Multi-group multi-verse optimizer for energy efficient for routing algorithm in wireless sensor network

Abstract

Wireless sensor network (WSN) is a network composed of a group of wireless sensors with limited energy. With the proliferation of sensor nodes, organization and management of sensor nodes become a challenging task. In this paper, a new topology is proposed to solve the routing problem in wireless sensor networks. Firstly, the sensor nodes are layered to avoid the ring path between cluster heads. Then the nodes of each layer are clustered to facilitate the integration of information and reduce energy dissipation. Moreover, we propose efficient multiverse optimization to mitigate the impact of local optimal solution prematurely and the population diversity declines prematurely. Extensive empirical studies on the CEC 2013 benchmark demonstrate the effectiveness of our new approach. The improved algorithm is further combined with the new topology to handle the routing problem in wireless sensor networks. The energy dissipation generated in routing is significantly lower than that of Multi-Verse Optimizer, Particle Swarm Optimization, and Parallel Particle Swarm Optimization in a wireless sensor network consisting of 5000 nodes.

Keywords

Routing clustering layering WSN multi-verse optimizer

1 Introduction

Wireless sensor networks (WSNs) [57] consist of a particular set of communicable sensor nodes that monitor changes in the physical environment [1, 3], such as natural disaster detection [20 , 46], healthcare [2 , 56], infrastructure status monitoring, and so on. The deployment of sensor nodes can be random, fixed or mobile, generating monitoring data through the sensor unit and transmitting data directly or indirectly to the base station (BS) using a transceiver. The base station has higher energy and processing capacity than other common nodes. However, due to the unconventional application environment, the power of sensor nodes is usually limited and cannot be charged. The energy limitation of sensor nodes is the biggest challenge for WSNs. Therefore, the energy-saving of sensor nodes has become an emerging research topic in WSNs [45].

Routing protocol, which solves the problem of data transmission, is one of the core technologies of WSNs. The performance of the routing protocol is closely related to the performance of the whole network. The routing protocol is responsible for forwarding messages from the source node to BS over the system, and this forwarding process is expected to be: 1. The message is forwarded along the optimal route from the source node to BS; 2. The message can reach BS correctly.

Existing Approaches and Challenges. In order to reduce the energy consumption of sensor nodes during data transmission, researchers propose many routing algorithms. Heinzelman proposes a cluster-based hierarchical routing protocol (LEACH) in [22]. To prolong the network life-span, the algorithm randomly selects nodes as cluster heads among sensor nodes to balance energy dissipation. Cluster head rotation has become an essential symbol of LEACH. However, LEACH is not suitable for large monitoring areas and requires a high range of transmission power. Hybrid energy-efficient distributed clustering (HEED) [59] chooses a cluster head periodically by combining two parameters. But, this cluster head selection method will bring additional energy consumption. Sensor protocol for information via negotiation (SPIN) [23] introduces a negotiation mechanism between nodes prior to data transmission, thus reducing data redundancy and network overhead. Unfortunately, this algorithm is not suitable for situations with a high density of nodes.

Our Approaches. This paper proposes a routing method for wireless sensor networks with a large range and high density. The method is automatically stratified according to the monitoring range. In order to retrench the energy of sensors, clustering is carried out within the layer. Through simulation experiment, the total energy dissipation of the network is lessened by using this method. We also propose a multi-group Multi-Verse Optimization (MVO) algorithm to assist the formation of wireless sensor network topology and the optimization of data transmission path selection. This algorithm introduces a new intergroup communication strategy, which enhances the optimization ability of the algorithm.

ContributionsOur primary contributions are as follows:

We propose a new topology to organize sensor nodes in the network. This structure can be applied to applications with large monitoring areas.

We also propose a multigroup Multi-Verse Optimization algorithm, which adopts a new intergroup communication strategy to avoid falling into the local optimal too early in the optimization process.

We propose a new fitness function for selecting the data path from the source node to the sink using the multigroup multi-verse optimization algorithm. The fitness function is combined with the new network topology so that the transmission path obtained by the multi-group multiverse optimization algorithm consumes less energy.

Organization. The rest of the paper is organized as follows. In section 2, we curtly look back the multiverse optimization, ladder diffusion algorithms and briefly introduce the clustering algorithm in WSNs. Section 3 presents the proposed multi-group MVO algorithm and its application in wireless network sensor routing problem. The experimental results on the CEC 2013 benchmark and the performance analysis applied to the routing problem are given in section 4. Section 5 finally concludes the paper.

2 Related work

2.1 Computational intelligence

In recent years, big data, 5G communications [52, 54], artificial intelligence and other technologies have developed rapidly, making people’s daily life more convenient and efficient. There is a lot of information hidden in big data, which can be analyzed to enable enterprises to provide more accurate services [5 , 53]. The development of 5G communication and the Internet of Things gives people a faster and richer Internet experience. The popularization of artificial intelligence makes people’s life more comfortable. The field of artificial intelligence is relatively broad, and computational intelligence is one of the most popular branches, and some mature algorithms have been successfully applied in the engineering field. Computational intelligence includes fuzzy [6 , 55], neural network and meta-heuristic algorithms. Meta-heuristic algorithms usually use simple formulas to simulate natural phenomena, which can effectively solve many practical problems [39 , 61]. After years of development, many scholars have proposed a variety of meta-heuristic algorithms, such as Differential evolution (DE) [49 , 60] is a swarm-based optimization algorithm [11]. It is a sort of evolutionary algorithm with easy realization, fast convergence and strong stability. Particle swarm optimization (PSO) [4 , 34] is a random searching algorithm based on swarm cooperation developed by simulating the foraging behavior of bird flock. Ant colony optimization (ACO) [12 , 16] is a probabilistic algorithm applied to search the shortest path. It is illuminated by the behavior of ants in way-finding while searching for aliment. Artificial bee colony (ABC) [9 , 58] is an optimization method proposed to imitate the behavior of bees. Its prime characteristic is that it does not need to know the extra information about the problem but only requires to contrast the benefits and drawbacks of the problem. This algorithm has a fast convergence rate. Symbiotic organism search (SOS) [8 , 19] is a meta-heuristic algorithm which refers to the interactive population relationship between different organisms in nature to enhance their adaptability to the environment to improve the survival ability of the population. The idea of Pigeon Inspired Optimization (PIO) is to simulate the nesting process of pigeons using the combination of earth’s magnetic field and landmarks [14 , 51]. The algorithm has the characteristics of parallelism and strong robustness, which can be used to solve complex continuous optimization problems. Cat swarm optimization (CSO) [13 , 44] is a global optimization algorithm based on cat behavior. Cats have an intense curiosity about active targets. Once they find targets, they can track them and quickly catch prey. The cat swarm algorithm focuses on the two behaviors of cat searching and tracking. QUasi-Affine TRansformation Evolutionary (QUATRE) [17 , 35] is inspired by a quasi-affine transformation in geometry. The algorithm can increase population diversity effectively and avoid premature convergence and stagnation.

2.2 Multi-verse optimizer

The multiverse optimization algorithm [36, 48] is illuminated by the multiverse theory and there are three important components, named white holes, black holes and wormholes respectively. Local search is done through white holes and black holes. Wormholes correspond to global searches. In this algorithm, a universe is regarded as a feasible solution, an individual of a universe is regarded as a component of the feasible solution, and the value of the fitness function is expressed as the inflation rate. Multiverse optimization algorithm acts up to the following rule:

A greater inflation rate increases the possibility of a white hole, while a smaller inflation rate increases the possibility of a black hole.

The universe with greater inflation rate has a higher probability of dispatch objects, and the universe with smaller inflation rate is more likely to receive objects.

All objects in the universe can randomly travel through the wormhole between this universe and the best universe we can find now, regardless of the inflation rate.

In each iteration, the roulette machine is used to build a white/black hole model, using the roulette wheel to select a universe with a white hole based on the inflation rate of each universe.

Assume that $U = [\begin{matrix} y_{11} & y_{12} & \dots & y_{1 p} \\ y_{21} & y_{22} & \dots & y_{2 p} \\ ⋮ & ⋮ & ⋮ & ⋮ \\ y_{n 1} & y_{n 2} & \dots & y_{np} \end{matrix}]$ (1) where p is the number of objects in each universe and n is the number of universes. $x_{i}^{j} = {\begin{matrix} x_{k}^{j} & r_{1} < NI (U_{i}) \\ x_{i}^{j} & r_{1} \geq NI (U_{i}) \end{matrix}$ (2) where $x_{i}^{j}$ indicates the jth object of ith universe, and $x_{k}^{j}$ denotes the jth object of kth universe on the basis of the roulette wheel mechanism, the ith universe is expressed by U_i, NI (·) represents regularization.

Wormholes are built between each universe and one that currently has a globally optimal inflation rate and help improve its inflation rate. The formula is shown below: $x_{i}^{j} = {\begin{matrix} {\begin{matrix} X_{j} + TDR \times (({ub}_{j} - \\ {lb}_{j}) \times r 4 + {lb}_{j}) & r_{3} < 0.5 \\ X_{j} - TDR \times (({ub}_{j} - \\ {lb}_{j}) \times r 4 + {lb}_{j}) & r_{3} \geq 0.5 \end{matrix} & r_{2} < WEP \\ x_{i}^{j} & r_{2} \geq WEP \end{matrix}$ (3) where X_j represents the jth component of the best universe, TDR is a coefficient called the traveling distance rate. WEP stands for white hole rate, ub_j is the upper bound on the jth component, lb_j is the lower bound on the jth component. r₂, r₃, and r₄ are random numbers from 0 to 1.

TDR and WEP are two key parameters. TDR defines the ratio of distance an object travels through wormhole to the universe with best inflation rate found so far, which decreases gradually with the number of iterations to achieve better local search results. $TDR = 1 - \frac{T^{1 / w}}{F^{1 / w}}$ (4) where T represents the iteration number at present, and F is maximum iteration number, w shows the local search capability of the algorithm, the greater the value of w, the more precise the local search ability is.

WEP defines the probability of wormhole occurrence, which increases with the iteration numbers. $WEP = W_{\min} + T \times (\frac{W_{\max} - W_{\min}}{F})$ (5) where W_min represents the minimum value of WEP and W_max represents the maximum value of WEP.

2.3 LD algorithm

Ho et al. [24] proposed a routing algorithm based on ladder diffusion and ant colony optimization called LD. The purpose of ladder diffusion is to layer the nodes and prohibit the transfer of data between nodes in the same layer to avoid the generation of circular paths. In the ant colony optimization stage, each node forms the appropriate path to the base station (BS).

2.4 Clustering algorithm

Although WSNs are thought to be self-organizing, network management has always been a challenge in networks of a given deployment size and associated requirements. Topology management is considered a possible technology to solve these problems [38, 47]. For large multi-hop wireless sensor networks, grouping sensor nodes into clusters is a progressive idea to facilitate topology management, reduce the energy consumption of sensor nodes, and obtain better network performance [41]. The sensor nodes are organized in the form of clusters, and a cluster head will be elected as a medium for the data transmission from a member node in the cluster to the base station. This structure has excellent self-organization and expansibility. In [42], a clustering method based on genetic algorithm and dominant set is proposed, which is called GADO. By using this algorithm, the distance between clustering center and sink node is small, which can effectively reduce data delay and delay the lifetime of cluster head.

Despite clustering mechanism simplifies the structure of WSN, and only CHs participate in forwarding data, which also makes the control of WSN easier. However, this method also has some disadvantages, for all data of member nodes in the cluster transmitted to the BS must pass through the CH and only CHs participates in data transmission, which causes too much load on the CHs and leads to the excessive energy consumption of the CHs. So in order to extend the lifetime of CHs, it may be a good idea to enhance the ability of CHs.

In some proposed algorithms, CHs in WSN are selected from common sensor nodes, such as LEACH. By constantly changing the role of each node as cluster head, LEACH made all nodes have the opportunity to become cluster head to attain the target of load balancing. Unfortunately, in LEACH, the data transmission between CHs and base station adopts single-hop mode, which is not suitable for the case of a large area.

In the other case, compared with ordinary nodes, cluster heads adopt some nodes with higher energy. The positions of these cluster heads are set in advance, thus to avoid rapid death of cluster heads and prolong the lifetime of the network. However, the introduction of high-energy nodes also increases the cost of WSN. In order to adapt to a wide range of monitoring areas, it is not enough to replace CHs with high-energy nodes, and we also need to make some improvements in the network topology. These improvements will be covered in the next section.

3 Multi-group MVO and its application in routing problem of wireless sensor network

3.1 Multi-group multi-verse optimizer

There is a problem in the canonical MVO algorithm, that is, it is likely to be caught in the local optimal solution prematurely and the population diversity declines prematurely. In order to mitigate the impact of this shortcoming, a multi-group MVO algorithm is derived from the standard MVO algorithm. Under the multi-group mechanism, all feasible solutions are divided into G groups, and each group executes the MVO algorithm in parallel, then periodically exchanges information with other groups, such as running the intergroup communication strategy every 20 iterations. In this paper, a neoteric intergroup communication strategy is proposed to improve the deficiencies of the classical MVO algorithm.

In our proposed approach, all universes are divided into four groups, G = {G₁, G₂, G₃, G₄}, and that all groups communicate with each other once every 20 generations. The group communication strategy first selects a few universes with poor fitness value in each group and replaces them with the best one in the next group with an adjacent number. $y_{ij} = {\begin{matrix} y_{b}^{2} & r_{5} \leq i \leq N / G \\ y_{b}^{3} & r_{6} \leq i \leq N / G \\ y_{b}^{4} & r_{7} \leq i \leq N / G \\ y_{b}^{1} & r_{8} \leq i \leq N / G \end{matrix}$ (6) where $y_{b}^{g}$ represents the greatest universe in gth group, r₅, r₆, r₇ and r₈ are nonce from 0 to 1.

Algorithm 1

Multi-Group MVO

Initialize: The dimension of each universe is D, and each universe U_i is initialized with D random numbers, i ∈ [1, N] and is divided into G groups. f (U_i) represents the fitness function of the universe U_i, The current number of iterations is T = 1, the maximum number of iterations is M, and R is the number of iterations executing the communication strategy.

Output: The global best university U_gbest, and the best inflation rate value f (U_gbest).

Iteration:

1: While T < M do

2: for gth = 1 to G do

3: The fitness value (i.e., the inflation rate) of each universe was evaluated and ranked according to the expansion rate to obtain the universe with the best expansion rate so far.

4: for i = 1 to N/G do

5: Select the white hole and update each component y_ij with a roulette wheel.

6: Influenced by wormholes, y_ij is based on best university mutation.

7: end for

8: end for

9: if T = = R then

10: Update y_ij with a mutation strategy

11: end if

12: T = T + 1

13: end while

3.2 Multi-group MVO for routing problem in WSN

3.2.1 Energy model

The radio energy model used in this paper refers to the model discussed in LEACH [22]. Slightly different is that the routing method we adopted does not allow sensor nodes to send data directly to BS, but must be passed through the CH to reach BS. E_elec,ε_amp represent the energy consumption of the sending (or receiving) circuit and the energy consumption of the sending circuit amplifier, respectively. We assume that E_elec = 50nJ/bit,ε_amp = 100pJ/bit/m².

The energy required to send k bits of data is as follows: $E_{T} (k, d) = E_{elec} * k + ε_{amp} * k * d^{2}$ (7) and to receive this data, the radio consumption: $E_{R} (k) = E_{elec} * k$ (8)

3.2.2 Network model

It is assumed that all sensor nodes are discretionarily arranged in a circle with a radius of 350 meters centered on BS. Once nodes are deployed, they will not change their positions. The location of cluster head nodes with high energy is determined according to the structure of the clustering algorithm. Similar to LEACH, the information collection task required several rounds to complete, in which all sensor nodes acquire information and transmit it to the corresponding cluster head in each round. After receiving the data, the CH transmits to BS via the CH of the next layer (the layer closer to BS).

3.2.3 Terminologies

In the algorithm description below, the following terminologies need to be used:

The set of sensor nodes is represented as $S = {s_{11}, s_{12}, \dots, s_{1 N_{1}}, \dots, s_{l 1}, \dots, s_{{lN}_{l}}}$ where l is the layer number and N_l is the node number of layer l.

The set of nodes at each level is represented as L_i = {s_i,1, s_i,2, …, s_{i,N_l}}.

The set of CHs is represented as CH = {c_1,1, c_1,2, …, c_l,1, …, c_{l,M_l}}. where l is the layer number and M_l is the CH number of layer l.

d_max represents the maximum communication distance of the node.

dist (s_i, s_j) is the distance between s_i and s_j,where s_i and s_j are members of S.

Meb (c_l,i) = {n₁, n₂, …, n_s} represents the collection of sensor nodes with c_l,i as CH, where n_i ∈ L_l, i = 1, 2, …, s, s is the size of the cluster with c_l,i as its CH.

LowerLayerCH (c_l,i) represents the set of lower layer cluster heads to which c_l,i can be connected.

NextHop (c_l,i) represents a cluster head selected in l + 1 layer of CH c_l,i as the next hop node to forward data.

E_residual (s_i) represents residual energy of the sensor node s_i.

3.2.4 layering

The routing algorithm proposed in this paper is divided into three steps. The first step is layering, the second step is to divide the nodes of each layer into several clusters, and the third step is to find the path (i.e., route) between the current node and BS. When the nodes of each layer want to transmit data to BS, they first transfer data to the CH they belong to, and then transfer the data from the CH to the CH in the lower layer until it reaches BS. The layering adopts the same mechanism as the ladder diffusion algorithm. Firstly, according to the maximum communication distance of nodes, all nodes that BS can connect to are denoted as the first layer, and the nodes that the first layer can connect to are denoted as the second layer, and so on.

Figure 1 is a quarter of the circular region. It is assuming that BS is at the origin of coordinates. The communication radius of the nodes is 35 meters, the blue node in the figure is within the communication range of BS, so it is the first layer, while the yellow node is within the radio range of the blue node, so it is the second layer, and so on. At the end of the layering, each node is numbered so that the nodes of the same layer are numbered consecutively. In this way, it is possible to determine which layer a node belongs to directly by numbering. This approach facilitates subsequent clustering and routing.

Fig. 1

A quarter of network structure.

3.2.5 Multi-group MVO for clustering

The fundamental goal of clustering is to maximize the WSN survival time and minimize the energy dissipation of sensor nodes.

The initialization of universes. Randomly generate cluster heads for each layer. Assume that the number of cluster heads in each layer is 20% of the number of sensor nodes in the layer. For example, the first layer has 1000 sensor nodes, whose numbers are from 1 to 1000, L₁ = {s_1,1, s_1,2, …, s_1,1000}, 200 different nodes are randomly selected as CHs from 1000 sensor nodes in the first layer, CH₁ = {c_1,1, c_1,2, …, c_1,200}. The CH that can communicate with it is searched by all sensor nodes in the first layer according to its maximum communication range d_max. If a node can be connected to multiple CHs at the same time, the nearest one will be selected. After the CH selection is completed, a temporary member information table is generated for each CH. Subsequently, the sensor node information is added, and the selected CH is marked in the sensor node. Then the CH serial number is regarded as the universe in the multi-group MVO algorithm, the inflation rate is evaluated, and the iteration is started. The fitness function is described in the next section. After the iteration, the new set of CHs is selected in the first layer, the CH tag of each node is changed, and the temporary member information table of the last selected CHs is officially recorded in the memory of the CHs. In this way, the cluster structure of the first layer is determined. In the same way, the cluster structure of each layer is determined from the layer nearest to BS outwards.

Fitness function. The determination of fitness function takes into account the energy dissipation of the CH, including the consumption of communication between the sensor nodes and the CH, the dissipation of data transmission between the cluster head and other layers. The connection rate between the CH and adjacent layer CH are also included.

Before introducing the calculation method of energy consumption for node communication, there are some other factors to consider. One of the most important factors is the coverage of the nodes in this layer. The coverage rate of nodes in this layer refers to the proportion of the number of hierarchical sensor nodes that the selected CHs can be connected to in the total number of sensor nodes in this layer. We want the ratio to be as large as possible. Another factor to consider is the number of adjacent layer CHs to which the CHs of this layer can be connected. The more adjacent CHs you can connect to, the better load balancing ability will be during the routing phase. Now let’s discuss the energy consumption of node communication.

Firstly, considering the communication energy consumption between sensor nodes and cluster heads, we hope that the average energy consumption of each sensor node is the lowest when sensor nodes in the cluster and their corresponding cluster heads carry out data transmission. It is assumed that cluster i in the first layer is composed of cluster head CH_1,i and sensor nodes (namely Meb (CH_1,i) that choose CH_1,i as cluster head in the cluster. The energy consumption of K-bit data transmitted between the CH and cluster members is shown as follows: $E_{intra} = \frac{\sum_{i = 1}^{M_{l}} \sum_{j = 1}^{N_{c}} E_{T} (k, dist (n_{j}, c_{l, i})) / N_{c}}{M_{l}}$ (9) where N_c denotes the size of Meb (c_l,i), n_j is a sensor node with c_l,i as CH, M_l is the number of clusters in the l layer.

Secondly, the communication between different clusters in two adjacent layers is considered. In this paper, we define a layer closer to BS than Layer l as the lower layer of l, and a layer farther from BS than layer l as the upper layer of l. Every layer has a lower layer except the first, and every layer has an upper layer except the last. The communication consumption of the adjacent layer should be considered in two parts, namely the energy consumption of the upper layer transferring data to this layer and the energy consumption of this layer transferring data to lower layer. And we determine cluster structure begins with the first layer, in each iteration, the cluster structure in upper layer is determined by the current iteration, and the cluster structure of in lower layer is determined by the previous iteration. However, because the network hierarchy is established layer by layer from the position close to BS, the high-layer structure has not been established when the current hierarchy is established. Therefore, only the transmission communication with the lower layer is considered for the time being.

In this paper, the energy consumed by adjacent layer cluster head communication is represented by the average energy consumption. For example, we now consider the communication energy consumption between the first layer and the adjacent layer CHs. Assume that the second layer has N₂ nodes, L₂ = {s_2,1, s_2,2, …, s_2,N₂}, with M₂ cluster heads CH₂ = {c_2,1, c_2,2, …, c_2,M₂}, and there are N₁ nodes in the first layer, L₁ = {s₁, 1, s₁, 2, …, s_1,N₁}, including M₁ cluster heads CH₁ = {c_1,1, c_1,2, …, c_1,M₁}, The cluster head to which c_2,p can be connected are shown as LowerLayerCH (c_2,p) = {nlc₁, nlc₂, …, nlc_{k
_p}}, where nlc_i ∈ CH₁, i = 1, 2, …, k₁, 1 ≤ k_p ≤ M₁. Then the energy consumption of data transmitted from the second layer to the first layer can be expressed as $E_{inter - lower} = \sum_{i = 1}^{M_{2}} \frac{\sum_{j = 1}^{k_{i}} E_{T} (k, dist (c_{2, i}, {nlc}_{j})) / k_{i}}{M_{2}}$ (10) Assuming that there are M_l cluster heads in the current layer, and there are k_i lower layer cluster heads to which the ith cluster head can be connected, the energy consumption of transmitting data from the current layer to the lower layer is as follows: $E_{inter - lower} = \sum_{i = 1}^{M_{l}} \frac{\sum_{j = 1}^{k_{i}} E_{T} (k, dist (c_{l, i}, {nlc}_{j})) / k_{i}}{M_{l}}$ (11) In addition, the number of nodes in this layer that the cluster head node selected in the current layer can connect to is also a factor to be considered. Some unreasonable cluster head node settings will make some nodes isolated so that they cannot connect to any cluster head node. We hope that such isolated nodes should be as few as possible. Therefore, we will also take into account the connection rate of cluster head nodes, expressed in R_connect.

$R_{connect} = \frac{M_{l} + \sum_{i = 1}^{M_{l}} S_{i}}{N_{l}}$ (12) Where, M_l is the number of cluster head nodes in this layer, S_i is the number of members of the ith cluster, and N_l is the number of all nodes in this layer.

An excellent hierarchy should also consider the possibility of connecting this layer with the higher layer and lower layer. When some nodes die, the data can still reach sink from other paths, which can ensure the reliability of the network. Here we describe this reliability by the number of nodes that can be connected to the upper and lower layers, expressed in Num_connect. Thus, the fitness function can be expressed as a linear combination of energy consumption required for the communication within the cluster, energy dissipation for communication between clusters (inter-layer), node coverage in the layer and connected number of CHs between adjacent two layers. $\begin{matrix} fitness = α \cdot E_{intra} + β \cdot E_{inter - lower} \\ - μ R_{connect} - η \cdot {Num}_{connect} \end{matrix}$ (13) where α, β, μ, η are four constants, μ and η are equilibrium coefficients, which are determined according to the values of the first two items in the formula.

3.2.6 Multi-group MVO for routing

When looking for the data transmission path of nodes, we still adopt multi-group MVO algorithm. In the initial stage of routing algorithm, the next hop of each sensor node except the cluster head is set as the corresponding CH. The dimension of the universe is one minus the number of layers where the node is located, and each dimension of the universe is initialized with a random number from 0 to 1. The ith dimension represents the ith cluster head involved in data transmission starting from the cluster head of the node. For example, suppose node s_3,k in the third layer wants to send data to BS, the path (i.e. the universe) should be two-dimensional, the assumption for {0.3, 0.6}, let’s say the cluster head of s_3,k is c_3,k′, and there are 5 cluster heads in the lower layer to which it can be connected, respectively is {c_2,k₁, c_2,k₂c_2,k₃, c_2,k₄, c_2,k₅}, because 5 times 0.3 round up is equal to 2, the next hop of c_3,k′ should be the second in the list of cluster heads to which it can connect to the lower layer, namely c_2,k₂. We continue to assume that c_2,k₂ can be connected to three cluster heads at the next layer, respectively is {c_1,k₁, c_1,k₂c_1,k₃}, since 3 times 0.6 round up is equal to 2, the next hop of c_2,k₂ should be c_1,k₂, and c_1,k₂ is the cluster head of the first layer, which can communicate directly with BS. So now we have a path from s_3,k to BS, which is s_3,k → c_3,k′ → c_2,k₂ → c_1,k₂ → BS.

Now that we have a way to encode paths, let’s talk about fitness functions. We want to find a path that minimizes the energy consumption of all nodes, and we also want to have as much energy left over from each node as possible. So let’s set up the fitness function from these two aspects. We represent the energy dissipation along the path by dividing the sum of energy dissipation of all nodes along the path by the number of layers from the source node to BS. The average residual energy and minimum remanent energy of all nodes on the path are used as two indexes to represent the remanent energy of sensor nodes on the route. We always want as little energy dissipation along the path as possible, and as much energy surplus as possible. Then the fitness function can be expressed as a linear combination of energy dissipation and residual energy. Suppose the path is: c_{l,k_l} → c_{l-1,k_l-1} → … → c_{1,k_p},the energy consumption on the path can be expressed as $E_{consumption} = \sum_{i = 1}^{l - 1} dist (c_{i, k_{i}}, c_{i + 1, k_{i + 1}}) / l$ (14) where c_{i,k_i} ∈ LowerLayerCH (c_{i+1,k_i+1}) , i ∈ [1, l - 1]. The average residual energy on the path can be shown as $E_{avg_resi} = \sum_{i = 1}^{l} E_{residual} (c_{i, k_{i}}) / l$ (15) the minimum residual energy on the path can be expressed as $\begin{matrix} E_{\min_resi} = MIN (E_{residual} (c_{1, k_{1}}), E_{residual} (c_{2, k_{2}}), . . ., \\ E_{residual} (c_{l, k_{l}})) \end{matrix}$ (16)

$\begin{matrix} fitness = & a \cdot E_{consumption} - b \cdot E_{avg_resi} \\ - c \cdot E_{\min_resi} \end{matrix}$ (17) where a, b, and c are three non-zero constants.

After several rounds of data transmission, some routing paths are invalid because a cluster-head node in the path dies due to exhaustion of energy, at which time the error message returns along the original route. Suppose the path is c₄ → c₃ → c₂ → c₁, After p rounds, cluster head c₂ dies, and the precursor c₃ of cluster head c₂ receives an error message. At which point the routing item whose next hop is c₂ in the routing table of c₃ will be deleted. Then cluster head c₃ looks for other routing items in the routing table and reroute from c₃. If the routing table of c₃ is empty, an error message is returned to c₄, c₄ performs the same operation as c₃. When c₄’s routing table is blank, the routing process of c₄ is declared a failure at this point.

4 Analysis of experimental results

In this section, the efficient and effectiveness of the proposed multi-group MVO algorithm will be evaluated on CEC 2013 and WSN routing problems.

4.1 Experimental results for global optimization

We used 28 benchmark functions from the CEC 2013 test set to evaluate the performance of the proposed multi-group MVO algorithm on real-parameter optimization. Among the 28 benchmark functions, the first five parts are unimodal functions, f₆-f₂₀ are fifteen basic multimodal functions, and f₂₁-f₂₈ are eight composition functions. So as to analyze the performance of multi-group MVO algorithm, we contrast it with the PSO algorithm and BHO algorithm [40]. The number of initial solutions is 100, the upper bound and the lower bound of the solution search range are 100 and -100 respectively, and 1200 iterations are carried out. In order to make the result fairer, each optimization algorithm runs 51 times for each test function to reduce the error.

The results are shown in Table 1. According to the analysis of the “best" column data, the multi-group MVO algorithm produces optimal results on 18 reference functions, including 3 unimodal functions (f₂, f₃, f₄), 7 multimodal functions (f₁₄-f₂₀) and all 8 composition functions. From “mean" perspective of view, multi-group MVO algorithm achieves best in 2 single-mode functions (f₃, f₄), 8 multimodal functions (f₁₃-f₂₀) and all 8 composition functions. In terms of the stability of the results obtained by running the algorithm 51 times, the multi-group MVO algorithm has excellent performance in 4 unimodal functions (f₁, f₃, f₄, f₅), 10 multimodal functions (f₆, f₇, f₁₀-f₁₅, f₁₇, f₁₉) and 4 composition functions (f₂₄-f₂₇). Overall, compared to PSO and BHO, the proposed multi-group MVO algorithm has a distinct advantage over f₃,f₄,f₁₄-f₁₈.

Table 1
Performance evaluation for Multi-Group MVO, PSO and BHO over CEC2013

PSO BHO Multi-Group MVO

Best Mean Std Best Mean Std Best Mean Std

1 -1.40E+03 -1.29E+03 9.55E+04 2.08E+04 2.39E+04 1.95E+06 5.11E-01 7.38E-01 1.58E-02

2 3.75E+06 1.01E+07 9.13E+12 1.52E+08 1.91E+08 6.01E+14 3.58E+06 1.12E+07 2.09E+13

3 7.71E+08 3.78E+09 9.45E+18 4.32E+10 5.64E+10 4.16E+19 2.36E+08 1.25E+09 6.94E+17

4 2.08E+03 4.73E+03 1.76E+06 5.50E+04 7.37E+04 6.24E+07 7.15E+02 1.63E+03 1.72E+05

5 -9.95E+02 -9.49E+02 1.65E+04 6.21E+02 1.11E+03 3.62E+04 7.41E-01 2.58E+01 2.89E+02

6 -8.56E+02 -8.00E+02 2.70E+03 3.31E+02 5.73E+02 1.51E+04 4.35E+01 5.05E+01 1.71E+02

7 -7.07E+02 -6.72E+02 6.18E+02 -6.72E+02 -5.48E+02 7.80E+03 5.85E+01 1.02E+02 5.46E+02

8 -6.79E+02 -6.79E+02 1.80E-03 -6.79E+02 -6.79E+02 1.80E-03 2.10E+01 2.12E+01 1.82E-03

9 -5.56E+02 -5.43E+02 1.65E+01 -5.39E+02 -5.30E+02 1.34E+01 2.80E+01 3.62E+01 1.86E+01

10 -4.92E+02 -4.37E+02 6.48E+03 1.90E+03 2.35E+03 5.64E+04 1.82E+00 3.20E+00 1.58E+00

11 -1.54E+02 2.38E+01 4.43E+03 1.77E+02 3.43E+02 8.12E+03 1.16E+02 2.31E+02 2.74E+03

12 2.16E+01 1.79E+02 6.91E+03 2.90E+02 5.05E+02 1.25E+04 1.33E+02 2.20E+02 2.13E+03

13 2.14E+02 4.17E+02 6.21E+03 5.25E+02 6.69E+02 4.28E+03 2.83E+02 3.92E+02 4.10E+03

14 4.72E+03 6.65E+03 7.08E+05 1.11E+04 1.30E+04 8.72E+05 4.46E+03 6.47E+03 6.85E+05

15 6.24E+03 8.74E+03 1.20E+06 1.13E+04 1.36E+04 7.60E+05 4.80E+03 6.85E+03 7.26E+05

16 2.02E+02 2.03E+02 2.33E-01 2.01E+02 2.03E+02 4.36E-01 4.89E-01 1.41E+00 2.47E-01

17 6.73E+02 8.35E+02 5.90E+03 9.59E+02 1.23E+03 1.59E+04 3.11E+02 4.17E+02 4.08E+03

18 8.51E+02 9.42E+02 2.96E+03 1.04E+03 1.32E+03 1.88E+04 2.77E+02 4.23E+02 4.46E+03

19 5.19E+02 5.35E+02 5.73E+01 1.60E+04 2.40E+04 1.44E+07 1.05E+01 2.17E+01 2.34E+01

20 6.20E+02 6.23E+02 1.07E+00 6.24E+02 6.24E+02 3.38E-02 2.03E+01 2.26E+01 2.00E+00

21 9.37E+02 1.62E+03 6.96E+04 3.89E+03 4.03E+03 2.19E+03 2.13E+02 8.53E+02 1.40E+05

22 9.03E+03 1.12E+04 2.08E+06 1.36E+04 1.58E+04 7.85E+05 5.24E+03 7.51E+03 1.55E+06

23 8.93E+03 1.20E+04 1.65E+06 1.44E+04 1.62E+04 4.40E+05 5.60E+03 7.92E+03 1.94E+06

24 1.34E+03 1.38E+03 3.51E+02 1.48E+03 1.54E+03 1.25E+03 2.86E+02 3.08E+02 1.46E+02

25 1.47E+03 1.54E+03 7.53E+02 1.64E+03 1.69E+03 3.55E+02 2.98E+02 3.38E+02 2.98E+02

26 1.40E+03 1.64E+03 3.66E+03 1.42E+03 1.62E+03 1.29E+04 3.59E+02 3.94E+02 1.45E+02

27 3.03E+03 3.30E+03 1.88E+04 3.60E+03 3.89E+03 1.55E+04 1.08E+03 1.33E+03 1.57E+04

28 1.82E+03 4.08E+03 4.72E+06 7.32E+03 8.59E+03 3.08E+05 4.04E+02 1.55E+03 2.44E+06

	PSO	BHO	Multi-Group MVO
1	-1.40E+03	-1.29E+03	9.55E+04	2.08E+04	2.39E+04	1.95E+06	5.11E-01	7.38E-01	1.58E-02
2	3.75E+06	1.01E+07	9.13E+12	1.52E+08	1.91E+08	6.01E+14	3.58E+06	1.12E+07	2.09E+13
3	7.71E+08	3.78E+09	9.45E+18	4.32E+10	5.64E+10	4.16E+19	2.36E+08	1.25E+09	6.94E+17
4	2.08E+03	4.73E+03	1.76E+06	5.50E+04	7.37E+04	6.24E+07	7.15E+02	1.63E+03	1.72E+05
5	-9.95E+02	-9.49E+02	1.65E+04	6.21E+02	1.11E+03	3.62E+04	7.41E-01	2.58E+01	2.89E+02
6	-8.56E+02	-8.00E+02	2.70E+03	3.31E+02	5.73E+02	1.51E+04	4.35E+01	5.05E+01	1.71E+02
7	-7.07E+02	-6.72E+02	6.18E+02	-6.72E+02	-5.48E+02	7.80E+03	5.85E+01	1.02E+02	5.46E+02
8	-6.79E+02	-6.79E+02	1.80E-03	-6.79E+02	-6.79E+02	1.80E-03	2.10E+01	2.12E+01	1.82E-03
9	-5.56E+02	-5.43E+02	1.65E+01	-5.39E+02	-5.30E+02	1.34E+01	2.80E+01	3.62E+01	1.86E+01
10	-4.92E+02	-4.37E+02	6.48E+03	1.90E+03	2.35E+03	5.64E+04	1.82E+00	3.20E+00	1.58E+00
11	-1.54E+02	2.38E+01	4.43E+03	1.77E+02	3.43E+02	8.12E+03	1.16E+02	2.31E+02	2.74E+03
12	2.16E+01	1.79E+02	6.91E+03	2.90E+02	5.05E+02	1.25E+04	1.33E+02	2.20E+02	2.13E+03
13	2.14E+02	4.17E+02	6.21E+03	5.25E+02	6.69E+02	4.28E+03	2.83E+02	3.92E+02	4.10E+03
14	4.72E+03	6.65E+03	7.08E+05	1.11E+04	1.30E+04	8.72E+05	4.46E+03	6.47E+03	6.85E+05
15	6.24E+03	8.74E+03	1.20E+06	1.13E+04	1.36E+04	7.60E+05	4.80E+03	6.85E+03	7.26E+05
16	2.02E+02	2.03E+02	2.33E-01	2.01E+02	2.03E+02	4.36E-01	4.89E-01	1.41E+00	2.47E-01
17	6.73E+02	8.35E+02	5.90E+03	9.59E+02	1.23E+03	1.59E+04	3.11E+02	4.17E+02	4.08E+03
18	8.51E+02	9.42E+02	2.96E+03	1.04E+03	1.32E+03	1.88E+04	2.77E+02	4.23E+02	4.46E+03
19	5.19E+02	5.35E+02	5.73E+01	1.60E+04	2.40E+04	1.44E+07	1.05E+01	2.17E+01	2.34E+01
20	6.20E+02	6.23E+02	1.07E+00	6.24E+02	6.24E+02	3.38E-02	2.03E+01	2.26E+01	2.00E+00
21	9.37E+02	1.62E+03	6.96E+04	3.89E+03	4.03E+03	2.19E+03	2.13E+02	8.53E+02	1.40E+05
22	9.03E+03	1.12E+04	2.08E+06	1.36E+04	1.58E+04	7.85E+05	5.24E+03	7.51E+03	1.55E+06
23	8.93E+03	1.20E+04	1.65E+06	1.44E+04	1.62E+04	4.40E+05	5.60E+03	7.92E+03	1.94E+06
24	1.34E+03	1.38E+03	3.51E+02	1.48E+03	1.54E+03	1.25E+03	2.86E+02	3.08E+02	1.46E+02
25	1.47E+03	1.54E+03	7.53E+02	1.64E+03	1.69E+03	3.55E+02	2.98E+02	3.38E+02	2.98E+02
26	1.40E+03	1.64E+03	3.66E+03	1.42E+03	1.62E+03	1.29E+04	3.59E+02	3.94E+02	1.45E+02
27	3.03E+03	3.30E+03	1.88E+04	3.60E+03	3.89E+03	1.55E+04	1.08E+03	1.33E+03	1.57E+04
28	1.82E+03	4.08E+03	4.72E+06	7.32E+03	8.59E+03	3.08E+05	4.04E+02	1.55E+03	2.44E+06

4.2 Experimental result for routing problem in wireless sensor network

In this subsection, we get some results by experimenting with routing algorithms for clustering in layers. The experiment assumes that WSN is a circular region with a radius of 350 meters, in which 5000 sensor nodes are deployed. The communication radius of each sensor node is 65 meters, and the BS is located at the center of the circle.The common sensor node has 2J of energy, and the CH energy is 20J. After the layered algorithm, 5000 sensor nodes are divided into 6 layers, and the number of nodes in each layer is 966, 898, 841, 930, 852, 513, and then the cluster is divided by the multi-group MVO algorithm. We also use the multi-group MVO algorithm to select the path of data transmission. In routing simulation, all nodes send data to the BS in turn. All sensor nodes must transmit data to the BS through the CH, and ordinary sensor nodes are not allowed to send data directly to another common sensor node.

The performance of multi-group MVO in multi-hop routing is evaluated by comparing with three excellent approaches –MVO, PPSO, and PSO. In the experiment, each algorithm went through 5000 rounds, and all nodes in each round sent data to BS once. We evaluated the algorithms from three aspects: the number of active nodes, data loss and energy consumption. The results are illustrated in Table 2. Multi-group MVO consistently outperforms other three approaches regarding all three measures. This is because Multi-group MVO considers both intergroup communication strategy and transmission path optimization.

Table 2
Comparative experiment on Multi-Group MVO, PPSO, MVO and PSO in routing problem

Criteria Multi-group MVO PPSO MVO PSO

Active nodes 571 568 543 566

Data loss 18,065,542 18,118,911 18,191,234 18,134,406

Power consumption 989,082,508.04 994,531,027.00 997,769,680.36 995,544,207.75

Criteria	Multi-group MVO	PPSO	MVO	PSO
Active nodes	571	568	543	566
Data loss	18,065,542	18,118,911	18,191,234	18,134,406
Power consumption	989,082,508.04	994,531,027.00	997,769,680.36	995,544,207.75

5 Conclusions

In this paper, a Multi-group MVO algorithm is proposed for routing problem in wireless sensor networks. The formation of ring routes is avoided by layering, energy consumption and connectivity rate of cluster structure are considered in the clustering, and energy consumption of CHs is effectively balanced. In data forwarding, the data is forwarded to BS after passing through layers of CHs. When the routing fails, it is rerouted from the node at the upper level of the failed node, which also saves part of the energy. Extensive empirical studies on benchmark CEC2013 demonstrate the effectiveness of our approach and the efficiency of our techniques. Furthermore, the comparative experiment shows our approach outperforms the other three approaches regarding the number of active nodes, data loss and energy consumption.

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	PSO			BHO			Multi-Group MVO
	Best	Mean	Std	Best	Mean	Std	Best	Mean	Std
1	-1.40E+03	-1.29E+03	9.55E+04	2.08E+04	2.39E+04	1.95E+06	5.11E-01	7.38E-01	1.58E-02
2	3.75E+06	1.01E+07	9.13E+12	1.52E+08	1.91E+08	6.01E+14	3.58E+06	1.12E+07	2.09E+13
3	7.71E+08	3.78E+09	9.45E+18	4.32E+10	5.64E+10	4.16E+19	2.36E+08	1.25E+09	6.94E+17
4	2.08E+03	4.73E+03	1.76E+06	5.50E+04	7.37E+04	6.24E+07	7.15E+02	1.63E+03	1.72E+05
5	-9.95E+02	-9.49E+02	1.65E+04	6.21E+02	1.11E+03	3.62E+04	7.41E-01	2.58E+01	2.89E+02
6	-8.56E+02	-8.00E+02	2.70E+03	3.31E+02	5.73E+02	1.51E+04	4.35E+01	5.05E+01	1.71E+02
7	-7.07E+02	-6.72E+02	6.18E+02	-6.72E+02	-5.48E+02	7.80E+03	5.85E+01	1.02E+02	5.46E+02
8	-6.79E+02	-6.79E+02	1.80E-03	-6.79E+02	-6.79E+02	1.80E-03	2.10E+01	2.12E+01	1.82E-03
9	-5.56E+02	-5.43E+02	1.65E+01	-5.39E+02	-5.30E+02	1.34E+01	2.80E+01	3.62E+01	1.86E+01
10	-4.92E+02	-4.37E+02	6.48E+03	1.90E+03	2.35E+03	5.64E+04	1.82E+00	3.20E+00	1.58E+00
11	-1.54E+02	2.38E+01	4.43E+03	1.77E+02	3.43E+02	8.12E+03	1.16E+02	2.31E+02	2.74E+03
12	2.16E+01	1.79E+02	6.91E+03	2.90E+02	5.05E+02	1.25E+04	1.33E+02	2.20E+02	2.13E+03
13	2.14E+02	4.17E+02	6.21E+03	5.25E+02	6.69E+02	4.28E+03	2.83E+02	3.92E+02	4.10E+03
14	4.72E+03	6.65E+03	7.08E+05	1.11E+04	1.30E+04	8.72E+05	4.46E+03	6.47E+03	6.85E+05
15	6.24E+03	8.74E+03	1.20E+06	1.13E+04	1.36E+04	7.60E+05	4.80E+03	6.85E+03	7.26E+05
16	2.02E+02	2.03E+02	2.33E-01	2.01E+02	2.03E+02	4.36E-01	4.89E-01	1.41E+00	2.47E-01
17	6.73E+02	8.35E+02	5.90E+03	9.59E+02	1.23E+03	1.59E+04	3.11E+02	4.17E+02	4.08E+03
18	8.51E+02	9.42E+02	2.96E+03	1.04E+03	1.32E+03	1.88E+04	2.77E+02	4.23E+02	4.46E+03
19	5.19E+02	5.35E+02	5.73E+01	1.60E+04	2.40E+04	1.44E+07	1.05E+01	2.17E+01	2.34E+01
20	6.20E+02	6.23E+02	1.07E+00	6.24E+02	6.24E+02	3.38E-02	2.03E+01	2.26E+01	2.00E+00
21	9.37E+02	1.62E+03	6.96E+04	3.89E+03	4.03E+03	2.19E+03	2.13E+02	8.53E+02	1.40E+05
22	9.03E+03	1.12E+04	2.08E+06	1.36E+04	1.58E+04	7.85E+05	5.24E+03	7.51E+03	1.55E+06
23	8.93E+03	1.20E+04	1.65E+06	1.44E+04	1.62E+04	4.40E+05	5.60E+03	7.92E+03	1.94E+06
24	1.34E+03	1.38E+03	3.51E+02	1.48E+03	1.54E+03	1.25E+03	2.86E+02	3.08E+02	1.46E+02
25	1.47E+03	1.54E+03	7.53E+02	1.64E+03	1.69E+03	3.55E+02	2.98E+02	3.38E+02	2.98E+02
26	1.40E+03	1.64E+03	3.66E+03	1.42E+03	1.62E+03	1.29E+04	3.59E+02	3.94E+02	1.45E+02
27	3.03E+03	3.30E+03	1.88E+04	3.60E+03	3.89E+03	1.55E+04	1.08E+03	1.33E+03	1.57E+04
28	1.82E+03	4.08E+03	4.72E+06	7.32E+03	8.59E+03	3.08E+05	4.04E+02	1.55E+03	2.44E+06

Multi-group multi-verse optimizer for energy efficient for routing algorithm in wireless sensor network

Abstract

Keywords

1 Introduction

2 Related work

2.1 Computational intelligence

2.2 Multi-verse optimizer

2.4 Clustering algorithm

3 Multi-group MVO and its application in routing problem of wireless sensor network

3.1 Multi-group multi-verse optimizer

3.2.1 Energy model

3.2.3 Terminologies

3.2.4 layering

4.1 Experimental results for global optimization

Table 2 Comparative experiment on Multi-Group MVO, PPSO, MVO and PSO in routing problem Criteria Multi-group MVO PPSO MVO PSO Active nodes 571 568 543 566 Data loss 18,065,542 18,118,911 18,191,234 18,134,406 Power consumption 989,082,508.04 994,531,027.00 997,769,680.36 995,544,207.75

References

Table 2
Comparative experiment on Multi-Group MVO, PPSO, MVO and PSO in routing problem

Criteria Multi-group MVO PPSO MVO PSO

Active nodes 571 568 543 566

Data loss 18,065,542 18,118,911 18,191,234 18,134,406

Power consumption 989,082,508.04 994,531,027.00 997,769,680.36 995,544,207.75