Modified hybrid fruit fly-based salp swarm optimization strategy for energy efficient optimization in MIMO Wireless Powered Communication Networks

Abstract

A potential way to handle the future requirements of wireless data traffic is the Massive Multiple Input Multiple Output (MIMO) antenna systems. The most effective method to satisfy the demand for wireless data traffic is to enhance the Spectral Efficiency of the existing spectrum since the wireless spectrum is a limited resource. In the MIMO network, cell-free, energy-efficient, and user-centric are considered as most important parameters to achieve effective communication. Therefore, a new energy efficiency optimization scheme is developed in a massive MIMO system to improve the system’s capacity and spectral efficiency. The multi-channel optimization problem is effectively rectified with the help of this newly designed energy efficiency optimization scheme. Here, the “Singular Value Decomposition (SVD)” method is utilized for the implementation of a sub-channel grouping scheme, where the sub-channels are arranged in descending order based on the results attained from SVD. After arranging the sub-channels, the sub-channel grouping is carried out, and then the energy efficiency optimization is provided with the help of Integrated Fruit Fly with Salp Swarm Optimization (IFFSSO). This energy-efficient algorithm improves the system capacity and spectral efficiency. The experimental outcome is revealed through various conventional models to ensure the energy efficiency of the recommended model.

Keywords

Massive Multiple Input Multiple Output Wireless Powered Communication Networks multi-channel optimization problem Integrated Fruit Fly with Salp Swarm Optimization

1. Introduction

MIMO is, commonly referred to as very large MIMO, increases the degree of interest from businesses and universities [30]. It is a vital technology for 5G wireless communication, and it is also used to boost the data speeds and service quality of the 5G network. Massive MIMO, comprising plenty of antennas, is able to provide enhanced spatial clarity and greatly increase the spectrum effectiveness of the system. Resource harvesting, which allows equipment to draw energy from environmental sources, attracts a lot of interest from both educators and companies [10]. Wireless communication networks may gather energy from abundant natural sources like the sun and wind [17]. Yet, renewable energy sources are often unstable, and the supply of power at the destination is uncontrollable; consequently, the communication instruments could fail to gather sufficient power [32]. The Wireless Energy Transfer (WET) method” can also extract energy from Radio Frequency (RF) transmissions [25]. This particular type of source of energy is more trustworthy than environmentally renewable sources because the RF waves are generated by specialized equipment [34]. In “Simultaneous Wireless Information and Power Transfer (SWIPT)”, the wireless equipment may separate the received signal into two parts; one portion is used to facilitate data decoding, and another is adopted to generate energy [37]. Numerous simple, low-power, uniform, or diverse sensors are used for sensing in short-range wireless communications networks [13]. Because of the constraints on energy resources and the easy availability of the actual sensors, the lifespan of these wireless sensor networks is limited [7].

The power acquired from deliberate or environmental authorities can be stored to restock the batteries, which has developed into an important strategy to offer a power supply for sustainable sensors [35]. While the RF signals generated by contextual transmitters are easily accessible, RF power capture becomes more versatile and efficient than solar or wind energy gathering [3]. The advantage of RF signals is used by multiple investigations in both “Wireless Information Transmission (WIT)” and WET [12]. Wireless-Powered Sensor Networks (WPSNs) employ WET in conventional wireless communication systems. The famous “harvest-then-transmit” approach has been implemented, where the system’s efficiency was enhanced simultaneously by maximizing the number of occasions and the conveying power allotted to the “Hybrid Access Point (H-AP)” [26]. Since that time, notable appropriate research has been done in the context of WPSNs using integrated fully duplex radio, intelligent radio, MIMO, and Non-Orthogonal Multiple Access (NOMA) methods. The above works merely target the spectral effectiveness of WPSNs, which can result in loss of power throughout the downlink WET [2]. In WPN, energy efficiency is considered as the critical parameter. The MIMO system consists of several numbers of antennas on the base station. So, it consumes more energy to maintain proper communication. Moreover, the condition of the channel also affects the energy competence of the network. Hence, the performance of the system is greatly affected. These issues are counteracted by the energy-efficient optimization process. The most effective communication process is achieved by the energy-efficient optimization process. The multimedia communication system is evaluated by the energy-efficient optimization process. In the MIMO network, energy efficiency is considered as one of the hot studies in recent days. The effects on antennas in the MIMO network are also determined by the energy-efficient optimization process.

Some studies have highlighted energy-efficient resource allocation systems that are merely used for radiated power minimization [16]. In wireless communication networks, energy is typically used for processing the signal at the receiver, which is not considered advantageous from the perspective of energy efficiency [31]. The latest study has changed the performance of resource allocation methods to optimize energy efficiency. So, the energy efficiency associated with wireless systems has increased, while they still have not cracked all the benefits [1]. Because the resource allocation methods ignore possible tuning controls on other layers and the interrelationships across all layers and modules, as well as the possibility of modifying the energy depending on data rate, are the issues to be addressed with the traditional energy optimization and resource allocation methods. Conventional techniques face lots of difficulties when identifying the data transmission characteristics. Moreover, the conventional techniques do not solve the multi-channel optimization problem in the network. As a consequence, energy efficiency optimization is crucial in WPCN, particularly in contrast to traditional wireless communication networks.

The heuristic-aided energy proficient optimization model in the MIMO network has several contributions and they are scheduled in the underneath parts.

To make a heuristic-aided energy-efficient optimization model in the MIMO network to lower the energy expenditure in the network during the transmission process. Hence, the spectral efficiency of the MIMO network is greatly increased.

To perform an energy-efficient optimization in the MIMO network, an IFFSSO is recommended. By using this algorithm, spectral effectiveness and the system capability of the MIMO network are highly enriched.

To alleviate the multi-channel optimization difficulty, the SVD method is utilized. It is used to group the sub-channels of the MIMO network.

The leftover parts of the IFFSSO-based energy-efficient optimization model in the MIMO network are outlined as follows. In Section 2, the existing energy-efficient optimization methods in the MIMO network and their advantages and disadvantages are portrayed in detail. The proposed methodology is provided in Section 3. In Section 4, optimized energy efficiency using the proposed hybrid optimization strategy in the MIMO system is briefly presented. Section 5 explains the SVD-based sub-channel grouping and energy efficiency optimization and its objective functions. The results generated by the IFFSSO-based energy efficient optimization model in the MIMO network and the discussion corresponding to the results are given in Section 6. At last, the conclusion of the IFFSSO-based energy efficient optimization model in the MIMO network is presented in Section 7.

2. Related works

In 2020, Ha et al. [11] have examined the EE of the recommended approach in “Heterogeneous Wireless Powered Communication Networks (HWPCNs)”. Due to non-convex fractional programming, the optimization problem has highly nonlinear since; it fails to provide optimal solutions. Based on this, convex programming has been applied in this research to provide efficient outcomes for the developed model. In 2016, Senning et al. [27] have offered a cross-layer optimization strategy to reduce the amount of energy used to process at each physical layer to reduce the energy consumption per information bit. In 2022, Pang et al. [22] have investigated energy-efficient optimization techniques to solve the resource optimization issue which has been faced by massive MIMO systems. The research has concentrated on efficiency in the offline policy with ideal suppositions. In order to forecast forthcoming information, the Markov chain method was applied in this system. In 2018, Tan et al. [29] have suggested a brand-new energy-efficient resource allocation scheme in terms of the Energy Efficiency (GEE) optimization approach. Here, the strength, duration of time, and baseline Quality-of-Service (QoS) requirements were considered to maximize the GEE in this system. The efficacy of the algorithms and the accuracy of their theoretical analysis were demonstrated by numerical results.

In 2013, Chen et al. [4] have explored an energy beamforming in the MIMO system and where the wireless power has transferred to collect energy from the transmitter in order to maximize the QoS requirement in this system. The resource allocation plan was constructed to solve the optimization issue. In 2018, Song and Zheng [28] have designed a Particle Swarm Optimization (PSO)-based approach for maximizing energy efficiency. The Non-Orthogonal Multiple Access (NOMA) strategy was applied to transfer data to the H-AP. Here, the simulation has shown that the suggested approach was converged with different environmental conditions. In 2019, Wang et al. [33] have developed an EE optimization for Wireless Power Transfer (WPT)-based huge MIMO systems with various Sensor Node (SN). The efficiency of the suggested technique and the influence of hardware shortcomings on system performance were finally demonstrated through simulation experiments. In 2020, Dong et al. [8] have implemented a module that combines the broadband wireless communication system with several cross-layer wireless communication systems to improve the performance in terms of energy efficiency in the communication network system. Finally, a controlled experiment was used to evaluate the algorithm’s energy.

2.1. Recent works based on energy efficiency in the MIMO system

In 2023, Reddy et al. [24] have developed a new hybridization model which was generally termed as Adaptive Shark Smell-Coyote Optimization (ASS-CO) algorithm for enhancing the energy efficiency in the MIMO system. The superior performance enhancement has been achieved based on the spectral and energy efficiency over the existing approaches. In 2023, Liu et al. [15] have designed the non-orthogonal based slicing framework for offering better spectral efficiency in the Distributed Massive Multiple-Input Multiple-Output (DM-MIMO) system. Here, the successive results were obtained DM-MIMO system using the developed model. In 2024, Gao et al. [9] have implemented a high energy-efficient uplink Multi-Users (MU) communication system with variable-resolution analog to digital converters (ADC). This developed EE model has provided a better convergence rate.

2.2. Problem statement

The signals are forwarded from the target place to the destination place by generating sufficient energy from the power station of the MIMO wireless-powered network. But, non-convexity is the greatest problem associated with the MIMO wireless-powered system during the communication process, and it greatly affects the usefulness of the system. In order to solve the non-convexity issues, numerous approaches are suggested to improve the performance of the system. By the utilization of the existing techniques, the user cannot develop energy from the MIMO wireless-powered network for transmitting the signals. The privileges and drawbacks of the existing energy-efficient optimization techniques are categorized in Table 1.

Table 1
Features and challenges of energy-efficient optimization approaches

Author [citation] Methodology Features Challenges

Ha et al. [11] Dinkelbach approach ∙ It is adopted to tackle the convex optimization issues in the network. ∙ It is used for downlink and uplink transmission activities. ∙ It is not suitable to solve joint design optimization problems. ∙ It develops high calibration errors in the optimization process.

Senning et al. [27] Energy-aware rate adaptation scheme ∙ It is used for the cross-layer optimization process. ∙ It is used to identify the condition of the channel with low energy. ∙ It takes more attributes and layers for the optimization process. ∙ If the wrong system mode is selected, it may affect the optimization process.

Pang et al. [22] Markov chain method ∙ It is utilized to predict the prospective information of the structure. ∙ It is utilized to finish the resource optimization process within a limited time. ∙ It is quite complex to implement. ∙ It does not identify the energy arrival and the channel information of the network.

Tan et al. [29] GEE ∙ It is used for maximizing the global energy efficiency of the network. ∙ It is employed to solve fractional and nonlinear convex optimization issues. ∙ It has more numbers of processing steps so it takes more time for the optimization process. ∙ It consumes very high transmission power.

Chen et al. [4] TDD ∙ It is used to perform the wireless transmission process. ∙ It is used to get high energy efficiency by considering the quality of service. ∙ It takes more computing resources and power for long-scale transmission. ∙ It has high latency.

Song and Zheng [28] NOMA ∙ It has a sufficient amount of convexity, so it can be used to solve global optimal issues. ∙ It is used to optimize the transmitting power and harvesting time of the structure. ∙ It is not suitable to solve the multi-hop issues in the wireless-powered network. ∙ It requires a high amount of global coupling variables in order to identify the nonconvexity issues.

Wang et al. [33] MRC ∙ It is utilized to detect the code transferred from the sensor nodes of the network. ∙ It is used to convert the energy efficiency maximization issues into concave linear fractional programming. ∙ It is not fit to defeat the non-convex issues in the network. ∙ It is not suitable for the maximum power transmission process.

Dong et al. [8] Resource allocation ∙ It is used to allocate the resources to the downlink of the wireless-powered network. ∙ It is also used to lower energy consumption in the resource allocation process. ∙ It is not suitable to solve optimization issues in a large-scale network environment.

Author [citation]	Methodology	Features	Challenges
Ha et al. [11]	Dinkelbach approach	∙ It is adopted to tackle the convex optimization issues in the network. ∙ It is used for downlink and uplink transmission activities.	∙ It is not suitable to solve joint design optimization problems. ∙ It develops high calibration errors in the optimization process.
Senning et al. [27]	Energy-aware rate adaptation scheme	∙ It is used for the cross-layer optimization process. ∙ It is used to identify the condition of the channel with low energy.	∙ It takes more attributes and layers for the optimization process. ∙ If the wrong system mode is selected, it may affect the optimization process.
Pang et al. [22]	Markov chain method	∙ It is utilized to predict the prospective information of the structure. ∙ It is utilized to finish the resource optimization process within a limited time.	∙ It is quite complex to implement. ∙ It does not identify the energy arrival and the channel information of the network.
Tan et al. [29]	GEE	∙ It is used for maximizing the global energy efficiency of the network. ∙ It is employed to solve fractional and nonlinear convex optimization issues.	∙ It has more numbers of processing steps so it takes more time for the optimization process. ∙ It consumes very high transmission power.
Chen et al. [4]	TDD	∙ It is used to perform the wireless transmission process. ∙ It is used to get high energy efficiency by considering the quality of service.	∙ It takes more computing resources and power for long-scale transmission. ∙ It has high latency.
Song and Zheng [28]	NOMA	∙ It has a sufficient amount of convexity, so it can be used to solve global optimal issues. ∙ It is used to optimize the transmitting power and harvesting time of the structure.	∙ It is not suitable to solve the multi-hop issues in the wireless-powered network. ∙ It requires a high amount of global coupling variables in order to identify the nonconvexity issues.
Wang et al. [33]	MRC	∙ It is utilized to detect the code transferred from the sensor nodes of the network. ∙ It is used to convert the energy efficiency maximization issues into concave linear fractional programming.	∙ It is not fit to defeat the non-convex issues in the network. ∙ It is not suitable for the maximum power transmission process.
Dong et al. [8]	Resource allocation	∙ It is used to allocate the resources to the downlink of the wireless-powered network. ∙ It is also used to lower energy consumption in the resource allocation process.	∙ It is not suitable to solve optimization issues in a large-scale network environment.

The weaknesses of the state-of-the-art approaches are listed below.

In a classical MIMO system, the transfer of data takes place with more than one antenna. To alleviate this, the massive MIMO is performed where multiple antennas are connected to the base station to transfer the data in an efficient way.

The cost, storage, and computational time become challenging issues in the classical MIMO system. Moreover, the SVD decomposition model is used in this research work to strengthen better computational time in the massive MIMO system.

Generally, the massive MIMO can be used to achieve better spectral efficiency with significant energy savings. With an increasing number of antennas, the consumption of power gets increased and also it prone to reduce the energy capacity. In addition to this, the developed IFFSSO approach is utilized for parameter optimization to provide better energy capacity in the massive MIMO system.

The large number of antennas are considered in the MIMO system since, the mutual coupling of the antenna needs to be required. In this developed methodology, the SVD method is utilized for the implementation of a sub-channel grouping scheme in order to provide an effective outcome.

3. Background

In this section, the overall background of the MIMO system is described. It is partitioned into two sections where the system model and energy efficiency of the MIMO system are clearly stated in Sections 3.1 and 3.2. Moreover, the basic characteristics of the system model and energy model are described in below sections. Here, the brief discussion related to the proposed model is discussed in Section 3.3.

3.1. MIMO: System model

The MIMO communication system is enhanced by merging with the OFDM. The data can be independently transferred via the parallel channels present in the MIMO system. Hence, the need of energy efficiency plays a significant role in the MIMO-OFDM communication system [5]. The salient features of the MIMO system are portrayed as follows.

File structure: The file system becomes more effective in the media systems. Here, the disk transmission rate is high in the media files on the network. However, the latency rate gets increased by lowering the disk transmission rate.

Software instruments: For multimedia programming language, different software tools are adopted to provide better communication in the MIMO system.

Advanced dispensation power: A huge volume of data is handled by the advanced dispensation power in the communication network.

Format of files in multimedia: In multi-media systems, the data is available in various formats like PNG, WAV, JPEG, DOC, AVI, GIF, MID, and MEPG.

Input and outcome: The input as well as the output are considered as most important parameters in the communication system.

Operating system: The main intent of this operating system is to provide better response while communication takes place. Here, the instantaneous programs and the superior throughput give a sophisticated feature for the communication system.

Memory space and storage: In wireless media communication, memory and storage are considered as significant parameters. More memory is occupied by compression tactics as well as the dependability of the audio and video in the communication system.

Network services: Multimedia communication always requires a huge amount of communication latency during the transmission process. In this system, the total amount is required to pick the data packets by means of communication latency.

Generally, the MIMO system [6] consists of several numbers of antennas are accomplished in the transmitter and receiver end. Here, the terms ${Tn}_{c}$ and ${Rc}_{c}$ is represented as a total number of transmitter antennas and receiver antennas. Hence, the antenna matrix is formed and it is represented as ${Tn}_{c} \times {Rc}_{c}$ . In this network, the OFDM signal is generated and they have particular bandwidth $Wb$ , subcarrier R, and frame extent $EG$ . The receiver signal of the communication system is attained using the OFDM signals in the particular frame and it is expressed in Eq. (1). $\begin{matrix} (1) & a_{M} (J) = {GE}_{M} z_{m} (J) + n \end{matrix}$

Thus, the additive noise vector in the communication system is represented as n. Moreover, the channel matrix based on the frequency is expressed by the term ${GE}_{M}$ , where $M = 1, 2 \dots R$ . Here, the term R is the subcarrier of the communication network. At Mth the subcarrier, the transmitter and the receiver signal vector are represented as $z_{m} (J)$ and $a_{M} (J)$ correspondingly in which $z_{m} \in E^{{Tn}_{c}}$ , $a_{m} \in E^{{Rc}_{c}}$ and ${GE}_{M} \in E^{{Tn}_{c} \times {Rc}_{c}}$ respectively. The simplification loss is does not taken into account while assuming the term $G {j j^{K}} = L^{{Tn}_{c} \times {Rc}_{c}}$ , and the term E signifies the complex space, and the operator of prospect is indicated as $G {∙}$ .

In the communication channel, the extension of the frame is less than the coherence time of the channel, so block fading is considered in the discrete-time channels. Here, the frame extent is taken as 64FDS. The frame extent is varied for the subsequent frames, and it is used to identify the modifications in the channel. The system model of the MIMO is delineated in Fig. 1.

Fig. 1.

System model of the MIMO.

3.2. Energy efficient model

In the MIMO model, several wireless nodes are connected via the communication link. The dispensation blocks of the transmitter and the receivers of the MIMO system [19] are taken into consideration to find the total energy consumption. Still, the baseband signal processing blocks of this system generate lots of complexities during this process, so this block is neglected at this phase. Moreover, the error correction codes are also considered in this system to neglect the complexities involved in this structure. As mentioned earlier, the transmitter and the receiver in this network are taken as ${Tn}_{c}$ , and ${Rc}_{c}$ respectively. The paths of the entire antennas in this network are used to transfer the frequency synthesizer. The power utilization and the power amplifiers of the MIMO network are taken as $Q_{D}$ , and $Q_{QB}$ respectively. The broadcast power $Q_{out}$ mainly relies on the power amplifier of the MIMO network, and it is identified by Eq. (2). $\begin{matrix} (2) & Q_{out} = {\bar{D}}_{c} S_{c} \times \frac{{(4 π e)}^{2}}{H_{u} H_{s} χ^{2}} N_{m} O_{g} \end{matrix}$

Here, the bit rate is represented as $S_{c}$ , and also the energy required for the receiver of the network is represented as ${\bar{D}}_{c}$ . Here, the variables $H_{u}$ , and $H_{s}$ is defined as the transmitter and the receiver of the MIMO network. Also, the span of the transmission is delineated as e, and also the background noise and the hardware process variation are compensated by the link margin denoted as $N_{m}$ . The size of the noise receiver is termed as $O_{g}$ , and it is predetermined by Eq. (3). $\begin{matrix} (3) & O_{g} = \frac{O_{s}}{O_{0}} \end{matrix}$

Here, the power spectral effectiveness of the signified as $O_{s}$ , and $O_{0} = - 171 dBm / Hz$ . The total power consumed by the power amplifiers of the MIMO network is evaluated by Eq. (4). $\begin{aligned} (4) & Q_{QB} = (1 + ℑ) Q_{out} \\ (5) & ℑ = \frac{o}{ς} - 1 \end{aligned}$

Here, the peak average ratio is indicated as o, and the exhaust efficiency is illustrated as ς.

The total power utilization is determined by Eq. (6). $\begin{aligned} Q_{D} & \approx N_{u} (Q_{EBD} + Q_{mer} + Q_{ftl ({Tn}_{c})}) + 2 Q_{cyn} \\ (6) & + N_{s} (\begin{array}{c} Q_{MOB} + Q_{mer} + Q_{JGB} \\ + Q_{ftl ({Rn}_{c})} + Q_{BED} \end{array}) \end{aligned}$

The power utilization of the digital to the analog transformer is represented as $Q_{EBD}$ and also the power utilization of the mixer is represented as $Q_{mer}$ , the power utilization of the transmitter and the receiver of the active filters are denoted as $Q_{ftl ({Tn}_{c})}$ , and $Q_{ftl ({Rn}_{c})}$ . Moreover, the terms $Q_{JGB}$ , $Q_{MOB}$ , $Q_{cyn}$ and $Q_{BED}$ define the power utilization of the midway frequency amplifier, squat noise amplifier, incidence synthesizer, and analog to digital transformer respectively. $\begin{matrix} (7) & F_{Cu} = \frac{(Q_{QB} + Q_{d})}{S_{c}} \end{matrix}$

The above Eq. (7) represents the entire energy utilization of the permanent structure.

3.3. Proposed methodology

An efficient energy efficiency optimization is needed where the research work is very helpful to develop a novel technique for enhancing the system’s capacity and spectral efficiency. Here, the SVD model has the ability to adapt a sub-channel grouping scheme. After rearranging all the sub-channels, the sub-channel grouping is taken, and also the energy efficiency optimization is done using the IFFSSO. However, it helps to enhance the system capacity and spectral efficiency. Moreover, the different experimental results are carried out and also it is revealed through various conventional models for further enhancement. The visualization illustration of the developed model is shown in Fig. 2.

Fig. 2.

Architectural representation of developed model based energy efficiency optimization model.

4. Optimized energy efficiency using the proposed hybrid optimization strategy in MIMO system

The background and general characteristics of the existing FFO and SSA algorithms are provided in below section. The rationality and the need for updating the given algorithms are depicted and also the mathematical model has been described. Moreover, the parameter tuning process and also the updation of random parameters for energy efficiency with the help of the developed IFFSSO algorithm. Especially, the advancements of the promoted IFFSSO algorithm are given as follows.

4.1. FFO algorithm

The FFO is mainly employed to find the global optimization, and also, the complex optimization issues are solved by this algorithm. This algorithm consists of a very simple implementation process, so it is adopted in all of the works. But, it is very difficult to handle the huge size of nonlinear optimization issues. The SSA is the meta-optimizer, and it can be prominently used to avoid the local optimal issues. Also, the primary random solutions are enriched by the SSA. But, it faces several complexities while maintaining the balance between the exploration and the exploitation phase. So, these issues are downcast by the newly developed IFFSSO. The developed IFFSSO is created by incorporating the conventional FFO and SSA algorithms. The main intent of the explored IFFSSO is to optimize the energy in the wireless network. This optimization of energy improves the communication process in the MIMO network. Hence, the performance of the network during the communication process is augmented. Here, the optimization defines to a process for discovering the input constraints to a function that provides the maximum or minimum findings of the function. Additionally, the optimization issues in expert systems are resolved by using intelligent techniques which provide effective outcomes. The advantages of the existing FFO and SSA algorithms in the MIMO system are described below. While considering the FFO algorithm, it tends to collect the overall optimum solution for providing better accurate performance in the MIMO system and also it helps to enhance the convergence rate. Also, the SSA algorithm tends to offer better QoS based on the resource constraints. The benefits of the hybridization of the FFA and SSA algorithm are described as follows. While optimizing the energy efficiency in the MIMO system, better resultant outcomes are provided to attain the efficient outcome where it helps to enhance the system performance. The developed IFFSSO is put into practice by the old position and the positions attained by the existing FFO and SSA. The process associated with the explored IFFSSO is formulated in Eq. (8). $\begin{matrix} (8) & Y_{new} = Y_{O} + (\frac{1}{(\frac{Y_{j}}{y_{k}^{j}})}) \end{matrix}$

Here, the innovated position accomplished by the explored IFFSSO is represented as $Y_{new}$ , the final position of the FFO is depicted as $Y_{j}$ , the final position in the SSA is expressed as $y_{k}^{j}$ , and the position in the 99th iteration is illustrated as $Y_{O}$ . The Background and characteristics of the FFO and SSA algorithm are described as follows.

The FFO [21] is considered as a strong optimization algorithm, and it is very simple to handle. This algorithm is executed by mimicking the food discovery characteristics of the fruit fly. The fruit fly can have the ability to smell all kinds of aromas developed in the surrounding environment. The fruit fly started flying towards the direction of the target food if it reached the location of the food.

The position of the fruit fly insects is signified in Eq. (9). $\begin{matrix} (9) & startY_axe; startZ_axe \end{matrix}$

The fruit fly insects search for their food using their smelling sense, and it is denoted in Eq. (10). $\begin{aligned} (10) & Y_{j} = Y_axe + arbi value \\ (11) & Z_{j} = Z_axe + arbi value \end{aligned}$

The fruit fly insect faces lots of complexities when it searches its food. To lower this complexity, the odor attentiveness verdict value and the place of the target food are initially determined by using Eq. (12) and Eq. (13). $\begin{aligned} (12) & {place}_{j} = \sqrt{Y_{j}^{2} + Z_{j}^{2}} \\ (13) & T_{j} = \frac{1}{{place}_{j}} \end{aligned}$

Here, odor attentiveness verdict value is delineated as $T_{j}$ , and the position of the target food is represented as ${place}_{j}$ .

For the purpose of identifying the odor attentiveness of the entire fruit fly, the value of $T_{j}$ is substituted in the fitness function, and it is given in Eq. (14). $\begin{matrix} (14) & {odur}_{j} = fit fun (T_{j}) \end{matrix}$

After this process, the fruit fly having the high odor attentiveness value is determined by Eq. (15). $\begin{matrix} (15) & (excellent odurindex) = max (odur) \end{matrix}$

The fruit fly started moving toward the direction of the target food by using its excellent eyesight, and it is represented in Eq. (16). $\begin{aligned} (16) & excellent odur = odur excellent \\ (17) & Y_axe = Y (excellindex) \\ (18) & Z_axe = Z (excellindex) \end{aligned}$

The above process is repeated until the best odor attentiveness verdict value is attained.

The SSA [20] algorithm is motivated by the team hunting characteristics of the Salp fish in the oceans or sea. Salp is the one type of jellyfish, and it is transparent in nature. This specifies the moves in water by pumping the water in the opposite direction. Mostly these types of species form a chain-like structure in the sea or ocean. This slap chain is mostly used for hunting and rapid displacements of the Salp fish.

Initially, the commanders and the supporters are selected in the Salp chain of this fish. In the Salp chain, the primal Salp fish is considered as the commander, and the remaining Salp fishes are taken as the supporters. The commander guides the total Salp chain in an excellent way.

In the particular search space o, the entire Salp fish is located in a uniform manner. The 2D matrix y is adopted to store the location information of all Salp fishes. At the search space o, the target of the Salp fish is indicated as G, and the spot of the commander fish is upgraded by Eq. (19). $\begin{matrix} (19) & y_{k}^{1} = \{\begin{array}{ll} G_{k} + d 1 ({ubou}_{k} - {lbou}_{k}) d 2 + {lbou}_{k} & d 3 ⩾ 0 \\ G_{k} - d 1 ({ubou}_{k} - {lbou}_{k}) d 2 + {lbou}_{k} & d 3 < 0 \end{array} \end{matrix}$

Here, at the dimension k, the upper and the lower bound is indicated as ${ubou}_{k}$ , ${lbou}_{k}$ , the location of the food destination is illustrated as $G_{k}$ , the arbitrary numbers are denoted as $d 1$ , $d 2$ , $d 3$ respectively, and the location of the commander Salp fish is signified as $y_{k}^{1}$ .

The exploitation and the exploration phase in this algorithm are maintained with the aid of the coefficient $d 1$ , and it is determined by Eq. (20). $\begin{matrix} (20) & d 1 = 2 e^{- (\frac{4 m}{M}) 2} \end{matrix}$

Thus, the supreme iteration value is expressed as M, and the existing iteration is depicted as m. The random numbers in the range of [0, 1] are indicated as $d 2$ , $d 3$ respectively.

The location of the supporters in the Salp chain is updated by talking about Newton’s law of motion, and it is provided in Eq. (21). $\begin{matrix} (21) & y_{k}^{j} = \frac{1}{2} b u^{2} + w_{0} u \end{matrix}$

Here, the primary velocity is signified as $w_{0}$ , at the dimension k, the spot of the Salp fish is elucidated as $y_{k}^{j}$ and here $k ⩾ 2$ . The value of $b and w$ is estimated by Eq. (22) and Eq. (23). $\begin{aligned} (22) & b = \frac{w_{end}}{w_{0}} \\ (23) & w = \frac{y - y_{0}}{u} \end{aligned}$

Here, the value of $w_{0}$ is taken as one. The location of the Salp fish is also upgraded by Eq. (24). $\begin{matrix} (24) & y_{k}^{j} = \frac{1}{2} (y_{k}^{j} + y_{k}^{j - 1}) \end{matrix}$

Here, the location of the Salp fish at kth dimension is elucidated as $y_{k}^{j}$ where $k ⩾ 2$ .

The flow representation of the offered IFFSSO is specified in Fig. 3, and the pseudocode of the offered IFFSSO is indicated in Algorithm 1.

Fig. 3.

Flow representation of the IFFSSO.

Algorithm 1

Implemented IFFSSO

5. SVD-based subchannel grouping and energy efficiency optimization and its objective functions

Overall this section shows the energy efficiency optimization and also the objective function for the developed model is clearly depicted in this section. Here, the basic introduction of SVD and also the channel grouping of MIMO are discussed in Sections 5.1 and 5.2. However, the description of energy-efficient optimization with fitness formulation is discussed in Section 5.3.

5.1. Basic SVD

The SVD method is used to resolve the multi-channel optimization problem in the wireless network. Moreover, the frame extension values are constantly varied for each frame in the network. Therefore, the SVD method is used to group the sub-channel in the network, and it is formulated in Eq. (25). $\begin{matrix} (25) & N (N = minimum (N_{{Tn}_{c}}, N_{{Rn}_{c}}) \end{matrix}$

The sub-channel grouping process is initiated in order to start up the energy efficiency process in the MIMO network. Here, the multichannel optimization issues are transformed into multi-target single-channel optimization issues. This transformation process is mainly achieved by the SVD-based sub-channel grouping system. The channel matrix ${GE}_{M}$ of each and every sub-carrier of the network is undergone for the SVD process, and it is indicated in Eq. (26). $\begin{matrix} (26) & {GE}_{M} = W_{M} \sqrt{{\tilde{υ}}_{M}} X_{M}^{GE} \end{matrix}$

Here, the unitary matrices are illustrated as $X_{M}$ , and $W_{M}$ , they are accompanied in the channel matrix. Here, the $X_{M} \in E^{{Tn}_{c} \times {Rc}_{c}}$ , and $W_{M} \in E^{{Tn}_{c} \times {Rc}_{c}}$ . Using aforementioned conditions, the two types of matrices are generated. The block matrix is taken as ${\tilde{υ}}_{M} = [υ_{M}, 0_{N_{{Tn}_{c}, {Tn}_{c} - {Rn}_{c}}}]$ if the receiver antenna’s count is lower than the transmitter antenna’s. If the transmitter antennas are greater than the receiver antenna, then the block matrix is adopted as ${\tilde{υ}}_{M} = [υ_{M}, 0_{N_{{Rn}_{c}, {Tn}_{c} - {Rn}_{c}}}]$ . The total number of sub-channel gain is signified using a block matrix termed as $υ_{M} = dig (κ_{1, M} \dots, κ_{0, M}) κ_{1, M} ⩾ 0, \forall_{o} = 1, \dots Q M = 1, \dots R$ . At the Mth subcarrier, the gain of the sub-channel set is expressed as ${κ_{1, M}}_{o = 1}^{Q}$ . The SISO sub-channel is developed as a result of the SVD techniques. For the orthogonal subcarrier R, the subchannels are further divided into $Q \times R$ parallel space-frequency sub channels. The structural outline of the SVD model is given in Fig. 4.

Fig. 4.

Structural outline of the SVD model.

5.2. Channel grouping

The MIMO system is highly prone to multi-channel optimization problems because of the numerous antennas in the network, so it greatly affects communication performance. So the sub-channel grouping is performed to solve the multi-channel optimization issues in the MIMO network. The channel grouping process is accomplished by the SVD process. Initially, the sub-channels are arranged in descending order. Subsequently, the grouping process is carried out with the assistance of SVD. The sub-channel grouping process is mainly used to neglect the multi-channel optimization problem in the MIMO network. So, the signals from several antennas are easily combined to achieve an effective communication process. Thus, the user capacity is greatly increased.

5.3. Energy-efficient optimization with fitness formulation

After the accomplishment of the sub-channel grouping process, the energy efficiency optimization process is carried out by the developed IFFSSO. Because of the developed IFFSSO, the spectral efficiency and the system capacity of the MIMO network are enriched without affecting the bandwidth of the wireless-powered network. Hence, the active antennas in the wireless-powered network are approximately identified as a result of this process; the development of wireless data traffic in the MIMO network is neglected. The objective function of the IFFSSO-based energy efficient optimization model in the MIMO network is given in Eq. (27). $\begin{matrix} (27) & F = \underset{{EE}}{arg min} (\frac{1}{SE + SC}) \end{matrix}$

Here, the energy efficiency is denoted by the term $EE$ , and it lies in the middle of $[0.025, 0.5]$ , the spectral efficiency $SE$ , and the spectral capacity $SC$ is calculated by Eq. (28) and Eq. (29). $\begin{matrix} (28) & SE = \frac{dr}{Bw} \end{matrix}$

Here, the data rate is represented as $dr$ , and the bandwidth of the channel is specified as $Bw$ . $\begin{matrix} (29) & SC = - \frac{1}{θ} log (\int_{0}^{\infty} e^{- EGD {log}_{2} (1 + ς (θ, κ) κ)} s \prod_{o, M} (κ) d κ) \end{matrix}$

Here, the allocated energy transmission in the sub-channels of the network is represented as $ς (θ, κ)$ ; and the sub-channel is depicted as $s \prod_{o, M} (κ)$ .

6. Results and discussion

In the result section, the detailed description of the implementation process for the designed energy efficient optimization model is stated in Section 6.1. In Sect. 6.2, the standard performance measures are evaluated for attaining better sufficient outcomes. The upcoming section briefly explains the superior performance in terms of IFFSSO-based energy optimization scheme in a MIMO wireless-powered network. In the end of this section, the obtained numerical findings of the developed model are described concisely.

6.1. Stimulation settings

MATLAB 2020a software was adopted to implement the IFFSSO-based energy optimization scheme in a MIMO wireless-powered network. The implementation required some additional parameters like population count and maximum iteration, and they were taken as 10, and 100, respectively. Here, the chromosome span was the same as the number of nodes in the MIMO network. Further, the effectiveness of the IFFSSO-based energy optimization scheme in the MIMO wireless-powered network was identified by comparing it with the existing algorithm such as “Electric Fish Optimization (EFO) [36], Tree Optimization Algorithm (TOA)” [18], FOA [21], SSA [20], and HFF-SSO [14]. Also, recent techniques like the Improved Butterfly Optimization (IBFO) algorithm [19], and the Adaptive Shark Smell-Coyote Optimization (ASS-CO) algorithm [24] are compared and validated with the developed model. The simulation parameters of the designed energy-efficient optimization model are shown in Table 2.

Table 2
Simulation parameters of the designed energy efficient optimization model

Parameter Values

Multiple Transmitters (MT) 4

Multiple Receivers (MR) 4

Theta (θ) $10^{- 3}$

Average transmission power constraint 0.1

Minimum value (multiple transmitters & multiple receivers) (M) 4

Number of subcarriers (N) 3

Time (ms) 1

Bandwidth (MHz) 1

Parameter	Values
Multiple Transmitters (MT)	4
Multiple Receivers (MR)	4
Theta (θ)	$10^{- 3}$
Average transmission power constraint	0.1
Minimum value (multiple transmitters & multiple receivers) (M)	4
Number of subcarriers (N)	3
Time (ms)	1
Bandwidth (MHz)	1

6.2. Evaluation metrics

The evaluation metrics for the recommended energy optimization scheme in the MIMO wireless-powered network are described as follows.

(a) Statistical test: The optimization approaches used for optimization that is “stochastic in nature”, it does not contain the capability to attain accurate results at a single implementation. Therefore, all the algorithms are needed for executing five times, and the “statistic of total validation” taking into consideration of “median, mean, standard deviations, best performance, and worst performance,” are calculated.

(b) Effective Capacity $C_{E} (θ)$ : It recognizes the higher constant data arrival rate at the transmitter buffer with the help of desired Quality of Service (QoS) constraints. It is equated in Eq. (30). $\begin{matrix} (30) & \begin{array}{c} C_{E} (θ) = max_{\begin{array}{c} H_{k} ≻ 0 \\ k t (H_{k}) ⩽ 1 \end{array}} - \frac{1}{θ SR} {log}_{e} F_{{\hat{J}}_{k}} {e^{- θ TN (y_{k} x_{k})}} \end{array} \end{matrix}$ Here, θ is an exponent of QoS, and also the term $H_{k}$ is denoted as the variation of time since it is a function of $F_{{\hat{J}}_{k}}$ . The total count of bits served from the transmitter is defined as $SR$ and the conditional probability density function is stated as $y_{k}$ and $x_{k}$ . The constraint ${e^{- θ TN (y_{k} x_{k})}}$ is termed as the lower bound of the effective capacity.

(c) Energy Efficiency (EE): It is the proposition of the network sum rate to the whole energy consumption. It is experimented in Eq. (31). $\begin{matrix} (31) & \begin{array}{c} EE = Capacity (C) / E where E = Ef + Lr \end{array} \end{matrix}$ Here, the term $Ef$ is denoted as the fixed energy consumption and also the constraint $Lr$ is stated as the average of energy efficiency.

(d) Spectral Efficiency (η): It is the data rate that can be communicated over a presented bandwidth in a communication system. It is expressed as bits-per-second per-hertz, (bits/s/Hz). $\begin{matrix} (32) & \begin{array}{c} η \approx S / A H (b/s/Hz/site) \end{array} \end{matrix}$ In the aforementioned equation, the term S is the bit rate, A is the bandwidth, and H is the cluster size.

6.3. Convergence study

The convergence study of the IFFSSO-based energy optimization scheme in the MIMO wireless-powered network is provided in Fig. 5. The cost utilization of the IFFSSO-based energy optimization scheme in the MIMO wireless-powered network is depleted than the EFO, TOA, FOA, SSA, and HFF-SSO with 50%, 83.33%, 50%, 50% and 20% at iteration 10. Hence, the convergence rate of the IFFSSO-based energy optimization model in a MIMO wireless-powered network is lower than the existing algorithms.

Fig. 5.

Convergence study of the heuristic-based energy efficient optimization model among several algorithms.

6.4. Energy capacity estimation

The energy capacity estimation of the IFFSSO-based energy efficient optimization model in MIMO wireless powered network is elucidated in Fig. 6. At average power constraints of 5, the effective capacity of the IFFSSO-based energy efficient optimization model in MIMO wireless powered network is upraised than the EFO, TOA, FOA, SSA, HFF-SSO with 26.66%, 20.63%, 18.75%, 8.57% and 2.70%. So, the energy capacity of the IFFSSO-based energy efficient optimization model in the MIMO wireless-powered network is emphasized more than the current algorithms.

Fig. 6.

Energy capacity estimation of the heuristic-based energy efficient optimization model based on (a) average power constraints, (b) QoS statistical exponent, and (c) iterations.

6.5. Energy efficiency examination

The energy efficiency study of the IFFSSO-based energy efficiency optimization in MIMO wireless powered network is illustrated in Fig. 7. At average power constraint 10, the energy efficiency of the IFFSSO-based energy efficiency optimization model is 26.08% improved than EFO, 25% improved than TOA, 13.28% improved than FOA, 8.20% improved than SSA and 7.40% improved than HFF-SSO. Therefore, the energy efficiency of the IFFSSO-based energy efficient optimization in the MIMO wireless-powered network model is more enriched than the conventional algorithms.

Fig. 7.

Energy efficiency evaluation of the developed model with various heuristic-based energy efficient optimization models in terms of (a) average power constraints, (b) QoS statistical exponent, and (c) iterations.

Fig. 8.

Analysis based on energy efficiency using heuristic algorithms in terms of (a) transmission power and (b) no. of users.

6.6. Spectral and energy efficiency of the developed model

The performance examination is done based on the energy and spectral efficiency of the developed model is illustrated in Fig. 8 and Fig. 9. Here, the performance of the developed model is enhanced with transmission power, and number of users are considered to show the effective outcomes. With high transmission power, the developed model offers better communication in the MIMO systems. In accordance, the existing EFO algorithm shows lower performance where traffic or congestion occurs which is not efficient for the MIMO system. Thus, the analysis is more beneficial to prove the developed model shows better performance than the existing heuristic algorithms.

Fig. 9.

Analysis based on spectral efficiency using heuristic algorithms in terms of (a) transmission power and (b) no. of users.

6.7. Statistical study

The statistical study of the IFFSSO-based energy efficiency optimization in MIMO wireless powered network is formulated in Table 3. The standard deviation of the IFFSSO-based energy efficiency optimization in MIMO wireless powered network is progressed than the EFO, TOA, FOA, SSA, and HFF-SSO with 54.54%, 12%, 53.68%, and 80.68%. Thus, the standard deviation of the IFFSSO-based energy efficiency optimization in the MIMO wireless-powered network is better than the conventional algorithms.

6.8. Comparative analysis of the offered model for energy efficiency

The comparative analysis is performed using the developed model for energy efficiency is shown in Table 4. Here, the validation takes place in terms of energy capacity and energy efficiency based on different configurations. This analysis is helpful to offer a reliable power supply in the energy efficiency optimization model for the MIMO system. Based on this, the developed model offers enhanced spectral efficiency in order to provide reliable performance. Moreover, the developed model shows the energy capacity value of 10403 (bits/Hz) at 3rd configuration. Throughout, the empirical findings, the offered IFFSSO model shows enriched performance while validating with recent approaches.

Table 3
Statistical analysis of heuristic-based energy efficiency optimization in MIMO network among several algorithms

Algorithms Best Worst Mean Median Standard deviation

EFO [36] 0.0552 0.0570 0.0548 0.0545 0.0547

TOA [18] 0.1441 0.1437 0.0679 0.1091 0.0679

FOA [21] 0.0604 0.0628 0.0575 0.0565 0.0564

SSA [20] 0.0553 0.0570 0.0555 0.0548 0.0547

HFF-SSO [14] 0.0133 0.0119 0.0041 0.0062 0.0030

Proposed IFFSSO 0.0552 0.0570 0.0548 0.0545 0.0547

Algorithms	Best	Worst	Mean	Median	Standard deviation
EFO [36]	0.0552	0.0570	0.0548	0.0545	0.0547
TOA [18]	0.1441	0.1437	0.0679	0.1091	0.0679
FOA [21]	0.0604	0.0628	0.0575	0.0565	0.0564
SSA [20]	0.0553	0.0570	0.0555	0.0548	0.0547
HFF-SSO [14]	0.0133	0.0119	0.0041	0.0062	0.0030
Proposed IFFSSO	0.0552	0.0570	0.0548	0.0545	0.0547

Table 4

State-of-art method comparison with developed model

Configurations	HFF-SSO [14]	IBFO [19]	ASS-CO [24]	IFFSSO
Energy capacity (bits/Hz)
1	7268.4	7472.2	7203.2	8320.3
2	8224	8227.4	7742.5	8869.8
3	8542.4	9661.1	8285.1	10403
4	7746.5	7850.1	7473.2	8595.3
5	8385.3	8946.4	8015.9	9638.5
Energy efficiency (bits/Hz/Joule)
1	64326	75110	71867	97248
2	$1.12 \times 10^{05}$	$1.24 \times 10^{05}$	$1.10 \times 10^{05}$	$1.45 \times 10^{05}$
3	$1.82 \times 10^{05}$	$1.53 \times 10^{05}$	$1.54 \times 10^{05}$	$2.49 \times 10^{05}$
4	88361	99391	91129	$1.21 \times 10^{05}$
5	$1.47 \times 10^{05}$	$1.38 \times 10^{05}$	$1.32 \times 10^{05}$	$1.97 \times 10^{05}$

6.9. Comparison of the developed model and existing approach using the Matlab platform and WEAK tool

The comparative analysis of the developed model and the existing approach using the MATLAB platform and WEKA tool is shown in Table 5. Here, the analysis is executed based on the number of users with different variations like 10, 20, 30, 40, and 50, and also the error analysis of MAE is taken for the experimentation. While analyzing the Table 5 result, the RF model shows a higher error rate than our proposed model regarding MAE metrics. Here, the given developed IFFSSO algorithm was experimented with using the MATLAB platform. Thus, the resultant findings of the developed model has clearly shown that the MATLAB platform provides better results than the WEKA tool.

Table 5
Comparison among the developed model and existing approach using Matlab platform and WEAK tool

MAE analysis

No. of users Random forest [23] using WEKA Proposed IFFSSO algorithm using MATLAB

10 16.832 8.1424

20 10.374 6.9915

30 8.953 6.1102

40 6.467 4.9191

50 21.398 4.0012

MAE analysis
10	16.832	8.1424
20	10.374	6.9915
30	8.953	6.1102
40	6.467	4.9191
50	21.398	4.0012

6.10. Discussion based on attained results

The experimentation of the given recommended energy efficiency optimization model in the MIMO network is conducted with the purpose of showing its effectiveness. Here, the Fig. 4 visualizes the convergence graph where it provides the better performance. At the 100th iteration, the designed method attains a better convergence rate. The EFO attains lower and also the HFF-SSO attains second better performance. Owing to the lowest performance the EFO easily falls into the local optimum. Figure 5 shows the validation of the energy capacity of the designed approach. Here, the EFO attains lower performance. While taking Fig. 6, the validation is conducted regarding energy efficiency where the recommended approach obtains better performance than the other baseline approaches. Table 2 shows the statistical validation of the offered regarding standard metrics. In this research work, the efficacy of the proposed model is validated based on the best metrics. Thus, the simulation outcome reveals that the given offered approach is statistically significant.

7. Conclusion

A heuristic-assisted energy efficiency optimization model in the MIMO network is adopted to optimize the energy efficiency of the MIMO network. So, the spectral efficiency and the system capacity of the MIMO network are greatly increased. The MIMO network was composed of several numbers of sensor nodes. All of these sensor nodes were used for the data transmission process, so more amount of energy was consumed by the sensor nodes. Therefore, the lifetime of the wireless network was greatly affected. In this work, the multi-channel optimization problem was solved by the SVD process. This SVD was used for the sub-channel grouping process. Before the initialization of the grouping process, the sub-channels were arranged in descending order, and the SVD was adopted for the grouping process. Hence, the multi-channel optimization problems were neglected, so the signal from the entire sensor nodes was effectively combined to perform the perfect communication process. After finishing the sub-channels grouping process, the developed IFFSSO was used for the energy-efficient optimization process. As a consequence of this optimization, the spectral efficiency and the system capacity of the network were greatly increased. So, huge amounts of data are transmitted via the antennas of the MIMO network. At average power constraints of 5, the effective capacity of the IFFSSO-based energy efficient optimization model in the MIMO wireless powered network was upraised than the EFO, TOA, FOA, SSA, HFF-SSO with 26.66%, 20.63%, 18.75%, 8.57%, and 2.70%. Hence, the performance of the IFFSSO-based energy efficiency optimization in the MIMO wireless-powered network was more privileged than the conventional approaches. A few of the limitations of this work are added as follows. Need to analyze the impact of diverse constraints on the whole performance. It is required to attain a better power consumption rate and also to deliver the requested UEs’ data rate with a better energy efficiency rate. In the future, we will investigate more details about the joint design optimization problems and also it offers high calibration errors in the optimization procedure. Additionally, we will try to add a high amount of global coupling variables to identify the non-convexity issues.

Conflict of interest

None to report.

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MAE analysis
No. of users	Random forest [23] using WEKA	Proposed IFFSSO algorithm using MATLAB
10	16.832	8.1424
20	10.374	6.9915
30	8.953	6.1102
40	6.467	4.9191
50	21.398	4.0012

Modified hybrid fruit fly-based salp swarm optimization strategy for energy efficient optimization in MIMO Wireless Powered Communication Networks

Abstract

Keywords

1. Introduction

2. Related works

2.1. Recent works based on energy efficiency in the MIMO system

2.2. Problem statement

3.1. MIMO: System model

3.3. Proposed methodology

4.1. FFO algorithm

5.1. Basic SVD

5.3. Energy-efficient optimization with fitness formulation

6. Results and discussion

6.1. Stimulation settings

6.3. Convergence study

6.8. Comparative analysis of the offered model for energy efficiency

Table 5 Comparison among the developed model and existing approach using Matlab platform and WEAK tool MAE analysis No. of users Random forest [23] using WEKA Proposed IFFSSO algorithm using MATLAB 10 16.832 8.1424 20 10.374 6.9915 30 8.953 6.1102 40 6.467 4.9191 50 21.398 4.0012

7. Conclusion

Conflict of interest

References

Table 5
Comparison among the developed model and existing approach using Matlab platform and WEAK tool

MAE analysis

No. of users Random forest [23] using WEKA Proposed IFFSSO algorithm using MATLAB

10 16.832 8.1424

20 10.374 6.9915

30 8.953 6.1102

40 6.467 4.9191

50 21.398 4.0012