Adaptive Shortest Path Routing Algorithms for Dynamic Network Environments

Adaptive Shortest Path Routing Algorithms for Dynamic Network Environments

Divyanshi Singh

Department of CSE Chandigarh University Mohali, India

Geetika Srivastava

Department of CSE Chandigarh University Mohali, India

Shashwat Sahni

Department of CSE Chandigarh University Mohali, India

Mandeep Kaur

Department of CSE Chandigarh University Mohali, India

Abstract – Due to the dynamic nature of MANETs, IoT, and VANETs, shortest path computation becomes a difcult endeavor due to their constantly changing topological structure. In this paper, we introduce a novel adaptive hybrid approach to nding the shortest route by employing heuristic-based optimization algorithms and real-time network awareness. In the proposed work, the following experimental parameters have been consid- ered: a number of nodes varying between 50 and 300; mobility speed between 525 m/s; and trafc load of 10100 packets/s. The proposed system will be evaluated based on important parameters: Packet Delivery Ratio (PDR); End-to-End Delay; Throughput; Routing Overhead; and Path Optimality Index. The experiments carried out show that the proposed algorithm provides a PDR of 96.8%, outperforming existing protocols like AODV (89.4%) and DSR (91.2%). The end-to-end delay is signicantly improved to only 48 ms, compared to previous systems 72 ms. At the same time, throughput is increased by 18.5% to 1.82 Mbps, with routing overhead minimized by 22%. Finally, according to the path optimality index, the shortest path can be found more accurately by 12%.The results validate that the proposed adaptive routing approach signicantly enhances shortest path computation efciency and reliability in dynamic network environments, making it suitable for real-time and large- scale applications.

Index TermsShortest Path Routing, Dynamic Networks, MANET, IoT, VANET, Adaptive Algorithms, Packet Delivery Ratio, End-to-End Delay, Throughput, Routing Overhead, Opti- mization Techniques, Network Performance.

1. Introduction

   Dynamic networks have become a core part of contempo- rary communication networks, especially in areas like Mobile Ad Hoc Networks (MANETs), Vehicular Ad Hoc Networks (VANETs) and Internet of Things (IoT) ecosystems. Such networks have a high turnover of topology, loose control and insufcient infrastructure support thus routing is a highly complex and required task. Shortest path routing problem, which seeks to nd the most efcient route between nodes, becomes much more complex in this kind of environment because of link breakages and node mobility are rife [1] [2] [3]. The conventional xed point routing algorithms cannot be sufcient to deal with such dynamic situations and the

   aspect of creating adaptive and intelligent routing mechanisms is therefore considered necessary [4]. Dijkstra and Bellman- Ford are traditional shortest path algorithms that are common in static or more dynamic networks; their deterministic nature and efciency make them popular and efcient. Nevertheless, these algorithms are based on scenarios of constant network conditions, and full information of the network structure which is not always possible in dynamic networks. Consequently, they signicantly deteriorate the performance in terms of delay, packet losses and routing overheads when used in highly dynamic environments [5] [6] [7]. This is the limitation that has caused researchers to look at other ways of being able to adjust to the changing states of the networks in real time [8]. Some of these challenges have been addressed in dynamic networks by the proposed reactive and proactive routing protocols such as the AODV and DSR. Whereas reactive protocols use fewer overhead (because they nd routes when required), proactive protocols maintain current routing tables at the expense of higher overhead control trafc. Although both methods have their merits, they experience problems of scalability and reliability in high mobility and dense network conditions [9] [10] [11]. In addition, the regular route nding and maintenance operations cause an even greater amount of latency, which affects the performance of the network as a whole [12]. To address these shortcomings, the current research has also been emphasizing on incor- poration of optimization methods and intelligent decision- making models in routing algorithms. Approaches based on metaheuristic algorithms, such as Ant Colony Optimization (ACO) and Genetic Algorithms (GA), have shown promising results in improving path selection and network efciency. Also, machine learning and reinforcement learning algorithms are more and more actively used to forecast the behavior of networks and dynamically change the routing decisions [13] [14] [15]. These techniques provide more exible and context- sensitive routing which greatly improves the performance of dynamic environments. The other signicant consideration of shortest path routing in dynamic networks is the consideration of various metrics of performance other than path length.

   Packet Delivery Ratio (PDR), End-to-End Delay, Throughput, Energy Consumption, and Routing Overhead are metrics that are important in measuring routing efciency. Multi-objective optimization is one of the methods that have been proposed to balance these parameters so that both efciency and reliability of network communication are guaranteed [16] [17] [18]. Quality of Service (QoS) requirements also introduce more complexity to the routing problem, particularly in real-time applications. Here, the current paper seeks to create a dynamic network-based adaptive shortest path routing system. The intended solution takes advantage of real-time network data and smart optimization techniques to improve the routing performance in different situations. This study will help to en- hance scalability, robustness and efciency of dynamic routing systems by eliminating the shortcomings of current approaches and integrating newest techniques. This research is likely to be of great relevance in the next-generation communication networks, such as smart cities, autonomous systems, and massive deployments of IoT [19] [20] [21].

2. Literature Review

   Research in the area of shortest path routing and intelligent network optimization has developed a lot, starting with clas- sic algorithmic methods and moving towards adaptable, AI- based systems. Dynamic routing in communication networks was pioneered by the shortest path rst strategy that uses emergency exits [4] as early as possible. Classical techniques of optimization of Mobile Ad Hoc Networks (MANETs) such as the fuzzy and rough set-based path selection [3], and uncertainty-based trust evaluation of secure routing [9] showed how decision-making in dynamic environments might improve the routing efciency and reliability. Also, early underwater sensor network protocols [20] and routing with memetic algorithms [21] occurred, and emphasized the role of heuristic and evolutionary methods in nding complex solutions to path optimization problems. The table 1 shows the Literature Review of Routing Strategies.

   As wireless sensor networks (WSNs) and IoT-based sys- tems started to emerge, energy efciency, sustainability, and environmental monitoring started to be included in routing strategies. To illustrate the use of routing algorithms in other elds, smart forest monitoring systems based on IoT and shortest path routing [2] and ecological monitoring systems with ant colony optimization [17] show the extension of routing algorithms to non-networking environments. Likewise, the increasing necessity to strike the balance between per- formance, energ consumption, and security in distributed systems are highlighted in energy efcient routing frame- works based on fuzzy multi-objective optimization and particle swarm optimization [6], as well as in cyber-resilient swarm routing in the case of fog assisted WSNs [18]. The routing strategies in the vehicular and transportation networks have been developed to real-time, adaptive, and AI-based routing strategies. Vehicle re-routing techniques to address congestion issues in a dynamic manner [1] and route guidance with reinforcement learning in mixed trafc situations [7] are a step

   in the right direction towards intelligent trafc management. More examples of the integration of AI, edge computing, and next-generation communication technologies include advanced vehicular ad hoc network (VANET) frameworks that use UAV assistance and 6G connectivity [5] and machine learning- assisted hybrid routing models in software-dened vehicular networks [15]. The analysis of routing metrics like OSPF [12] also offers information on the issues of optimising routing decisions in dynamic and secure network settings. Lately, the emphasis in routing optimization has been on articial intelligence, machine learning, and reinforcement learning. The adaptability and scalability are considerably enhanced by AI-controlled routing pipelines based on deep Q-learning (DQL) [19] and reinforcement learning-based algorithms to operate in large-scale street networks [13]. Transfer learning with deep reinforcement learning [7] is more resilient to dynamic environments, and intelligent controller selection in the software-dened vehicular systems [5] is representative of the increased intersection of AI and networking. Such methods facilitate predictive and contextual routing choices which are more successful than the conventional xed algorithms. Specically, routing protocols in specialized elds have also been developed to cater to the demands of their applications. Shortest path routing in healthcare wireless sensor networks that monitor patients physiological activities is an example [14]. Other examples include UAV routing in sustainable supply chains with the use of three-dimensional path planning [10], and electric vehicle routing in which charging and travel times are considered [8]. In addition, software-dened man- agement architectures in IP-based WSNs are also an important area of research [16]. Generally, the existing literature review shows that there has been a denite shift from the use of conventional algorithms to advanced techniques for routing. The implementation of AI, IoT, and SDN has improved routing in terms of efciency, scalability, and robustness. Nevertheless, issues like security attacks, changes in network topology, and power management are still crucial aspects that need to be investigated. The combination of new technologies like 6G, edge computing, and federated learning is anticipated to revolutionize routing in the future.

3. Methodology

   The research proposal suggests that the adaptive algorithm for shortest path routing is designed and evaluated using simulation-based techniques. The simulations are based on the well-known network simulator NS-3 Mobility Trace Dataset (Random Waypoint Model) and CRAWDAD dataset. The node movement characteristics used for this research include a square terrain with a size of 1000 m x 1000 m and different node movement speeds between 5 m/s and 25 m/s. The number of nodes used during simulation experiments varies between 50, 100, 200, and 300. Packet generation for simulation is based on Constant Bit Rate (CBR) ows with different sizes (512 bytes) and speeds between 10 to 100 packets per second. Figure 1 shows the proposed methodology used in this research paper.

   TABLE I

   Literature Review of Routing Strategies

   Ref No	Title	Author & Year	Findings	Research Gaps
   [1]	Dynamic adaptive vehicle re- routing strategy for trafc con- gestion mitigation of grid net- work	Wang et al., 2024	Proposed adaptive re-routing to re- duce congestion in grid networks, improving travel time and trafc ow efciency.	Limited scalability in large hetero- geneous trafc systems and lack of real-time AI integration.
   [2]	Smart forest monitoring: IoT framework with shortest path routing	Etaati et al., 2024	Introduced IoT-based monitoring with efcient shortest path routing for environmental sustainability.	Energy efciency and long-term deployment challenges in harsh en- vironments not fully addressed.
   [3]	Optimal path management in MANET using fuzzy and rough set theory	Seethalakshmi et al., 2011	Combined fuzzy logic and rough set theory to enhance routing de- cisions under uncertainty.	Outdated approach lacking inte- gration with modern AI/ML tech- niques and scalability issues.
   [4]	Shortest path rst with emer- gency exits	Wang & Crowcroft, 1990	Introduced enhanced shortest path routing with backup paths for fault tolerance.	Does not consider dynamic net- works or real-time adaptive routing requirements.
   [5]	6G SDVN: UAV-Assisted VANETs for AI-enabled controller selection	Rad et al., 2026	Proposed UAV-assisted SDVN with AI-based controller selection for improved connectivity and perfor- mance.	High computational complexity and challenges in real-world deployment and standardization.

   1. Adaptive Link Cost Function

      Cij

      = · 1

      Sij

      + · Qj

      + · 1

      Ej

      (1)

      Where: Cij is the cost of the link between node i and j, Sij represents link stability, Qj is the queue length at node j, and Ej denotes the residual energy of node j. , , and are weighting coefcients such that + + = 1.

      Explanation: This equation dynamically computes the rout- ing cost by considering stability, congestion, and energy, ensuring reliable and efcient path selection.

   2. Path Cost Aggregation Equation

      Pcost = I:

      (i,j)P

      Cij (2)

      Where: Pcost is the total cost of path P , and Cij represents the cost of each link along the path.

      Explanation: This equation calculates the overall path cost by summing individual link costs, enabling shortest path determination in dynamic networks.

   3. Packet Delivery Ratio (PDR)

      PDR = Preceived × 100 (3)

      Psent

      Where: Preceived is the number of packets successfully received at the destination, and Psent is the total number of packets transmitted.

      Explanation: This metric evaluates the reliability of the routing protocol by measuring successful data delivery.

      t

      k

   4. Average End-to-End Delay

      Davg =

      N

      P

      k=1

      k recv

      (t

      N

      send)

      (4)

      Fig. 1. Proposed Methodology

      Where: tk

      k recv

      are the transmission and reception

      send

      and t

      times of packet k, and N is the total number of received packets.

      Explanation: This equation computes the average delay experienced by packets, reecting the timeliness of data trans- mission.

      Algorithm 1 Adaptive Shortest Path Routing Algorithm

      1: Initialize network graph G(V, E)

      2: Assign initial weights using Eq. (1)

      3: for each node i V do

      4: Discover neighbors and update link stability

      5: end for

      6: while network is active do

      7: for each source node do

      8:

      9:

      p>10:

      11:

      12:

      13:

      Compute shortest path using Eq. (2)

      if link failure detected then Update link cost dynamically Recompute shortest path

      end if

      Forward packets along optimal path

      Fig. 2. PDR vs Node Density

      mobility speeds, and it shows that even at very fast speed rates such as 25 meters/second, the algorithm performs well

      14: end for

      15: Measure performance using Eq. (3) and Eq. (4)

      16: end while

      17: Output routing performance metrics

      Algorithm 1 shows the Adaptive Shortest Path Routing Algorithm. The suggested routing scheme includes dynamic calculation of shortest path and topology updating. At rst, the network topology is built according to node connection data obtained from mobility traces. An advanced version of Dijkstra algorithm is implemented, which includes dynamic weighting of links according to link stability (weighting coefcient 0.6), node energy (weighting coefcient 0.2), and node queue level (weighting coefcient 0.2). Topology changes monitoring is provided at time interval equal to 1 second; routing recalcula- tions are made in case of probability of link break exceeding

      0.3 threshold value that helps minimize the level of packet loss. For the purpose of performance analysis the following criteria were chosen: Packet Delivery Ratio (PDR), End-to-End Delay, Throughput, Routing Overhead, and Path Optimality Index. Proposed model has been compared with AODV and DSR standard protocols under similar conditions. All experiments have been carried out for 10 times independently to prove their statistically valid results. The range of delivery ratio values equals 92.5%-96.8%; end-to-end delay ranges from 45 ms to 60 ms according to node density; throughput equals 1.45 Mbps-1.82 Mbps respectively. Routing overhead was found to be 18%-22% lower than in standard protocols; path optimality index is better in 10%-12%. To check for robustness, a scalability test is carried out by changing the node density and the amount of trafc together. In terms of efciency, the algorithm proves to have high levels of robustness, maintaining a constant performance even at 300 nodes and 100 packets per second of trafc, showing just 6 percent decrease in packet delivery ratio and an additional 12 ms in delay, which is impressive. In addition, sensitivity tests are run by changing

      compared to other existing approaches.

4. Result and Evaluation

   The performance of the adaptive shortest path routing technique is tested on different node densities of 50, 100, 200, and 300 nodes and various speeds of mobility starting from 5m/s to 25m/s. The PDR performance metric is very efcient with 96.8% at 50 nodes and sustaining 93.1% even when the number of nodes is 300; on the other hand, the AODV and DSR protocols were found to provide a value of 89.4% and 91.2%, respectively. The average delay per packet for the suggested technique is 48ms while AODV and DSR techniques give delays of 72ms and 65ms, respectively. The table 2 shows the Performance Evaluation of Routing Algorithms.

   TABLE II

   Performance Evaluation of Routing Algorithms

   Metric	Proposed	AODV	DSR
   Packet Delivery Ratio	96.8	89.4	91.2
   End-to-End Delay (ms)	48	72	65
   Throughput (Mbps)	1.82	1.35	1.42
   Routing Overhead Reduction	22	0	0
   Path Optimality Improvement	12	0	0
   Energy Consumption Reduction	15	0	0
   PDR at 300 Nodes	93.1	84.7	87.3
   Delay at High Mobility (ms)	60	85	78
   Throughput at High Trafc	1.57	1.21	1.29

   The throughput analysis shows that the proposed algorithm has a peak throughput of 1.82 Mbps for medium trafc load (50 packets/s) and a steady state throughput of 1.57 Mbps for heavy trafc load (100 packets/s). On the other hand, the average throughput of AODV and DSR was estimated to be

   1.35 Mbps and 1.42 Mbps, respectively. Figure 2 shows the PDR vs Node Density.

   The number of control packets has been decreased by 22% for AODV and by 18% for DSR due to a more efcient approach to route maintenance. The Path Optimality Index is

   Fig. 3. Throughput Distribution

   also enhanced by 12%, which means that the chosen routes have become more similar to the actual shortest routes. Figure 3 shows the Throughput Distribution.

   The evaluation results of scalability and robustness proper- ties show that proposed algorithm demonstrates better scala- bility. In case the number of nodes was increased from 50 up to 300, the PDR decreased by only 3.7%, and delay increased by 12 ms. In high mobility environment with 25 m/s speed, the algorithm demonstrates a high PDR rate higher than 92% even with high speed; however, AODV PDR decreased to less than 85%. The energy consumption of proposed algorithm demonstrated a decrease of about 15% in comparison with baseline protocols, which leads to network lifetime increase.

5. Challenges and Limitations

   In spite of the positive results, however, the suggested adaptive shortest path routing technique encounters a number of problems in highly dynamic networks. Firstly, there is the considerable computational cost of the constant topology observation and path recomputation every second that will result in extra processing work in resource-limited nodes. With the number of nodes increasing up to 300 and more, it becomes harder for the algorithm to cope with memory demands and delays related to link state maintenance. Another drawback of the routing method is connected with the use of weights: incorrect values assigned to such parameters as link stability (0.6), energy level of the node (0.2) and queue size (0.2) reduce performance by 8-10% depending on PDR and delay. A major limitation in this regard concerns the performance when there is a highly mobile environment and an heterogeneous wireless network. At very high mobility levels, i.e., greater than 25 m/s, the rate of link failures rises considerably, resulting in occasional uctuations in routing and a decline in PDR to around 9092%. Moreover, the framework has been analyzed mostly in a controlled environment through simulation data, e.g., NS-3 mobility traces and CRAWDAD data set, which may fail to reect the uncertainty factors of the environment in reality, e.g., interference and obstacle effects. The issue

   of security is also not considered in its entirety; there is no explicit solution to routing attacks, such as the black hole attack or sybil attack.

6. Future Outcomes

   In the future, research may be undertaken to extend the pro- posed adaptive shortest path routing approach through the use of advanced intelligent systems including deep reinforcement learning and federated learning. This way, nodes are expected to learn effective routing policies using both past and present information to increase Packet Delivery Ratio to more than 97% while minimizing end-to-end delays to less than 40 ms. Furthermore, the employment of predictive mobility models is expected to help predict future topology changes to decrease route failures to about 2025%. In addition, the incorporation of multi-objective optimization algorithms will ensure that the algorithm dynamically balances metrics such as energy ex- penditure, end-to-end delay, and throughput efciency. Other avenues worth exploring include the extension of th approach to cater for secure and scalable routing for heterogeneous and large scale networks with over 500-1000 nodes. By utilizing blockchain based trust management as well as lightweight encryption approaches, resilience against routing attacks will be enhanced leading to decreased packet losses by 30-35%. Practical testing of the system in an IoT testbed as well as edge computing environment will help demonstrate its performance under real-world limitations like interference and differences in the hardware. Other improvements that can enhance energy efciency of the system and lower power consumption by 18- 25% can be considered. This will make the routing technique viable for use in 6G systems and other advanced systems.

7. Conclusion

In summary, this research offered an adaptive shortest path routing algorithm specically developed to tackle the problem of route selection and maintenance in networks that frequently experience changes in their topology due to movement and fre- quent recongurations. Specically, the algorithm incorporated real-time awareness of the network topology and considered several weighted optimization criteria, namely link stability, energy levels, and queue loads. As evidenced by the experi- mental results, the algorithm provided better performance than other routing protocols. In particular, the maximum value of Packet Delivery Ratio was 96.8% with an end-to-end delay of roughly 48 ms, throughput of 1.82 Mbps, and routing overhead reduction between 18-22%. In addition, the method proved to be scalable and robust, maintaining acceptable performance in the case of 300-node network with 25 m/s speed. It should be pointed out that the proposed approach managed to improve path optimality index and reduce energy consumption, ensuring that the chosen path is as close to optimal as possible. Even though there are some limitations associated with computation costs and parameter adjustment, overall this paper has shown that the developed algorithm works well.

References

1. C. Wang, T. Atkison, and H. Park, Dynamic adaptive vehicle re-routing strategy for trafc congestion mitigation of grid network, International Journal of Transportation Science and Technology, vol. 14, pp. 120136, 2024, doi: 10.1016/j.ijtst.2023.04.003.

2. A. Etaati, M. Bastam, and E. Ataie, Smart forest monitoring: A novel Internet of Things framework with shortest path routing for sustainable environmental management, IET Networks, vol. 13, no. 56, pp. 528 545, 2024, doi: 10.1049/ntw2.12135.

3. P. Seethalakshmi, M. Joseph Auxilius Jude, and G. Rajendran, An optimal path management strategy in Mobile Ad Hoc Network using fuzzy and rough set theory, American Journal of Applied Sciences, vol. 8, no. 12, pp. 13141321, 2011, doi: 10.3844/ajassp.2011.1314.1321.

4. Z. Wang and J. Crowcroft, Shortest path rst with emergency exits, in

   Proc. ACM SIGCOMM, 1990, pp. 166176, doi: 10.1145/99508.99548.

5. M. Rad, A. Afridi, S. Sualiheen, A. Iqbal, I. Ali, and A. Akhunzada, 6G SDVN: UAV-Assisted VANETs for AI-Enabled Controller Selection and Heterogeneous Multi-Band Connectivity, IEEE Open Journal of the Communications Society, 2026, doi: 10.1109/OJCOMS.2026.3678705.

6. M. A. Tawfeek, I. Alrashdi, M. Alruwaili, and F. M. Talaat, A Fuzzy Multi-Objective Framework for Energy Optimization and Reliable Routing in Wireless Sensor Networks via Particle Swarm Optimization, Computers, Materials and Continua, vol. 83, no. 2, pp. 27732792, 2025, doi: 10.32604/cmc.2025.061773.

7. D. Lee, Transfer Learning-Based Deep Reinforcement Learning Ap- proach for Robust Route Guidance in Mixed Trafc Environment, IEEE Access, vol. 12, pp. 6166761680, 2024, doi: 10.1109/AC- CESS.2024.3395430.

8. S. Shao, W. Guan, B. Ran, Z. He, and J. Bi, Electric Vehicle Routing Problem with Charging Time and Variable Travel Time, Mathematical Problems in Engineering, vol. 2017, Art. no. 5098183, 2017, doi: 10.1155/2017/5098183.

9. S. Muthuramalingam and T. Suba Nachiar, Enhancing the security for MANET by identifying untrusted nodes using uncertainty rules, Indian Journal of Science and Technology, vol. 9, no. 4, pp. 19, 2016, doi: 10.17485/ijst/2016/v9i4/87043.

10. M. Ikram and R. Sroufe, A novel sequential block path planning method for 3D unmanned aerial vehicle routing in sustainable supply chains, Supply Chain Analytics, vol. 9, Art. no. 100094, 2025, doi: 10.1016/j.sca.2024.100094.

11. S. Ebadinezhad, Design and performance evaluation of Improved DFACO protocol based on dynamic clustering in VANETs, SN Applied Sciences, vol. 3, no. 4, Art. no. 486, 2021, doi: 10.1007/s42452-021-

    04494-8.

12. C. Thaenchaikun and K. Kanjanasit, A Comparative Study of OSPF Metrics in Routing Algorithms for Dynamic Path Selection in Network Security, ASEAN Journal of Scientic and Technological Reports, vol. 28, no. 2, Art. no. e256556, 2025, doi: 10.55164/ajstr.v28i2.256556.

13. D. Li et al., A reinforcement learning-based routing algorithm for large street networks, International Journal of Geographi- cal Information Science, vol. 38, no. 2, pp. 183215, 2024, doi: 10.1080/13658816.2023.2279975.

14. R. Gill and T. K. Dubey, Application of Shortest Path Algorithm for Patient Routing in Healthcare Wireless Sensor Networks, Jour- nal of Applied Bioanalysis, vol. 11, no. 2, pp. 234245, 2025, doi: 10.53555/jab.v11i2.203.

15. P. A. D. S. N. Wijesekara and S. Gunawardena, A Machine Learning- Aided Network Contention-Aware Link Lifetime- and Delay-Based Hybrid Routing Framework for Software-Dened Vehicular Networks, Telecom, vol. 4, no. 3, pp. 393458, 2023, doi: 10.3390/telecom4030023.

16. F. F. Jurado-Lasso, K. Clarke, and A. Nirmalathas, A Software-Dened Management System for IP-Enabled WSNs, IEEE Systems Journal, vol. 14, no. 2, pp. 23352346, 2020, doi: 10.1109/JSYST.2019.2946781.

17. G. Zhang, Y. Gong, X. He, G. Wang, Z. Hu, and H. Wang, Ecological Environment Monitoring of Open Pit Abandoned Mines Combining Internet of Things and Improved Ant Colony Optimization, Engineering Reports, vol. 7, no. 11, Art. no. e70500, 2025, doi: 10.1002/eng2.70500.

18. A. Upadhiyay and A. Jain, Cyber resilient framework with energy efcient swarm routing and ensemble threat detection in fog assisted wireless sensor networks, Scientic Reports, vol. 15, no. 1, Art. no. 36461, 2025, doi: 10.1038/s41598-025-21368-w.

19. D. Goteti and V. K. Reddy, AI-driven routing pipeline in software- dened networks using DQL: a mini review, Frontiers in Articial Intel- ligence, vol. 8, Art. no. 1685155, 2025, doi: 10.3389/frai.2025.1685155.

20. N. Javaid et al., An efcient data-gathering routing protocol for underwater wireless sensor networks, Sensors, vol. 15, no. 11, pp. 2914929181, 2015, doi: 10.3390/s151129149.

21. N. R. Sabar, A. Song, Z. Tari, X. Yi, and A. Zomaya, A memetic algorithm for dynamic shortest path routing on mobile ad-hoc networks, in Proc. ICPADS, 2016, pp. 6067, doi: 10.1109/ICPADS.2015.16.