Quantum adaptive clonal genetic algorithm for low-energy clustering in agricultural WSNs

Abstract

Agricultural Wireless Sensor Networks (AWSNs) are essential for real-time monitoring in precision farming, yet their lifetime is severely constrained by limited node energy and the difficulty of battery replacement in large-scale deployments. This study proposes a Quantum Adaptive Clonal Genetic Algorithm (QACGA) to achieve energy-efficient clustering in AWSNs. The algorithm combines quantum-inspired adaptive operators with dynamic adjustments in cluster-head selection, mutation, and cloning rates, while integrating multi-objective constraints related to node distribution, residual energy, and communication distance. Simulation results demonstrate that QACGA consistently reduces energy consumption compared with established clustering algorithms, achieving savings of up to 38.1% relative to PSO, SFLA, and WOA, and also surpassing MRCH under equivalent conditions. In addition to lowering energy costs, QACGA improves clustering stability and extends overall network lifetime across diverse deployment scales. These findings highlight QACGA as a robust and practical optimization framework, providing new benchmarks for energy management in AWSNs and offering valuable insights for smart agriculture applications.

Introduction

An agricultural wireless sensor network (AWSN), a core component of the Internet of Things (IoT), provides solid support for the development of smart agriculture through real-time monitoring and data collection, and its importance is becoming increasingly prominent¹. Large-scale farmland monitoring networks are characterized by extensive coverage, long planting cycles, restricted energy supply, and variable environments². Achieving stable, reliable, and efficient data transmission and collection under these conditions has become a challenge in current research and applications³. At the same time, the wireless sensor network itself faces problems of limited node energy, high energy consumption, poor scalability of routing protocols, and low throughput⁴. Therefore, given the limited energy resources of sensor nodes, it is important to study how to extend the network life cycle while guaranteeing the quality of network information to improve the quality of environmental monitoring in agricultural wireless sensor networks^5,6.

As a key component of network data collection, the performance of routing protocols directly affects the overall performance of the network and has thus been a hot research topic in recent years^7–9. Various clustering methods have been proposed to address the resource-constrained characteristics of sensor networks. However, these methods often suffer from insufficient practical applications in the field, and most protocols are deficient in cluster head selection and life cycle management. Therefore, the design of low-energy clustering routing protocols for agricultural wireless sensor networks (AWSNs) has become a pressing issue.

To reduce the energy consumption of agricultural AWSNs, a new clustering model and heuristic algorithm, QACGA, is proposed in this paper. It utilizes the advantages of quantum adaptive operators and quantum computation to improve the performance of the algorithm and obtain an ideal cluster head selection scheme. The simulation results show that the QACGA-based clustering model outperforms the other AWSN methods in terms of energy consumption.

The main contributions of this paper are as follows:

1. A new cluster model for Agricultural Wireless Sensor Networks (AWSN) is proposed to solve the problem of excessive sensor transmission energy consumption in AWSN. The model optimizes the cluster head election process by introducing the cluster head competition radius parameter to reduce the communication distance between sensors, thus improving the communication transmission energy efficiency.

2. An adaptive mechanism was designed to improve the search efficiency of the clustering process. The mechanism considers the position of sensor nodes, residual energy, communication distance, and other key parameters, guides the evolution direction of the cloning operator and genetic algorithm, makes full use of the global search capability of the algorithm, avoids premature convergence, and falls into a local optimum.

3. Introducing a quantum computing mechanism to enhance the search ability of the optimal solution during cluster head selection. By introducing an adaptive rotational step mechanism, the quantum operation can guide the evolution direction and speed of the quantum chromosome in the quantum population update process, optimize the search efficiency of the solution space, and improve the accuracy of the algorithm. Compared with genetic algorithms, quantum search algorithms exhibit superior global search capabilities and enhanced exploration of the solution space.

The remainder of this paper is organized as follows: Sect. 2 introduces the work related to the AWSN clustering method; Sect. 3 shows the AWSN clustering model; Sect. 4 introduces in detail the QACGA method used for solving the AWSN clustering problem; Sect. 5 validates the effectiveness of QACGA in reducing energy consumption through simulation experiments and explains the experimental results in detail; and finally, Sect. 6 summarizes the conclusions of this study and discusses future research directions.

Related work

In AWSNs, routing protocols play a role in ensuring reliable data transmission between sensor nodes and aggregation nodes¹⁰. With the progress of science and technology, traditional simple protocols are gradually becoming unable to meet the increasing number of application scenarios^11,12. Therefore, it is necessary for people to combine routing protocols with the needs of specific applications. Therefore, a large number of protocols that meet these requirements have been proposed by scholars^13,14. According to the topology into which sensor networks are divided, current routing protocols are mainly divided into three categories: Flat, Hierarchical/Clustering, and Geographic^15–18.

Planar routing protocols have been designed for small-scale AWSNs in network architectures with a small number of nodes^19–21. However, they have limitations in terms of network latency, scalability, and energy consumption^22,23. Typical planar routing protocols include Flooding, SPIN, and Directed Diffusion (DD) protocols²⁴.

The hierarchical routing protocol is suitable for large-scale AWSNs, which divides the sensor nodes into two different levels: cluster head nodes and ordinary nodes. Ordinary nodes collect data and send it directly to the cluster head nodes of their respective clusters, which receive the sensed data, and then perform data aggregation and send it to the base station. Typical hierarchical routing protocols include LEACH, TEEN, HEED, and DEEC protocol^25,26. The low-energy adaptive clustering hierarchy (LEACH)²⁷ is the most widely used hierarchical routing protocol. It uses a roulette to elect cluster heads randomly and divides different rounds to rotate the cluster heads to balance the network energy consumption²⁸. However, it also has some limitations. For example, nodes with low residual energy may also be elected as cluster heads, the problem of unreasonable distance between the cluster heads accelerates the energy consumption of nodes, and network load balancing cannot be guaranteed²⁹.

Many parts of the clustering process are NP-hard problems. therefore, an increasing number of swarm intelligence optimization algorithms are applied to the clustering process. For example, PSO³⁰ is used in the clustering process and exhibits excellent performance owing to its advantages such as easy implementation and fast convergence. Hu and Yu introduced PSO^31,32 in the cluster head selection process of AWSN clustering, which improved the efficiency of node energy utilization in AWSNs. Singh incorporated the idea of uniform clustering into an octopus algorithm³³ to reduce node energy consumption. Suresh also applied the Fuzzy Firebug Swarm Optimization Algorithm³⁴ principle to the clustering process of AWSN to avoid the premature appearance of blind nodes. Wang proposed an energy-aware clustering algorithm that considers both intra-cluster distance and network energy consumption dimensions in the process of clustering using Ant Colony Optimization³⁵. Yao adapted the transfer operator weights of the Archimedes Optimization Algorithm³⁶ to transform the AWSN clustering problem into a nonlinear optimization problem, thereby proposing an improved particle swarm optimization algorithm (MPSO). The Mohan metaheuristic algorithm³⁷ was used to divide the nodes in the AWSN into clusters of varying sizes, and the size of the clusters was determined based on the distance of the nodes from the base station, which allowed more intra-cluster energy to be set aside and achieved the purpose of prolonging the network life cycle. The EEHCHR algorithm³⁸ integrates Euclidean distance, Fuzzy C-Means clustering, node residual energy and base-station proximity into a two-tier hierarchy (Direct and Central Cluster Heads) to cut energy use and extend network life; the EOCGS method³⁹ analytically computes the optimal cluster count and dynamically assigns Cluster Heads and Grid Heads via a fitness function based on residual energy, inter-node distance and grid-centroid location to boost energy savings, stability and coverage; and MRCH⁴⁰ builds on RCH-LEACH by embedding active-node residual energy into a percentage-based CH selection process—evaluated under varied base-station placements—to achieve marked gains in energy efficiency and network longevity.

Existing clustering methods for AWSNs still have room for improvement in terms of energy optimization and global search capability. To address these limitations, this paper proposes a new clustering model and heuristic method based on quantum computing and adaptive strategies. The proposed method aims to increase the convergence speed by introducing a novel adaptive strategy and multi-objective strategy and to improve the search capability of the solution space by introducing quantum computing methods. Thus, optimal clustering solutions were obtained. This study aims to fill the research gap in this area.

System model

In the application of AWSNs, the randomness of the cluster head selection of traditional algorithms leads to an uneven distribution of cluster heads in the network. The distribution of cluster heads in the network is too centralized, or electing nodes with less remaining energy as cluster head nodes can lead to rapid energy depletion, thus affecting the lifecycle and overall performance of the network. In this study, we designed a uniform clustering model for AWSNs and introduced the parameter values of node location, denseness, communication distance, and residual energy to design the probability of a node being elected as a cluster head in the process of cluster head election.

Network model

Agricultural monitoring sensor nodes were deployed in a two-dimensional planar coordinate area of farmland, including sensor nodes and base stations. The locations of these sensor nodes were randomly distributed within a specified area and then divided into multiple clusters of varying sizes using a clustering protocol, each with a cluster head node. The base station nodes, on the other hand, are located at a known location. All sensor nodes possess the same attributes, such as the initial energy, communication capability, and data fusion capability. Despite their identical attributes, each node has a unique ID, which is used to distinguish the other nodes. During the communication process, the position of the sensor node is fixed until the end of the communication. The base station can provide a steady supply of energy; therefore, we did not need to consider its energy consumption. However, sensor nodes have limited energy, and data transmission consumes energy and is not replenished. The nodes determine the distance and location information from the base station based on the magnitude of the received signal. A schematic diagram of the AWSNs network model is shown in Fig. 1.

Fig. 1.

AWSNs clustered network model.

Energy consumption model

AWSNs are deployed in the field farmland environment, where the shading effect on the wireless signals produced by the luxuriant branches and leaves of the crops is very obvious; therefore, the free-space fading model and multipath fading model in the general-purpose channel model are introduced. The energy consumption for data transmission is mainly in the transmitting circuit and power amplifier circuit, and the energy consumption for receiving data is mainly concentrated in the receiving circuit. QACGA adopts the energy model^18,41,42 proposed by the researchers.

The energy consumption expression for a node to send and receive bit data to and from a node at distance is given by Eqs. (1) and (2), respectively:

1

2

where is the length of the transmitted packet and . When , the power amplification loss adopts free-space mode, whereas when , it adopts multipath attenuation mode. , and are the energy consumption coefficients of the circuit amplifier in the two modes.

After successful cluster establishment, the member nodes send sensory data to the cluster head node, which identifies the received data, and then forwards the data to the base station.

Multi-objective fitness function

Network communication energy consumption and communication distance affects the performance of AWSNs, the shorter the sum of the distances between the cluster head and the nodes within the cluster the more uniform the distribution of the cluster head and the lower the energy consumption of the network, then the communication distance adaptation function in the network is shown in Eq. (3).

3

where denotes the coordinate value of the i-th node and  denotes the coordinate value of the cluster head node which is in the same cluster with that node.

The overall energy consumption of a network is the most important parameter for evaluating the performance of AWSNs. The overall communication energy adaptation function of the network is expressed by Eq. (4).

4

where,  denotes the energy consumption of the i-th node. It can be expressed as .

According to the communication distance adaptation function and network communication energy consumption adaptation function, the multi-objective adaptation function is shown in Eq. (5).

5

where and denote the evaluation constants used to evaluate the weights of the multi-objective fitness function, which was set as .

QACGA-based low energy clustering method for AWSNs

Quantum chromosome initialization

For an AWSNs with m nodes, where each node has and only has a unique ID¹⁷ in the network, the quantum chromosome coding for the clustering model can be expressed as Eq. (6).

6

where denotes the quantum chromosome of the i-th individual in generation . and denote the probability amplitude of a node being selected as a normal node “0” and a node being selected as a cluster head node “1,, " respectively.

The quantum chromosome was measured to obtain a binary chromosome, as shown in Eq. (7).

7

where denotes the binary code of the i-th individual and denotes the random collapse probability during the quantum measurement. The binary chromosome after quantum measurement is given by Eq. (8).

8

If the number of cluster heads is too low, the radius range of a single cluster will be too large, and the distance between nodes in the cluster and the cluster head and between the cluster head and the base station will be too large, which will lead to an increase in the energy consumption of all the nodes in the network, which in turn will affect the reliability and life cycle of the entire network. If the number of cluster heads is too high, it will lead to unnecessary network energy consumption, which will affect the performance and reliability of the network. The maximum number of cluster heads was set to M. The corrected binary chromosome is given by Eq. (9).

9

where  is bounded by the maximum number of cluster heads. If the number of cluster heads exceeds the maximum number of cluster heads, a new quantum measurement of the quantum chromosome is required.

Adaptive factors

The angle of the quantum rotating gate can guide the evolution direction of the population and affect the convergence speed of the algorithm, QACGA designed an adaptive rotation angle strategy, which can adaptively adjust the size of the rotation angle of the quantum rotating gate according to the evolution process, as shown in Eq. (10).

10

where denotes the minimum rotation angle, the maximum rotation angle, and the adaptive factor, as shown in Eq. (11).

11

where denotes the Hamming distance between the current individual and the current optimal individual , that is, the magnitude of the individual difference between the two binary strings.

In the iterative process of the population, with the number of iterations in the population of individuals in the adjustment of the magnitude tending to stabilize, the design of the adaptive iteration factor shown in Eq. (12).

12

where, denotes the maximum number of iterations. The adaptive selection probability is given by Eq. (13).

13

The adaptive catastrophe probability is shown in Eq. (14).

14

Population renewal

The quantum chromosome was updated using a quantum revolving door, as shown in Eq. (15).

15

where denotes the angle of rotation in the-direction, as shown in Eq. (16).

16

where is the direction of rotation of the quantum-revolving door, which ensures that the individual to be updated is rotated in the direction of the optimal individual.

An adaptive quantum catastrophe factor is introduced to enhance the global space search capability of the algorithm and prevent it from falling into local solutions. The chromosome quantum catastrophe process is given by Eq. (17).

17

where denotes the random catastrophe probability and denotes the boundary probability amplitude of the quantum chromosome to prevent the algorithm from falling into a local optimal solution at this point .

Use of clone pools to preserve globally optimal chromosomes and guide the direction of population iterations. The clone pool is updated as shown in Eq. (18).

18

where denotes the fitness function of the optimal chromosome after iteration and denotes the fitness function of the optimal chromosome before iteration. If the fitness value of the optimal individual after iteration is better than that of the optimal individual before iteration, then the optimal individual after iteration is saved in the clone pool, which is used to guide the iterative direction of the population.

The complete algorithm flowchart of QACGA is shown in Fig. 2.

Fig. 2.

Algorithm flowchart of QACGA.

Algorithm complexity analysis

Cloning, adaptive computing, and quantum computing are the main sources of complexity in the QACGA. The cloning operator designs a triple loop that includes the number of iterations, population size, and number of nodes, which results in the maximum computational complexity. The complexity of the cloning operator is given by Eq. (19).

19

where n denotes the number of chromosomes in the population.

The complexity of the adaptive operator consists of calculating the adaptive rotation step and adaptive catastrophe probability, which must be executed twice in each iteration. Complexity is given by Eq. (20).

20

The complexity is multiplied by because the Hamming distance between the current individual and optimal chromosome must be calculated.

The complexity of quantum computation involves updating the quantum probability amplitude of each individual. In each iteration, the quantum revolving door and quantum measurement are executed once, and the complexity is given by Eqs. (21).

21

The total computational complexity of QACGA is shown in Eq. (22).

22

The heuristic algorithms PSO, shuffled frog-leaping algorithm (SFLA), and Whale Optimization Algorithm (WOA) are commonly used for score-clustering models. The algorithmic complexity of the PSO is given by Eq. (23).

23

The algorithmic complexity of SFLA is shown in Eq. (24).

24

The algorithmic complexity of WOA is shown in Eq. (25).

25

The algorithmic complexity of QACGA is shown in Eq. (26).

26

Through the algorithm complexity analysis, the QACGA proposed in this paper is higher than PSO in terms of complexity and has the same algorithm complexity as SFLA and WOA. However, according to the simulation test, the algorithm performance of QACGA was better than those of PSO, SFLA, and WOA. The effectiveness of the QACGA was verified in complex scenarios with a large number of nodes.

Results and discussion

To validate the effectiveness of QACGA in clustering AWSNs, this study compares it with other state-of-the-art clustering methods, including WOA⁴³, PSO⁴⁴, SFLA⁴⁵, and MRCH⁴⁰. In this study, clustering experiments were conducted using the MATLABR2018b simulation platform. Mode testing was performed on a Windows 11 device equipped with a 12th generation Intel (R) Core (TM) i5-12400 F 2.50 GHz. The experimental data involved in this study are the averages of the results of 100 experiments. The environmental parameters used in the QACGA experiments are presented in Table 1.

Table 1.

Algorithm parameter setting.

Parameter	Value

The simulation was performed using a clustering method based on the QACGA, WOA, PSO, SFLA, and MRCH. In the QACGA, the number of iterations of the algorithm was 500, and the number of populations was 100. By contrast, in SFLA, the frog overview was 100, the number of populations was 10, the number of frogs in each population was 10, and the maximum step size was 40 m. In the WOA, the population magnitude was set to 100 and the number of iterations was 500. In PSO, the number of particles is 100, the individual acceleration constant is 2, the social acceleration constant is 2, the inertia weight is 0.9, and the number of iterations is 500. Table 2 presents the detailed simulation setup.

Table 2.

Simulation setup.

Sensor nodes	Cluster-head ratio	Area size
600	5%
700	10%
800	15%
900	20%

The cluster-head ratio was set to 0.05. The setup area was . The simulation results are shown in Fig. 3, representing cases with 600, 700, 800, and 900 sensor nodes. The cluster-head ratio is simply the proportion of nodes elected as cluster heads.

Fig. 3.

Variation of network communication energy consumption with 600 sensors.

In Fig. 3, 4, 5 and 6 shows the variation in network communication energy consumption in AWSNs after QACGA, WOA, PSO, SFLA, and MRCH clustering when the cluster-head ratio is 20%, and the number of sensor nodes varies with the number of iterations of the algorithm. From the simulation results, it can be seen that the QACGA reduces the energy consumption by 13.56%, 26.45%, 38.13%, and 2.2% compared to the WOA, PSO, SFLA, and MRCH, respectively. QACGA can obtain better results at the beginning of the iteration and still obtains a lower-energy-consumption clustering scheme as the number of iterations increases. This is due to the powerful global search capability of the QACGA quantum operator. The SFLA and PSO can reduce the energy consumption of the network at the early iteration stage, but they easily fall into the local optimal solution, which ultimately leads to stagnation of their evolution, and the final result is not ideal. The WOA, owing to the cyclic iterative idea, also optimizes the iterative process to search for the lowest energy-consuming clustering scheme; however, owing to its limited computational capacity, it leads to a lower evolutionary speed. is limited, resulting in a slow evolutionary speed. The MRCH, the imposition of constraints on auxiliary node parameters during cluster-head selection limits its global exploration capability, causing the optimization to converge more slowly toward the optimal head configuration in the initial iterations. Therefore, the QACGA can obtain the lowest energy-consumption clustering scheme at a faster speed when the number of nodes is small. When the number of nodes increases, QACGA uses the powerful solution space searching ability of quantum computing to obtain a clustering scheme with lower energy consumption than the comparison algorithm. This means that the QACGA is more energy-efficient with the same amount of transmitted data.

Fig. 4.

Variation of network communication energy consumption with 700 sensors.

Fig. 5.

Variation of network communication energy consumption with 800 sensors.

Fig. 6.

Variation of network communication energy consumption with 900 sensors.

Figure 7, 8, 9 and 10 show a comparison of network communication energy consumption with different clustering schemes when 800 to1100 sensor nodes are randomly deployed in a area. Variation in network communication energy consumption of AWSNs when the cluster head ratio was set to 5%, 10%, 15%, and 20%. When the cluster head ratio was 5%, the communication energy consumption of the QACGA was reduced by 1.52%, 3.70%, 5.24%, and 0.91% compared with the WOA, PSO, SFLA, and MRCH, respectively. At lower cluster head proportions, the energy performance of the QACGA clustering scheme differs significantly from those of the comparison algorithms, WOA, PSO, SFLA, and MRCH. This is because the QACGA uses adaptive factors to adjust the clustering scheme. When the number of cluster head nodes is small, QACGA can make full use of the nodes’ own position information, remaining energy consumption, and communication distance and use a multi-objective strategy for constraints to obtain the clustering scheme with optimal energy performance. At a cluster head ratio of 20%, the communication energy consumption of the QACGA was reduced by 0.22%, 1.26%, 1.54%, and 0.18%, compared with the WOA, PSO, SFLA, and MRCH, respectively. When the number of cluster heads is large, QACGA can still solve the optimal clustering scheme using its powerful search capability for quantum computing. The results show that QACGA can achieve lower network communication energy consumption and improve the life cycle of AWSNs with fewer cluster head nodes under the same environmental parameters.

Fig. 7.

Variation of network communication energy consumption with 800 sensors.

Fig. 8.

Variation of network communication energy consumption with 900 sensors.

Fig. 9.

Variation of network communication energy consumption with 1000 sensors.

Fig. 10.

Variation of network communication energy consumption with 1100 sensors.

Figure 11 shows the end-to‐end communication delay for five algorithms at cluster‐head ratios of 5%, 10%, 15%, and 20%. QACGA achieves the lowest delay in every case. At a 5% ratio, QACGA records about 1138 ms, compared with 1255 ms for MRCH and nearly 1300 ms for PSO, WOA, and SFLA. At 10%, QACGA drops to roughly 1140 ms, while MRCH and the other methods remain near 1157 ms and 1165 ms, respectively. Even at 20%, QACGA maintains the best performance at approximately 1079 ms versus 1086 ms for MRCH and 1095 ms for the meta‐heuristics. These results confirm that QACGA’s quantum‐inspired multi‐objective clustering and hierarchical routing significantly reduce communication delay across all tested configurations.

Fig. 11.

End-to-end communication delay for QACGA, MRCH, PSO, WOA, and SFLA at varying cluster-head ratios.

Table 3 shows that the network communication energy consumption of AWSNs varies with the deployment area when the number of nodes is 800 and the cluster head ratio is 5%. Table 2 shows the network communication energy performance of the QACGA, WOA, PSO, SFLA, and MRCH clustering schemes when the area varies from 200 m to 450 m. At the deployment area of , the communication energy consumption of QACGA is reduced by 1.99 µJ, 1.56 µJ, 0.98 µJ, and 0.33 µJ, compared with WOA, PSO, SFLA, and MRCH, respectively. When the deployment area is , the communication energy consumption of QACGA is reduced by 10.32 µJ, 7.42 µJ, 4.45 µJ, and 1.66 µJ, than WOA, PSO, SFLA, and MRCH, respectively. As the area increases, the communication distance between nodes increases, the distribution of nodes becomes sparse, and the difficulty in solving the AWSNs clustering scheme increases. From the results, it can be seen that QACGA is better overall than the comparison algorithms in terms of network energy consumption when nodes are dense. When nodes are sparse, QACGA’s clustering scheme has a lower energy consumption performance than WOA, PSO, SFLA, and MRCH. This is because the adaptive and cloning operators used by QACGA adjust the clustering scheme by considering the communication distance between nodes when the communication distance between nodes increases while using the cloning pool to preserve the optimal clustering result and directing the population to search for the optimal result. Using the powerful search capability of quantum computing, QACGA can avoid falling into local optimal solutions while searching for the optimal results. Compared with WOA, PSO, SFLA, and MRCH, QACGA has greater adaptability and lower network energy performance when changing the size of the deployment area, which is the ability to quickly configure QACGA cluster heads under different environmental conditions.

Table 3.

Variation of network communication energy consumption with deployment area.

Algorithm	200 m*200m	250 m*250m	300 m*300m	350 m*350m	400 m*400m	450 m*450m
SFLA	0.2393 J	0.2431 J	0.2474 J	0.2526 J	0.2570 J	0.2646 J
PSO	0.2389 J	0.2424 J	0.2461 J	0.2511 J	0.2559 J	0.2617 J
WOA	0.2383 J	0.2415 J	0.2447 J	0.2491 J	0.2539 J	0.2588 J
MRCH	0.2377 J	0.2409 J	0.2438 J	0.2478 J	0.2516 J	0.2559 J
QACGA	0.2374 J	0.2399 J	0.2428 J	0.2466 J	0.2499 J	0.2543 J

Figure 12 shows the box plots of the energy consumption of the QACGA, WOA, PSO, SFLA, and MRCH clustering schemes when the number of nodes was 800, the area was and the cluster head ratio was 0.05. From the results, it can be observed that the maximum value of the network energy consumption of the QACGA clustering scheme was still smaller than the minimum value of the comparison algorithms WOA, PSO, SFLA, and MRCH. This indicates that the communication energy consumption of the QACGA is better than those of the comparison algorithms WOA, PSO, SFLA, and MRCH. The QACGA has the smallest box, and the difference between the maximum and minimum values of network energy consumption is also the smallest, indicating that the robustness of the QACGA is the best compared to the WOA, PSO, SFLA, and MRCH. This is due to the multi-objective strategy introduced by QACGA, which takes the communication distance as a constraint while considering the overall energy consumption. With the adjustment of adaptive factors, the QACGA can achieve lower network energy consumption while maintaining better robustness. From the results, it can be seen that the complexity of the problem grows exponentially with an increase in the number of nodes, deployment area, and proportion of cluster heads, but QACGA still has a significant performance advantage over WOA, PSO, SFLA, and MRCH.

Fig. 12.

Box diagram of QACGA, WOA, PSO SFLA, and MRCH communication energy consumption.

Conclusions

AWSNs were evaluated as critical to smart agriculture, yet their deployment is hindered by substantial energy demands. Clustering approaches have been shown to alleviate energy constraints and extend network longevity. In this study, a quantum-inspired adaptive clustering algorithm (QACGA) was developed, incorporating node spatial coordinates, residual energy, and inter-node communication distance into a multi-objective optimization framework executed via quantum computation. The adaptive factor adjustment mechanism for cluster head selection enables balanced energy distribution and reduces total energy expenditure across the network. Comparative experiments demonstrated that QACGA outperforms WOA, PSO, SFLA, and MRCH in both energy efficiency and network robustness. By adapting a quantum-inspired genetic framework to the unique spatial heterogeneity and energy dynamics of crop-field deployments, the proposed QACGA delivers a flexible clustering solution that balances energy savings with communication reliability. The algorithm’s multi‐objective design provides practical guidelines for cluster‐head ratios, mutation/cloning dynamics, and environmental constraints, enabling seamless integration into real‐world AWSN deployments. Moreover, extensive evaluation under diverse network conditions establishes QACGA as a new performance benchmark for AWSN energy management and offers a clear roadmap for future precision‐agriculture IoT implementations. Notwithstanding these advances, current validation is limited to two-dimensional homogeneous AWSN models. Future work will extend QACGA to three-dimensional deployments, incorporate heterogeneous energy profiles, and optimize performance in anisotropic environments.

Author contributions

J.Z. conceived and designed the study. J.Z., B. L., and L. Z. performed experiments. J.Z., B. L., and L. Z. wrote the manuscript. J.Z., B. L., and L. Z. reviewed and edited the manuscript. J.Z., B. L., and L. Z. have read and approved the manuscript.

Funding

This research was funded by the Corps Guiding Scientific and Technological Plan Project(grant number 2023ZD055), Shihezi University Young Innovative Talent Program Project (grant number CXPY202204) and National Science and Technology Major Project (grant number 2022ZD0115800).

Data availability

The data presented in this study are available upon request from the corresponding author. The data are not publicly available because of privacy concerns.

Declarations

Competing interests

The authors declare no competing interests.