided, congestion is reduced, and traffic safety is improved, since long queues may provoke dangerous maneuvers (e.g., overtaking) and increase the risk of secondary delays, since long queues can block nearby intersections. The number of vehicles in the queue is obtained using the following Equation (15) in accordance with ref. [47]:

$$N=q·r_{ef}+N_0$$

(15)

Meanwhile, the queue length is obtained using the following Equation (16):

$$Lq=N·l$$

(16)

Criterion C₅: The degree of green time utilization indicates how effectively the allocated green time is used relative to the traffic demand. This criterion is a key indicator of the balance of the signal timing plan and helps ensure that green time is distributed efficiently to reduce delays. The value of the degree of utilization of the green time is obtained using Equation (17) in accordance with [45]. The objective is for the utilization degree to be as close as possible to the value of 0.95, since values greater than 1 indicate an oversaturated phase, which may lead to congestion. When evaluating this criterion, the degree of green time utilization is analyzed separately for the major roadway (C₅₁) and for the minor roadway (C₅₂), which are defined as sub-criteria.

$$U={\displaystyle \frac{Q}{S·\frac{g_{ef}}{C}}}$$

(17)

Criterion C₆: Pedestrian delay [s/ped] is defined as the time pedestrians spend waiting at the intersection before being given the pedestrian right of way (green light). The minimization of pedestrian delay is a key criterion when the goal is sustainable and inclusive mobility. It enables a safer, faster, and more efficient movement of pedestrians through the intersection and contributes the balance between motorized and non-motorized traffic. Within this criterion, two sub-criteria are considered: average pedestrian delay on the major roadway (C₆₁) and on the minor roadway (C₆₂). The average delay of the pedestrian signals is determined based on Equation (18), in accordance with ref. [48]:

$$d_{ped}={\displaystyle \frac{0.5·{(C-g_{efpeš})}^2}{C}}$$

(18)

Criterion C₇: Emission of exhaust fumes is defined linguistically in the proposed model. Since various pollutants are produced during the combustion of fossil fuels, CO₂ (C₇₁) and NO_x—nitrogen oxides (C₇₂)—are selected as the most significant and are treated as sub-criteria. Estimated CO₂ emissions represent the amount of carbon dioxide emitted by vehicles during movement, idling, and acceleration at intersections. The objective in forming the signal timing plan is to minimize total CO₂ emissions in order to improve the environmental sustainability of traffic [49]. The minimization of CO₂ emissions reduces negative environmental impacts, supports the goals of green and smart cities, and improves air quality in urban areas. NO_x emissions arise from the combustion of fuel in vehicle engines and have severe negative effects on air quality, human health, and the environment (acid rain, smog). The minimization of nitrogen oxide emissions is becoming an increasingly important criterion in modern signal timing plans, especially in urban environments.

Criterion C₈: Fuel consumption is defined as the total estimated fuel consumption per traffic signaling cycle. Although the unit of measurement for average fuel consumption per vehicle is typically (L/veh), in the proposed model fuel consumption is defined linguistically due to large variations among the defined alternatives. The minimization of fuel consumption serves as a secondary indicator of efficiency, but is often a significant user-oriented or system-level criterion during traffic signal timing plan optimization because it directly reduces vehicle operating costs, contributes to environmental goals, and mitigates the negative effects of traffic congestion and delay. This parameter is determined based on the average unit fuel consumption under the corresponding vehicle operating regime within the zone of influence of an intersection on traffic flow. The average fuel consumption can be estimated using Equation (19) in accordance with ref. [46]:

$$P_{fuel}=\alpha ·d+(\beta -\alpha ·d_{ad})·h$$

(19)

Criterion C₉: In the proposed model, the uninterrupted public transport vehicle throughput is defined linguistically, based on multiple simulation runs for a given signal timing plan. This criterion represents the maximization of unobstructed movement of public transport vehicles (buses, trams, trolleybuses) through the intersection, with the objective of reducing the number of stops, shortening public transport travel times, and improving schedule adherence and arrival punctuality. The importance of uninterrupted public transport flow and signal priority strategies for public transport vehicles at signalized intersections has been widely recognized in recent studies [50].

The proposed framework represents a two-level decision architecture rather than a purely single-objective optimization model. The Genetic Algorithm is employed as a structured search mechanism to generate a feasible and diversified set of candidate signal timing plans under operational and technical constraints, where delay minimization serves primarily as a feasibility-oriented filtering criterion rather than the final optimization objective. The final selection of the optimal signal timing plan is performed within a fuzzy MCDM environment that simultaneously considers operational, environmental, energy-related, and public transport performance indicators. Since these criteria are inherently conflicting (e.g., delay reduction versus emission minimization or pedestrian service quality), the decision stage preserves the multi-criteria nature of the problem and enables sustainability-oriented evaluation of alternative solutions. In this framework, the GA stage ensures exploration and feasibility of candidate solutions, while the MCDM stage constitutes the actual MCDM layer responsible for final solution selection.

2.2. Applied Methods for Determining the Optimal Signal Timing Plan

The Genetic Algorithm is one of the most well-known and most frequently applied metaheuristic methods for solving optimization problems of varying complexity. Developed on principles inspired by natural selection and evolutionary processes, the GA employs mechanisms of biological evolution, such as selection, crossover, and mutation, to explore the space of possible solutions and gradually converge toward the global optimum [51]. Unlike classical deterministic optimization methods, which often encounter difficulties of local optima and require strictly defined mathematical models, the GA is stochastic in nature and capable of efficiently solving nonlinear, multi-criteria, and complex problems where the number of feasible solutions is extremely large and the relationships among variables are difficult to predict. Its robustness and flexibility make it suitable not only for theoretical research but also for solving practical real-world problems.

Multi-criteria decision-making methods are used to generate decision-making rules based on which a given set of alternatives is evaluated according to multiple criteria, with corresponding criteria weight coefficients. Managing imprecision and uncertainty in the decision-making process is enabled through fuzzy MCDM methods, which can integrate different types of criteria and allow the processing of qualitative information and linguistic variables alongside numerical data. Determining criteria weight coefficients is not a straightforward task and essentially depends on the subjective judgments of experts. Depending on the chosen MCDM method, the influence of criteria weight coefficients on the final solution changes, and even slight modifications in their values may lead to different rankings of alternatives. Numerous approaches to determining criteria weight coefficients have been investigated for many years. Expert judgment can significantly influence the selection of the optimal solution, as the evaluation must take into account multiple and often conflicting criteria. In order to make the determination of weight coefficients as objective as possible, it is necessary to involve a larger number of experts; therefore, robust group decision-making methods must be applied to integrate conflicting opinions, viewpoints, and proposed solutions. This problem is addressed by introducing mathematical aggregation operators to obtain aggregated initial decision matrices or aggregated criteria weight coefficients. The advantage of using aggregation operators, compared to other methods, lies in their objective synthesis of diverse expert opinions, even when the experts belong to different stakeholder groups.

Based on the previously reviewed literature, the aim of this study was the application of a multimodal hybrid approach using three well-known fuzzy MCDM methods for determining the criteria weight coefficients—F-AHP, F-FUCOM, and F-PIPRECIA—and the introduction of an aggregation operator, in this case the F-GM, which combines individual values into a single aggregated value while taking into account information on variations, dependencies, and expert preferences, after which the alternatives were ranked using F-TOPSIS, F-WASPAS, and F-ARAS, thereby providing a more robust and objective basis for decision-making. Finally, the RDMR method was applied as a tool for generating robust decision-making rules, yielding the final complete ranking of alternatives. Sensitivity analysis was performed using Kendall’s ${\tau }_b$ and Spearman’s $\rho$ tests. In the conducted study, expert evaluations were obtained independently to avoid mutual influence during the assessment process, while aggregation and subsequent robustness analysis ensured mitigation of potential individual judgment bias. Furthermore, the simultaneous application of multiple fuzzy weighting methods was intended to enable cross-validation of obtained criteria weights and to reduce sensitivity to method-specific assumptions. The aggregation of results using the F-GM operator therefore represents a robustness-oriented procedure aimed at minimizing subjectivity rather than increasing it.

The F-AHP method constitutes an extension of the conventional AHP through the integration of fuzzy numbers into the pairwise comparison process. The earliest applications of the F-AHP method could be seen in [52], while subsequent research introduced numerous variations and improvements to the algorithm. The fundamental idea of the F-AHP approach is that expert pairwise comparisons are expressed using fuzzy numbers (typically triangular or trapezoidal), which effectively model uncertainty, subjectivity, and imprecision in decision-making process. Owing to these characteristics, F-AHP is today regarded as one of the key tools of modern MCDM, and its flexibility and ability to integrate with other methods make it a suitable basis for the development of new hybrid and robust MCDM approaches. In this study, the fuzzy scale proposed in [53] was applied.

The FUCOM method is based on pairwise comparison of criteria and the assessment of deviations from maximal consistency thus ensuring stable and reliable weight determination with a minimal number of comparisons. Its main advantage over traditional methods is that it requires fewer pairwise criteria comparisons while still ensuring a high degree of consistency in the results. In order to provide additional flexibility and take into account the uncertainty in expert evaluations, the fuzzy extension F-FUCOM was developed. In this study, the weighting scale presented in [54,55] was used.

The PIPRECIA method [56] is based on comparisons with a reference criterion, without the need to pre-rank the criteria according to importance. This procedure enables a relatively simple and intuitive weighting process that requires fewer comparisons than methods such as AHP. Given that fuzzy logic is based on the transformation of qualitative evaluations into quantitative values, this method provides an ideal framework for integration within fuzzy MCDM models. In the proposed framework, the scale referred to in [57] was applied.

The F-GM operator is an extension of the classical geometric mean within fuzzy set theory, enabling uncertainty and subjectivity in expert evaluations to be adequately modeled and incorporated into the decision-making process. Compared to the fuzzy arithmetic mean, F-GM reduces the influence of extreme values and provides more stable results in cases with substantial variability among assessments. The application of the F-GM operator is particularly important in group decision-making, as it allows all individual expert evaluations to be aggregated into a single unified value, providing a balanced and robust basis for further MCDM analysis and alternative ranking.

The main limitation of the classical TOPSIS method lies in the assumption that all input values are precisely defined. In real-world decision-making conditions, expert assessments are often vague, subjective, and expressed in the form of linguistic variables. In order to overcome this limitation, the F-TOPSIS method was developed [58]. F-TOPSIS integrates the classical TOPSIS algorithm with fuzzy set theory, wherein the criteria and alternative evaluations are defined using fuzzy numbers.

The WASPAS method is based on combining the advantages of the WSM and WPM through a linear combination of their optimality criteria. In this way, greater accuracy and stability of the results are achieved compared to the individual application of either the WSM or WPM. Although the classical WASPAS method ensures a high degree of reliability, it is based on the assumption that both the criteria values and the weights are precisely defined [59]. In real decision-making environments, this is often not the case, as expert assessments are subject to subjectivity, imprecision, and uncertainty. Therefore, the fuzzy extension F-WASPAS was developed. The general characteristic of this method is its ability to evaluate and rank alternatives with a high level of reliability.

The F-ARAS method integrates fuzzy set theory with the classical ARAS algorithm [60] based on a proportional assessment of alternatives. The fundamental idea of the method is that the optimality of each alternative directly depends on the proportional relationship between its criteria’s values and in relation to the reference solution. In this way, the method enables the determination of alternative priorities through linear normalization of criteria and calculating the overall utility degree of each alternative.

RDMR is an approach developed to form robust decision rules within MCDM problems. Instead of direct alternative ranking, RDMR combines the results of multiple MCDM methods, enabling the identification of stable and reliable solutions, especially when different MCDM approaches yield conflicting rankings. The approach is based on quality engineering principles inspired by the Taguchi method, specifically through the calculation of the S/N ratio for each alternative to generate a robust decision-making rule [61].

3. Case Study

In this study, an isolated four-leg signalized intersection located in Vranje, Serbia, shown in Figure 2, was selected as a real-world test environment for validation of the proposed traffic signal optimization framework. The intersection consists of two traffic lanes on each of the three adjacent roadways, and one adjacent roadway with three traffic lanes.

The traffic demand data used in this case study were obtained through field measurements conducted at the analyzed intersection under different traffic load levels. These observed traffic volumes were directly incorporated into the analytical evaluation framework. Since the proposed model operates on established capacity-based formulations rather than behavioral microsimulation, traditional microsimulation calibration procedures were not required.

Multiple traffic demand scenarios were defined to enable a comprehensive performance assessment, including low, moderate, peak-hour, and oversaturated traffic conditions. Within this framework, the microsimulation environment was employed as a controlled comparative platform for consistent benchmarking of alternative control strategies under equivalent operating conditions, thereby ensuring a methodologically sound validation of the proposed model’s performance.

The selected intersection is used as a representative real-world test environment for methodological validation purposes, while the proposed hybrid framework itself is not location-specific and can be applied to other signalized intersections through adaptation of traffic input data and evaluation criteria.

The determination of the optimal cycle length and green time allocation was performed for a one-hour time interval, and the obtained results constitute the alternatives within the MCDM framework. Based on the collected data from the analyzed intersection over a seven-day period, 50 alternatives were generated using Equation (12), i.e., the corresponding cycle lengths and green time allocations shown in

Table 1. Alternatives obtained using the GA.

Alternatives (A1–A50)
A1	(30, 10.8, 13.2)	A11	(30, 13.9, 10.1)	A21	(30, 15.3, 8.7)	A31	(40, 20, 14)	A41	(40, 22.3, 11.7)
A2	(30, 11.4, 12.6)	A12	(30, 14, 10)	A22	(30, 15.9, 8.1)	A32	(40, 20.1, 13.9)	A42	(40, 22.5, 11.5)
A3	(30, 12.4, 11.6)	A13	(30, 14.1, 9.9)	A23	(30, 16, 8)	A33	(40, 20.4, 13.6)	A43	(50, 22.9, 21.1)
A4	(30, 12.7, 11.3)	A14	(30, 14.2, 9.8)	A24	(30, 16.3, 7.7)	A34	(40, 20.5, 13.5)	A44	(50, 23.9, 20.1)
A5	(30, 13, 11)	A15	(30, 14.3, 9.7)	A25	(30, 17.4, 6.6)	A35	(40, 21.2, 12.8)	A45	(50, 24.7, 19.3)
A6	(30, 13.1, 10.9)	A16	(30, 14.4, 9.6)	A26	(30, 8.8, 15.2)	A36	(40, 21.3, 12.7)	A46	(50, 25, 19)
A7	(30, 13.2, 10.8)	A17	(30, 14.5, 9.5)	A27	(40, 17.6, 16.4)	A37	(40, 21.4, 12.6)	A47	(50, 25.5, 18.5)
A8	(30, 13.4, 10.6)	A18	(30, 14.8, 9.2)	A28	(40, 18.2, 15.8)	A38	(40, 21.7, 12.3)	A48	(50, 26.8, 17.2)
A9	(30, 13.5, 10.5)	A19	(30, 15, 9)	A29	(40, 18.3, 15.7)	A39	(40, 21.9, 12.1)	A49	(50, 30, 14)
A10	(30, 13.6, 10.4)	A20	(30, 15.1, 8.9)	A30	(40, 19.5, 14.5)	A40	(40, 22.1, 11.9)	A50	(60, 31.7, 22.3)

. The adopted data collection horizon allowed the optimization process to account for temporal variations in traffic demand and operational conditions, thereby ensuring that the generated alternative set reflects realistic and representative operating regimes of the analyzed intersection. This approach ensures that the generated alternatives are derived from observed traffic variability, providing a reliable basis for subsequent multi-criteria evaluation and robust decision-making.

In accordance with the actual operational configuration of the analyzed intersection, a two-phase signal control scheme was adopted for the determination of candidate signal timing plans. Nevertheless, the proposed optimization framework is not inherently restricted to this phase structure. Intersections with additional phases, including protected or dedicated turning movements, can be incorporated through straightforward extension of the decision variable set and the corresponding constraint formulation. Accordingly, the adopted two-phase configuration represents a case-specific implementation reflecting existing field conditions rather than a methodological limitation of the proposed model. Therefore, the analyzed intersection should be interpreted as a representative implementation environment, while the proposed hybrid framework constitutes a generalized decision-support architecture applicable to signalized intersections with varying geometric layouts and operational configurations.

The first value in the generated alternatives denotes the cycle length, the second value stands for the duration of the green time in the first phase, and the third value stands for the duration of the green time in the second phase.

The fuzzy decision-making matrix, based on the previously described alternatives and the defined set of criteria, was constructed and is shown in

Table 2. Performance evaluations of cycle lengths and green time allocations—fuzzy decision-making matrix.

Ai	C1 [veh]	C2 [s/vehicle]	C3 [stops]	C4 [m]	C5 [%]		C6 [s]		C7 [−]		C8 [−]	C9 [−]
					C51	C52	C61	C62	C71	C72
	Max	Min	Min	Min	Max		Min		Min		Min	Max
A1	3887	(9.59, 9.81, 10.05)	(771, 835, 899)	(32.03, 34.78, 37.53)	(0.45, 0.49, 0.52)	(0.26, 0.28, 0.3)	6.14	4.70	(0.17, 0.33, 0.5)	(0.17, 0.33, 0.5)	(0.17, 0.33, 0.5)	(0, 0, 0.25)
A2	3853	(8.59, 8.77, 8.96)	(466, 528, 590)	(19.35, 21.97, 24.6)	(0.25, 0.29, 0.32)	(0.17, 0.19, 0.21)	5.77	5.05	(0.17, 0.33, 0.5)	(0, 0.17, 0.33)	(0, 0.17, 0.33)	(0, 0, 0.25)
A3	3798	(8.77, 8.97, 9.18)	(855, 914, 972)	(35.64, 38.05, 40.47)	(0.45, 0.49, 0.52)	(0.32, 0.34, 0.36)	5.16	5.64	(0.17, 0.33, 0.5)	(0.17, 0.33, 0.5)	(0.33, 0.5, 0.67)	(0, 0, 0.25)
A4	3781	(8.7, 8.9, 9.11)	(896, 954, 1011)	(37.32, 39.68, 42.03)	(0.48, 0.51, 0.54)	(0.33, 0.35, 0.37)	4.99	5.83	(0.17, 0.33, 0.5)	(0.17, 0.33, 0.5)	(0.33, 0.5, 0.67)	(0, 0, 0.25)
A5	3765	(8.84, 9.05, 9.28)	(1024, 1080, 1137)	(42.58, 44.87, 47.16)	(0.56, 0.59, 0.62)	(0.37, 0.39, 0.41)	4.82	6.02	(0.17, 0.33, 0.5)	(0.33, 0.5, 0.67)	(0.33, 0.5, 0.67)	(0, 0, 0.25)
A6	3759	(7.24, 7.37, 7.51)	(228, 284, 341)	(9.58, 11.85, 14.12)	(0.11, 0.14, 0.17)	(0.09, 0.12, 0.14)	4.76	6.08	(0, 0.17, 0.33)	(0, 0, 0.17)	(0, 0, 0.17)	(0, 0, 0.25)
A7	3754	(8.37, 8.56, 8.76)	(908, 964, 1020)	(37.83, 40.08, 42.33)	(0.46, 0.49, 0.52)	(0.35, 0.38, 0.4)	4.70	6.14	(0, 0.17, 0.33)	(0.33, 0.5, 0.67)	(0.33, 0.5, 0.67)	(0, 0, 0.25)
A8	3743	(7.53, 7.68, 7.83)	(559, 614, 670)	(23.45, 25.66, 27.87)	(0.24, 0.27, 0.3)	(0.25, 0.27, 0.3)	4.59	6.27	(0, 0.17, 0.33)	(0.17, 0.33, 0.5)	(0.17, 0.33, 0.5)	(0, 0.25, 0.5)
A9	3737	(8.58, 8.78, 9)	(1078, 1133, 1188)	(44.84, 47.03, 49.22)	(0.56, 0.59, 0.61)	(0.41, 0.44, 0.47)	4.54	6.34	(0.17, 0.33, 0.5)	(0.33, 0.5, 0.67)	(0.33, 0.5, 0.67)	(0, 0.25, 0.5)
A10	3731	(8.04, 8.22, 8.4)	(894, 948, 1003)	(37.31, 39.48, 41.65)	(0.43, 0.45, 0.48)	(0.37, 0.4, 0.42)	4.48	6.40	(0, 0.17, 0.33)	(0.33, 0.5, 0.67)	(0.33, 0.5, 0.67)	(0, 0.25, 0.5)
A11	3715	(8.3, 8.5, 8.71)	(1061, 1114, 1168)	(44.04, 46.14, 48.25)	(0.55, 0.58, 0.6)	(0.41, 0.44, 0.47)	4.32	6.60	(0, 0.17, 0.33)	(0.33, 0.5, 0.67)	(0.33, 0.5, 0.67)	(0, 0.25, 0.5)
A12	3709	(7.81, 7.97, 8.15)	(917, 971, 1024)	(38.35, 40.43, 42.51)	(0.42, 0.44, 0.47)	(0.4, 0.43, 0.46)	4.27	6.67	(0, 0.17, 0.33)	(0.33, 0.5, 0.67)	(0.33, 0.5, 0.67)	(0, 0.25, 0.5)
A13	3704	(7.45, 7.6, 7.77)	(719, 772, 825)	(29.99, 32.05, 34.11)	(0.35, 0.37, 0.4)	(0.3, 0.33, 0.35)	4.21	6.73	(0, 0.17, 0.33)	(0.17, 0.33, 0.5)	(0.17, 0.33, 0.5)	(0, 0.25, 0.5)
A14	3698	(7.88, 8.05, 8.23)	(1025, 1077, 1130)	(42.81, 44.85, 46.89)	(0.46, 0.49, 0.51)	(0.46, 0.48, 0.51)	4.16	6.80	(0, 0.17, 0.33)	(0.33, 0.5, 0.67)	(0.33, 0.5, 0.67)	(0, 0.25, 0.5)
A15	3693	(7.46, 7.61, 7.77)	(803, 855, 907)	(33.48, 35.5, 37.52)	(0.38, 0.4, 0.43)	(0.35, 0.37, 0.4)	4.11	6.87	(0, 0.17, 0.33)	(0.17, 0.33, 0.5)	(0.17, 0.33, 0.5)	(0, 0.25, 0.5)
A16	3687	(7.71, 7.88, 8.05)	(1017, 1069, 1121)	(42.53, 44.53, 46.53)	(0.44, 0.47, 0.5)	(0.47, 0.5, 0.52)	4.06	6.94	(0, 0.17, 0.33)	(0.33, 0.5, 0.67)	(0.33, 0.5, 0.67)	(0, 0.25, 0.5)
A17	3682	(7.46, 7.62, 7.78)	(859, 911, 963)	(35.75, 37.73, 39.71)	(0.41, 0.44, 0.46)	(0.37, 0.4, 0.42)	4.00	7.00	(0, 0.17, 0.33)	(0.33, 0.5, 0.67)	(0.33, 0.5, 0.67)	(0, 0.25, 0.5)
A18	3665	(7.32, 7.48, 7.64)	(918, 969, 1020)	(38.31, 40.23, 42.14)	(0.41, 0.44, 0.46)	(0.42, 0.45, 0.48)	3.85	7.21	(0, 0.17, 0.33)	(0.33, 0.5, 0.67)	(0.33, 0.5, 0.67)	(0, 0.25, 0.5)
A19	3654	(7.54, 7.71, 7.89)	(1114, 1164, 1214)	(46.44, 48.32, 50.19)	(0.49, 0.52, 0.54)	(0.53, 0.55, 0.58)	3.75	7.35	(0, 0.17, 0.33)	(0.5, 0.67, 0.83)	(0.33, 0.5, 0.67)	(0, 0.25, 0.5)
A20	3648	(7.19, 7.35, 7.51)	(934, 984, 1033)	(38.83, 40.68, 42.54)	(0.43, 0.45, 0.48)	(0.43, 0.46, 0.49)	3.70	7.42	(0, 0.17, 0.33)	(0.33, 0.5, 0.67)	(0.33, 0.5, 0.67)	(0, 0.25, 0.5)
A21	3637	(6.43, 6.55, 6.68)	(536, 585, 634)	(22.4, 24.21, 26.02)	(0.24, 0.26, 0.29)	(0.25, 0.28, 0.31)	3.60	7.56	(0, 0.17, 0.33)	(0, 0.17, 0.33)	(0, 0.17, 0.33)	(0, 0.25, 0.5)
A22	3604	(5.88, 5.99, 6.1)	(341, 388, 435)	(13.95, 15.64, 17.33)	(0.19, 0.21, 0.23)	(0.13, 0.16, 0.2)	3.31	7.99	(0, 0.17, 0.33)	(0, 0.17, 0.33)	(0, 0.17, 0.33)	(0, 0.25, 0.5)
A23	3598	(6.63, 6.76, 6.91)	(991, 1038, 1085)	(41.43, 43.1, 44.77)	(0.4, 0.43, 0.45)	(0.53, 0.56, 0.6)	3.27	8.07	(0, 0.17, 0.33)	(0.17, 0.33, 0.5)	(0.33, 0.5, 0.67)	(0, 0.25, 0.5)
A24	3582	(6.04, 6.15, 6.27)	(685, 731, 777)	(28.49, 30.09, 31.69)	(0.3, 0.32, 0.34)	(0.36, 0.39, 0.43)	3.13	8.29	(0, 0.17, 0.33)	(0, 0.17, 0.33)	(0.17, 0.33, 0.5)	(0, 0.25, 0.5)
A25	3521	(4.65, 4.72, 4.79)	(31, 73, 115)	(1.65, 3.02, 4.4)	(0.01, 0.03, 0.05)	(0.01, 0.05, 0.09)	2.65	9.13	(0, 0, 0.17)	(0, 0, 0.17)	(0, 0, 0.17)	(0, 0.25, 0.5)
A26	3997	(9.34, 9.53, 9.73)	(36, 107, 178)	(1.24, 4.4, 7.57)	(0.03, 0.07, 0.11)	(0.02, 0.04, 0.05)	7.49	3.65	(0.17, 0.33, 0.5)	(0, 0, 0.17)	(0, 0, 0.17)	(0, 0, 0.25)
A27	4034	(11.75, 12.03, 12.32)	(1201, 1257, 1313)	(74.08, 77.5, 80.92)	(0.55, 0.58, 0.61)	(0.49, 0.51, 0.53)	6.27	6.96	(0.33, 0.5, 0.67)	(0.5, 0.67, 0.83)	(0.67, 0.83, 1)	(0, 0.25, 0.5)
A28	4009	(9.07, 9.23, 9.41)	(170, 224, 279)	(10.53, 13.82, 17.11)	(0.08, 0.1, 0.13)	(0.07, 0.09, 0.11)	5.94	7.32	(0.17, 0.33, 0.5)	(0, 0, 0.17)	(0, 0, 0.17)	(0.25, 0.5, 0.75)
A29	4005	(10.65, 10.89, 11.14)	(890, 944, 999)	(54.86, 58.13, 61.4)	(0.45, 0.47, 0.5)	(0.34, 0.36, 0.38)	5.89	7.38	(0.33, 0.5, 0.67)	(0.33, 0.5, 0.67)	(0.5, 0.67, 0.83)	(0.25, 0.5, 0.75)
A30	3955	(11.03, 11.3, 11.59)	(1288, 1340, 1391)	(79.34, 82.36, 85.38)	(0.61, 0.64, 0.66)	(0.52, 0.55, 0.57)	5.25	8.13	(0.33, 0.5, 0.67)	(0.67, 0.83, 1)	(0.67, 0.83, 1)	(0.25, 0.5, 0.75)
A31	3934	(8.79, 8.96, 9.13)	(474, 524, 574)	(29.15, 32.07, 34.98)	(0.24, 0.27, 0.29)	(0.18, 0.2, 0.23)	5.00	8.45	(0.17, 0.33, 0.5)	(0.17, 0.33, 0.5)	(0.17, 0.33, 0.5)	(0.25, 0.5, 0.75)
A32	3930	(9.97, 10.19, 10.43)	(1038, 1088, 1137)	(63.88, 66.78, 69.67)	(0.49, 0.51, 0.54)	(0.43, 0.46, 0.48)	4.95	8.52	(0.17, 0.33, 0.5)	(0.5, 0.67, 0.83)	(0.5, 0.67, 0.83)	(0.25, 0.5, 0.75)
A33	3918	(9.27, 9.46, 9.66)	(792, 841, 890)	(48.61, 51.44, 54.27)	(0.4, 0.42, 0.44)	(0.31, 0.34, 0.37)	4.80	8.71	(0.17, 0.33, 0.5)	(0.33, 0.5, 0.67)	(0.33, 0.5, 0.67)	(0.25, 0.5, 0.75)
A34	3913	(9.8, 10.01, 10.24)	(1093, 1142, 1191)	(67.4, 70.21, 73.02)	(0.48, 0.51, 0.53)	(0.48, 0.51, 0.54)	4.75	8.78	(0.17, 0.33, 0.5)	(0.5, 0.67, 0.83)	(0.67, 0.83, 1)	(0.25, 0.5, 0.75)
A35	3884	(8.53, 8.69, 8.86)	(664, 711, 758)	(40.69, 43.36, 46.03)	(0.32, 0.35, 0.37)	(0.28, 0.3, 0.33)	4.42	9.25	(0.17, 0.33, 0.5)	(0.17, 0.33, 0.5)	(0.33, 0.5, 0.67)	(0.25, 0.5, 0.75)
A36	3880	(9.12, 9.31, 9.52)	(956, 1002, 1049)	(58.56, 61.2, 63.85)	(0.46, 0.48, 0.5)	(0.41, 0.44, 0.46)	4.37	9.32	(0.17, 0.33, 0.5)	(0.5, 0.67, 0.83)	(0.5, 0.67, 0.83)	(0.25, 0.5, 0.75)
A37	3876	(9.71, 9.93, 10.17)	(1274, 1320, 1367)	(78.42, 81.04, 83.67)	(0.55, 0.58, 0.6)	(0.6, 0.62, 0.65)	4.32	9.38	(0.17, 0.33, 0.5)	(0.5, 0.67, 0.83)	(0.67, 0.83, 1)	(0.25, 0.5, 0.75)
A38	3864	(7.59, 7.72, 7.85)	(320, 366, 412)	(19.8, 22.37, 24.93)	(0.15, 0.17, 0.19)	(0.14, 0.17, 0.2)	4.19	9.59	(0.17, 0.33, 0.5)	(0, 0.17, 0.33)	(0, 0.17, 0.33)	(0.25, 0.5, 0.75)
A39	3847	(7.2, 7.31, 7.43)	(218, 263, 308)	(13.72, 16.2, 18.68)	(0.08, 0.1, 0.13)	(0.11, 0.14, 0.17)	4.01	9.87	(0.17, 0.33, 0.5)	(0, 0, 0.17)	(0, 0.17, 0.33)	(0.5, 0.75, 1)
A40	3848	(6.23, 6.33, 6.44)	(107, 151, 196)	(0.66, 5.22, 9.79)	(0.01, 0.03, 0.05)	(0, 0.02, 0.03)	4.01	4.10	(0, 0.17, 0.33)	(0, 0, 0.17)	(0, 0, 0.17)	(0.5, 0.75, 1)
A41	3839	(9.15, 9.35, 9.56)	(1351, 1395, 1439)	(83.63, 86.07, 88.51)	(0.52, 0.54, 0.56)	(0.72, 0.75, 0.78)	3.92	10.01	(0.17, 0.33, 0.5)	(0.5, 0.67, 0.83)	(0.83, 1, 1)	(0.5, 0.75, 1)
A42	3830	(7.06, 7.17, 7.29)	(192, 236, 280)	(11.51, 13.91, 16.31)	(0.13, 0.15, 0.17)	(0.05, 0.08, 0.11)	3.83	10.15	(0.17, 0.33, 0.5)	(0, 0.17, 0.33)	(0, 0.17, 0.33)	(0.5, 0.75, 1)
A43	4172	(13.63, 13.94, 14.27)	(1034, 1089, 1143)	(84.73, 89.12, 93.52)	(0.49, 0.52, 0.55)	(0.4, 0.42, 0.44)	7.34	8.35	(0.67, 0.83, 1)	(0.67, 0.83, 1)	(0.83, 1, 1)	(0.5, 0.75, 1)
A44	4139	(13.51, 13.83, 14.17)	(1139, 1191, 1243)	(93.22, 97.41, 101.6)	(0.55, 0.58, 0.61)	(0.44, 0.46, 0.48)	6.81	8.94	(0.5, 0.67, 0.83)	(0.83, 1, 1)	(0.83, 1, 1)	(0.5, 0.75, 1)
A45	4112	(12.54, 12.82, 13.12)	(986, 1037, 1087)	(80.73, 84.76, 88.78)	(0.47, 0.5, 0.53)	(0.39, 0.41, 0.43)	6.40	9.42	(0.5, 0.67, 0.83)	(0.67, 0.83, 1)	(0.67, 0.83, 1)	(0.5, 0.75, 1)
A46	4102	(13.56, 13.89, 14.25)	(1339, 1389, 1439)	(109.65, 113.61, 117.56)	(0.62, 0.65, 0.67)	(0.55, 0.57, 0.59)	6.25	9.61	(0.5, 0.67, 0.83)	(0.83, 1, 1)	(0.83, 1, 1)	(0.5, 0.75, 1)
A47	4086	(12.3, 12.56, 12.85)	(1077, 1126, 1175)	(88.22, 92.08, 95.93)	(0.48, 0.51, 0.53)	(0.45, 0.48, 0.5)	6.00	9.92	(0.5, 0.67, 0.83)	(0.67, 0.83, 1)	(0.83, 1, 1)	(0.5, 0.75, 1)
A48	4043	(11.34, 11.58, 11.84)	(980, 1027, 1073)	(80.14, 83.72, 87.3)	(0.45, 0.47, 0.5)	(0.42, 0.44, 0.47)	5.38	10.76	(0.33, 0.5, 0.67)	(0.5, 0.67, 0.83)	(0.67, 0.83, 1)	(0.75, 1, 1)
A49	3936	(10.56, 10.79, 11.04)	(1376, 1416, 1456)	(112.25, 115.16, 118.08)	(0.57, 0.59, 0.61)	(0.73, 0.76, 0.79)	4.00	12.96	(0.33, 0.5, 0.67)	(0.67, 0.83, 1)	(0.83, 1, 1)	(0.75, 1, 1)
A50	4167	(14.52, 14.86, 15.21)	(1132, 1180, 1227)	(115.67, 120.32, 124.97)	(0.54, 0.56, 0.59)	(0.45, 0.48, 0.5)	6.67	11.84	(0.83, 1, 1)	(0.83, 1, 1)	(0.83, 1, 1)	(0.75, 1, 1)

.

A team of six experts, with a minimum of 10 years of experience in traffic management, was selected to evaluate the relative levels of importance of the criteria. Experts were selected according to predefined eligibility criteria, including professional experience in traffic management practice, direct involvement in traffic signal control analysis, and demonstrated expertise in urban traffic engineering. In order to better capture subjective opinions, as well as the knowledge and expertise of decision-makers in the group decision-making process, three fuzzy subjective criteria weight coefficients methods were applied: F-AHP, F-FUCOM, and F-PIPRECIA. After performing pairwise comparisons of each criterion, the corresponding criteria weight coefficients were determined. In this way, the experts were able to express their assessments within a broader interval of values, in accordance with their beliefs and confidence levels. The aggregation of the computed criteria weight coefficients obtained from all applied fuzzy MCDM methods was carried out using the F-GM aggregation operator, and the aggregated weights are presented in

Table 3. Aggregated criteria weight coefficients obtained by the F-GM operator.

	C1	C2	C3	C4	C5	C6	C7	C8	C9
F-AHP
m 1	0.16226	0.17606	0.16246	0.12458	0.16493	0.07524	0.01826	0.03699	0.07923
F-FUCOM
l 2	0.06749	0.07642	0.05619	0.05138	0.05778	0.04575	0.03262	0.05749	0.0381
m	0.14362	0.12959	0.10858	0.13248	0.10871	0.10045	0.09215	0.12286	0.07384
u 3	0.14452	0.13136	0.10859	0.13562	0.11491	0.10047	0.10027	0.14089	0.07593
F-PIPRECIA
l	0.04991	0.05222	0.03998	0.03256	0.04451	0.02817	0.01976	0.01712	0.02057
m	0.1506	0.16927	0.12602	0.10381	0.15203	0.08672	0.05788	0.05037	0.06586
u	0.55513	0.57406	0.4232	0.3388	0.47564	0.27034	0.18802	0.16817	0.25462

¹ middle, ² lower, ³ upper.

.

It can be concluded that the values of almost all criteria weight coefficients are relatively close to each other. The F-FUCOM method indicated that some criteria weight coefficients have identical or very close values compared to their real and maximum expected values.

4. Results

The results obtained using the F-GM aggregation operator for each fuzzy MCDM method were used for further computations, i.e., for ranking the alternatives. The F-GM weight coefficients were combined with another set of three fuzzy MCDM methods, namely F-TOPSIS, F-WASPAS, and F-ARAS, with the aim of generating a more robust decision-making rule. The resulting rankings are shown in

Table 4. Ranking of alternatives according to different sets of criteria weight coefficients.

	F-AHP			F-FUCOM			F-PIPRECIA			RDMR Rank
	F-TOPSIS	F-WASPAS	F-ARAS	F-TOPSIS	F-WASPAS	F-ARAS	F-TOPSIS	F-WASPAS	F-ARAS
A1	48	50	50	50	48	50	50	50	50	50
A2	49	45	11	12	11	11	31	25	11	26
A3	44	49	49	48	50	49	48	49	49	49
A4	43	48	48	47	49	48	47	48	48	48
A5	34	47	46	45	46	47	45	47	47	47
A6	45	43	4	5	6	3	15	10	4	19
A7	39	46	28	29	28	26	32	38	26	34
A8	46	40	25	32	23	24	39	24	25	31
A9	19	42	41	35	35	44	30	29	44	39
A10	31	41	24	25	25	25	23	23	24	27
A11	10	35	16	17	19	17	13	15	17	13
A12	28	39	22	23	24	23	21	22	22	23
A13	35	34	23	26	15	22	27	21	23	24
A14	18	38	19	20	22	20	18	19	19	20
A15	33	32	21	24	14	21	24	17	21	22
A16	16	37	18	19	20	19	16	18	18	16
A17	26	36	20	22	21	18	20	20	20	21
A18	21	33	17	21	18	16	19	16	16	15
A19	8	31	14	14	17	14	10	13	14	10
A20	12	30	15	16	16	15	14	14	15	12
A21	15	8	7	4	5	6	4	4	6	4
A22	17	7	5	3	4	5	3	3	5	3
A23	5	29	13	13	13	13	8	12	13	8
A24	11	21	12	11	12	12	5	8	12	7
A25	2	2	2	2	2	2	2	2	2	2
A26	41	13	3	6	7	4	12	11	3	9
A27	36	44	47	46	47	46	44	46	46	46
A28	47	4	6	9	3	7	28	5	7	14
A29	38	22	45	43	40	45	43	42	45	44
A30	9	20	34	31	38	37	26	31	37	30
A31	50	11	44	49	29	42	49	39	43	45
A32	27	18	40	39	36	41	37	33	40	38
A33	37	16	43	42	33	43	42	36	42	41
A34	22	19	39	36	37	39	33	32	39	35
A35	42	12	42	44	30	40	46	34	41	42
A36	25	14	37	38	32	38	36	30	38	33
A37	7	15	31	28	31	33	22	28	34	25
A38	40	6	10	10	10	10	17	9	10	11
A39	29	5	9	7	8	8	7	6	9	6
A40	1	1	1	1	1	1	1	1	1	1
A41	4	9	27	18	26	28	9	26	27	17
A42	23	3	8	8	9	9	6	7	8	5
A43	32	28	38	41	45	36	41	45	36	43
A44	20	26	33	34	42	32	29	40	31	32
A45	30	25	36	40	43	35	40	43	35	40
A46	6	23	29	27	39	30	25	35	29	28
A47	24	24	35	37	41	34	35	41	32	37
A48	13	17	30	30	34	29	34	37	30	29
A49	3	10	26	15	27	27	11	27	28	18
A50	14	27	32	33	44	31	38	44	33	36

.

Based on the comparison of the results of the fuzzy MCDM methods, it can be observed and concluded that the first alternative, i.e., the best-ranked option, is A₄₀ (40, 22.1, 11.9). Furthermore, the second-ranked alternative is A₂₅, and this result is consistent across all combinations of fuzzy MCDM methods, whereas the rankings of the remaining alternatives are not aligned to the same extent as for the top two. The greatest discrepancies among the fuzzy MCDM combinations are evident for the F-AHP + F-TOPSIS and F-AHP + F-WASPAS methods.

In such situations where discrepancies arise in the ranking of alternatives, it is appropriate to apply the RDMR approach. This approach generates a robust decision-making rule by incorporating multiple rankings derived from solving the same decision-making problem with different MCDM methods. In its practical implementation, the RDMR procedure involves calculating the S/N ratio for each evaluated alternative (A₁, …, A₅₀), which is an indication of their stability under varying conditions. The final step consists of ranking these S/N values, whereby the alternative with the highest S/N ratio is identified as the most favorable alternative, while the lowest value corresponds to the least desirable option.

In this study, although all rankings of the alternatives were obtained using different fuzzy MCDM methods and approaches, they exhibit varying levels of similarity. To analyze the degree of similarity between the complete rankings, Kendall’s ${\tau }_b$ and Spearman’s $\rho$ tests were selected. These two non-parametric statistical tests were applied to measure the correlation between the rankings obtained through ten combinations of fuzzy MCDM methods and the RDMR concept. Kendall’s ${\tau }_b$ indicates the similarity in the ordering of ranked alternatives (i.e., the number of concordant and discordant paired observations), whereas Spearman’s $\rho$ measures the strength of the linear relationship between two complete rankings. The results of Kendall’s ${\tau }_b$ and Spearman’s $\rho$ tests are shown in

Table 5. Performance test results (Kendall’s and Spearman’s rank correlation coefficients).

			F-AHP			F-FUCOM			F-PIPRECIA			RDMR
			Fuzzy TOPSIS	Fuzzy WASPAS	Fuzzy ARAS	Fuzzy TOPSIS	Fuzzy WASPAS	Fuzzy ARAS	Fuzzy TOPSIS	Fuzzy WASPAS	Fuzzy ARAS
F-AHP	Fuzzy TOPSIS	${\tau }_b$	1.0000	0.2588	0.2604	0.3584	0.1314	0.2261	0.4841	0.2571	0.2343	0.3829
		$\rho$	1.0000	0.3548	0.3080	0.4115	0.1738	0.2797	0.6342	0.3345	0.2846	0.5181
	Fuzzy WASPAS	${\tau }_b$	0.2588	1.0000	0.2637	0.2931	0.3927	0.2653	0.3208	0.3812	0.2604	0.3633
		$\rho$	0.3548	1.0000	0.3766	0.4226	0.4311	0.3723	0.4341	0.4586	0.3725	0.4900
	Fuzzy ARAS	${\tau }_b$	0.2604	0.2637	1.0000	0.8955	0.8090	0.9624	0.7371	0.8204	0.9706	0.8449
		$\rho$	0.3080	0.3766	1.0000	0.9773	0.9392	0.9967	0.8784	0.9358	0.9969	0.9478
F-FUCOM	Fuzzy TOPSIS	${\tau }_b$	0.3584	0.2931	0.8955	1.0000	0.7698	0.8678	0.8351	0.7976	0.8694	0.8743
		$\rho$	0.4115	0.4226	0.9773	1.0000	0.9148	0.9656	0.9338	0.9315	0.9667	0.9654
	Fuzzy WASPAS	${\tau }_b$	0.1314	0.3927	0.8090	0.7698	1.0000	0.8106	0.6310	0.8580	0.8024	0.7322
		$\rho$	0.1738	0.4311	0.9392	0.9148	1.0000	0.9377	0.8091	0.9632	0.9346	0.8998
	Fuzzy ARAS	${\tau }_b$	0.2261	0.2653	0.9624	0.8678	0.8106	1.0000	0.7061	0.7992	0.9788	0.8139
		$\rho$	0.2797	0.3723	0.9967	0.9656	0.9377	1.0000	0.8597	0.9234	0.9985	0.9358
F-PIPRECIA	Fuzzy TOPSIS	${\tau }_b$	0.4841	0.3208	0.7371	0.8351	0.6310	0.7061	1.0000	0.7404	0.7241	0.8629
		$\rho$	0.6342	0.4341	0.8784	0.9338	0.8091	0.8597	1.0000	0.8879	0.8653	0.9642
	Fuzzy WASPAS	${\tau }_b$	0.2571	0.3812	0.8204	0.7976	0.8580	0.7992	0.7404	1.0000	0.8073	0.8318
		$\rho$	0.3345	0.4586	0.9358	0.9315	0.9632	0.9234	0.8879	1.0000	0.9236	0.9498
	Fuzzy ARAS	${\tau }_b$	0.2343	0.2604	0.9706	0.8694	0.8024	0.9788	0.7241	0.8073	1.0000	0.8286
		$\rho$	0.2846	0.3725	0.9969	0.9667	0.9346	0.9985	0.8653	0.9236	1.0000	0.9381
RDMR		${\tau }_b$	0.3829	0.3633	0.8449	0.8743	0.7322	0.8139	0.8629	0.8318	0.8286	1.0000
		$\rho$	0.5181	0.4900	0.9478	0.9654	0.8998	0.9358	0.9642	0.9498	0.9381	1.0000
Sum		${\tau }_b$	3.5935	3.7992	7.5641	7.5608	6.9371	7.4302	7.0416	7.2931	7.4759	7.5347
		$\rho$	4.2993	4.7127	8.3569	8.4893	8.0033	8.2694	8.2667	8.3084	8.2806	8.6090

.

Taking into account the results of Kendall’s ${\tau }_b$ and Spearman’s $\rho$ tests—which generate values within the interval [−1, +1], whereby +1 indicates a complete positive association between two rankings, whereas −1 indicates a complete negative association, and 0 denotes the absence of association between the compared ranking sets—it can be concluded that higher values of Sum (${\tau }_b$) and Sum ($\rho$) indicate smaller variations in the ranking order. It is evident that RDMR achieves the highest cumulative value of Spearman’s $\rho$ (8.6090), whereas its cumulative Kendall’s ${\tau }_b$ value is also high (7.5347). Only two combinations show slightly higher but not significantly different ${\tau }_b$ values: F-AHP + F-ARAS (7.5641) and F-FUCOM + F-TOPSIS (7.5608). Therefore, it can be concluded that RDMR provides a more robust and comprehensive decision-making rule, which can be highly useful in solving real-world decision-making problems.

Furthermore, a general characteristic of the proposed approach is that a wide dispersion of rankings obtained using different fuzzy MCDM methods and RDMR was not observed, which is confirmed by the high values of Sum (${\tau }_b$) and Sum ($\rho$), except in the case of applying the F-AHP + F-TOPSIS and F-AHP + F-WASPAS combinations, where a certain level of inconsistency in the alternative ranking order is noticeable compared to that with the other approaches.

5. Discussion

The obtained results confirm that the integration of metaheuristic optimization and fuzzy MCDM enables a comprehensive evaluation of traffic signal timing plans that cannot be achieved using single-objective optimization approaches. Unlike traditional fixed-time strategies or purely optimization-based models, the proposed hybrid framework simultaneously considers operational, environmental, and public transport performance indicators, thereby enabling a more balanced and sustainable traffic control decision. The comparative analysis of the existing fixed signal timing plan for the analyzed intersection and the optimized proposed plan clearly highlights the benefits of applying the proposed hybrid optimization framework. Figure 3 presents the key performance indicators and the achieved relative improvements.

The most significant improvement is observed in the average vehicle delay, which is reduced by 3.09 s, corresponding to an improvement of 40.82%. This reduction indicates that the optimized plan allocates green time much more efficiently in accordance with actual traffic demand, thereby reducing vehicle delay and accelerating the traffic flow through the intersection. A notable improvement is also achieved in the average pedestrian delay, which decreases by 24.19%. This result shows that the optimized plan successfully balances the needs of both vehicles and pedestrians, enabling faster and more efficient pedestrian crossings without disrupting vehicle flow.

The average queue length is reduced by 24.86%, confirming that the optimized plan not only decreases delay, but also contributes to reduction in vehicle queuing in the adjacent lanes. Shorter queues directly reduce the risk of congestion increase and propagation onto surrounding roadways. Regarding green time utilization, the optimized plan increases efficiency from 0.69% to 0.77%, representing an improvement of 10.39%. Although the absolute values are small due to the nature of the metric, the relative increase indicates better use of the available intersection capacity.

Two criteria show minimal or negative deviations. The number of stops increases by 5.02%, which may be a consequence of the optimization primarily favoring the minimization of total delay rather than reducing the frequency of stops. Such trade-offs are common in multi-criteria optimization problems where objectives may be mutually conflicting. Similarly, fuel consumption shows only a marginal change of 0.23%, which is expected because fuel usage is highly dependent on acceleration patterns that are not fully optimized solely by adjusting cycle length and green time allocation.

Overall, the results confirm that the proposed optimization model significantly improves key operational metrics, especially those directly related to intersection efficiency (delays, queue lengths, green time utilization). The minimal or negative changes observed in secondary criteria highlight the complexity of multi-criteria traffic management but do not diminish the overall benefits of the proposed solution, thereby confirming its robustness and practical value.

6. Conclusions

The selection of the optimal signal timing plan at a signalized intersection constitutes a crucial stage in effective traffic flow management, where it is necessary to take into account all relevant criteria that influence vehicle, passenger, and pedestrian delays, traffic safety, energy consumption, and exhaust fumes emissions. In this study, an integrated hybrid framework for signal timing plan optimization was developed, combining a GA for determining the optimal cycle length and green time allocation, fuzzy MCDM methods for system performance evaluation, and the RDMR approach to enhance the stability and reliability of decision-making outcomes.

The results of the experimental analysis clearly confirm the practical advantages of the proposed framework. The comparative evaluation of the existing fixed signal timing plan and the optimized proposed plan demonstrated substantial improvements across key operational metrics. Average vehicle delay was reduced by 40.82% and pedestrian delay by 24.19%, while average queue length decreased by 24.86%. Green time utilization increased by 10.39%, indicating more effective use of the available intersection capacity. Although minor or negative deviations were observed for the number of stops and fuel consumption, their relatively small magnitude reflects expected trade-offs as a result of mutually conflicting objectives. Considering the discussion presented in the previous section, these results show that the integrated hybrid approach provides a more robust, stable, and practically applicable solution compared to traditional methods of traffic control devices management.

The hybrid framework integrates metaheuristic optimization with fuzzy MCDM techniques to enable systematic generation, evaluation, and robust selection of signal timing alternatives. The application of aggregation-based decision rules and correlation-based sensitivity analysis confirms stability and reliability of the obtained decision outcomes, demonstrating suitability of the proposed approach for real-world traffic management applications.

The obtained results further indicate that the proposed hybrid optimization and fuzzy MCDM framework enables effective selection of optimal traffic signal timing plans under varying traffic demand conditions, contributing to improved intersection performance and decision-making reliability. From a practical implementation perspective, the framework operates using traffic data commonly available in existing urban traffic management systems and does not require deployment of advanced adaptive infrastructure. Consequently, the proposed approach is particularly suitable for small and medium-sized urban environments where implementation of fully adaptive signal control systems is often constrained by infrastructural or economic limitations. Overall, the multi-scenario evaluation based on real traffic data, combined with metaheuristic optimization, aggregated group decision-making procedures, and ranking stability verification, confirms that the proposed hybrid framework represents a reliable and robust decision-support approach for traffic signal timing optimization under realistic urban traffic conditions. Although correlation-based sensitivity analysis confirms stability of decision rankings, investigation of operational robustness under incident-related disturbances such as traffic surges, lane blockages, or detector failures represents an important direction for future research.

The proposed model exhibits a general and flexible structure, enabling its adaptation to various intelligent and adaptive traffic management applications. The generation of candidate signal timing plans can be further enhanced through integration of additional metaheuristic optimization techniques, deep learning approaches, or reinforcement learning models. Future research will therefore focus on extending the proposed framework toward network-level traffic control applications and incorporating disturbance-aware optimization mechanisms aimed at improving the resilience of intelligent traffic management systems. Moreover, integration with microsimulation environments represents a promising direction for further validation of the proposed decision-support framework under stochastic traffic conditions. In this context, the proposed framework provides a scalable foundation for future development of intelligent and data-driven traffic signal control systems.