An adaptive and hybrid Ant colony optimization algorithm for multi-constrained QoS routing in MANETs

1 Introduction

Mobile Ad Hoc Networks (MANETs) are infrastructure-less distributed networks characterized by self-organization and self-healing capabilities (Mohsin, 2022). They have demonstrated significant application potential in fields such as emergency communication, military reconnaissance, the Internet of Things (IoT), and environmental monitoring (Gulati and Kumar, 2013; Sahoo et al., 2024).

With the evolution towards sixth-generation (6G) mobile networks, MANETs are emerging as a fundamental connectivity architecture for realizing Smart Cities and Digital Twins, where ubiquitous sensing and ultra-reliable communications are required. In the 6G era, Integrated Sensing and Communication (ISAC) equips MANET nodes with unprecedented environmental awareness. For instance, advanced techniques such as ISAC imaging utilizing channel state information via ray tracing (Bazzi et al., 2025), and compressed multiband sensing in the FR3 band using the Alternating Direction Method of Multipliers (ADMM) (Wang et al., 2026), significantly enhance the joint detection and localization of nodes in multipath-rich environments. Furthermore, advanced physical-layer technologies like beamforming and waveform design can fundamentally mitigate the severe multi-user interference typical in highly dynamic MANETs. Designing waveforms with adjustable peak-to-average power ratio (PAPR) maximizes the sum-rate while minimizing interference (Bazzi and Chafii, 2025), and outage-based robust beamforming designs for dual-functional radar-communication (DFRC) systems ensure stable target detection and communication quality even under imperfect channel state information (Bazzi and Chafii, 2023).

However, despite these physical layer advancements, the inherent node mobility, time-varying wireless channels (Vivekananda et al., 2021), and limited network resources make providing reliable end-to-end Quality of Service (QoS) guarantees a critical challenge in MANETs at the network layer (Suganya and David, 2021; Palacios Jara et al., 2021). The management of QoS is increasingly shifting towards application-driven requirements (Alaya et al., 2021). For instance, recent developments in Software-Defined Networking (SDN) have demonstrated the necessity of translating high-level application QoS metrics (e.g., interactive response time) into low-level network policies (Gorlatch and Humernbrum, 2015), and utilizing flexible control planes to construct efficient routing topologies, such as scalable multicast trees (Humernbrum et al., 2016). In MANETs, QoS routing similarly aims to discover transmission paths that not only satisfy multiple conflicting constraints (e.g., bandwidth, delay, and packet loss rate) driven by application demands but also optimize overall network performance (Sensarma et al., 2012; Chen et al., 2020; Khanh et al., 2025).

The multi-constrained QoS routing problem in MANETs is fundamentally an NP-hard problem (Surendran and Prakash, 2015). Traditional routing protocols, such as AODV and DSR, primarily prioritize connectivity maintenance and often struggle to perform effective path optimization under complex multi-objective constraints (Patel et al., 2014; Shirkande and Vatti, 2013). Recently, meta-heuristic algorithms, particularly Ant Colony Optimization (ACO) (Kumari et al., 2021), have been widely applied to this field due to their effectiveness in solving combinatorial optimization problems (Wong Yoon Khang et al., 2020). Extensive research has demonstrated that metaheuristics, especially when hybridized with other techniques or when their parameters are properly tuned, can achieve near-optimal solutions with remarkable computational efficiency. For example, hybridizing ACO with simulated annealing and applying dynamic parameter tuning have shown significant success in accelerating complex industrial combinatorial optimization problems (Nisar et al., 2020; Borisenko and Gorlatch, 2019; Borisenko and Gorlatch, 2021).

However, traditional ACO algorithms face significant limitations when applied to MANET routing (Surendran and Prakash, 2015). First, fixed parameter settings (e.g., the pheromone evaporation coefficient) hinder the balance between exploration (global search) and exploitation (local search), often leading to premature convergence and entrapment in local optima (Ahirwar et al., 2023). Second, single pheromone update strategies often result in a conflict between convergence speed and solution quality (Ramalingam et al., 2022; Vargheese et al., 2023). These issues are particularly pronounced in dynamic MANET environments, where the robustness and convergence of traditional ACO are often unsatisfactory. To overcome the aforementioned defects and enhance adaptability across varying network scales and highly dynamic environments, this paper proposes an Adaptive and Hybrid Ant Colony Optimization (AH-ACO) algorithm. The main contributions of this study are as follows:

Construction of a Multi-Constraint Comprehensive Cost Model: To overcome the limitations of single-objective optimization, this study established a mathematical model aimed at minimizing the overall network cost. The model innovatively constructs a weighted product function that includes hop count, delay, packet loss rate, and the inverse of bandwidth, thereby enabling a comprehensive quantitative evaluation of overall path performance while satisfying various strict QoS constraints.

Design of an Adaptive Hybrid Update Mechanism: To address the bottleneck problem of traditional ACO algorithms being prone to local optima, an adaptive pheromone evaporation mechanism that dynamically adjusts during iterations was designed to effectively balance the algorithm’s exploration and exploitation capabilities at different stages. At the same time, a hybrid pheromone update strategy was introduced, which integrates rewards from both the global optimal path and elite paths. This not only maintains population diversity but also significantly accelerates the convergence speed of the algorithm.

Systematic Performance Evaluation: The proposed algorithm was validated through discrete event simulation. Experimental results show that compared with the Dijkstra algorithm and traditional ACO algorithms, the AH-ACO algorithm not only demonstrates excellent convergence speed and optimization quality but also significantly reduces end-to-end delay and packet loss rate in complex scenarios with large-scale networks and high-speed mobile nodes. This fully confirms that the algorithm possesses strong robustness and scalability in dynamic MANET environments.

2 Applicability of ACO in MANET multi-constrained QoS problems

Ant Colony Optimization is a bionic optimization algorithm simulating the foraging behavior of natural ant colonies, first proposed by Muruganandam and Renjit (2021), Tamizharasi et al. (2023). Its core inspiration comes from the positive feedback mechanism of pheromones demonstrated by ants when finding paths between food sources and their nests (Singaravelan and Mariappan, 2022; Shokouhifar, 2021). In nature, ants release a volatile chemical substance called pheromone on their path (Zhou et al., 2022). Other ants can sense this substance and tend to choose paths with higher pheromone concentrations (Zhao et al., 2022).

As shown in Figure 1, in the initial stage of the algorithm, the ant colony is in a completely blind state. Ants start from the nest and randomly choose paths (Path A, Path B, Path C shown as dashed lines in the figure) to find food. At this time, no pheromone exists on the paths in the environment (or the pheromone concentration is set to the same initial value), so the probability of ants choosing any path is basically equal (Wu et al., 2024). Ants release pheromones (blue lines in the figure) on the path while moving (Meng et al., 2023). Ants taking the shorter path (Path A) require less time for a round trip and make more trips per unit of time (Hu et al., 2024). Therefore, within the same timeframe, more pheromones will accumulate on Path A than on the longer paths (Path B, Path C). The “rain cloud” icon in the figure represents the natural evaporation of pheromones; if a path is rarely traveled, the pheromone on it will gradually disappear over time. Ants departing subsequently no longer choose paths completely randomly but tend to select paths with higher pheromone concentrations (thicker blue arrows in the figure), forming a positive feedback loop: Path A is shorter ➡ Ants return faster ➡ Pheromone accumulates faster ➡ Attracts more ants to choose Path A. Over time, the positive feedback loop causes the vast majority of ants to gather on the shortest path (Path A), while the signals on longer paths (Path B and Path C) become extremely weak or disappear due to fewer ants selecting them and continuous pheromone evaporation (Chen et al., 2022; Blum, 2024). Eventually, the entire colony “calculates” the global optimal solution (Optimal Path) from the nest to the food source.

ACO algorithms demonstrate significant advantages in multi-constrained QoS routing problems, thanks to their unique distributed, self-organizing, and positive feedback mechanisms. Firstly, their parallel search mechanism can efficiently explore the solution space, approximating the global optimal path in polynomial time through pheromone feedback, effectively addressing computational bottlenecks of NP-hard problems. Secondly, the algorithm possesses inherent dynamic adaptability; the pheromone evaporation mechanism can automatically eliminate invalid paths, continuously explore new paths, and adapt to the highly dynamic changes of MANET topology. Meanwhile, the algorithm framework is flexible, allowing multiple constraints such as bandwidth and delay to be incorporated into the heuristic function, meeting the core requirements of QoS routing. These characteristics enable it to achieve both solution efficiency, robustness, and multi-objective optimization capabilities in the dynamic environment of MANETs.

3 Modeling the multi-constrained QoS routing problem

MANETs face a core challenge in providing reliable QoS guarantees due to their centerless nature, dynamic topology, and limited resources. An effective QoS architecture must be able to dynamically perceive the network environment, make intelligent decisions, and coordinate resource control to achieve end-to-end performance goals.

A typical solution is a layered, closed-loop control system, as shown in Figure 2. The core idea is that the upper-layer application proposes QoS requirements, and the system continuously perceives the network status. A centralized “brain” then makes comprehensive decisions on routing, resources, and access, finally driving the network to complete data forwarding, forming a complete adaptive cycle from demand to assurance.

Support and Sensing System: This is the system’s requirements interface. It receives QoS requirements from applications on one hand and continuously perceives the network status on the other, providing a real-time, coordinated decision-making basis for the entire system.

QoS Core Processing System: This is the command center of the system. It receives signals from the sensing layer and executes key functions including QoS routing discovery and decision-making, resource reservation and management, access control, and data forwarding.

End-to-End QoS Assurance: This is the final output and goal of the entire architecture. Through the close collaboration of the Perceive-Decide-Control chain described above, the system can realize stable and reliable service quality assurance from the source node to the destination node in a dynamically changing network environment.

This architecture integrates demand perception, intelligent decision-making, and precise control, forming a closed loop capable of adapting to network changes.

Regarding the selection of QoS metrics, research usually focuses on different aspects depending on the application scenario. In multi-hop wireless networks, end-to-end path quality is determined jointly by the quality of every link. Common QoS metrics can be classified into three categories based on how QoS parameters aggregate along the path, as shown in Table 1.

TABLE 1. Attribute classification of key QoS metrics in MANETs.

We model the network as an undirected graph G = V , E, where V is the set of all mobile nodes in the network, and E is the set of all edges in the graph, representing available wireless communication links between nodes. A routing path from source node s to destination node d is P s , d = s , i , j , . . . , d, as shown in Figure 3. The end-to-end QoS metrics for this path are calculated as follows: Where d e l a y P is the total delay of path P, l o s t P is the total packet loss rate of path P, and b a n d w i d t h P is the available bandwidth of path P. Therefore, the final multi-constrained QoS routing problem can be formulated as: In the undirected graph G = V , E, find an optimal path P for traffic flow s , d , D max ⁡ , L max ⁡ , B min such that:

d e l a y P = ∑ e ∈ P d e l a y e + ∑ n ∈ P d e l a y n (1)

l o s t P = 1 − ∏ e ∈ E p 1 − l e (2)

b a n d w i d t h P = min b a n d w i d t h e (3)

d e l a y P ≤ D max l o s t P ≤ L max b a n d w i d t h P ≥ B min (4)

Among all paths that satisfy the above three constraints, our goal is to find the path with the lowest cost. To this end, we need to define a cost function that integrates multiple optimization objectives into one. To address the problem of inconsistent dimensions of different QoS metrics and to strictly enforce constraint thresholds, before calculating the comprehensive cost, we map the absolute physical values to dimensionless penalty functions and utility functions. Specifically, the delay penalty f D P, packet loss penalty f L P, and bandwidth utility f B P are defined as follows:

f D P = D max D max − d e l a y P (5)

f L P = L max L max − l o s t P (6)

f B P = b a n d w i d t h P − B min B min (7)

Therefore, the integrated multi-constraint cost function defined in this paper is restated as:Where h o p s P is the routing hop count, and, ω 1 , ω 2 and ω 3 are proportional coefficients set according to the weight of delay, packet loss rate, and bandwidth in QoS routing. As seen from the equation, the cost function is inversely proportional to bandwidth and directly proportional to delay, packet loss rate, and hop count. This algorithm aims to solve the above optimization problem: finding a path P for traffic flow s , d , D max ⁡ , L max ⁡ , B min that minimizes the comprehensive cost function under the premise of satisfying bandwidth, delay, and packet loss rate constraints.

Cos t P = h o p s P × ω 1 × f D P + ω 2 × f L P ω 3 × f B P (8)

4 Solving multi-constrained QoS routing with AH-ACO

4.1 Flow of the Ant colony optimization algorithm

Initialize algorithm control parameters, including: number of ants m; pheromone heuristic factor α controlling the influence of pheromone concentration; expectation heuristic factor β controlling the influence of heuristic information; pheromone evaporation coefficient ρ 0 < ρ < 1; and pheromone intensity coefficient Q. Initialize pheromones, usually setting the initial pheromone τ i j on all paths to a small constant to ensure the randomness of the initial exploration. The Tabu list is a key mechanism in the ACO algorithm to prevent repeated visits and the formation of invalid loops. Before each ant K starts constructing a path, an empty Tabu list belonging to it is initialized. After the ant starts from the origin, the origin is immediately added to the Tabu list and marked as visited.

Ants start from the source node and select the next node j to visit based on a probability rule. The most commonly used is the pseudo-random proportional rule, calculated as:Where τ i j is the pheromone concentration on edge i , j, and η i j is the heuristic information, usually a priori knowledge, such as 1 d i j. In QoS routing, this can be a QoS metric function defined for the link. The calculation range a l l o w e d k for the next node j is strictly defined as: all neighbor nodes of the current node i that are not recorded in that ant’s Tabu list, avoiding the formation of loops.

P i j = τ i j α η i j β ∑ j ∈ a l l o w e d k τ i j α η i j β , j ∈ a l l o w e d k 0 (9)

For the complete path T k constructed by each ant, its objective function value L k is calculated. After all ants have completed path construction, global pheromone updates are performed. First, pheromones on all edges are reduced by a certain proportion to simulate the natural evaporation process, preventing the algorithm from converging to local optima too early and helping to explore new areas:

τ i j t = 1 − ρ τ i j t − 1 (10)

Secondly, each ant releases pheromones on its constructed path T k. Typically, the lower the path cost L k, the more pheromone Δ τ i j is released. A common ACO model is the Ant-Cycle model:

Δ τ i j k = Q L k , i f the k − th ant passes through nodes i , j in this cycle 0 , o t h e r w i s e (11)

Finally, the pheromones released by all ants are accumulated onto the corresponding edges:

τ i j t + 1 = 1 − ρ τ i j t + Δ τ i j (12)

The loop ends when the termination condition is met, outputting the global optimal path found during the entire iteration process.

4.2 Design of core elements of the AH-ACO

4.2.1 Heuristic information and state transition probability

The path optimization process is guided jointly by pheromone concentration and heuristic information, and its design directly affects the algorithm’s performance and direction. To effectively integrate the QoS constraints of MANETs into the path construction process, we perform a refined design.

Heuristic information η i j is used to quantitatively assess the local desirability of choosing neighbor node j from node i at each step of path construction. Its core design goal is to guide ants to prioritize links that have excellent physical characteristics and help improve the quality of the path. Considering the multi-constrained nature of the problem, we adopt a local cost-driven design approach. That is, the lower the local cost of a link, the greater its attraction should be. Therefore, we first define a local cost c i j for each link i , j. This function is a local manifestation of the macroscopic path cost function, aimed at estimating the contribution to the overall cost through obtainable local information:Where d e l a y i j, l o s t i j, and b a n d w i d t h i j are the delay, packet loss rate, and bandwidth of link i , j, respectively. Since this is a local cost, the hop count is set to 1. Based on this local cost, the heuristic information η i j is its reciprocal, realizing the mapping “the lower the cost, the stronger the attraction”:

c i j = 1 × ω 1 × d e l a y i j + ω 2 × l o s t i j ω 3 × b a n d w i d t h i j (13)

η i j = 1 c i j (14)

This means that the lower the local cost of a hop, the larger its heuristic information value, and the stronger its attraction to ants. This provides strong positive guidance for ants to quickly gather in high-quality path areas when pheromones are scarce in the early stages of the algorithm.

Based on this, the probability of ant k choosing the next node j at node i is determined by the weighted product of pheromone concentration and heuristic information, following the classic random proportional rule:

P i j = τ i j α η i j β ∑ j ∈ a l l o w e d k τ i j α η i j β , j ∈ a l l o w e d k 0 (15)

In this model, τ i j is the pheromone concentration on edge i , j, representing the collective wisdom accumulated by the ant colony in past searches. α and β are the pheromone and heuristic factors, respectively. When α > β, the algorithm tends to utilize historical experience; conversely, it relies more on exploring links with better local properties. a l l o w e d k is a key link in the implementation of constraint handling. It is not simply the set of unvisited neighbors but a feasible candidate set pre-screened by QoS constraints: a l l o w e d k = j | j ∉ t a b u k , b i j ≥ B min. Here, t a b u k is the Tabu list of visited nodes for ant k to prevent loops. This step mandatorily satisfies the bandwidth constraint at every step of path construction, limiting the search space to the feasible solution range and greatly improving algorithm efficiency.

This probability formula ensures that the algorithm balances utilizing known excellent paths (pheromone-guided) and exploring potential high-quality paths (heuristic-guided): on one hand, ants tend to choose links with high pheromone concentration and strong heuristic information; on the other hand, the probabilistic selection mechanism provides opportunities for exploring other potential quality paths.

4.2.2 Improved pheromone update strategy

The pheromone update mechanism is the core of the ant colony algorithm’s optimization search, governing the accumulation, inheritance, and evolution of collective knowledge. Traditional ant colony algorithms typically use a fixed pheromone evaporation coefficient and a single global optimal update strategy. However, when solving complex MANET multi-constraint QoS routing problems, this approach can easily lead to an imbalance between convergence speed and global search capability, manifesting as premature convergence or excessively slow convergence of the algorithm. To overcome these shortcomings, this paper proposes a collaborative optimization strategy that integrates local updates, adaptive global updates, and elite guidance. This strategy achieves a dynamic balance between exploration and exploitation during the search process through multi-level and adaptive pheromone adjustment, thereby improving the algorithm’s convergence performance while ensuring global optimization capability.

Pheromone Local Update: During the path construction process of ants, we introduce a local pheromone update mechanism. When an ant completes the movement from node i to node j, it immediately performs a micro-adjustment to the pheromone on that link i , j:

τ i j t + 1 = 1 − ξ · τ i j t + ξ · τ 0 (16)

Here, ξ ∈ 0 , 1 is the local evaporation coefficient, and τ 0 is the initial value of the pheromone. The core function of this operation is to introduce a dynamic negative feedback mechanism. When a link is visited by an ant, a portion of its pheromone is immediately evaporated, temporarily reducing its attractiveness to subsequent ants.

The value of the local evaporation coefficient ξ is crucial to the strength of this negative feedback mechanism. If ξ in Formula 16 is set too small (for example, ξ ≤ 0.01), the negative feedback effect will be negligible, causing ants from the same batch to gather too quickly on a suboptimal path. This may lead the algorithm to lose population diversity and fall into a local optimum. Conversely, if ξ is set too large (for example, ξ ≥ 0.5), ants will excessively erase the pheromone on the path they traverse, potentially almost reducing it to zero before the iteration ends. This severely undermines the accumulation of global positive feedback signals, causing the algorithm to degenerate into a blind search state that is difficult to converge.

The results of the parameter sensitivity simulation experiment are shown in Figure 4. When ξ is in the interval [0.1, 0.2], the AH-ACO algorithm achieves the optimal dynamic balance between exploration and exploitation. Within this optimal range, with the main simulation setting of ξ = 0.15, the local update works just right: by appropriately reducing the attractiveness of paths that have already been visited, it effectively encourages other ants in the same iteration cycle to explore alternative paths that have not yet been traversed, significantly increasing the algorithm’s exploration breadth of the solution space in a single iteration. Moreover, this mechanism successfully prevents all ants from being rapidly attracted to a potentially suboptimal path in the early stage of the algorithm, serving as a solid defense for maintaining population diversity and avoiding getting trapped in local optima.

Pheromone Global Update: After all ants complete one cycle and construct paths, global pheromone updates are performed. We adopt a strategy combining elite guidance and adaptation. The rules are as follows:

τ i j t = 1 − ρ · τ i j t − 1 + Δ τ i j a l l + Δ τ i j e l i t e (17)

First, calculate the sum of pheromone increments for all feasible solution ants. For all ants k that successfully found a feasible path P k in this iteration, calculate their pheromone contribution Δ τ i j k. The contribution is inversely proportional to the comprehensive cost of the path Cos t k; the better the path, the larger the contribution:Where Q is a constant used to adjust the pheromone magnitude. Then, calculate the sum of pheromones released by all feasible solution ants on link i , j:

Δ τ i j k = Q Cos t k , i f i , j ∈ P k 0 , e l s e (18)

Δ τ i j a l l = ∑ Δ τ i j k (19)

Second, calculate the additional reward for the global optimal ant. Find the path P g b with the lowest cost among all feasible solutions in this iteration (i.e., the global optimal solution of this iteration) and calculate its pheromone increment. This increment will serve as an additional reward:

Δ τ i j e l i t e = Q Cos t g b , i f i , j ∈ P g b 0 , e l s e (20)

Adaptive Evaporation Mechanism: The evaporation term ρ simulates the natural decay of information. In this scheme, we discard the practice of fixed evaporation coefficients and introduce a time-varying adaptive evaporation coefficient:Where ρ i n i is the initial evaporation coefficient, and i t e r and i t e r max are the current iteration number and the maximum iteration number, respectively. The motivation for this design is to dynamically adjust the evaporation coefficient during the search process. In the early stage of exploration, pheromones evaporate quickly, rapidly weakening the influence of historical paths, and the algorithm tends to rely on heuristic information for bold exploration. In the later stage of exploration, pheromones evaporate slowly, allowing knowledge accumulated on elite paths and optimal paths to be retained and reinforced, guiding the population to converge to the optimal solution.

ρ = ρ i n i 1 − i t e r i t e r max (21)

4.2.3 Overall algorithm flow

Based on the above design, the complete procedure of the AH-ACO is as follows:

Initialization: Set the algorithm parameters, including the number of ants m, parameters λ , μ , Q, initial evaporation coefficient ρ i n i, and various weight coefficients. Initialize the pheromone value on all links to τ 0.

Path Construction and Local Pheromone Update: For each ant K = 1 to m, set the starting node s as the current node and add it to the tabu list. While the current node is not the destination node d, check all neighbors of the current node i and include those nodes j that satisfy b i j ≥ B min and are not in the tabu list of ant k into the feasible neighbor set N i k. If N i k is empty, mark the path construction for this ant as failed, release the ant, and proceed to the next ant. According to the state transition rule, select the next node j from N i k, add it to the tabu list, move to node j, and perform a local pheromone update. After ant k successfully constructs a path P k, calculate the cost function Cos t P, end-to-end delay d e l a y P, and packet loss rate l o s t i j of the path.

QoS Constraint Validation and Global Pheromone Update: From all paths constructed in the previous step, filter out those that do not satisfy the delay constraint d e l a y P ≤ D max and the packet loss constraint l o s t P ≤ L max. Update the pheromone values on the links of the remaining valid paths according to the pheromone update strategy.

Iteration and Output the Result: Repeat Step 2 and Step 3 until the maximum number of iterations is reached or a satisfactory solution is found. Output the global optimal path.

The pseudo-code for the AH-ACO algorithm is shown in Algorithm 1.

Algorithm 1 Adaptive and hybrid Ant colony optimization (AH-ACO).

5 Experimental results and discussion

5.1 Experimental setup and parameter settings

To validate the effectiveness of the AH-ACO algorithm in solving multi-constrained QoS routing problems in MANETs, this study constructed a discrete event simulation environment based on the Python platform. The experiment adopted the Random Waypoint Model to simulate the dynamic distribution of nodes within a 1000 m × 1000 m area. To comprehensively evaluate the Scalability and Dynamic Robustness of the algorithm, two independent test scenarios were designed:

Varying Network Scale Scenario: The maximum node movement speed was fixed at 10 m / s, and five scale gradients were set with node counts ranging from 20 to 100: {20,40,60,80,100}.

Varying Mobility Speed Scenario: The network scale was fixed at 60 nodes, and six speed gradients were set ranging from 0 m / s to 25 m / s: 0 , 5 , 10 , 15 , 20 , 25 m / s.

The specific simulation scenario parameters are detailed in Table 2.

TABLE 2. Network topology and simulation environment parameters.

The simulation environment is illustrated in Figure 5.

The QoS parameters of the network links follow a uniform distribution to simulate the stochastic nature of heterogeneous wireless environments. The QoS constraints are detailed in Table 3.

TABLE 3. Link QoS attributes and service constraints.

Furthermore, to ensure fairness in comparison, both the ACO algorithm and the AH-ACO algorithm adopted identical population sizes and iteration counts. The specific algorithm control parameters are set as shown in Table 4.

TABLE 4. Algorithm control parameters.

5.2 Convergence performance analysis

Figure 6 shows a comparison of the change curves of the objective function values between the AH-ACO algorithm and the traditional ACO algorithm in a typical network scenario. It can be observed that the traditional ACO algorithm exhibits a rapid decline in the early stages (approximately the first 15 iterations), but enters a stagnation period around the 25th iteration. Notably, the curve of the traditional ACO does not form a smooth asymptote thereafter; instead, it continues to oscillate between cost values of 20–24. In metaheuristic algorithms, this kind of sustained oscillation in the later stage indicates that the algorithm has not truly achieved convergence. Instead, due to a fixed pheromone evaporation coefficient and a single update strategy, the ant colony keeps wandering among several suboptimal paths, failing to generate sufficiently strong positive feedback to lock onto a single steady state.

In contrast, the AH-ACO algorithm demonstrates excellent steady-state behavior. Although its initial convergence speed is slightly slower, in the middle and later stages (iterations 20–60), as the adaptive evaporation mechanism gradually reduces the evaporation rate ρ, combined with the hybrid elite update strategy, the pheromone on the global optimal path accumulates steadily and strongly. Finally, around the 85th iteration, the cost value of AH-ACO stops oscillating and smoothly stabilizes at approximately 8.3. This indicates that the entire ant colony has fully converged, with all ants stably focusing on the global optimal solution, achieving true algorithmic convergence and steady state.

5.3 QoS Performance evaluation under different network scales

To verify the scalability of the algorithm regarding multi-constrained QoS problems, this experiment compared and analyzed the performance of Dijkstra, ACO, and AH-ACO across three key metrics—delay, packet loss rate, and bandwidth—under different network node densities. The specific comparative results of these metrics as a function of network scale are illustrated in Figure 7.

End-to-End Delay: As shown in Figure 7a, although the Dijkstra algorithm demonstrates the advantage of precise optimization in small-scale topologies, as the network scale increases, its latency performance deteriorates sharply due to its rigid constraint pruning strategy. In contrast, the AH-ACO algorithm, with its excellent global search capability, maintains the average latency around 72.4 m s in large networks. This is mainly attributed to the algorithm’s introduction of multi-objective heuristic information, which effectively guides the ant colony to quickly converge to low-cost paths that meet latency constraints within the solution space.

End-to-End Packet Loss Rate: Figure 7b reveals significant differences in communication reliability among the algorithms. For packet loss rate, a typical multiplicative metric, the AH-ACO algorithm shows a clear advantage. By explicitly incorporating link reliability into the comprehensive cost model and using a hybrid pheromone update strategy to enhance the selection weight of highly reliable links, the algorithm effectively reduces end-to-end packet loss rate, with overall performance significantly outperforming the comparison algorithms.

Path Available Bandwidth: As shown in Figure 7c, due to the greedy nature of the Dijkstra algorithm in seeking maximum bottleneck bandwidth, it achieves the highest bandwidth values. Although the bandwidth performance of the AH-ACO algorithm is slightly lower than that of Dijkstra, it is significantly better than traditional ACO. In fact, the performance of AH-ACO represents a strategic trade-off: the algorithm sacrifices a minimal amount of redundant bandwidth to achieve substantial improvements in latency and packet loss performance, thereby maximizing overall QoS utility in complex network environments.

When scaling up the network, if one blindly pursues the maximum bottleneck bandwidth, the routing often has to choose detour paths with a higher hop count. However, since delay is an additive metric and packet loss rate is a multiplicative metric, an increase in the hop count can cause these two performance aspects to deteriorate sharply. The AH-ACO algorithm effectively curbs the greedy pursuit of redundant bandwidth by explicitly introducing a hop count penalty factor (h o p s P) into the cost function. The algorithm proactively makes a strategic compromise, sacrificing a negligible amount of non-essential bandwidth in exchange for a significant reduction in end-to-end delay and packet loss rate, thereby maximizing the comprehensive QoS utility in complex-scale networks.

5.4 QoS Performance evaluation under different node mobility speeds

To further evaluate the robustness of the algorithm in dynamic environments, this experiment compared and analyzed the performance of Dijkstra, ACO, and AH-ACO across the three key metrics under different maximum node movement speeds, as illustrated in Figure 8.

End-to-End Delay: As shown in Figure 8a, as the node movement speed increases, the frequency of route reconstruction increases sharply due to frequent network topology changes, causing an upward trend in delay for all algorithms. However, the AH-ACO algorithm exhibits the flattest delay growth curve.

End-to-End Packet Loss Rate: As shown in Figure 8b, link breakage caused by high-speed mobility is the primary cause of data packet loss. The AH-ACO algorithm maintained the lowest packet loss rate across all tested speeds, significantly outperforming traditional ACO and Dijkstra. AH-ACO’s Hybrid Pheromone Update Strategy enables the utilization of elite ants to rapidly discover and reinforce potential alternative paths, thereby achieving seamless path switching before the current link fails.

Path Available Bandwidth: As shown in Figure 8c, although the Dijkstra algorithm can search for the theoretical maximum bottleneck bandwidth in static scenarios, its performance drops precipitously as movement speed increases. In contrast, although AH-ACO has a slightly lower peak bandwidth in static conditions, it demonstrates extremely strong stability in high-dynamic scenarios, capable of providing continuous and reliable Effective Bandwidth.

The high-speed movement of nodes significantly increases link instability. If the algorithm becomes overly greedy for instantaneous high-bandwidth links, once a link breaks due to node movement, frequent route reconstruction will lead to a sharp increase in delay and a substantial loss of data packets. Leveraging its hybrid elite update strategy, the AH-ACO algorithm, while reinforcing the optimal solution, consistently maintains a high-quality pool of alternative paths. This mechanism, which sacrifices a slight amount of static peak bandwidth in exchange for path diversity and stability, enables seamless switching when link failures occur. Consequently, it maintains extremely low delay and stable effective bandwidth even in highly dynamic environments.

5.5 Theoretical boundaries and limitations of AH-ACO

Although the AH-ACO algorithm demonstrates excellent multi-objective optimization performance in medium to large-scale MANET scenarios with good connectivity, its effectiveness is limited by specific theoretical boundaries. When the network environment approaches these boundaries, the algorithm’s convergence and optimization capabilities decline significantly.

In extremely sparse networks, the state transitions of AH-ACO rely heavily on a pre-filtered feasible candidate set a l l o w e d k = j | j ∉ t a b u k , b i j ≥ B min. In networks with very low node density, the average degree of nodes is small. During pathfinding, ants can easily hit dead ends, causing a l l o w e d k to frequently become an empty set. According to the algorithm design, this forces the construction of an ant’s path to terminate and the ant to be released. A large number of ant “deaths” drastically reduces the number of successfully constructed complete paths in a single iteration, severely weakening the effective accumulation of global pheromones and causing the algorithm to degrade into inefficient random search, or even completely stall after several consecutive iterations with no feasible solutions.

In overly constrained scenarios, when QoS constraints from the application layer (like extremely high B min or extremely low D max) are strict to the limits of the network’s physical topology, the algorithm’s pruning mechanism also causes the search space to shrink sharply. At this point, the guiding effect of heuristic information is greatly weakened, making it difficult for the algorithm to explore an initial feasible solution that satisfies all stringent conditions within a reasonable time, showing poor convergence robustness.

Therefore, AH-ACO is more suitable for dynamic network environments with relatively dense node distribution and a certain degree of link redundancy. For scenarios that are extremely sparse or prone to frequent network partitioning, it is necessary to incorporate topology control or introduce underlying mechanisms like the store-carry-forward principle from Delay-Tolerant Networks (DTN) as a supplement.

6 Conclusion

In response to the complexity of multi-constraint QoS routing issues in MANETs, this paper proposes an Adaptive Hybrid Ant Colony Optimization algorithm. By constructing a multidimensional comprehensive cost model and organically integrating an adaptive pheromone evaporation mechanism with a hybrid update strategy, the algorithm successfully achieves a dynamic balance between global exploration and local exploitation. This approach effectively overcomes the inherent shortcomings of traditional metaheuristic algorithms, such as slow convergence and susceptibility to being trapped in local optima. Simulation results indicate that under different network scales and highly dynamic scenarios, AH-ACO significantly reduces end-to-end delay and packet loss while maintaining high effective bandwidth. Compared with the Dijkstra algorithm and traditional ACO algorithms, the proposed algorithm demonstrates superior convergence performance and robustness, providing an efficient and reliable solution for quality of service assurance in dynamic network environments.

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Footnotes

Edited by: Jules M. Moualeu, University of the Witwatersrand, South Africa

Reviewed by: Ahmad Bazzi, New York University Abu Dhabi, United Arab Emirates

Sergei Gorlatch, University of Münster, Germany