Low power energy balanced clustering routing scheme based on improved SSA and Multi-Hop transmission in IoT

Abstract

In the large scale monitoring application of the IoT, the power carried by a single sensor node is limited, and it may not be replenished in the later stage. Therefore, it is required that the sensor nodes should save power when working, and the power consumption among the sensor nodes should be balanced to avoid the early death of some nodes and the occurrence of monitoring blind spots in the monitor area. Communication is the main part of power loss for sensor nodes. For this reason, this paper introduces a new low power energy balanced clustering routing scheme. Firstly, the sparrow search algorithm is improved by adding adaptive sine function and Cauchy random number to raise the search capability of the discoverer; The standard normal distribution random number is used to enhance the vigilant escape from the limit of local optimal value. Then the enhanced SSA algorithm can be used for cluster head selection. A fitness function with five key parameters is constructed by using the residual energy, the member number within a cluster, the intra-cluster distance in a cluster, the distance among clusters, and the distance from cluster head to base station, which effectively realizes the energy consumption balance among sensors in each round. At the same time, in the data forwarding stage, the multi-hop forwarding rules are designed to further reduce energy loss, greatly delay the arrival of the first dead node, and keep the sensor node working in the low power mode for a long time. Experimental results show that this scheme not only significantly prolongs the sensor lifetime, but also balances the power consumption among sensor nodes. This scheme provides a new idea for IoT sensor nodes to work in low power and ultra long standby mode, especially suitable for large scale and long term deployment scenarios such as ecological monitoring and industrial equipment state perception.

Introduction

For the IoT, a diverse array of sensor devices is emerging in the market, all sharing a common characteristic: reliance on battery power¹. However, the capacity of these batteries is often limited. Thus, how can we extend the operational time of devices with constrained battery life? The most effective approach is to maintain low power consumption during operation. Consequently, low power technology plays a critical role in IoT applications. Minimizing energy consumption is essential for prolonging device lifespan and enhancing energy efficiency². As on-chip systems and integrated circuits continue to evolve, researchers have discovered that devices themselves do not require significant amounts of electricity for data processing and storage. Instead, it is communication among devices that accounts for the majority of energy consumption³.

Data communication technology encompasses two primary components: route discovery and data forwarding. Generally speaking, when deploying large scale networked devices, cluster routing tends to be prioritized⁴, as it demonstrates superior low power consumption and scalability compared to flat routing approaches. LEACH (Low-Energy Adaptive Clustering Hierarchy) represents one of the earliest clustering routing protocols and serves as a quintessential example of distributed routing methodologies. In LEACH, each sensor node has an equal opportunity to function as a cluster head over time. This strategy aims to distribute energy consumption evenly across all sensor nodes.

These concepts used to balance consumption and improve network lifetime have been adopted by subsequent protocols. The LEACH-C routing protocol serves as a representative of centralized clustering routing protocols. It employs a stochastic optimization approach, specifically Simulated Annealing (SA), to identify a relatively optimal set of cluster heads. Consequently, the cluster structure formed by these cluster head nodes effectively reduces energy consumption during data communication in each round. Both of these routing protocols have become classic low power solutions for the IoT. In the process of forming clusters and establishing forwarding routes, LEACH-C demonstrates significant advantages in energy savings compared to LEACH due to its implementation of optimization algorithms in every round. As a result, later researchers have sought to introduce various swarm intelligence optimization algorithms into clustering processes and analyze their performance concerning energy consumption balance and network lifetime extension. Furthermore, some scholars have endeavored to improve or enhance swarm intelligence algorithms or combine different search methodologies for more comprehensive studies on energy consume⁵. In addition, some researchers try to save energy in the data forwarding phase; thus, concepts such as relay nodes and multi-hop strategies have been successively proposed⁶. These innovative methods realize the expansion of the scale of the IoT, and make the application scenarios more diversified⁷.

This article adopts an improved Sparrow Search Algorithm combined with a multi-hop data forwarding strategy to develop a novel low power energy balanced clustering routing scheme. Its primary contributions include:

(1) It proposes an enhanced sparrow search algorithm. It adds adaptive sine function and Cauchy random number to the original sparrow algorithm, and their combination enhances the ability of the discoverer to expand the search range. In addition, it introduces the standard normal distribution random number to help the vigilant jump out of the local extreme value.

(2) It applies the improved SSA for cluster head selection. It also designs a fitness function containing five key factors, including remaining energy, number of members, intra-cluster distance, inter-cluster distance, and distance from cluster heads to BS. This method can not only ensure that a group of cluster heads with minimum total energy loss are selected, but also in each round effectively balance the energy loss among sensors.

(3) It introduce the concept of relays and establish selection criteria for multi-relay configurations. The algorithm can adopt a multi-hop mode to further reduce energy consumption. It also verifies the operational advantages of our proposed scheme in prolonging network lifetime and balancing energy consumption under different initial energy and deployment area. It provides a feasible low power routing scheme for large scale monitoring of the IoT.

This paper is structured as follows: Section “Related Work” provides an overview of existing research for low power energy balanced clustering routing methods. We analyze and compare these literature, and put forward our own scheme. In “Methods”, we firstly give the improvement of SSA and then applied it to clustering. By designing a fitness function with five key parameters, a set of optimal cluster heads are selected. In addition, we have also designed multi-hop forwarding rules. The “Results” section demonstrates our algorithm’s effectiveness through experimental comparisons with four other algorithms in network lifetime and energy balance. In the “Discussion” section, we discussed the scalability of the scheme and provided validation for different initial energies and region areas. Finally, we summarize our findings and propose future research directions.

Related work

Traditional internet routing algorithm designs often prioritize the most efficient path for data forwarding, with minimal consideration given to energy loss. In the context of limited energy resources in sensor nodes within the IoT, it is essential to prioritize energy factors when designing routing protocols in order to extend network lifetime^8,9,10. Consequently, some designed routing protocol must account for router paths that minimize power loss while also ensuring balanced energy usage for the entire network^11,12.

Many researchers try to utilize swarm intelligence optimization algorithms or their improved algorithms to solve the cluster head selection and clustering problems in cluster routing protocols. For instance, Chang et al.¹³ propose a clustering protocol that integrates an improved Artificial Fish Swarm Algorithm (IAFSA) with Fuzzy C-means (FCM). This approach first enhances both the search space and step size of the artificial fish swarm algorithm before employing FCM to identify cluster centers and select an optimal set of cluster heads. It does not consider the energy consumption balance among nodes when selecting cluster heads. Wang et al.¹⁴ introduce a clustering routing scheme based on the Artificial Bee Colony (ABC) algorithm. This protocol incorporates factors such as cluster head energy, position, and centripetal rate into ABC theory, optimizing both cluster head quality and overall clustering effectiveness; thus balancing node energy consumption while extending network lifespan. However, it does not consider the distance between clusters when selecting cluster heads. In another study¹⁵, an enhanced version of the ABC algorithm is proposed for planning relay node deployment aimed at prolonging network longevity. Additionally, Yu et al.¹⁵ present a novel dynamic search balance strategy within this framework. However, the effectiveness of the algorithm in larger scale deployment needs to be further verified. A routing algorithm for Wireless Sensor Networks (WSNs) based on Cuckoo-optimized K-means is proposed¹⁶. During the clustering stage, the Cuckoo algorithm is initially employed to choose the initial cluster centers, followed by clustering calculations using K-means. In the data transfer process, in conjunction with the Cuckoo algorithm, it devises an energy-efficient route for the cluster head. This routing design fully leverages the optimization capabilities of Cuckoo search. The CS-K algorithm effectively maintains low-power operational modes. An energy-optimized bat algorithm known as ECO-BAT is introduced to identify an optimal set of cluster heads for clustering purposes¹⁷. When implementing this algorithm, not only is the maximum distance between Cluster Heads (CHs) and their respective members considered, but also the remaining energy levels of CH candidates are taken into account. It focuses on cluster heads selection, and adopts single hop mode during the data transmission phase. Qiu et al.¹⁸ have improved the original SSA by introducing chaotic initialization, sine cosine mutation, and adaptive population adjustment strategy, and applied it to the selection of cluster heads to ensure that a set of optimal cluster heads is selected. This method can effectively reduce energy loss by 26.8%. Sun et al.¹⁹ propose an Improved SSA (ISSA), which utilizes adaptive t-distribution for cluster head selection within a clustering routing framework. The results indicate that this improved SSA significantly enhances the distribution of cluster head selection in accordance with LEACH protocol principles and effectively reduces overall network energy loss. However, its effectiveness of the improved algorithm needs to be verified on more test functions. Yang et al.²⁰ enhance the original Butterfly Optimization Algorithm (BOA) by introducing a nonlinear dynamic convergence factor and Circle chaotic mapping to regulate parameter values; this modification improves both optimization speed and convergence accuracy of BOA while endowing it with stronger search capabilities. Ultimately, this refined Butterfly Optimization Algorithm (IBOA) addresses issues related to random selection of cluster heads and enables a comprehensive identification of more optimal cluster head nodes. He et al.²¹ propose a strategy that builds upon an improved Sine Cosine Algorithm (SCA). This enhancement utilizes an inertia weight factor, resulting in a refined sine cosine algorithm. The improved algorithm facilitates node position updates, ultimately leading to a more optimal set of cluster head. However, the design of its inertia weight factor needs to be further optimized. Sun et al.²² proposed a WSN clustering routing optimized by firefly algorithm. This method uses the firefly algorithm enhanced by chaos optimization technology to cluster the network nodes for balancing the load of nodes. It proposes to select two cluster heads in each cluster. The primary cluster head is responsible for data collection and fusion, and the secondary cluster head is responsible for data transmission. However, it does not pay attention to the residual energy during building clusters. Kiamansouri et al.²³ proposed a two-level clustering based on fuzzy logic. In the first level clustering, several parameters are applied: energy, node capacity and neighbor number. In the secondary clustering, the centrality formula is used to select the super cluster head node. The algorithm tries to make the cluster structure as uniform as possible. However, from the experimental results, the energy consumption of each round fluctuates greatly. He proposed an efficient periodic cluster head selection strategy based on three key factors: neighbors, residual energy, and inter-cluster distance, but the first dead node appeared earlier.

Several researchers have employed various swarm intelligence optimization algorithms to enhance cluster structures. During the process of forming clusters, self-organizing neural network mapping (SOM) is initially utilized to group sensor nodes; subsequently, an improved Grey Wolf Optimization (GWO) method is applied to determine the optimal cluster head selection²⁴. However, it does not consider the distance between clusters in the process of rebuilding clusters. Zhao et al.²⁵ introduce a heterogeneous sensor network routing protocol known as SA-MGWO (SA-modified Grey Wolf Optimizer), which integrates Simulated Annealing (SA) with an enhanced GWO approach. This protocol dynamically adjusts prey weights within the GWO framework and employs SA for selecting an optimal set of cluster heads. However, it can be improved in achieving energy balance among nodes. Dai et al.²⁶ propose a non-uniform clustering protocol based on an enhanced firefly algorithm optimized back propagation neural network. By introducing weight factors and incorporating four evaluation indicators within the firefly algorithm, they achieve a balanced intra-cluster load and reduce communication distances among clusters. When combined with the BP neural network, the methods for path selection and cluster head election are optimized to attain superior clustering performance. But its time complexity is a little high. Sefatiet et al.²⁷ employ a black hole algorithm for path planning alongside an ant colony optimization (ACO) algorithm for search routing, effectively merging the strengths of both approaches to enhance network longevity. However, the algorithm does not consider the size of clusters when selecting cluster heads. Vikhyathet et al.²⁸ introduce CIOO for cluster head selection in each round utilizing Osprey and Chimp Optimization algorithms, thereby fully capitalizing on their respective advantages. The algorithm saves node energy to a certain extent, however it does not consider the energy balance among nodes. Zhao et al.²⁹draw from Beetle Antennae Search and Whale Optimization Search methodologies to establish data forwarding paths formed by clustering that minimize energy consumption. However, it only cares the distance to BS. K-medoids integrated with an improved artificial bee colony (ABC) algorithm is utilized for cluster formation³⁰, followed by proposing a cross-layer Harris hawks optimization route. However, its energy consumption cannot be fully minimized. Ajmi et al.³¹present MWCSGA, which combines swarm cooperative optimization (SCO) with genetic algorithms (GA), also introducing concepts such as multi-weight clustering models. However, it still has high energy consumption. This paper³² is based on genetic algorithm (GA) and BS location to look for the best cluster head. For the high-level routing between cluster heads, the so-called onion method is defined to reduce the overhead between cluster heads. This method effectively prolongs the lifetime of a single sensor node, but it can be further improved in terms of energy balance among nodes and the whole network life cycle. Akbari et al.³³ proposed a cluster head selection method based on distance, residual energy, received signal strength and link expiration time. Simulation results show that it is good in packet delivery rate, delay, response time and network lifetime. However, it is only verified in a small range of node deployment, lacking more data support. Hameed et al.³⁴ proposes a scheme based on cuckoo algorithm and sensor device scheduling mechanism. It uses DBSCAN^34,35 algorithm in the clustering stage, which is relatively early and has strong limitations, the first dead node appeared earlier in the algorithm. Idrees et al.³⁶ proposes EL-RPL routing protocol and a PP algorithm for load balancing. For saving energy, it fully considers residual energy and the number of packets received by its parent node during selecting the relay node. But the algorithm is also limited to the original hierarchy.

In the data forwarding stage, scholars strive to further reduce energy consumption by integrating relay nodes and multi-hop strategies. Zhang³⁷proposes a cellular virtual grid wireless sensor network (WSN) clustering method employing multi-hop routing techniques; this involves single-hop communication within clusters while utilizing mixed hops between them to optimize path planning, resulting in significant reductions in energy expenditure compared to traditional algorithms. But its first death node appeared earlier. Xu³⁸ introduces threshold correction multi-hop routing wherein energy levels and relative distances are employed to calculate moderation factors for cluster heads during inter-cluster multi-hop routing stages. Compared to conventional LEACH routing protocols, TCCR routing effectively prolongs the onset of node depletion and improves data transmission efficiency. However, the energy balance performance of this algorithm is relatively poor. Zhang et al.³⁹ propose a fuzzy control based clustering routing algorithm FCRA, which incorporates a fuzzy controller for cluster head election based on node distance and residual energy to determine the probability of a node being selected as a cluster head. The data transmission employs an inter-cluster multi-hop mode, with the next hop relay node identified through the weight function associated with each transmission path. The algorithm performs well in prolonging the network life cycle. Jin et al.⁴⁰ introduce the LEACH-DC hierarchical multi-hop routing protocol that utilizes dual cluster heads, effectively addressing data conflict issues and further extending lifespan. he effectiveness of the algorithm needs to be further verified in different environments. Miao et al.⁴¹ present a multi-hop method known as MRGK, which integrates genetic algorithms and K-means clustering techniques. This approach optimizes candidate relay node selection by considering factors such as remaining energy levels, member counts, and forwarding numbers to select an appropriate next hop relay while preventing potential failures of relay nodes due to excessive or insufficient forwarded data volumes. However, its relay node selection rules need to be improved. Tian et al.⁴² propose an energy-efficient multi-hop multi-path protocol called EMHMP based LEACH principles. In this scheme, when forwarding data packets, relay nodes are chosen according to criteria including average remaining energy along paths, minimum hops required for data transmission, and packet sizes involved in communication processes. The optimal data transmission path is selected from a backup routing table before transmitting information to the base station. However, its energy efficiency balance ability is general. Ye et al.⁴³ introduce an improved LEACH protocol termed LEACH-CIE. During data transmission phases within MFRCRE (Multi-hop Forwarding Routing Considering its own residual energy), various factors such as energy consumption rates and communication distances are taken into account when designing conditions for node forwarding. However, the failure node appeared earlier. Nodes compute the weights of cluster heads based on neighbor distribution and their own energy levels⁴⁴, taking turns to select cluster heads. During the data forwarding stage, a routing scheme is designed utilizing the Particle Swarm Optimization (PSO) algorithm to avoid including nodes with lower energy in the transmission path, thereby enhancing the energy efficiency of inter-cluster data transmission. However, it may be improved in improving network lifetime and throughput. Djéné et al.⁴⁵ propose a multi-hop clustering scheme that incorporates lightweight blockchain technology, which enhances the operational lifespan, scalability, load balancing, and packet transfer capabilities of WSNs by rotating the responsibilities of cluster heads among different nodes within each cluster. However, the algorithm needs authentication proof of blockchain technology. Lv et al.⁴⁶ introduce a method for monitoring residual energy in sensor nodes based on a multi-hop clustering algorithm. This approach utilizes a multi-hop mechanism for packet transmission via cluster heads while implementing global updates and modifying heuristic factors to determine the minimum energy loss router from the cluster head to BS. The algorithm also needs further optimization to improve the convergence speed.

SSA is a new heuristic algorithm with a simple structure, easy implementation, and strong search ability. At present, this algorithm and improved algorithms have been widely applied in various fields. We applied the improved algorithm to cluster head selection, attempting to find a cluster head set with the least energy consumption in each round. In addition, we also found that when the network is deployed on a large scale, the distance between clusters is still relatively long. At this time, selecting relay nodes and multi-hop can further reduce energy consumption. So we propose an improved Sparrow Search Algorithm combined with a multi-hop data forwarding strategy to develop a novel low power energy balanced clustering routing.

Methods

Improved sparrow search algorithm

The SSA⁴⁷ was mentioned firstly by Xue and Shen from Donghua University in 2020. This algorithm simulates the collective intelligent predation behavior of sparrows. The algorithm divides sparrows into discoverers and followers. Discoverers can actively seek food sources, while followers obtain food based on the discoverers. Their identities can be exchanged, and they all have the potential to act as warning agents. The mathematical representation of the population formed by sparrows is provided in Eqs. (1)-(2). Here, d represents dimension, n denotes sparrow number, f indicates the fitness value.

(1)

$${F_x}=\left[ {\begin{array}{*{20}{c}} {f([\begin{array}{*{20}{c}} {x_{1}^{1}}&{x_{1}^{2}}& \cdots &{x_{1}^{d}} \end{array}])} \\ {f([\begin{array}{*{20}{c}} {x_{2}^{1}}&{x_{2}^{2}}& \cdots &{x_{2}^{d}} \end{array}])} \\ {\begin{array}{*{20}{c}} {}& \cdots &{}&{} \end{array}} \\ {f([\begin{array}{*{20}{c}} {x_{n}^{1}}&{x_{n}^{2}}& \cdots &{x_{n}^{d}} \end{array}])} \end{array}} \right]$$

(2)

In SSA, the discoverers provide predatory direction for all followers. The position update description for discoverers are expressed in Eq. (3):

(3)

$X_{{i,j}}^{t}$ is position in the t iteration. $\alpha$ is a random number, and $\alpha \in \left( {0,1} \right]$. ${T_{\hbox{max} }}$ is the maximum iteration number. R is a random number that follows a normal distribution. L is a matrix of $1 \times d$. The value of each element is 1. ${R_2}$ represents the warning value,${R_2} \in [0,1]$.$ST$ represents the safety value, $ST \in [0.5,1]$.

When ${R_2}<ST$, it means that no predators are found around the discoverer, and the discoverers are relatively safe and can perform a wide range search. While the new position of the original algorithm is related to the population number i. As i increases, the range of values for the algorithm gradually narrows. This approach is not conducive to population diversity, as illustrated in Fig. 1(a). In contrast, the improved formula incorporates a sine function and is dependent on the number of iterations, as presented in Eq. (4). Its value range progressively expands with an increasing number of iterations. The significance of this approach lies in its ability to retain previous optimal values while simultaneously enhancing both search range and diversity, as demonstrated in Fig. 1(b).

Fig. 1

(a) Population value. (b) Iteration value.

(4)

When ${R_2} \geqslant ST$, this indicates that a predator has been detected and an alert has been issued to other sparrows, who must quickly flee toward other safe places. While the original SSA algorithm employs a standard normal distribution for positional updates. The enhanced SSA modifies this approach by utilizing a Cauchy distribution instead, as shown in Eq. (5). The original SSA relies on random numbers drawn from a standard normal distribution; consequently, its variation factor range is depicted in Fig. 2(a). In comparison, the improved algorithm utilizes random numbers derived from a Cauchy distribution; its variation factor range is displayed in Fig. 2(b). It becomes evident that this enhancement significantly broadens both value ranges and search space.

Fig. 2

(a) Standard normal distribution. (b) Cauchy distribution.

(5)

Figure 2(a). Standard normal distribution Fig. 2(b). Cauchy distribution.

The iterative formula governing position updates for discoverers for improved SSA algorithm is outlined in Eq. (6). Prior to each iteration, this enhanced SSA first ranks fitness functions from previous populations, selecting only the top 30% as discoverers while designating the remaining 70% as followers with an established safety threshold set at 0.6.

(6)

For followers in the region, they follow the discoverers’ position, and their position update through Eq. (7):

$$X_{{i,j}}^{{t+1}}=\left\{ \begin{gathered} R \cdot \exp (\frac{{X_{{worst}}^{t} - X_{{i,j}}^{t}}}{{{i^2}}}),i>n/2 \hfill \\ X_{p}^{{t+1}}+\left| {X_{{i,j}}^{t} - X_{p}^{{t+1}}} \right| \cdot {A^+} \cdot L,i \leqslant n/2 \hfill \\ \end{gathered} \right.$$

(7)

$X_{{worst}}^{t}$ is the worst location of current population globally. $X_{p}^{{t+1}}$ denotes current optimal locations identified by discoverers. A is a matrix of $1 \times d$, where its element is randomly distributed 1 or − 1, and ${A^+}={A^T}{(A{A^T})^{ - 1}}$.

Warners are randomly assigned within a population. Their positions update are described as follows in Eq. (8).

$$X_{i}^{{t+1}}=\left\{ \begin{gathered} X_{{best}}^{t}+\beta .\left| {X_{i}^{t} - X_{{best}}^{t}} \right|,{f_i} \ne {f_g} \hfill \\ X_{i}^{t}+K.(\frac{{\left| {X_{i}^{t} - X_{{worst}}^{t}} \right|}}{{({f_i} - {f_w})+\varepsilon }}),{f_i}={f_g} \hfill \\ \end{gathered} \right.$$

(8)

$X_{{best}}^{t}$ is current global optimal position. $\beta$ is a random number that follows a normal distribution with a mean of 0 and a variance of 1. ${f_i}$ is the current fitness value, and ${f_g}$ and ${f_w}$ are the current global best and worst fitness values. And K is a random number between $[ - 1,1]$. $\varepsilon$ is a very small constant.

When ${f_i} \ne {f_g}$, a uniform random distribution is used as the watchman. The algorithm takes values between $[0,1]$, as shown in Fig. 3(a). After improvement, by replacing it with a standard normal distribution $\delta$, the range of values can be increased to$[ - 2.58,2.58]$, as shown in Fig. 3(b). Its function is to jump out of the current extreme. The improved vigilante formula is shown in Eq. (9). In the article, the warning randomly selected 40% nodes from each population.

Fig. 3

(a) Uniform random distribution. (b) Standard normal distribution.

$$X_{i}^{{t+1}}=\left\{ \begin{gathered} X_{{best}}^{t}+\delta .\left| {X_{i}^{t} - X_{{best}}^{t}} \right|,{f_i} \ne {f_g} \hfill \\ X_{i}^{t}+K.(\frac{{\left| {X_{i}^{t} - X_{{worst}}^{t}} \right|}}{{({f_i} - {f_w})+\varepsilon }}),{f_i}={f_g} \hfill \\ \end{gathered} \right.$$

(9)

Test of improved sparrow search algorithm

To measure the feasibility and effectiveness for improved SSA, we test it with original algorithm. This article uses MATLAB for experiments, running on a 64 bit Windows 11 operating system. The common parameter settings for the algorithms in the simulation program are: population size = 30, maximum iteration times = 500, spatial dimension = 30. Six classic test functions are introduced in the experiment, as shown in Table 1. Among them, F1-F3 are unimodal functions, and local optima is global optima, commonly used to test the convergence speed and optimization accuracy; F4-F6 are multimodal functions with multiple local extrema, commonly used to test the algorithm’s ability to escape from local optima and explore globally. To reduce experimental randomness, 50 times independent experiments were conducted on each test function. The test results in Fig. 4; Table 2.

Table 1 Test function.

Fig. 4

(a) The convergence curve of F1 (b) The convergence curve of F2. (c) The convergence curve of F3. (d).The convergence curve of F4. (e) The convergence curve of F5. (f) The convergence curve of F6.

According to Table 2, in the unimodal test function, the convergence accuracy of the improved SSA is superior to the original algorithm, especially for functions F1 and F2, where the improved algorithm can achieve the theoretical optimal value. For function F3, although it did not reach the theoretical optimal value, it still reached the order of magnitude of E- 04. In the multi-modal test function, the convergence accuracy of the improved algorithm is also better, especially for functions F4 and F6, which have reached the theoretical optimal value; Although function F5 did not reach the theoretical optimum, its convergence accuracy reached the order of E- 16. From the perspective of convergence speed, F3, F4, F5 and F6 can all converge to a certain optimal value at a very fast speed. In the comparison of variances, F1, F2, F4, F5 and F6 reaches all 0, which proves that the stability of improved SSA is also fine.

Table 2 Test result.

Cluster head election algorithm

(1)Set of candidate cluster head nodes.

Before starting in every round, a group of candidate cluster heads is constructed, its elements in the set are composed of the high energy nodes. In each round, calculate the times a surviving sensor can be used as a cluster head according to Eq. (10), denoted as CHNumbers, and sort them in descending order by CHNumbers.

(10)

$E(i)$ represents current node energy. ${E_{CH}}$ represents average energy consumption when serving as a cluster head. It includes energy consumption from receiving members, data fusion, and transferring to BS.

①. Before a dead node appears, select the top 40% of nodes with larger CHNumbers as high-energy nodes;

②. After a dead node appears, select the top 25% of nodes with larger CHNumbers as high-energy nodes.

(2)The optimal number for cluster heads.

Generally, in each round there is an approximate optimal number for cluster heads, which can keep the lowest energy consumption. Here, the optimal number is shown in Eq. (11):

$${K_{{\text{opt}}}}=P*{N_{alive}}$$

(11)

(3)Initial population.

The population Q initialization is determined via randomly choosing ${K_{{\text{opt}}}}=p*{N_{alive}}$ cluster heads from the candidate set, a total of q times.

(4)Fitness function.

The fitness function of algorithms consists of the following five parts in Eq. (12):

$$F={F_1}+{F_2}+{F_3}+{F_4}+{F_5}$$

(12)

The fitness function fully considers the distance from member to cluster heads, from cluster heads to BS, and member numbers in a cluster. It makes the energy loss of each round as balanced as possible, prolongs the running lifetime as much as possible, and delays the arrival of the first dead node. Wherein, ${F_1} - {F_5}$ factors are respectively shown in Eqs. (13)-(17).

(13)

N represents the total nodes. ${K_{opt}}$ represents cluster heads or clusters number at each round, and ${m_i}$ represents member numbers in i-th cluster. ${F_1}$ is the standard deviation of member numbers in a cluster. It tries to make member numbers in each cluster as close as possible, making the distribution of cluster structures more uniform.

(14)

${d_{ijtoCHj}}$ is the distance among the i-th member of the j-th cluster head. ${m_{ij}}$ is member numbers in j-th cluster. ${F_2}$ is average standard deviation of the squared distance between members and cluster head. It strives to ensure that the distance from members to cluster head is consistent.

(15)

${d_{toBS}}$ is the distance from any node to BS. ${d_{CHitoBS}}$ is the distance from i-th cluster head to BS. Its function is to make the distance from cluster head and BS significantly different. It can enable cluster heads to be distributed in various positions within the region.

(16)

M is the edge length of the region. ${d_{CHitoCHj}}$ is the distance from i-th cluster head to j-th cluster head. This function ${F_4}$ helps to distribute cluster heads evenly in the region.

(17)

${d_{itoCH}}$ represents the distance between i-th cluster member and its cluster head. ${F_5}$ is the average of the sum of squared distances from all members to cluster head. This can reduce the distance between members and cluster head.

(5)Cluster head election.

The improved SSA is applied to cluster head selection, which is called LEACH-SSA. Cluster head election refers to the use of improved SSA algorithm and its fitness function to update the position of a population, with a total of iterations, ultimately electing a set of individuals with the least power dissipation. When performing position updates, the improved SSA algorithm reorders individuals based on their own fitness function, selecting top 30% of individuals with a smaller fitness function to update according to Eq. (6), the remaining 70% of individuals to update according to Eq. (7), and randomly selecting 40% of all individuals to update position according to Eq. (9). Steps of Cluster head election algorithm can be summarized in algorithm LEACH-SSA.

(6)Cluster formation algorithm.

During cluster formation, it is to first select cluster head and then form cluster structure. The member nodes in the range will select its cluster head closest to them to cluster together.

(7)Time complexity.

The time for constructing the candidate cluster head set is O (N_alive), and the time for clustering is O (N * Kopt). The time for iteratively selecting cluster heads is O (Q * Tmax), so the time for each round is O (N_alive+N * Kopt + Q * Tmax), which means the maximum time complexity is O (N²). In addition, the assumption of our algorithm is that the energy of the BS is infinite, and all calculations are completed by the BS and then transfered to terminal sensor nodes execution. So there is no need to consider the energy loss caused by calculations. Another issue is that our data transmission may take a long time to be executed once, such as in long-term ecological environment monitoring applications, where we have a high tolerance for the time required for early routing formation.

Data forwarding algorithm

(1)First-order radio model.

In general, when discussing the energy consumption of routing transmission protocols, we adopt first-order Radio communication mode in Fig. 5. The parameters used in the communication model are shown in Table 3. There are three types of energy consumption by nodes: sending data, receiving data, and fusing data. Their calculation formulas are as follows in Eqs. (18)-(20). It is obvious that energy drained by a node is related to transmission length and the amount of data transmitted.

Fig. 5

First-Order Radio Model.

Table 3 Model parameters.

(18)

(19)

(20)

(2)Data forwarding.

There are three types of data transmission methods, direct transfer, single hop transfer, and multi hop transfer in Fig. 6.

Fig. 6

Transmission methods.

Direct transmission refers to member nodes transfer data directly to cluster head, and cluster head node forwards data directly to BS. This transmission method is very suitable for situations where the distance among nodes is relatively close or the regional range is relatively small. Here, The direct transmission method is shown in the Eq. (21).

(21)

Multi-hop transmission refers to the process of forwarding data through multiple intermediate nodes. This approach is particularly suitable for scenarios where the distance between nodes is relatively long or when the area covered is extensive. In this context, multi-hop transmission can facilitate data transfer from cluster heads to BS. Building upon LEACH-SSA, if a single-hop data transmission method is employed, we refer to it as the LEACH-SSSA algorithm. Conversely, if a multi-hop data transmission method is utilized, it is designated as the LEACH-MSSA algorithm. The criteria for selecting relay nodes are outlined in Eq. (22).

Single-Hop: Data forwarding occurs exclusively through one intermediate relay node. That is there is only one relay node from cluster head to BS.

Multi-Hop: Data forwarding traverses multiple intermediate relay nodes. That is there may be multiple relay nodes from cluster head to BS, and the number is uncertain.

(22)

Results

Parameter settings

In this study, algorithms are programmed and simulated using MATLAB 2023. We will compare five algorithms—LEACH, LEACH-C, LEACH-SSA, LEACH-SSSA, and LEACH-MSSA.We use three metrics to measure and compare the effectiveness of algorithms: including clustering structure, network lifetime, and energy consumption balance. The parameter settings in Table 4.

The simulation experiment was conducted in a 200 * 200 monitoring area, with 200 sensor nodes randomly deployed, each carrying an initial energy of 0.5 joules. The base station is located outside the monitoring area, and the two are far apart. Assuming the probability of the optimal number of cluster heads in each round is 0.05. In cluster head elections, the population size is 15 and there are 20 iterations.

Table 4 Parameters and values.

Clustering and data forwarding structure

Initially, the LEACH-SSA algorithm selects cluster heads. Subsequently, other member nodes identify and select the nearest cluster head to build their respective clusters. During data transfer process, member nodes send their data directly to their corresponding cluster head nodes; this direct approach is feasible because distance considerations have already been addressed during clustering. Members are chosen based on proximity to their closest cluster head; thus this distance tends to be relatively short enough for direct transmission, as illustrated in Fig. 7(a).

Fig. 7

(a) Clustering diagram and direct transmission. (b) Clustering diagram and single-hop forwarding. (c)Clustering diagram and multi-hop forwarding.

During the process of transmitting data from cluster heads to BS, the uncertainty associated with this distance allows for both direct transmission and multi-hop data transmission. When the distance from cluster head to BS is less than${d_0}$, direct transmission can be used. If it is relatively long, relay nodes can be used for forwarding. As illustrated in Fig. 7(b), only one relay node is selected for certain cluster heads; whereas in Fig. 7(c), multiple relay nodes can be chosen for forwarding tasks related to cluster head nodes. It is evident from Fig. 7(b) and Fig. 7(c) that these schemes have thoroughly considered the impact of distance on data transmission, resulting in a more uniform clustering structure in LEACH-SSSA and LEACH-MSSA compared to that observed in the directly transmitted LEACH-SSA algorithm.

Network lifetime

In IoT applications, it is crucial to delay the onset of the first dead node as much as possible since once a node depletes its battery, it creates a monitoring blind spot which compromises reliability in monitoring tasks. Furthermore, there is an emphasis on achieving prolonged operational time across the entire network rather than focusing solely on individual or select nodes’ performance; ultimately requiring all nodes within the network to collaborate effectively to complete monitoring tasks efficiently. In other words, energy consumption must be balanced throughout each round of operation. Here, the rounds in which the first dead node occurs is defined as the lifetime. If 80% nodes die, monitoring has become very unreliable, and we believe that the operation of the network is over. The lifetimes associated with various algorithms currently implemented within our network are summarized below in Table 5.

FND (First Node Dead): This refers to the rounds in which the first node dies.

HND (Half Node Dead): This indicates the rounds when 40% of nodes are dead.

LND (Last Node Dead): This denotes the rounds at which 80% of nodes have died.

Table 5 The lifetime of various algorithms.

Figure 8 presents a graph generated from Table 5, illustrating the cumulative number of dead nodes across each round. It vividly reflects the lifetime and energy consumption patterns of different algorithms. From both Table 5; Fig. 8, it is evident that LEACH-SSA experiences its first dead node later than both LEACH and LEACH-C, suggesting that improved SSA algorithm offers advantages in cluster head election and significantly extends network lifetime. Furthermore, the node death curve for LEACH-SSA is relatively linear, spanning from 692 rounds to 847 rounds. In contrast, LEACH-C exhibits a more gradual decline in its node death curve, ranging from 480 rounds to 820 rounds. The energy consumption within LEACH-SSA is notably balanced; all nodes exhibit similar energy usage leading to their demise over a shorter time. Conversely, energy consumption among nodes in LEACH-C is uneven: some deplete their resources more rapidly and die earlier while others retain more energy and survive longer.Moreover, algorithms such as LEACH-SSSA and LEACH-MSSA demonstrate significant advantages due to their implementation of relay methods during data forwarding stages. Their lifetimes are comparatively extended, reaching up to 903 and 1050 rounds respectively. Notably, multi-hop communication proves superior over single-hop methods by delaying the occurrence of the first dead node by approximately 150 rounds under single-hop conditions. Additionally, these two algorithms maintain relatively balanced energy consumption profiles; they take only about 25 rounds for transitions from one dead node to an overall mortality rate of up to 80%.

Fig. 8

Cumulative dead nodes diagram in each round.

Energy consumption balance ability

The entire network emphasizes coordination and the joint completion of tasks, necessitating that all nodes function properly. If a node fails prematurely, it creates monitoring dead spots within the network, which is unacceptable. Therefore, the objective of the algorithm is to extend network lifetime as long as possible. From an energy consumption perspective, if the algorithm can conserve energy in sensor nodes for each round while striving to balance and minimize overall energy consumption among nodes, it can effectively prolong network longevity. In light of these considerations, the algorithm aims to comprehensively account for all nodes in the region when designing fitness functions and multi-hop rules.

Fig. 9

Energy consumption in each round.

As illustrated in Fig. 9, LEACH-MSSA exhibits very uniform and minimal energy consumption until a dead node appears; its consumption remains below 0.1 J. The second most efficient is the LEACH-SSSA algorithm, which also maintains balanced energy consumption per round. Although LEACH-SSA demonstrates lower energy usage than LEACH-C initially, its per-round energy consumption increases during later stages of operation and becomes unbalanced compared to earlier rounds, indicating that both single-hop and multi-hop methods possess certain capabilities for maintaining energy balance when forwarding data from cluster heads to BS. Conversely, LEACH shows significant fluctuations in energy consumption across rounds due to its random selection of cluster heads without consideration for remaining energy levels.

Discussion

To evaluate whether this scheme possesses good scalability, different initial energies and area sizes were tested. Initial energies ranged from 0.3 J to 0.7 J while area sizes varied from 100 × 100 to 400 × 400 units. Table 6 compares lifetimes across various algorithms under differing initial energies and area dimensions; results indicate that this scheme adapts well to changes in both parameters, demonstrating notable adaptability and superiority over others tested.

Table 6 Comparison of lifetimes of algorithms with different initial energies and regions.

In Table 6, as the initial energy increases, the lifetime of the nodes also extends. This is attributed to the fact that a higher initial energy allows algorithms to operate for a longer duration. For instance, in a scenario where M*M = 200 * 200 and E₀ = 0.7, the first dead node in the LEACH-MSSA algorithm was observed after 1479 rounds, with 80% of nodes failing by round 1498. In contrast, when considering M*M = 200 * 200 with E₀ = 0.5, not only was the round count for the first dead node significantly lower, but also approximately 80% of nodes perished within about 20 rounds; this indicates that energy consumption remained relatively uniform. Upon increasing the area to M*M = 300 * 300 with E₀ = 0.7, it was noted that the first dead node in the LEACH-MSSA algorithm occurred at round 1290 and that 80% of nodes failed by round 1369. The expansion of regional area has led to an increase in transmission distances between nodes, resulting in an earlier occurrence of failure for the first dead node. Consequently, this suggests a diminished capacity for balancing energy consumption within our algorithm; thus indicating a need for further multi-hop adaptation strategies tailored to larger regions. Figure 10(a)−(b) provide a three-dimensional comparison illustrating lifetimes across various algorithms under different initial energies and regional areas. It is evident that our proposed scheme performs well within the range of M = 200 ~ 300 and demonstrates adaptability across varying initial energies.

Fig. 10

(a) Comparison diagram of lifetimes in LEACH. (b) Comparison diagram of lifetimes in LEACH-SSA.

LEACH-C and LEACH-SSA LEACH-SSSA and LEACH-MSSA.

For enhanced clarity in comparisons, Fig. 11(a)− (d) and Fig. 12(a)− (d) have been presented accordingly. Figure 11(a)− (d) depict lifetimes associated with each algorithm at differing initial energies while Fig. 12(a)− (d) illustrate lifetime distributions among various algorithms across distinct regions.

Fig. 11

(a) M*M = 200 * 200, N = 200, BS=(100, 250), E₀ = 0.3 (b) M*M = 200 * 200, N = 200, BS=(100, 250), E₀ = 0.4. (c). M*M = 200 * 200, N = 200, BS=(100, 250), E₀ = 0.6 (d). M*M = 200 * 200, N = 200, BS=(100, 250), E₀ = 0.7.

Fig. 12

(a) M*M = 100 * 100, N = 50, BS=(50, 150), E₀ = 0.5 (b) M*M = 200 * 200, N = 200, BS=(100, 250), E₀ = 0.5. (c) M*M = 300 * 300, N = 450, BS=(150, 350), E₀ = 0.5. (d). M*M = 400 * 400, N = 800, BS=(200, 450), E₀ = 0.5.

Conclusion

In order to extend the operational lifespan, reduce energy loss, and ensure the collaborative execution of monitoring tasks in the entire IoT network, this paper proposes a low-power, energy-balanced centralized clustering routing protocol. Firstly, we have enhanced the SSA algorithm. During the discovery iteration process, adaptive sine function influence factors and Cauchy distribution random numbers are incorporated to improve search capabilities and increase population diversity among individuals. In the vigilance iterative phase, standard normal distribution random numbers are introduced to enhance the watchman’s ability to escape from regional extremes. Subsequently, the LEACH-SSA algorithm is employed in cluster head election. A fitness function has been constructed based on several criteria: remaining energy of nodes, number of members within each cluster, intra-cluster distances, inter-cluster distances, and distances from cluster heads to BS. The scheme is not only to elect a cluster head scheme that minimizes consumption but also to ensure that energy consumption remains as balanced as possible throughout the entire network’s lifetime. Additionally, during inter-cluster data transmission stages, we introduce two forwarding methods: single-hop and multi-hop transmissions. By identifying relay nodes with lower energy expenditure rates, we can further mitigate energy depletion and prolong their operational lifetimes. Experimental results demonstrate that our proposed low-power clustering routing scheme effectively maintains low power usage. Notably, with multi-hop data forwarding implemented, the network exhibits adaptability for larger-scale application scenarios while enhancing protocol scalability. Future work will focus on assessing this scheme’s adaptability across different region sizes and validating its performance in practical settings while also considering node data transmission dynamics in heterogeneous environments.