This section delves into the computational complexity of the IZOACP. The initialization phase of ZOA has a complexity of , where denotes the count of zebras and signifies the number of variables associated with the problem. The algorithm encompasses iterations, during which each member of the population undergoes updates in two distinct phases, and the objective function is assessed for each member. The complexity associated with this updating procedure is . Consequently, the overall computational complexity of ZOA can be encapsulated as . Pseudo Code of Proposed IZOACP is shown in Algorithm 1.

This research employed MATLAB 2020a to perform simulation experiments aimed at assessing the effectiveness of several algorithms, including LEACH, DMaOWOA, and ARSH-FATI-CHS, alongside the newly introduced IZOACP method, in tackling critical challenges like energy consumption, network longevity, and data transmission quality in AWSNs. The evaluation of the proposed algorithm was based on several key performance indicators, such as the number of operational rounds before varying levels of node failure, the mean residual energy across nodes, data throughput, and latency in transmission. The specific experimental configuration information is shown in Table 1 and Table 2. The baseline algorithm analysis is shown in Table 3.

The performance evaluation included comparative experiments on lifecycle, energy consumption, throughput, and network latency.

Figure 3 presents the relationship between the number of surviving nodes and the number of rounds in IWSNs for two scenarios. Subfigure (a) corresponds to Scenario 1, while subfigure (b) represents Scenario 2. Each subfigure includes four curves representing the algorithms LEACH, DMaOWOA, ARSH-FATI-CHS, and IZOACP. In Scenario 1, the number of surviving nodes decreases as the rounds progress. IZOACP consistently maintains the highest number of alive nodes throughout the rounds, demonstrating superior network longevity. LEACH shows the fastest decline in surviving nodes, while DMaOWOA and ARSH-FATI-CHS perform moderately. In Scenario 2, a similar trend is observed over a larger range of rounds (up to 1500). IZOACP again outperforms the other algorithms, maintaining a significantly higher number of alive nodes even in later rounds. LEACH exhibits the poorest performance, with nodes depleting rapidly. DMaOWOA and ARSH-FATI-CHS show intermediate results but are consistently surpassed by IZOACP. Overall, the results highlight that IZOACP significantly extends the network lifetime in both scenarios, outperforming LEACH, DMaOWOA, and ARSH-FATI-CHS in terms of node survivability. IZOACP achieves the highest number of rounds with the most surviving nodes, making it the best-performing algorithm.

Figure 4 consists of two bar charts, labeled (a) and (b), comparing the number of rounds achieved by four algorithms -- LEACH, DMaOWOA, ARSH-FATI-CHS, and IZOACP -- under different node death ratios in Scenario 1 and Scenario 2. The x-axis represents three node death conditions: "One node dies," "Half of the nodes die," and "All nodes die," while the y-axis indicates the number of rounds. The bars are color-coded: blue for LEACH, yellow for DMaOWOA, green for ARSH-FATI-CHS, and red for IZOACP. In Scenario 1, the number of rounds for "One node dies" are 164 for LEACH, 215 for DMaOWOA, 257 for ARSH-FATI-CHS, and 324 for IZOACP. IZOACP achieves the highest number of rounds, demonstrating a 97.56% improvement over LEACH in this condition. For "Half of the nodes die," the rounds are 155, 216, 261, and 355, respectively, with IZOACP showing a 129.03% improvement over LEACH. For "All nodes die," the rounds are 191, 261, 299, and 355, with IZOACP achieving an 85.86% improvement over LEACH. In Scenario 2 (Chart (b)), the number of rounds for "One node dies" are 462 for LEACH, 751 for DMaOWOA, 767 for ARSH-FATI-CHS, and 904 for IZOACP. IZOACP outperforms LEACH by 95.67%. For "Half of the nodes die," the rounds are 442, 590, 741, and 926, respectively, with IZOACP showing a 109.50% improvement over LEACH. For "All nodes die," the rounds are 576, 741, 1025, and 1286, with IZOACP achieving a 123.26% improvement over LEACH. Overall, Figure 3 highlights that IZOACP consistently achieves the highest number of rounds across all node death conditions in both scenarios, significantly outperforming LEACH, DMaOWOA, and ARSH-FATI-CHS. This demonstrates IZOACP's superior ability to extend network lifetime under varying levels of node failure.

Figure 5 presents two line charts, labeled (a) and (b), comparing the total energy consumption (in joules) of four schemes -- LEACH, DMaOWOA, ARSH-FATI-CHS, and IZOACP -- across different rounds in Scenario 1 and Scenario 2. In Scenario 1, the total energy consumption increases with the number of rounds, with LEACH showing the steepest rise, followed by DMaOWOA and ARSH-FATI-CHS, while IZOACP demonstrates the slowest and most stable increase, maintaining the lowest energy consumption throughout. In Scenario 2, a similar trend is observed over a larger range of rounds (up to 1200), where LEACH again exhibits the fastest energy depletion, DMaOWOA and ARSH-FATI-CHS perform moderately, and IZOACP consistently maintains the lowest energy consumption. Overall, IZOACP stands out as the most energy-efficient scheme, significantly outperforming the other methods in minimizing energy consumption and ensuring prolonged network operation in both scenarios.

Figure 6 consists of two subfigures, labeled (a) and (b), comparing the packet sizes received by cluster nodes for four schemes -- LEACH, DMaOWOA, ARSH-FATI-CHS, and IZOACP -- across different rounds in Scenario 1 and Scenario 2. The x-axis represents the number of rounds, while the y-axis indicates the number of data packets received. In Scenario 1 (Subfigure (a)), the packet sizes for all four schemes stabilize quickly within fewer rounds, with IZOACP achieving the highest data reception at 9410 bits, representing a 45.65% improvement over LEACH. In Scenario 2 (Subfigure (b)), the packet sizes increase linearly with the number of rounds, and IZOACP again outperforms the other schemes, reaching 155656 bits, which is a 93.88% improvement over LEACH. Overall, the figure demonstrates that IZOACP consistently achieves the highest data packet reception in both scenarios, highlighting its superior performance in enhancing data transmission efficiency in AWSNs. The clear color distinction and concise layout of the figure facilitate easy comparison of the four schemes.

Figure 7 presents a bar chart comparing the average network delay (in milliseconds) of four algorithms -- LEACH, DMaOWOA, ARSH-FATI-CHS, and IZOACP -- in two scenarios: Scenario 1 and Scenario 2. In Scenario 1, the average delays are 172.94 ms for LEACH, 167.49 ms for DMaOWOA, 159.37 ms for ARSH-FATI-CHS, and 155.40 ms for IZOACP, representing reductions of 10.12%, 7.23%, and 2.49% respectively compared to LEACH. In Scenario 2, the delays are 165.76 ms for LEACH, 163.91 ms for DMaOWOA, 154.82 ms for ARSH-FATI-CHS, and 153.92 ms for IZOACP, showing reductions of 1.12%, 6.60%, and 0.58% respectively compared to LEACH. The results show that IZOACP consistently achieves the lowest average delay in both scenarios, demonstrating its superior efficiency in minimizing network latency, while LEACH exhibits the highest delay, and DMaOWOA and ARSH-FATI-CHS perform moderately, with ARSH-FATI-CHS showing better performance than DMaOWOA. Overall, the chart highlights that IZOACP outperforms the other algorithms in reducing network delay, making it the most effective solution for improving data transmission responsiveness in WSNs.

Table 4 summarizes the network lifetime performance of several advanced clustering and relay node placement protocols across two different scenarios. SEP and Z-SEP, as traditional clustering protocols, achieve moderate network lifetimes of 217-714 rounds, reflecting their limited ability to balance energy consumption among nodes. MOCRNP and MOFF-RNP, which incorporate multi-objective relay node placement strategies using Firefly-based optimization, significantly improve network longevity by optimizing connectivity and coverage, achieving lifetimes of 299-1078 rounds. GAFOR further enhances energy efficiency through integrated clustering and relay node optimization, reaching up to 1153 rounds in Scenario 2. Among all the evaluated methods, the proposed IZOACP consistently outperforms the others, achieving network lifetimes of 355 rounds in Scenario 1 and 1286 rounds in Scenario 2. This demonstrates that the integration of zebra optimization, Gaussian mutation, opposition-based learning, and dynamic adaptive inter-cluster routing effectively balances residual energy, reduces intra-cluster distances, and improves communication efficiency. Overall, these results confirm that IZOACP provides a robust and energy-efficient framework for extending the operational lifetime of wireless sensor networks under diverse deployment scenarios.

Table 5 presents the results of the ablation experiments conducted to evaluate the computational overhead of different strategies employed in the IZOACP algorithm. The table compares the computational overhead (measured in seconds) for four different scenarios: the basic ZOA algorithm, ZOA augmented with Gaussian Mutation, ZOA augmented with Opposition-Based Learning, and a combination of ZOA with both Gaussian Mutation and Opposition-Based Learning. The experiments were conducted under two distinct scenarios (Scenario 1 and Scenario 2) to assess the impact of these strategies on computational efficiency. In Scenario 1, the basic ZOA algorithm had a computational overhead of 2.08 seconds. When Gaussian Mutation was added, the computational overhead increased to 2.73 seconds. The addition of Opposition-Based Learning alone resulted in a computational overhead of 2.16 seconds, while the combination of both Gaussian Mutation and Opposition-Based Learning led to a higher computational overhead of 3.27 seconds. In Scenario 2, the basic ZOA algorithm had a computational overhead of 20.64 seconds. With Gaussian Mutation, this increased to 23.15 seconds, while Opposition-Based Learning alone resulted in a computational overhead of 21.28 seconds. The combined strategy of Gaussian Mutation and Opposition-Based Learning had the highest computational overhead at 25.03 seconds. These results highlight the trade-off between the enhanced performance provided by the additional strategies and the increased computational overhead they introduce. The ablation experiments provide valuable insights into the efficiency and effectiveness of each strategy, aiding in the optimization of the IZOACP algorithm for practical applications.

Table 6 presents a detailed comparison of the scalability performance of various advanced protocols in terms of their ability to handle different numbers of nodes. The table includes eight protocols: LEACH, DMaOWOA, ARSH-FATI-CHS, SEP, Z-SEP, MOCRNP, MOFF-RNP, GAFOR, and IZOACP. The scalability is evaluated across four different node counts: 50 nodes, 200 nodes, 500 nodes, and 1000 nodes. The results show that IZOACP consistently outperforms the other protocols, achieving the highest scalability values across all node counts, with values of 355, 388, 426, and 462 for 50, 200, 500, and 1000 nodes, respectively. This indicates that IZOACP is particularly effective in maintaining high performance as the number of nodes increases. Other protocols such as GAFOR and MOFF-RNP also demonstrate strong scalability, with GAFOR achieving values of 319, 357, 391, and 429, and MOFF-RNP achieving values of 311, 348, 382, and 414 for the respective node counts. In contrast, protocols like LEACH and SEP show relatively lower scalability values, with LEACH achieving 191, 223, 258, and 289, and SEP achieving 217, 245, 278, and 307 for the respective node counts. This comprehensive comparison highlights the varying degrees of scalability among the protocols, with IZOACP emerging as the most scalable protocol in this study.

The proposed IZOACP protocol, despite its advantages, has some limitations. It has high computational complexity, which may reduce efficiency on devices with limited resources. Its adaptability to highly dynamic network environments with frequent node mobility and topology changes hasn't been fully explored. Also, while the protocol focuses on optimizing energy consumption and cluster head selection, its ability to handle multi-objective optimization scenarios that involve multiple performance metrics like energy consumption, latency, and network coverage hasn't been thoroughly investigated. Additionally, the integration of IZOACP with edge computing and machine learning for intelligent Internet of Things applications is still in the early stages and needs further research.