Green concept of neuromarketing based on a systematic review using the bibliometric method

Negin Sangari; Payvand Mirzaeian Khamseh; Shib Sankar Sana; Negin Sangari; Payvand Mirzaeian Khamseh; Shib Sankar Sana

doi:10.3934/GF.2023016

Green Finance

2023, Volume 5, Issue 3: 392-430. doi: 10.3934/GF.2023016

Previous Article Next Article

Review Special Issues

Green concept of neuromarketing based on a systematic review using the bibliometric method

1.
Department of Management, Faculty of Social Sciences and Economics, Alzahra University, Tehran, Iran
2.
Department of Mathematics, Kishore Bharati Bhagini Nivedita College, Ramkrishna Sarani, Behala, Kolkata, 700060, India

Received: 02 August 2023 Revised: 25 August 2023 Accepted: 30 August 2023 Published: 18 September 2023
JEL Codes: G41, M31, Z33

Unlike traditional marketing methods, neuromarketing has shown new insights and higher prediction accuracy. This research uses the bibliometric method to analyze the objectives like the analysis and integration of the green concept of neuromarketing, recognition of the useful authors, the years of publication of documents, authoritative journals that publish articles in this field and keywords around the concept of neuromarketing. The tools presented in neuromarketing expand and improve the perception of the enthusiasts and researchers in this field, and it compares the results obtained from different approaches. From the methodological point of view, this research is qualitative and based on Iden et al.'s (2017) model, consisting of four steps of planning, selecting, extracting and implementing and combining it with setting of Silva's (2015) articles in the form of a review. A bibliometric system is implemented, and VOS viewer software was used to analyze the results.

The findings are presented in two phases. In the first phase, the performance analysis, the share of the annual production of neuromarketing documents, the percentage of the production of authoritative quarterly journals of this field, the share of the output of related subject areas, the share of the countries' published articles and the share of the documents by productive authors were identified and studied. Also, knowledge maps were drawn in the second phase, and 17 clusters are found, including 109 items and 131 keywords. The theoretical contribution of this article consists of the field of green neuromarketing, which is categorized into four clusters with themes of sustainability and green consumption. The results of this study were obtained based on the framework of theory, context, method, antecedents, decisions, and outcomes. All the keywords related to neuromarketing were categorized from the analysis of the previous articles and its features were studied in the proposed model.

Keywords:

Citation: Negin Sangari, Payvand Mirzaeian Khamseh, Shib Sankar Sana. Green concept of neuromarketing based on a systematic review using the bibliometric method[J]. Green Finance, 2023, 5(3): 392-430. doi: 10.3934/GF.2023016

Related Papers:

[1]	Xiangyang Ren, Shuai Chen, Kunyuan Wang, Juan Tan . Design and application of improved sparrow search algorithm based on sine cosine and firefly perturbation. Mathematical Biosciences and Engineering, 2022, 19(11): 11422-11452. doi: 10.3934/mbe.2022533
[2]	Anlu Yuan, Tieyi Zhang, Lingcong Xiong, Zhipeng Zhang . Torque control strategy of electric racing car based on acceleration intention recognition. Mathematical Biosciences and Engineering, 2024, 21(2): 2879-2900. doi: 10.3934/mbe.2024128
[3]	Shijing Ma, Yunhe Wang, Shouwei Zhang . Modified chemical reaction optimization and its application in engineering problems. Mathematical Biosciences and Engineering, 2021, 18(6): 7143-7160. doi: 10.3934/mbe.2021354
[4]	Guowen Li, Ying Xu, Chengbin Chang, Sainan Wang, Qian Zhang, Dong An . Improved bat algorithm for roundness error evaluation problem. Mathematical Biosciences and Engineering, 2022, 19(9): 9388-9411. doi: 10.3934/mbe.2022437
[5]	Shenghan Li, Linlin Ye . Multi-level thresholding image segmentation for rubber tree secant using improved Otsu's method and snake optimizer. Mathematical Biosciences and Engineering, 2023, 20(6): 9645-9669. doi: 10.3934/mbe.2023423
[6]	Chikun Gong, Yuhang Yang, Lipeng Yuan, Jiaxin Wang . An improved ant colony algorithm for integrating global path planning and local obstacle avoidance for mobile robot in dynamic environment. Mathematical Biosciences and Engineering, 2022, 19(12): 12405-12426. doi: 10.3934/mbe.2022579
[7]	Yijie Zhang, Yuhang Cai . Adaptive dynamic self-learning grey wolf optimization algorithm for solving global optimization problems and engineering problems. Mathematical Biosciences and Engineering, 2024, 21(3): 3910-3943. doi: 10.3934/mbe.2024174
[8]	Ning Zhou, Chen Zhang, Songlin Zhang . A multi-strategy firefly algorithm based on rough data reasoning for power economic dispatch. Mathematical Biosciences and Engineering, 2022, 19(9): 8866-8891. doi: 10.3934/mbe.2022411
[9]	Junjie Liu, Hui Wang, Xue Li, Kai Chen, Chaoyu Li . Robotic arm trajectory optimization based on multiverse algorithm. Mathematical Biosciences and Engineering, 2023, 20(2): 2776-2792. doi: 10.3934/mbe.2023130
[10]	Di-Wen Kang, Li-Ping Mo, Fang-Ling Wang, Yun Ou . Adaptive harmony search algorithm utilizing differential evolution and opposition-based learning. Mathematical Biosciences and Engineering, 2021, 18(4): 4226-4246. doi: 10.3934/mbe.2021212

Abstract

1. Introduction

The sparrow search algorithm ^[1] is a new SI algorithm put forward by Xue in 2020. By observing the predation behavior and reconnaissance mechanism of sparrow populations in nature, the intelligent algorithm has the advantages of high search accuracy, fast optimization and few parameters, which has attracted more and more scholars' attention. Furthermore, as a kind of SI algorithm, the sparrow search algorithm also has some shortcomings, such as premature convergence and easy to fall into local optimization.

For the improvement and application of the sparrow search algorithm, many scholars have done a lot of research. GAO et al. ^[2] put forward a multi-strategy improved evolutionary sparrow search algorithm by adding tent chaos in the initialization population phase, which sped up convergence and improved convergence precision. Additionally, the algorithm used a greedy strategy to fully utilize each individual sparrow to increase its capability to deal with the global optimal solution. Liu et al. ^[3] added the circle chaotic mapping into the sparrow search algorithm to improve the global search ability of the algorithm in population initialization and introduce t-distribution in the position update formula for different iteration cycles of the sparrow to facilitate the algorithm to jump out of the local optimum. Ren et al. ^[4] proposed a sparrow search algorithm based on sine cosine and firefly disturbance. The sine cosine algorithm with random inertia weight was added to the finder position update, and all sparrows were updated using the optimal sparrows obtained by firefly disturbance method to improve the sparrows search ability. Brezočnik et al. ^[5] analyzed various methods of SI algorithms in feature selection problems, provided a unified framework for SI algorithms to solve feature selection and discussed the application prospects of feature selection methods based on SI in different application fields. Zhang et al. ^[6] proposed a random configuration network based on the chaotic sparrow search algorithm, the chaotic sparrow search algorithm mainly uses logistic mapping, adaptive hyperparameters and variational operators to enhance the global optimization capability of the sparrow search algorithm. The accuracy of the random configuration network is affected by the allocation and selection of some network parameters. The chaotic sparrow search algorithm is used to optimize the random configuration network to provide better parameters for the network. Fan et al. ^[7] used the hybrid sparrow search algorithm to optimize the hyperparameters of the deep learning algorithm. The hybrid sparrow search algorithm is a hyperparameter optimization method combining the sparrow search algorithm and particle swarm optimization, which avoids the local optimal solution in the sparrow search algorithm and the search efficiency of the particle swarm optimization algorithm. Dong et al. ^[8] used an improved multi-objective sparrow search algorithm to distribute the capacity of distributed power generation, introduced Levy flight strategy to enhance the ability of multi-objective sparrow search algorithm to jump out of local optimum and established a multi-objective optimization model with investment cost, environmental protection and power supply quality and used the multi-objective sparrow search algorithm to optimize the solution. Zhu et al. ^[9] used an improved sparrow search algorithm to optimize the control of a chilled water system, disturbed the sparrow by random walk strategy to improve the global search ability of the sparrow and added Gaussian mutation in the iterative process of the algorithm to enhance the local search capability, which effectively solves the problem of large time lag and inertia of the chilled water system. Li et al. ^[10] proposed an improved sparrow search algorithm to solve the problem of super-parameter selection of the support vector machine (SVM) model. Through a new dynamic adaptive t- distribution mutation, the performance of the sparrow search algorithm was enhanced, and the proposed method can effectively improve the prediction accuracy.

Although the aforementioned revised approaches have helped the algorithm's search performance to some degree, there is still much potential for advancement. In order to improve the algorithm's convergence performance and convergence accuracy simultaneously, we propose a multi-strategy improved sparrow search algorithm based on the existing research. The major contributions of this article are as follows:

1) A multi-strategy improved sparrow search algorithm (ISSA) has been proposed, with mostly the following three points.

a) Dynamically adjust the number of discoverers and joiners in the population, which facilitates the algorithm to make a balance between search and global search.

b) The update the strategy of the mining phase of the honeypot optimization algorithm (HBA) is introduced to improve the location update of the joiners in SSA and enhance the global exploitation capability of the algorithm.

c) The optimal position of the discoverer is disturbed by the disturbance operator and levy flight to increase the algorithm's capacity to depart from the local optimum.

2) Compared with five basic algorithms on 13 benchmark functions, the effectiveness of the proposed algorithm is verified. The results demonstrate that the proposed algorithm has faster convergence speed and higher convergence accuracy in solving functional optimization problems.

3) Applying ISSA to the pilot optimization problem in channel estimation, the bit error rate is greatly improved, indicating the superiority of the proposed algorithm in engineering applications.

The organizational structure of the remaining parts of this article is as follows: The second section discusses the basic sparrow search algorithm, describing the population distribution and update method of the original algorithm. In the third section, an improved sparrow search algorithm (ISSA) was proposed, and three improved strategies were introduced. In the fourth section, we conducted simulation experiments on the proposed method, conducted experiments on unimodal and multimodal test functions and conducted Wilcoxon rank sum tests. The fifth section applies the proposed algorithm to channel estimation in the OFDM system, and finally, a summary is provided in the sixth section.

2. Basic sparrow search algorithm

The sparrow search algorithm is put forward by observing the predation behavior and reconnaissance mechanism of sparrow populations in nature. The sparrow population is divided into two categories: finders and participants, in which the finders account for 30% of the population and supply the foraging guidance for the whole sparrow population, and the remaining sparrows are participants, which search for food around the discoverers with the best fitness value. Additionally, certain sparrows were chosen at random to serve as scouts to add an early warning mechanism.

In SSA, discoverers are sparrows with higher fitness values and they supply foraging directions and locations for the joiners. The location formula of the discoverers is as follows:

$X_i^{t + 1} = \left\{ \begin{array}{l} X_i^t \cdot \exp ( - \frac{i}{{a \cdot T}})\quad \quad {\text{ }}\;{R_2} < ST \hfill \\ X_i^t + Q \cdot L\quad \quad \quad \quad \quad \quad \;{R_2} \geqslant ST \hfill \\ \end{array} \right.$

(2.1)

$t$ indicates the current iteration number, $T$ is the maximum iteration number, ${X}_{i}^{t}$ indicates the location of the $i$ sparrow in the $t$ iteration, $a$ is the random number of (0, 1), $Q$ satisfies normal distribution, $L$ is the matrix of $1\times D$ with all elements in it are 1 and $D$ is the maximum dimensional value. ${R}_{2}$ and $ST$ represent the alert values and security values. When ${R}_{2} < ST$ , it means that the current environment is free of pouncers and the discoverer can conduct an extensive search. When ${R}_{2}\ge ST$ , it indicates that a portion of the population has found a predator and an alert has been issued, and all sparrows need to move closer to the safety zone at this time.

Joiners always observe the behavior of discoverers and they adjust their positions based on the information from the discoverers. The location formula of the participants is as follows:

$X_i^{t + 1} = \left\{ \begin{array}{l} Q \cdot \exp ( - \frac{{{X_{worst}} - X_i^t}}{{{i^2}}})\quad \quad \quad \quad \quad \quad \;i > n/2 \hfill \\ X_p^t + \left| {X_i^t - X_p^t} \right| \cdot {A^ + } \cdot L\quad \quad \quad \quad \quad \quad otherwise \hfill \\ \end{array} \right.$

(2.2)

where ${X}_{worst}$ denotes the global worst location, ${X}_{p}^{t}$ denotes the optimal position currently occupied by the discoverer, $A$ is a matrix of $1\times D$ with values randomly assigned to 1 or -1 and ${A}^{+} = {A}^{T}(A{A}^{T}{)}^{-1}$ . When $i > n/2$ , it indicates that the $i$ sparrow with low adaptability is not getting sufficient nutrition and needs to fly to other places to forage for better food, otherwise, the joiner searches near the optimal location searched by the finder.

During sparrow foraging, in order to avoid attacks from predators, the population randomly selects sparrows from 10-20% to scout, and when danger is detected, individuals in the population will make corresponding adjustments. The location formula of the scouts is as follows:

$X_i^{t + 1} = \left\{ \begin{array}{l} X_i^t + \beta \cdot \left| {X_i^t - X_{best}^t} \right|\quad \quad \quad \quad \quad {\text{ }}{f_i} > {f_g} \hfill \\ X_i^t + K \cdot \left( {\frac{{\left| {X_i^t - X_{worst}^t} \right|}}{{({f_i} - {f_w}) + \varepsilon }}} \right)\quad \quad {\text{ }}\quad {f_i} = {f_g} \hfill \\ \end{array} \right.$

(2.3)

${X}_{best}^{t}$ is the current global optimum position and $\beta$ is the step control variable, which satisfies the standard normal distribution, $K$ is a random number between (-1, 1) and ${f}_{g}\mathrm{a}\mathrm{n}\mathrm{d}{f}_{w}$ are the global highest and lowest fitness values, respectively. $\epsilon$ is a constant to prevent the denominator from being 0. When ${f}_{i} > {f}_{g}$ , the sparrow is at the edge of the population and is vulnerable to attack by predators, sparrows need to move to the best individual position of the population. ${f}_{i} = {f}_{g}$ indicates that the sparrow in the middle of the population is aware of the danger and needs to move closer to other sparrows to reduce the risk of being pounced.

3. Multi-strategy improved sparrow search algorithm (ISSA)

First, the population dynamic adjustment strategy is used to control the number of sparrow population discoverers and joiners. The number of discoverers and joiners of the original sparrow search algorithm is fixed and the discoverers perform global search and the joiners perform local search. With the increase of iterations, the algorithm tends to fall into a local optimum and requires more discoverers for global search, so the population dynamic adjustment strategy is designed to balance the algorithm's global search and local search capabilities of the algorithm to avoid falling into a local optimum. Then, the joiner's position update formula in the algorithm is improved. The joiner's position update formula for conducting global search in the original algorithm is a step length multiplied by a normally distributed random number, which is determined by the current position and the global worst position, and only the global worst position is considered, while the global optimal position is ignored. In the improved position update formula, the mining phase of the honeypot optimization algorithm (HBA) is introduced, and the global optimal position and the global worst position are added to enhance the global exploration capability of the algorithm. Finally, the optimal position of the population discoverer is perturbed using the perturbation operator and levy flight strategy. In the original algorithm, the joiner always searches near the optimal position of the discoverer, the optimal position of the discoverer may be in the local optimum, at which time it is necessary to perturb the move step using the perturbation operator. Levy flight is added at the optimal position to enhance the ability of the algorithm to depart the local optimum.

3.1. Sparrow species dynamic adjustment strategy

Discoverers in the sparrow population primarily undertake worldwide searches, while joiners' activity is classified into two categories. One portion of the joiners conducts local searches in the discoverer's optimal location, while the other part conducts worldwide searches. The number of discoverers and joiners in the sparrow population is fixed in the original sparrow search algorithm, and a fixed number of discoverers always undertake global searches in each iteration. The joiners then seek, depending on the direction supplied by the discoverer. Once the discoverer's ideal location falls into a local optimum, a set number of joiners do a local search at the optimal point, followed by a global search, making it difficult to exit the local optimum. Later in the algorithm iteration process, a bigger number of discoverers are necessary to conduct global searches in order to explore better sites all over the world. Moreover, a greater proportion of sparrows are required to do global searches among joiners. To balance the algorithm's ability to do global and local searches, a dynamic adjustment approach for the number of sparrow discoverers and participants has been created. The dynamic adjustment strategy is as follows:

$\begin{array}{l} P{D_1} = PD + {R_1}(t/T) \hfill \\ P{D_2} = {R_2} + {R_3}(t/T) \hfill \\ \end{array}$

(3.1)

$P{D}_{1}$ is the proportion of improved discoverers, $PD$ is the original discoverers' ratio, generally set at 20%, ${R}_{1}$ is the upper limit for the set discoverer ratio column increase, which is equal to 0.1, $t$ is the current iteration number and $T$ is the maximum iteration number. $P{D}_{2}$ is the comparison column of sparrows in the population for global search, ${R}_{2}$ is the original set ratio, generally set to 0.5, ${R}_{3}$ is the upper limit of the increased global search sparrow ratio, taken as 0.1. With the increase of the number of times, the number of discoverers and global search joiners are increasing, and the number of joiners searching near the optimal position of the discoverer is decreasing, which is conducive to the algorithm to jump out of the local optimum and increase the ability of global search.

3.2. Honeypot optimization strategy

The honeypot optimization algorithm ^[11] is a new meta-heuristic intelligent algorithm proposed by Fatma A. Hashim in 2021. The HBA algorithm is mainly used to find the optimal by mimicking the honey badger foraging behavior, the algorithm model has few parameters and has a better global search capability. There are two phases in the search process, tracking around the excavation and following existing guides to find foraging honey. Thus, we mainly introduce the update strategy of the tracking around the excavation phase of HBA, and in the excavation phase, the formula for updating the position of the honeypot algorithm is as follows:

${x_{new}} = {x_{prey}} + F \times \beta \times I \times {x_{prey}} + F \times {r_1} \times \alpha \times {d_i} \times \left| {\cos \left( {2\pi {r_2}} \right) \times \left[ {1 - \cos (2\pi {r_3})} \right]} \right|$

(3.2)

${x}_{prey}$ is the location of the prey and is the best location globally. $\beta \ge 1$ (Default is 6) represents the honey badger's ability to find food. ${d}_{i}$ is the distance between the prey and the $i$ th honey badger, and ${r}_{1}$ , ${r}_{2}$ and ${r}_{3}$ are three different random numbers between 0 and 1. $F$ as a sign to change the search direction, the following equation is used to update:

$F = \left\{ \begin{array}{l} 1\quad \quad {\text{ }}{r_4} \leqslant 0.5 \hfill \\ - 1\quad {\text{ }}\, else\quad \hfill \\ \end{array} \right.$

(3.3)

$I$ is the definition of olfactory intensity, if the odor is high, the movement will be fast and vice versa, which is given by the inverse square law. $\alpha$ is the time-varying search decay factor, which indicates the randomness of the search process over time. $\alpha$ value decreases with increasing number of iterations and is defined by equation.

$\begin{array}{l} I = {r_5} \times \frac{S}{{4\pi {d^2}}} \hfill \\ S = {({x_i} - {x_{i + 1}})^2} \hfill \\ d = {x_{prey}} - {x_i} \hfill \\ \alpha = 2 \times \exp (\frac{{ - t}}{{{t_{\max }}}}) \hfill \\ \end{array}$

(3.4)

In the mining phase of the honeypot optimization algorithm, the search is mainly carried out near the global optimal position, and two random steps are added. In other words, a position is randomly selected from the current and optimal positions as the update position for the next iteration. In the original sparrow search algorithm, the update formula of the participant's location for global search only takes into account the current and worst positions, leaving out the ideal position. The search strategy of the honeypot algorithm is applied to the position update formula of the joiners in SSA, and the optimal position of the discoverer is introduced into the global search update formulas, randomly select a position between the optimal and worst positions as the step size for position update in the next iteration. The improved discoverer location update formula is as follows:

$X_i^{t + 1} = \left\{ \begin{array}{l} Q \cdot \exp (\frac{{X_p^t + F \times \beta \times I \times (X_p^t - {X_{worst}})}}{{{i^2}}})\quad \quad \quad {\text{ }}\;i > n.(1 - P{D_2}) \hfill \\ X_p^t + \left| {X_i^t - X_p^t} \right| \cdot {A^ + } \cdot L\quad \quad \quad \quad \quad \quad {\text{ }}otherwise \hfill \\ \end{array} \right.$

(3.5)

Among them, $n$ represents the number of sparrow populations. When $i > n(1-P{D}_{2})$ , it indicates that the current enrollee has not found a better location, so it is necessary to expand the search interval for global search. In other cases, the participants need to use the information provided by the discoverer for local search.

3.3. Perturbation operator and levy flight strategy

In the original algorithm, the joiner is searching at the optimal position found by the discoverer, and in the multi-peak test function, if the discoverer finds the local optimal location, then the joiner searches at the local optimal position of the algorithm. If it is difficult to depart from the local optimum, it is necessary to perturb the joiner position update formula with a small perturbation when the current sparrow's fitness value is low, and a larger perturbation when the fitness value is larger, which is also affected by the number of iterations, while adding levy flight ^[12] near the optimal position of the discoverer ${X}_{P}^{t}$ to facilitate the algorithm to depart from the local optimum. The perturbation operator and levy flight are defined as follows:

$\begin{array}{l} w = {w_{\min }} + ({w_{\max }} - {w_{\min }}) \times (\frac{{{f_i} - {f_g}}}{{{f_w} - {f_g}}}) \times \frac{t}{T} \hfill \\ Levy(\beta ) = \alpha \cdot \frac{u}{{{{\left| v \right|}^{\frac{1}{\beta }}}}} \hfill \\ \end{array}$

(3.6)

where $w$ is the current perturbation, ${w}_{max}$ and ${w}_{min}$ are the highest and lowest perturbations, respectively, which take the values of 0.5 and 1.5 here, $Levy\left(\beta \right)$ is the levy flight's step size, $u$ , $v$ satisfy the normal distribution and $\alpha$ is the step scaling factor. In the experiment, levy flight requires small changes, so the value of a should not be too large. After repeated experiments, we found that the performance is best when $\alpha$ is set to 0.01 and $\beta$ is the random number of [0, 2], when taken as 1.5. Levy flight involves performing small step size transformations over a long period of time, with occasional large step size transformations. By introducing levy flight into the optimal position in the local search formula of the joiners, the optimal position can be perturbed, resulting in a small deviation of the discoverer's optimal position with a high probability and a large deviation with a low probability. The joiners not only retain the discoverer's position information, but helps the algorithm depart from local optima. The improved algorithm updates the formula as follows:

$X_i^{t + 1} = \left\{ \begin{array}{l} Q \cdot \exp (\frac{{X_p^t + F \times \beta \times I \times (X_p^t - {X_{worse}})}}{{{i^2}}})\quad \quad \quad {\text{ }}\;i > n.(1 - P{D_2}) \hfill \\ Levy(\beta ) \cdot X_p^t + w \cdot \left| {X_i^t - Levy(\beta ) \cdot X_p^t} \right| \cdot {A^ + } \cdot L\quad \quad {\text{ }}otherwise \hfill \\ \end{array} \right.$

(3.7)

$n$ represents the number of sparrow populations. In the global search stage of the discoverer, we added the search strategy of the honeypot algorithm, expanding the search space and global search ability of the algorithm. In the local search stage, we added perturbation operators and levy flight, which can break free from the constraints of the optimal position of the discoverer and have the ability to jump out of the local optimum.

3.4. Steps for a multi-strategy improved sparrow search algorithm

The specific implementation steps of the ISSA algorithm are as follows:

Step 1. Set the population size $N$ , maximum number of iterations $T$ , scout ratio $SD$ , alarm value ${R}_{2}$ and security value $ST$ .

Step 2. Calculate each sparrow's fitness value individually using the fitness function, then rank them, record the best position ${X}_{best}$ and the best fitness value ${f}_{g}$ , the worst position ${X}_{worst}$ and the worst fitness value ${f}_{w}$ in the population.

Step 3. Calculate the proportion of discoverers $P{D}_{1}$ and the proportion of joiners performing a global search $P{D}_{2}$ according to Eq (3.1).

Step 4. The population is separated into discoverers and participants according to the ratio calculated in step 3, and the locations of discoverers and joiners are updated according to Eqs (2.1) and (3.7).

Step 5. Update the location of the scout according to Eq (2.3).

Step 6. Update the best position ${X}_{best}$ and best fitness value ${f}_{g}$ , the worst position ${X}_{worst}$ and the worst fitness value ${f}_{w}$ .

Step 7. When the maximum number of iterations has been achieved, the best outcome is produced and the algorithm is finished, otherwise go to step 3.

The pseudocode of the ISSA algorithm is shown in Table 1.

Table 1. Pseudocode for ISSA.

Algorithm multi-strategy improved sparrow search optimization algorithm
Input: the population size $N$ , maximum number of iterations $T$ , scout ratio $SD$ , alarm value ${R}_{2}$ and security value $ST$ .
Output: global minimum fitness value ${f}_{best}$ and the global optimal position ${X}_{best}$
1. set t = 0
2. initialize the position vector of sparrow individuals ${X}_{i}^{t}(i=\mathrm{1, 2}, ..., N)$
3. calculate the fitness value of each sparrow individual based on the fitness function and sort them, recording the best position ${X}_{best}$ and best fitness value ${f}_{g}$ , the worst position ${X}_{worst}$ and the worst fitness value ${f}_{w}$
4. while (t < T) do
calculate the proportion of discoverers $P{D}_{1}$ and the proportion of global searchers $P{D}_{2}$ according to Eq (3.1)
For $i=1:N\cdot P{D}_{1}$ do
update the discoverer's position ${X}_{i}^{t}$ according to Eq (2.1) and calculate the fitness value ${f}_{i}$
update discoverer's optimal location ${X}_{p}^{t}$
End for
For $i=N\cdot P{D}_{1}+1:N$ do
update the position ${X}_{i}^{t}$ of the enrollee according to Eq (3.7) and calculate the fitness value ${f}_{i}$
End for
For $i=1:N\cdot 0.2$ do
update the position ${X}_{i}^{t}$ of the scout according to Eq (2.3) and calculate the fitness value ${f}_{i}$
End for
update the best position ${X}_{best}$ and best fitness value ${f}_{g}$ , the worst position ${X}_{worst}$ and the worst fitness value ${f}_{w}$
t = t + 1
End while
5. return ${f}_{best}$ , ${X}_{best}$

| Show Table

DownLoad: CSV

4. Simulation experiments

4.1. Benchmarking functions

In order to test the performance of the improved sparrow algorithm (ISSA), 13 distinct standard test functions were selected for testing. To ensure the reliability of the algorithm, these functions include single-peak and multi-peak. ${F}_{1}-{F}_{7}$ is the single-peak benchmark test function and ${F}_{8}-{F}_{13}$ is the multi-peak benchmark test function, and the specific function information is shown in , where $D$ represents the dimension of function, range represents the upper and lower limits of each dimension and Fmin is the theoretical optimal value of the test function.

Table 2. Benchmarking function.

Function	D	Range	Fmin
${F_{\text{1}}}(x) = \sum\limits_{i = 1}^n {x_i^2}$	$30$	$[-100, 100]$	${\text{ }}0$
${F_{\text{2}}}(x) = \sum\limits_{i = 1}^n {\left\| {{x_i}} \right\|} + \prod\limits_{i = 1}^n {\left\| {{x_i}} \right\|}$	$30$	$[-100, 100]$	${\text{ }}0$
${F_{\text{3}}}(x) = {\sum\limits_{i = 1}^n {(\sum\limits_{j = 1}^n {{x_j}})} ^2}$	$30$	$[-100, 100]$	${\text{ }}0$
${F_{\text{4}}}(x) = \max \left\{ {\left\| {{x_i}} \right\|, \quad 1 \leqslant i \leqslant n} \right\}$	${\text{ }}30$	$[-100, 100]$	${\text{ }}0$
${F_{\text{5}}}(x) = \sum\limits_{i = 1}^n {\left[{100{{({x_{i + 1}}- {x_i})}^2} + {{({x_i}- 1)}^2}} \right]}$	$30$	$[-100, 100]$	${\text{ }}0$
${F_{\text{6}}}(x) = \sum\limits_{i = 1}^n {({{\left\| {{x_i} + 0.5} \right\|}^2})}$	${\text{ }}30$	$[-100, 100]$	${\text{ }}0$
${F_{\text{7}}}(x) = \sum\limits_{i = 1}^n {ix_i^4 + random[0, 1)}$	$30$	$[-100, 100]$	${\text{ }}0$
${F_8} = \sum\limits_{i = 1}^n { - {x_i}\sin (\sqrt {\left\| {{x_i}} \right\|})}$	${\text{ 30}}$	$[- 500{\text{.500]}}$	$- 12569{\text{.5}}$
${F_9} = \sum\limits_{i = 1}^n {[x_i^2- 10\cos (2\pi {x_i})} {\text{ + 10]}}$	$30$	$[- 5{\text{.12, 5}}{\text{.12]}}$	$0$
$\begin{array}{l} {F_{10}}{\text{ = - 20exp}}\left({{\text{ - 0}}{\text{.2}}\sqrt {1/n\sum\limits_{i = 1}^n {x_i^2} } } \right){\text{ - exp}} \hfill \\ \left({1/n\sum\limits_{i = 1}^n {\cos (2\pi {x_i})} } \right){\text{ + 20 + e }} \hfill \\ \end{array}$	${\text{ 30}}$	$[32, 32]$	$0$
${F_{11}} = 1/4000\sum\limits_{i = 1}^n {x_i^2 - \prod\limits_{i = 1}^n {\cos ({x_i}/\sqrt i })} {\text{ + 1}}$	$30$	$[-600, 600]$	$\; {\text{ 0}}\,$
$\begin{array}{l} {F_{12}} = \pi /n\left\{ {10\sin (\pi {y_i}) + y} \right\} + \sum\limits_{i = 1}^n {u({x_i}, 10, 100, 4)} \hfill \\ \left\{ \begin{array}{l} y = \sum\limits_{i = 1}^{n - 1} {{{({y_i} - 1)}^2}[1 + 10{{\sin }^2}(\pi {y_{i + 1}})] + {{({y_n} - 1)}^2}} {\text{ }} \hfill \\ {y_i} = 1 + ({x_i} + 1)/4 \hfill \\ \hfill \\ {\text{u(}}{x_i}, a, k, m) = \left\{ \begin{array}{l} k{({x_i} - a)^m}{\text{ }}{x_i} > a \hfill \\ 0{\text{ }} - a < {x_i} < a \hfill \\ k{(- {x_i} - a)^m}{\text{ }}{x_i} < - a \hfill \\ \end{array} \right. \hfill \\ \end{array} \right.{\text{ }} \hfill \\ \end{array}$	$30$	$[-50, 50]$	$\; {\text{ }}\; {\text{ 0}}$
$\begin{array}{l} {F_{13}} = 0.1\left\{ {{{\sin }^2}(3\pi {x_i}) + y} \right\} + \sum\limits_{i = 1}^n {u({x_i}5, 100, 4)}\; {\text{ 0}} \hfill \\ {\text{ }} \hfill \\ \left\{ \begin{array}{l} y = \sum\limits_{i = 1}^n {{{({x_i} - 1)}^2}[1 + 10{{\sin }^2}(3\pi {x_i} + 1)] + {{({x_n} - 1)}^2}[1 + {{\sin }^2}(2\pi {x_n}]} \hfill \\ {y_i} = 1 + ({x_i} + 1)/4{\text{ }} \hfill \\ \hfill \\ {\text{u(}}{x_i}, a, k, m) = \left\{ \begin{array}{l} k{({x_i} - a)^m}{\text{ }}{x_i} > a \hfill \\ {\text{ }} - a < {x_i} < a \hfill \\ k{(- {x_i} - a)^m}{\text{ }}{x_i} < - a \hfill \\ \end{array} \right. \hfill \\ \end{array} \right. \hfill \\ \hfill \\ \end{array}$	${\text{ 30 }}$	$\; {\text{ [-50, 50] }}$	$0$

| Show Table

DownLoad: CSV

4.2. Algorithm performance testing

The improved algorithms in this paper were compared with the initial sparrow search algorithm (SSA) ^[1], gray wolf algorithm (GWO) ^[13], particle swarm algorithm (PSO) ^[14], whale algorithm (WOA) ^[15] and harris hawk algorithm (HHO) ^[16] with a population setting of 50 and an iteration number of 500, which were run in 13 basic test functions. To verify the improved accuracy and reliability of the algorithms, each algorithm was run 30 times independently to obtain the best value, the worst value, the mean value and the standard deviation. The experimental data are shown in Table 3.

Table 3. Statistical results of test functions.

Function	Algorithm	Best Value	Worst Value	Mean	Standard Deviation
${F_1}$	$ISSA$	0	0	0	0
	$SSA$	0	3.1864e-167	1.0621e-168	0
	$GWO$	1.3421e-35	9.5061e-33	1.8382e-33	2.2221e-33
	$PSO$	6.2326e-01	4.0682e+00	1.9043e+00	7.8942e-01
	$WOA$	1.2048e-97	2.4256e-79	8.0858e-81	4.4285e-80
	$HHO$	3.1580e-115	1.1840e-101	4.3698e-103	2.1566e-102
F₂	$ISSA$	0	0	0	0
	$S S A$	0	8.0286e-73	2.7546e-74	1.4649e-73
	$G W O$	1.0171e-20	1.6197e-19	1.8382e-33	4.0183e-20
	$PSO$	2.1010e+00	8.8391e+00	3.7033e+00	1.5229e+00
	$WOA$	1.1144e-60	1.6915e-51	5.7178e-53	3.0868e-52
	$HHO$	1.5936e-63	5.4539e-52	3.7851e-53	1.2047e-52
${F_3}$	$ISSA$	0	0	0	0
	$SSA$	0	3.2933e-97	1.0977e-98	6.0128e-98
	$GWO$	8.8323e-05	1.1289e-01	1.4057e-02	2.4901e-02
	$PSO$	8.3009e+02	2.3863e+03	1.5807e+03	3.6382e+02
	$WOA$	8.7232e+04	2.2099e+05	1.5590e+05	3.0711e+04
	$HHO$	6.6572e-104	7.5648e-80	2.6622e-81	1.3800e-80
${F_4}$	$ISSA$	0	0	0	0
	$SSA$	0	3.3360e-79	1.1304e-80	6.0882e-80
	$GWO$	1.8481e-09	2.0828e-07	2.1830e-08	3.6978e-08
	$PSO$	1.5610e+00	2.1636e+00	1.8451e+00	1.5855e-01
	$WOA$	1.0979e+00	8.0088e+01	4.0919e+01	2.6874e+01
	$HHO$	6.5401e-59	9.4584e-51	6.7262e-52	1.7779e-51
${F_5}$	$ISSA$	5.0702e-08	6.6256e-04	1.2085e-04	1.8009e-04
	$SSA$	8.0695e-09	6.9311e-04	4.3963e-05	4.6962e-05
	$GWO$	2.5409e+01	2.7947e+01	2.6763e+01	6.3084e-01
	$PSO$	2.0406e+02	2.0100e+03	6.2682e+02	3.6003e+02
	$WOA$	2.6745e+01	2.8735e+01	2.7510e+01	5.1895e-01
	$HHO$	1.4009e-05	4.0703e-02	6.4049e-03	9.0201e-03
${F_6}$	$ISSA$	3.2625e-09	1.7089e-04	8.5505e-06	3.0861e-05
	$SSA$	8.3945e-14	7.5595e-08	3.5915e-09	8.5505e-06
	$GWO$	2.9951e-05	1.0066e+00	4.0874e-01	2.9877e-01
	$PSO$	4.7765e-01	3.4218e+00	1.6663e+00	8.5085e-01
	$WOA$	1.4147e-02	4.1637e-01	7.8582e-02	8.2848e-02
	$HHO$	5.8989e-08	4.2385e-04	5.3248e-05	9.4043e-05
${F_7}$	$ISSA$	5.008e-06	2.7466e-04	7.4644e-05	7.6159e-05
	$SSA$	2.3711e-05	1.2953e-03	3.1855e-04	3.4020e-04
	$GWO$	1.9770e-04	3.3204e-03	1.1363e-03	8.0935e-04
	$PSO$	2.7306e+00	3.7821e+01	1.1836e+01	9.0431e+00
	$WOA$	3.4660e-05	7.3887e-03	2.0482e-03	2.1898e-03
	$HHO$	2.7638e-06	4.1441e-04	9.7169e-05	1.0390e-04
${F_8}$	$ISSA$	-1.2569e+04	-7.4191e+03	-1.1887e+04	1.2782e+03
	$SSA$	-9.2134e+03	-6.5663e+03	-8.2420e+03	5.5573e+02
	$GWO$	-7.9246e+03	-5.0894e+03	-6.4129e+03	6.0860e+02
	$PSO$	-8.8566e+03	-3.1261e+03	-6.5984e+03	1.2449e+03
	$WOA$	-1.2569e+04	-8.7211e+03	-1.1390e+04	1.0232e+03
	$HHO$	-1.2569e+04	-1.2346e+04	-1.2562e+04	4.0822e+01
$F_9$	$ISSA$	0	0	0	0
	$S S A$	0	0	0	0
	$G W O$	0.0000e+00	1.1286e+01	2.6422e+00	3.4938e+00
	$PSO$	8.9641e+01	2.2799e+02	1.5502e+02	3.2893e+01
	$WOA$	0.0000e+00	1.2864e+02	4.2878e+00	2.3485e+01
	$HHO$	0	0	0	0
${F_{10}}$	$ISSA$	8.8818e-16	8.8818e-16	8.8818e-16	0
	$SSA$	8.8818e-16	8.8818e-16	8.8818e-16	0
	$GWO$	3.6415e-14	5.7732e-14	4.4231e-14	5.2281e-15
	$PSO$	1.5364e+00	3.2912e+00	2.3790e+00	4.6682e-01
	$WOA$	8.8818e-16	7.9936e-15	4.5593e-15	2.1847e-15
	$HHO$	8.8818e-16	8.8818e-16	8.8818e-16	0.0000e+00
${F_{11}}$	$ISSA$	0	0	0	0
	$SSA$	0	0	0	0
	$GWO$	0.0000e+00,	2.1431e-02	3.5261e-03	6.2577e-03
	$PSO$	4.1021e-02	1.7217e-01	8.9648e-02	3.1821e-02
	$WOA$	0.0000e+00	1.0747e-01	3.5825e-03	1.9622e-02
	$HHO$	0	0	0	0
${F_{12}}$	$ISSA$	2.5567e-14	1.0504e-05	8.2340e-07	2.0803e-06
	$SSA$	7.2294e-12	1.1659e-07	1.3818e-08	2.4578e-08
	$GWO$	7.0921e-06	6.2996e-02	2.6369e-02	1.2897e-02
	$PSO$	3.8811e-03	2.2942e-01	3.3481e-02	4.6857e-02
	$WOA$	1.5657e-03	9.3638e-02	9.9804e-03	1.6518e-02
	$HHO$	1.0840e-07	1.7123e-05	3.7877e-06	4.1722e-06
${F_{13}}$	$ISSA$	5.0710e-10	2.5597e-05	2.9599e-06	5.4241e-06
	$SSA$	8.9927e-10	2.0121e-06	1.9305e-07	3.8369e-07
	$GWO$	4.7668e-05	7.5600e-01	4.0804e-01	2.1821e-01
	$PSO$	2.1080e-01	7.0900e-01	4.0368e-01	1.4349e-01
	$WOA$	2.7551e-02	5.8833e-01	2.1351e-01	1.5308e-01
	$HHO$	1.2643e-09	2.2246e-04	3.6326e-05	5.1000e-05

| Show Table

DownLoad: CSV

As shown in , for the single-peak test function ${F}_{1}-{F}_{4}$ , the proposed ISSA has a higher finding effect than SSA, GWO, PSO, WOA and HHO. All can find the theoretical optimal value with a standard deviation of 0, and the optimization effect is stable. For the ${F}_{5}$ and ${F}_{6}$ functions, ISSA's optimization is lower than that of SSA, but the accuracy loss is not great. For the ${F}_{7}$ function, ISSA has little improvement, and the standard deviation and mean value are the lowest. For the ${F}_{8}$ function, HHO achieves the best result, the optimal value and the average value are close to the theoretical optimal value, the performance of ISSA has improved significantly and the average value has been greatly enhanced compared with SSA. For the ${F}_{9}-{F}_{11}$ function, ISSA, SSA and HHO have similar performance and have discovered the test function's ideal value, which means that ISSA has maintained the optimization-seeking ability of SSA and has not reduced the optimization-seeking ability of the algorithm. For the ${F}_{12}-{F}_{13}$ function, SSA outperforms ISSA, which comes in second only to SSA and also achieves good optimization results. In summary, ISSA performs poorly on ${F}_{5}$ , ${F}_{6}$ , ${F}_{12}$ , ${F}_{13}$ and achieves better performance on other test functions.

In order to highlight the superiority of the algorithm more intuitively and to facilitate the presentation of experimental results, the first 12 test functions were selected for testing, each algorithm was independently executed 30 times and the average convergence curves of the test functions were plotted according to the fitness function value and the number of iterations. Specifically, as shown in , it can be observed that the improved algorithm in this paper has a faster convergence speed and higher convergence accuracy on most test functions. In the ${F}_{1}-{F}_{4}$ function, the improved algorithm is able to converge to 0, and ISSA has a huge improvement in both convergence speed and convergence accuracy. In ${F}_{5}$ , ${F}_{6}$ , ISSA has poorer performance compared to SSA, but there is no major loss in accuracy, and it is still more accurate than GWO, HHO, PSO and WOA. In the ${F}_{7}$ function, ISSA has the greatest optimization finding precision among the six algorithms, and in the ${F}_{8}$ function, ISSA has lower performance than HHO, but still higher than SSA, GWO, PSO and WOA. In ${F}_{9}-{F}_{11}$ , ISSA, SSA and HHO all find the theoretical optimum, but ISSA has higher convergence speed, and the convergence speed improvement is very large. In the ${F}_{12}$ function, the convergence accuracy of ISSA is lower than that of SSA, but the difference is not large. In summary, ISSA has good performance in both single-peak and multi-peak functions.

Figure 1. Average convergence curve of test function.

DownLoad: Full-Size Img PowerPoint

Due to the improvement of the original algorithm, ISSA has higher computational complexity, and the running time can indirectly reflect the complexity of the algorithm. Therefore, we have made statistics on the running time of each algorithm, in which the number of iterations is set to 500, and the population is set to 50, running for a total of 100 times. The average running time of the six algorithms obtained is in Table 4, and the time unit is seconds. It can be seen that the average running time of ISSA is longer than that of SSA and other algorithms. The running time of SSA is longer than that of GWO and PSO, because these two algorithms are traditional SI algorithms with low complexity and poor performance in optimization, so the time is short. HHO and WOA are new SI algorithms, and the calculation time of SSA is longer than WOA and shorter than HHO. ISSA is improved on the basis of SSA, adding three strategies, which increases the computational complexity and running time, but has better convergence speed and accuracy.

Table 4. Function run schedule.

Function	ISSA	SSA	GWO	PSO	WOA	HHO
${F}_{1}$	4.5601e-01	2.5262e-01	1.8739e-01	2.2744e-01	8.7704e-02	1.1250e-01
${F}_{2}$	5.2522e-01	2.9624e-01	2.1472e-01	3.1399e-01	1.0855e-01	1.3769e-01
${F}_{3}$	1.7906e+00	1.5361e+00	1.2834e+00	2.6802e+00	1.1424e+00	1.1655e+00
${F}_{4}$	4.7572e-01	2.6550e-01	1.8347e-01	2.7232e-01	8.5454e-02	1.1064e-01
${F}_{5}$	6.4553e-01	2.9481e-01	2.2528e-01	4.0675e-01	1.1273e-01	1.4183e-01
${F}_{6}$	5.7290e-01	2.4893e-01	1.8573e-01	3.1503e-01	8.5637e-02	1.1233e-01
${F}_{7}$	7.2310e-01	3.9009e-01	2.9794e-01	5.2787e-01	1.9761e-01	2.2544e-01
${F}_{8}$	6.4317e-01	3.0312e-01	2.2628e-01	4.2769e-01	1.3433e-01	1.5224e-01
${F}_{9}$	4.5420e-01	2.6201e-01	1.9559e-01	3.4739e-01	1.0720e-01	1.1922e-01
${F}_{10}$	5.1214e-01	2.9018e-01	2.1408e-01	3.9707e-01	1.2929e-01	1.4188e-01
${F}_{11}$	5.5401e-01	3.2185e-01	2.3612e-01	6.4961e-01	1.4446e-01	1.6124e-01
${F}_{12}$	9.1667e-01	7.0514e-01	5.4576e-01	1.1828e+00	4.4232e-01	4.6976e-01
${F}_{13}$	1.0942e+00	7.1022e-01	5.4974e-01	1.1907e+00	4.4634e-01	4.7318e-01

| Show Table

DownLoad: CSV

4.3. Wilcoxon rank sum test

To more thoroughly evaluate the effectiveness of the proposed algorithm, we introduce the Wilcoxon rank sum test ^[17] to test the significance of the optimal results of ISSA algorithm and other algorithms under 30 independent runs to evaluate whether there is a significant difference between the proposed ISSA and other algorithms. The original hypothesis is ${H}_{0}$ : there is no significant difference between the two algorithms, and the alternative hypothesis is ${H}_{1}$ : there is a significant difference between the two algorithms. When $P < 5\%$ , the original hypothesis ${H}_{0}$ is rejected and the alternative hypothesis ${H}_{1}$ is accepted, which means that there is a significant difference between the two algorithms, and when $P > 5\%$ , the original hypothesis is accepted, which implies that there is no significant difference between the two algorithms, indicating that the two algorithms are equivalent in finding the optimal results. The rank sum test results of ISSA and SSA, GWO, PSO, WOA and HHO are shown in , where $N/A$ indicates that the two algorithms have equivalent performance and cannot be compared.

Table 5. Wilcoxon rank sum test P value table.

Function	SSA	GWO	PSO	WOA	HHO
${F_1}$	5.8522e-09	1.2118e-12	1.2118e-12	1.2118e-12	1.2118e-12
${F_2}$	5.7720e-11	1.2118e-12	1.2118e-12	1.2118e-12	1.2118e-12
${F_3}$	1.9346e-10	1.2118e-12	1.2118e-12	1.2118e-12	1.2118e-12
${F_4}$	1.6572e-11	1.2118e-12	1.2118e-12	1.2118e-12	1.2118e-12
${F_5}$	1.4532e-01	3.0199e-11	3.0199e-11	3.0199e-11	1.4733e-07
${F_6}$	8.1014e-10	3.0199e-11	3.0199e-11	3.0199e-11	1.3111e-08
${F_7}$	6.0459e-07	3.0199e-11	3.0199e-11	1.4643e-10	8.0727e-03
${F_8}$	1.6132e-10	3.0199e-11	3.4971e-09	8.5641e-04	3.2651e-02
${F_9}$	N/A	1.1586e-11	1.2118e-12	1.2118e-12	N/A
${F_{10}}$	N/A	9.0844e-13	1.2118e-12	1.0793e-09	N/A
${F_{11}}$	N/A	2.7880e-03	1.2118e-12	1.2118e-12	N/A
${F_{12}}$	4.9752e-11	3.0199e-11	3.0199e-11	3.0199e-11	2.1959e-07
${F_{13}}$	3.4971e-09	3.0199e-11	3.0199e-11	3.0199e-11	1.4733e-07

| Show Table

DownLoad: CSV

According to , the performance of ISSA is equivalent to that of SSA and HHO in the ${F}_{9}-{F}_{11}$ function, which shows that the three algorithms can determine the best value of the test function pair in each experiment. According to the convergence curve, it is known that ISSA has faster convergence velocity and higher stability. The rest of the p-values are less than 0.05, indicating that there is a significant difference between the proposed ISSA and the other algorithms.

4.4. Robustness analysis

shows the boxplot of the optimal value for each test function of six algorithms. Each algorithm runs independently 50 times in the test function, selecting ${F}_{1}$ , ${F}_{3}$ , ${F}_{5}$ and ${F}_{7}$ from the single-peak function and ${F}_{8}$ and ${F}_{11}$ from the multi-peak function. It can be seen that in ${F}_{1}$ and ${F}_{3}$ , the ISSA algorithm has a maximum, minimum and median of 0 in the boxplot, which is much smaller than other algorithms, indicating that ISSA has strong balance ability and high robustness. In ${F}_{5}$ , the optimal value accuracy of ISSA is lower than ISSA, but much higher than other algorithms. However, its upper quartile is smaller than ISSA, and the optimal value distribution is relatively concentrated, improving the robustness of the original algorithm. In ${F}_{7}$ , the accuracy of the optimal value solved by ISSA is greater than that of SSA, and the entire boxplot of ISSA is below SSA, which also improves the robustness of the original algorithm. The search accuracy of ISSA and HHO is the same, the median and mean values of ISSA are lower than HHO and the stability of ISSA is higher. In ${F}_{8}$ , HHO has greater robustness, the accuracy of the ISSA is significantly higher than that of SSA and it is concentrated close to the theoretical ideal value with minimal variation in the optimal value, which further increases robustness. For ${F}_{11}$ , the optimal value for ISSA, SSA and HHO is 0, and each of these three algorithms has a high level of robustness. Based on the corresponding ${F}_{11}$ convergence curve in Figure 1, it can be seen that ISSA has a faster convergence speed. In summary, ISSA not only improves search accuracy, but also has high robustness.

Figure 2. Boxplot for algorithm.

DownLoad: Full-Size Img PowerPoint

5. Engineering applications

Orthogonal frequency division multiplexing (OFDM) ^[18] is the core technology of 4G networks, as a low-complexity transmission technology, it is widely used in broadcast systems as well as wireless LAN standards and has great advantages in terms of resistance to multipath fading, narrowband interference, multiple access and signal processing. The difficulty of this system is mainly to obtain the channel state information matrix accurately so as to recover the transmitted signal at the receiver side, so channel estimation is the key to achieve this step.

The major traditional channel estimation methods are least squares (LS) ^[19], minimum mean square error (MMSE) ^[20], maximum likelihood ^[21] and Bayesian channel estimation ^[22]. The three major orthogonal frequency division multiplexing (OFDM) channel estimation methods are non-blind channel, blind channel and semi-blind channel estimation ^[23]. Among them, the performance of the blind channel estimation method is better than the semi-blind channel estimation, but its complexity is quite high and there are not many practical use cases. Non-blind channel estimation is based on pilots or training sequences. In order to track channel changes in real-time and reduce errors, pilot-based channel estimation algorithms are generally used. This method has problems such as high pilot overhead and poor robustness and performs poorly in low signal-to-noise ratio situations.

The LS algorithm is used in pilot-based channel estimation to obtain the channel at the pilot location. Then, estimate the whole channel through interpolation algorithm and finally get the signal sent by the sender. The channel estimation based on pilot focuses on the design of pilot, the traditional guide frequency design method is fixed, generally using equal interval into the pilot. This pilot arrangement order is manually set, so it is impossible to obtain a lower bit error rate. Aiming at the defects of traditional pilot design, we designed a least square method based on an improved sparrow search algorithm (ISSA-LS). The improved sparrow search algorithm is used to determine the optimal position of pilots, the fitness value is taken as the average bit error rate (BER) of each experiment and ISSA is utilized to identify the pilot arrangement order with the lowest average bit error rate.

The experimental signal modulation method are phase shift keying modulation (PSK) and quadrature amplitude modulation (QAM), the signal-to-noise ratio is 0-30, the number of subcarriers is 52, the number of guide frequency is 12, the number of population of the improved sparrow search algorithm is taken as 30 and the number of iterations is set to 50 (Figure 3). In 4PSK signals, the LS algorithm reduces the bit error rate to 0 when the SNR (signal-to-noise ratio) is 5, while ISSA-LS already reduces it to 0 when the SNR is 3. In the 8PSK signal, when the SNR reaches 8, the LS method decreases the bit error rate to 0, but ISSA-LS already does so when the ratio is 7. The bit error rate of ISSA-LS is significantly lower than LS at both low and high signal-to-noise ratios when the transmitter uses PSK as the modulation method. The bit error rate in 16QAM signals is reduced to 0 by the LS algorithm at a SNR of 7, whereas it has already fallen to 0 by ISSA-LS at a SNR of 6. As the SNR of 64QAM signals reaches 14, the LS algorithm reduces the bit error rate to 0, whereas the ISSA-LS method has already achieved 0 at 11. The performance of ISSA-LS at low signal-to-noise ratios is comparable to that of the LS algorithm when the modulation mode of the modulation transmitter is QAM. ISSA-LS has a substantially lower bit error rate than LS at high SNR. The performance of ISSA-LS improves as the SNR increases.

Figure 3. Bit error rate curve after pilot optimization.

DownLoad: Full-Size Img PowerPoint

Figure 4 shows the error bar of the bit error rate curves of ISSA-LS and LS, twenty experiments were conducted, and error bars were drawn based on the mean and standard deviation of the bit error rate at different signal-to-noise ratios. It can be seen that the bit error rate of ISSA-LS algorithm is lower than that of LS. Overall, whether it is PSK modulation or QAM modulation, the least squares method optimized by the improved sparrow search algorithm (ISSA-LS) has a lower bit error rate. The performance is superior to traditional least squares (LS) methods in both low signal-to-noise and high signal-to-noise ratios.

Figure 4. Error bar of bit error rate.

DownLoad: Full-Size Img PowerPoint

6. Conclusions

In this paper, a multi-strategy improved sparrow search algorithm is proposed. First, a sparrow population dynamic adjustment strategy is added to dynamically adjust the population size of discoverers and joiners, and with the increase of iterations, more discoverers find foraging directions for the whole population, the number of joiners for global search increases, which facilitates the algorithm to depart from a local optimum. In the position formula of the finders, an update mechanism in the mining stage of the honeypot optimization algorithm is introduced. After changing the location update formula, the algorithm's global search ability increases and can search in a larger range; the update formula of the joiners is perturbed by the perturbation operator and levy flight strategy, which further improves the algorithm's capacity to depart from the local optimum. Finally, the algorithm is tested in 13 test functions to verify the superiority of the algorithm with other algorithms, and the algorithm is applied to the pilot optimization in channel estimation and achieves a lower BER. However, there are some defects in this paper. For instance, the improved algorithm does not achieve better performance on ${F}_{5}$ , ${F}_{6}$ , ${F}_{12}$ and ${F}_{13}$ in the pilot optimization in the channel estimation; and the performance of the improved sparrow search algorithm is equivalent to that of the least square method when the signal-to-noise ratio is low. In a future study, we will strive to use various ways to improve the algorithm and its convergence accuracy in these test functions. The enhanced algorithm will then be applied to pilot optimization to increase the channel estimate accuracy even more.

Use of AI tools declaration

The authors declare they have not used Artificial Intelligence (AI) tools in the creation of this article.

Acknowledgments

This work is supported by the Tianjin Natural Science Foundation (No. 20JCYBJC00320), College Students' innovation and Entrepreneurship Project (No. 2022SKYZ313, No. 2022SKYZ390) and Innovation and Entrepreneurship Project for College Students.

Conflict of interest

The authors declare there is no conflict of interest.

References

[1]	Adebayo TS (2023) Trade‐off between environmental sustainability and economic growth through coal consumption and natural resources exploitation in China: New policy insights from wavelet local multiple correlation. Geol J 58: 1384–1400. https://doi.org/10.1002/gj.4664 doi: 10.1002/gj.4664
[2]	Adil S, Lacoste-Badie S, Droulers O (2018) Face presence and gaze direction in print advertisements: how they influence consumer responses—an eye-tracking study. J Advertising Res 58: 443–455. https://doi.org/10.2501/JAR-2018-004 doi: 10.2501/JAR-2018-004
[3]	Akhter S, Pauyo T, Khan M (2019) What is the difference between a systematic review and a meta-analysis? Basic methods handbook for clinical orthopaedic research: a practical guide and case-based research approach, 331–342. https://doi.org/10.1007/978-3-662-58254-1_37 doi: 10.1007/978-3-662-58254-1_37
[4]	Aly E, Elsawah S, Ryan MJ (2022) A review and catalogue to the use of models in enabling the achievement of sustainable development goals (SDG). J Clean Prod 340: 130803. https://doi.org/10.1016/j.jclepro.2022.130803 doi: 10.1016/j.jclepro.2022.130803
[5]	Bakalash T, Riemer H (2013) Exploring ad-elicited emotional arousal and memory for the ad using fMRI. J Advert 42: 275–291. https://doi.org/10.1080/00913367.2013.768065 doi: 10.1080/00913367.2013.768065
[6]	Baldo D, Viswanathan VS, Timpone, RJ, et al. (2022) The heart, brain, and body of marketing: complementary roles of neurophysiological measures in tracking emotions, memory, and ad effectiveness. Psyc Mark 39: 1979–1991. https://doi.org/10.1002/mar.21697 doi: 10.1002/mar.21697
[7]	Bandari R, Moallemi EA, Lester RE, et al. (2022) Prioritising Sustainable Development Goals, characterising interactions, and identifying solutions for local sustainability. Env Sci Pol 127: 325–336. https://doi.org/10.1016/j.envsci.2021.09.016 doi: 10.1016/j.envsci.2021.09.016
[8]	Bergamaschi M, Randerson K (2016) The futures of family businesses and the development of corporate social responsibility. Futures 75: 54–65. https://doi.org/10.1016/j.futures.2015.10.006 doi: 10.1016/j.futures.2015.10.006
[9]	Berkman ET, Falk EB (2013) Beyond brain mapping: Using neural measures to predict real-world outcomes. Curr Direc Psych Sci 22: 45–50. https://doi.org/10.1177/0963721412469394 doi: 10.1177/0963721412469394
[10]	Biglari S, Beiglary S, Arthanari T (2022) Achieving sustainable development goals: Fact or Fiction?. J Clean Prod 332: 130032. https://doi.org/10.1016/j.jclepro.2021.130032 doi: 10.1016/j.jclepro.2021.130032
[11]	Cahn BR, Delorme A, Polich J (2013) Occipital gamma activation during vipassana meditation. Cogn Proces 14: 393–406. https://doi.org/10.1007/s10339-009-0352-1 doi: 10.1007/s10339-009-0352-1
[12]	Cakir MP, Çakar T, Girisken Y, et al. (2018) An investigation of the neural correlates of purchase behavior through fNIRS. Eur J Mark 52: 224–243. https://doi.org/10.1108/EJM-12-2016-0864 doi: 10.1108/EJM-12-2016-0864
[13]	Carroll AB (2016) Carroll's pyramid of CSR: Taking another look. Int J Corp Soc Res 1: 1–8. https://doi.org/10.1186/s40991-016-0004-6 doi: 10.1186/s40991-016-0004-6
[14]	Chang L, Tsao DY, Liu T (2021) Distributed representation of visual objects by single neurons in macaque visual cortex. Nat Commun 12: 1–13. https://doi.org/10.1523/JNEUROSCI.1958-14.2015 doi: 10.1038/s41467-020-20314-w
[15]	Chen JE, Glover GH (2021) Advances in BOLD fMRI methodology. Tren Cogn Sci 25: 511–527. https://doi.org/10.1016/j.tics.2017.09.010 doi: 10.1016/j.tics.2017.09.010
[16]	Cheng Y, Yang CY, Lin CP, et al. (2008) The perception of pain in others suppresses somatosensory oscillations: a magnetoencephalography study. Neuroimage 40: 1833–1840. https://doi.org/10.1016/j.neuroimage.2008.01.064 doi: 10.1016/j.neuroimage.2008.01.064
[17]	Ćirović M, Dimitriadis N, Janić M, et al. (2022) More than words: Rethinking sustainability communications through neuroscientific methods. J Cons Behav. https://doi.org/10.1002/cb.2125 doi: 10.1002/cb.2125
[18]	Clark KR, Leslie KR, Garcia-Garcia M, et al. (2018) How advertisers can keep mobile users engaged and reduce video-ad blocking: Best practices for video-ad placement and delivery based on consumer neuroscience measures. J Adv Res 58: 311–325. https://doi.org/10.2501/JAR-2018-036 doi: 10.2501/JAR-2018-036
[19]	Daugherty T, Hoffman E, Kennedy K, et al. (2018) Measuring consumer neural activation to differentiate cognitive processing of advertising: Revisiting Krugman. Eur J Mark 52: 182–198. https://doi.org/10.1108/EJM-10-2017-0657 doi: 10.1108/EJM-10-2017-0657
[20]	de Oliveira JHC, Giraldi JDME (2017) What is neuromarketing? A proposal for a broader and more accurate definition. Glob Bus Manage Res 9: 19–29. Available from: http://gbmrjournal.com/pdf/vol.%209%20no.%202/V9N2-2.pdf
[21]	de Oliveira L, Prado JW (2021) Emotion and advertising effectiveness: A facial analysis study. Int J Adv 40: 455–472. Available from: http://www.gbmrjournal.com/pdf/vol.%209%20no.%202/V9N2-2.pdf
[22]	De Vries EL, Fennis BM, Bijmolt TH, et al. (2018) Friends with benefits: Behavioral and fMRI studies on the effect of friendship reminders on self-control for compulsive and non-compulsive buyers. Int J Res Mark 35: 336–358. https://doi.org/10.1016/j.ijresmar.2017.12.004 doi: 10.1016/j.ijresmar.2017.12.004
[23]	Donthu N, Kumar S, Pandey N, et al. (2021) Mapping the electronic word-of-mouth (eWOM) research: A systematic review and bibliometric analysis. J Bus Res 135: 758–773. https://doi.org/10.1016/j.jbusres.2021.07.015 doi: 10.1016/j.jbusres.2021.07.015
[24]	Farooq O, Rupp DE, Farooq M (2017) The multiple pathways through which internal and external corporate social responsibility influence organizational identification and multifoci outcomes: The moderating role of cultural and social orientations. Acad Manage J 60: 954–985. https://doi.org/10.5465/amj.2014.0849 doi: 10.5465/amj.2014.0849
[25]	Figner B, Murphy RO, Siegel P (2019) Measuring electrodermal activity and its applications in judgment and decision-making research, In: A Handbook of Process Tracing Methods, Routledge, 161–183. https://doi.org/10.4324/9781315160559-12
[26]	Foroudi P, Akarsu TN, Marvi R, et al. (2021) Intellectual evolution of social innovation: A bibliometric analysis and avenues for future research trends. Ind Mark Manage 93: 446–465. https://doi.org/10.1016/j.indmarman.2020.03.026 doi: 10.1016/j.indmarman.2020.03.026
[27]	Fortunato VCR, Giraldi JDME, de Oliveira JHC (2014) A review of studies on neuromarketing: Practical results, techniques, contributions and limitations. J Manage Res 6: 201–220. https://doi.org/10.5296/jmr.v6i2.5446 doi: 10.5296/jmr.v6i2.5446
[28]	Frederick DP (2022) Recent Trends in Neuro marketing–An Exploratory Study. Int J Case Stud Bus IT Edu. (IJCSBE), 6: 38–60. https://doi.org/10.47992/IJCSBE.2581.6942.0148 doi: 10.47992/IJCSBE.2581.6942.0148
[29]	Garczarek-Bąk U, Szymkowiak A, Gaczek P, et al. (2021) A comparative analysis of neuromarketing methods for brand purchasing predictions among young adults. J Brand Manage 28: 171–185. https://doi.org/10.1057/s41262-020-00221-7 doi: 10.1057/s41262-020-00221-7
[30]	Gazzaniga MS, Ivry RB, Mangun GR (2021) Cognitive neuroscience: The Biology of the Mind (5th ed.), W. W. Norton & Company. Available from: https://www.amazon.com/Cognitive-Neuroscience-Biology-Mind-Fifth/dp/0393603172
[31]	Ghaffar A, Islam T (2023) Factors leading to sustainable consumption behavior: an empirical investigation among millennial consumers. Kyber. https://doi.org/10.1108/K-12-2022-1675 doi: 10.1108/K-12-2022-1675
[32]	Gómez-Carmona D, Marín-Dueñas PP, Tenorio RC, et al. (2022) Environmental concern as a moderator of information processing: A fMRI study. J Clean Prod 369: 133306. https://doi.org/10.1016/j.jclepro.2022.133306 doi: 10.1016/j.jclepro.2022.133306
[33]	Gountas J, Gountas S, Ciorciari J, et al. (2019) Looking beyond traditional measures of advertising impact: Using neuroscientific methods to evaluate social marketing messages. J Bus Res105: 121–135. https://doi.org/10.1016/j.jbusres.2019.07.011 doi: 10.1016/j.jbusres.2019.07.011
[34]	Hakim A, Klorfeld S, Sela T, et al. (2021) Machines learn neuromarketing: Improving preference prediction from self-reports using multiple EEG measures and machine learning. Int J Res Mark 38: 770–791. https://doi.org/10.1016/j.ijresmar.2020.10.005 doi: 10.1016/j.ijresmar.2020.10.005
[35]	Hakimi N, Shahbakhti M, Sappia S, et al. (2022) Estimation of respiratory rate from functional near-infrared spectroscopy (fNIRS): A new perspective on respiratory interference. Bios 12: 1170. https://doi.org/10.3390/bios12121170 doi: 10.3390/bios12121170
[36]	Halkiopoulos C, Antonopoulou H, Gkintoni E, et al. (2022) Neuromarketing as an indicator of cognitive consumer behavior in decision-making process of tourism destination—An overview, In: Transcending Borders in Tourism Through Innovation and Cultural Heritage: 8th International Conference, IACuDiT, Hydra, Greece, 2021, Cham: Springer International Publishing, 679–697. https://doi.org/10.1007/978-3-030-92491-1_41
[37]	Hamelin N, Thaichon P, Abraham C, et al. (2020) Story telling, the scale of persuasion and retention: A neuromarketing approach. J Retail Cons Serv 55: 102099. https://doi.org/10.1016/j.jretconser.2020.102099 doi: 10.1016/j.jretconser.2020.102099
[38]	Holmqvist K, Örbom SL, Hooge IT, et al. (2023) Eye tracking: empirical foundations for a minimal reporting guideline. Behav Res Method 55: 364–416. https://doi.org/10.3758/s13428-021-01762-8 doi: 10.3758/s13428-021-01762-8
[39]	Hsu M (2017) Neuromarketing: inside the mind of the consumer. Calif Manage Rev 59: 5–22. https://doi.org/10.1177/0008125617720208 doi: 10.1177/0008125617720208
[40]	Hsu MYT, Cheng JMS (2018) fMRI neuromarketing and consumer learning theory: word-of-mouth effectiveness after product harm crisis. Eur J Mark 52: 199–223. https://doi.org/10.1108/EJM-12-2016-0866 doi: 10.1108/EJM-12-2016-0866
[41]	Iden J, Methlie LB, Christensen GE (2017) The Nature of Strategic Foresight Research: A Systematic Literature Review. Technol Forecast Social Change 116: 87–97. https://doi.org/10.1016/j.techfore.2006.10.001 doi: 10.1016/j.techfore.2016.11.002
[42]	Jai TM, Fang D, Bao FS, et al. (2021) Seeing it is like touching it: Unraveling the effective product presentations on online apparel purchase decisions and brain activity (An fMRI Study). J Int Mark 53: 66–79. https://doi.org/10.1016/j.intmar.2020.04.005 doi: 10.1016/j.intmar.2020.04.005
[43]	Kansra P, Oberoi S, Gupta SL, et al. (2022) Factors limiting the application of consumer neuroscience: A systematic review. J Cons Behav. https://doi.org/10.1002/cb.2131 doi: 10.1002/cb.2131
[44]	Khashei V, Harandi AO (2015) Explaining strategic control model in weight industry: discourse exploration using grounded theory strategy. J Strat Manage Stud 6: 81–80.
[45]	Keles HO, Karakulak EZ, Hanoglu L, et al. (2022) Screening for Alzheimer's disease using prefrontal resting-state functional near-infrared spectroscopy. Front Hum Neur 16: 1061668. https://doi.org/10.3389/fnhum.2022.1061668 doi: 10.3389/fnhum.2022.1061668
[46]	Kirschstein T, Köhling R (2009) What is the source of the EEG? Clin. EEG Neur 40: 146–149. https://doi.org/10.1177/155005940904000305 doi: 10.1177/155005940904000305
[47]	Knutson B, Genevsky A (2018) Neuroforecasting aggregate choice. Curr Direct Psych Sci 27: 110–115. https://doi.org/10.1177/0963721417737877 doi: 10.1177/0963721417737877
[48]	Kolar T, Batagelj Z, Omeragić I, et al. (2021) How moment-to-moment EEG measures enhance ad effectiveness evaluation: Peak emotions during branding moments as key indicators. J Adv Res 61: 365–381. https://doi.org/10.2501/JAR-2021-014 doi: 10.2501/JAR-2021-014
[49]	Krampe C, Strelow E, Haas A, et al. (2018) The application of mobile fNIRS to "shopper neuroscience"–first insights from a merchandising communication study. Eur J Mark 52: 244–259. https://doi.org/10.1108/EJM-12-2016-0727 doi: 10.1108/EJM-12-2016-0727
[50]	Kumar B, Sharma A, Vatavwala S, et al. (2020) Digital mediation in business-to-business marketing: A bibliometric analysis. Ind Mark Manage 85: 126–140. https://doi.org/10.1016/j.indmarman.2019.10.002 doi: 10.1016/j.indmarman.2019.10.002
[51]	Le TT (2023) The association of corporate social responsibility and sustainable consumption and production patterns: The mediating role of green supply chain management. J Clean Prod 414: 137435. https://doi.org/10.1016/j.jclepro.2023.137435 doi: 10.1016/j.jclepro.2023.137435
[52]	Lee EJ, Kwon G, Shin HJ, et al. (2014) The spell of green: Can frontal EEG activations identify green consumers? J Bus Eth 122: 511–521. https://doi.org/10.1007/s10551-013-1775-2 doi: 10.1007/s10551-013-1775-2
[53]	Lee N, Brandes L, Chamberlain L, et al. (2017).This is your brain on neuromarketing: Reflections on a decade of research. J Mark Manage 33: 878–892. https://doi.org/10.1080/0267257X.2017.1327249 doi: 10.1080/0267257X.2017.1327249
[54]	Lee N, Broderick AJ, Chamberlain L (2007) What is 'neuromarketing'? A discussion and agenda for future research. Int J Psych 63: 199–204. https://doi.org/10.1016/j.ijpsycho.2006.03.007 doi: 10.1016/j.ijpsycho.2006.03.007
[55]	Lee N, Chamberlain L, Brandes L (2018) Welcome to the jungle! The neuromarketing literature through the eyes of a newcomer. Eur J Mark 52: 4–38. https://doi.org/10.1108/EJM-02-2017-0122 doi: 10.1108/EJM-02-2017-0122
[56]	Levallois C, Smidts A, Wouters P (2021) The emergence of neuromarketing investigated through online public communications (2002–2008). Bus Hist 63: 443–466. https://doi.org/10.1080/00076791.2019.1579194 doi: 10.1080/00076791.2019.1579194
[57]	Li SZ, Jain AK, Huang T, et al. (2005) Face recognition applications. Hand Face Recog, 371–390.
[58]	Lim WM (2018) Demystifying neuromarketing. J Bus Res 91: 205–220. https://doi.org/10.1016/j.jbusres.2018.05.036 doi: 10.1016/j.jbusres.2018.05.036
[59]	Lim WM, Yap SF, Makkar M (2021) Home sharing in marketing and tourism at a tipping point: What do we know, how do we know, and where should we be heading? J Bus Res 122: 534–566. https://doi.org/10.1016/j.jbusres.2020.08.051 doi: 10.1016/j.jbusres.2020.08.051
[60]	Liu Y, Zhao R, Xiong X, et al. (2023) A Bibliometric analysis of consumer neuroscience towards sustainable consumption. Behav Sci 13: 298–315. https://doi.org/10.3390/bs13040298 doi: 10.3390/bs13040298
[61]	Luna-Nevarez C (2021) Neuromarketing, ethics, and regulation: An exploratory analysis of consumer opinions and sentiment on blogs and social media. J Cons Pol 44: 559–583. https://doi.org/10.1007/s10603-021-09496-y doi: 10.1007/s10603-021-09496-y
[62]	Mariani MM, Al-Sultan K, De Massis A (2023). Corporate social responsibility in family firms: A systematic literature review. J Small Bus Manage 61: 1192–1246. https://doi.org/10.1080/00472778.2021.1955122 doi: 10.1080/00472778.2021.1955122
[63]	Marzouk OA, Mahrous AA (2020) Sustainable consumption behavior of energy and water-efficient products in a resource-constrained environment. J Glob Mark 33: 335–353. https://doi.org/10.1080/08911762.2019.1709005 doi: 10.1080/08911762.2019.1709005
[64]	McDonald MA, Tayebi M, McGeown JP, et al. (2022) A window into eye movement dysfunction following mTBI: a scoping review of magnetic resonance imaging and eye tracking findings. Brain Behav 12: e2714. https://doi.org/10.1002/brb3.2714 doi: 10.1002/brb3.2714
[65]	Meyerding SG, Mehlhose CM (2020) Can neuromarketing add value to the traditional marketing research? An exemplary experiment with functional near-infrared spectroscopy (fNIRS). J Bus Res 107: 172–185. https://doi.org/10.1016/j.jbusres.2018.10.052 doi: 10.1016/j.jbusres.2018.10.052
[66]	Mishra S, Malhotra G, Chatterjee R, et al. (2021) Impact of self-expressiveness and environmental commitment on sustainable consumption behavior: The moderating role of fashion consciousness. J Strat Mark, 1–23. https://doi.org/10.1080/0965254X.2021.1892162 doi: 10.1080/0965254X.2021.1892162
[67]	Motoki K, Sugiura M, Kawashima R (2019). Common neural value representations of hedonic and utilitarian products in the ventral stratum: An fMRI study. Sci Rep 9: 1–10. https://doi.org/10.1038/s41598-019-52159-9 doi: 10.1038/s41598-018-37186-2
[68]	Motoki K, Suzuki S, Kawashima R, et al. (2020) A combination of self-reported data and social-related neural measures forecasts viral marketing success on social media. J Interact Mark 52: 99–117. https://doi.org/10.1016/j.intmar.2020.06.003 doi: 10.1016/j.intmar.2020.06.003
[69]	Murphy ER, Illes J, Reiner PB (2008) Neuroethics of neuromarketing. J Cons Behav An Int Res Rev 7: 293–302. https://doi.org/10.1002/cb.252 doi: 10.1002/cb.252
[70]	Nasir O, Javed RT, Gupta S, et al. (2023) Artificial intelligence and sustainable development goals nexus via four vantage points. Techn Soc 72: 102171. https://doi.org/10.1016/j.techsoc.2022.102171 doi: 10.1016/j.techsoc.2022.102171
[71]	Negrete-Cardoso M, Rosano-Ortega G, Álvarez-Aros EL, et al. (2022) Circular economy strategy and waste management: A bibliometric analysis in its contribution to sustainable development, toward a post-COVID-19 era. Env Sci Poll Res 29: 61729–61746. https://doi.org/10.1007/s11356-022-18703-3 doi: 10.1007/s11356-022-18703-3
[72]	Nemorin S (2017) Neuromarketing and the "poor in world" consumer: how the animalization of thinking underpins contemporary market research discourses. Cons Mark Cult 20: 59–80. https://doi.org/10.1080/10253866.2016.1160897 doi: 10.1080/10253866.2016.1160897
[73]	Nilashi M, Samad S, Ahmadi N, et al. (2020). Neuromarketing: a review of research and implications for marketing. J Soft Comp Dec Supp Sys 7: 23–31.
[74]	Oliveira PM, Guerreiro J, Rita P (2022) Neuroscience research in consumer behavior: A review and future research agenda. Int J Cons Stud 46: 2041–2067. https://doi.org/10.1111/ijcs.12800 doi: 10.1111/ijcs.12800
[75]	Pagan NM, Pagan KM, Teixeira AA, et al. (2020) Application of neuroscience in the area of sustainability: Mapping the territory. Glob J Flex Sys Manage 21: 61–77. https://doi.org/10.1007/s40171-020-00243-9 doi: 10.1007/s40171-020-00243-9
[76]	Paul J, Benito GRG (2018) A review of research on outward foreign direct investment from emerging countries, including China: what do we know, how do we know and where should we be heading? Asia Pac Bus Rev 24: 90–115. https://doi.org/10.1080/13602381.2017.1357316 doi: 10.1080/13602381.2017.1357316
[77]	Paul J, Parthasarathy S, Gupta P (2017) Exporting challenges of SMEs: A review and future research agenda. J World Bus 52: 327–342. https://doi.org/10.1016/j.jwb.2017.01.003 doi: 10.1016/j.jwb.2017.01.003
[78]	Pérez-Martínez J, Hernandez-Gil F, San Miguel G, et al. (2023) Analysing associations between digitalization and the accomplishment of the Sustainable Development Goals. Sci Total Env 857: 159700. https://doi.org/10.1016/j.scitotenv.2022.159700 doi: 10.1016/j.scitotenv.2022.159700
[79]	Piracci G, Casini L, Contini C, et al. (2023) Identifying key attributes in sustainable food choices: An analysis using the food values framework. J Clean Prod 416: 137924. https://doi.org/10.1016/j.jclepro.2023.137924 doi: 10.1016/j.jclepro.2023.137924
[80]	Plassmann H, Venkatraman V, Huettel S, et al. (2015) Consumer neuroscience: applications, challenges, and possible solutions. J Mark Res 52: 427–435.https://doi.org/10.1509/jmr.14.0048 doi: 10.1509/jmr.14.0048
[81]	Powers A, Fani N, Murphy L, et al. (2019) Attention bias toward threatening faces in women with PTSD: Eye tracking correlates by symptom cluster. Eur J Psy 10: 1568133. https://doi.org/10.1080/20008198.2019.1568133 doi: 10.1080/20008198.2019.1568133
[82]	Qananwah Q, Alqudah AM, Alodat MD, et al. (2022) Detecting cognitive features of videos using EEG signal. Comp J 65: 105–123. https://doi.org/10.1093/comjnl/bxaa180 doi: 10.1093/comjnl/bxaa180
[83]	Qasim MS, Bari DS, Martinsen ØG (2022) Influence of ambient temperature on tonic and phasic electrodermal activity components. Phys Meas 43: 065001. https://doi.org/10.1088/1361-6579/ac72f4 doi: 10.1088/1361-6579/ac72f4
[84]	Qazi A, Simsekler MCE, Al-Mhdawi MKS (2023) Exploring network-based dependencies between country-level sustainability and business risks. J Clean Prod 418: 138161. https://doi.org/10.1016/j.jclepro.2023.138161 doi: 10.1016/j.jclepro.2023.138161
[85]	Ramsøy TZ (2019) Building a foundation for neuromarketing and consumer neuroscience research: How researchers can apply academic rigor to the neuroscientific study of advertising effects. J Adv Res 59: 281–294.https://doi.org/10.2501/JAR-2019-034 doi: 10.2501/JAR-2019-034
[86]	Rana IA, Khaled S, Jamshed A, Nawaz A (2022) Social protection in disaster risk reduction and climate change adaptation: A bibliometric and thematic review. J Integ Env Sci 19: 65–83. https://doi.org/10.1080/1943815X.2022.2108458 doi: 10.1080/1943815X.2022.2108458
[87]	Rawnaque FS, Rahman K M, Anwar SF, et al. (2020). Technological advancements and opportunities in neuromarketing: a systematic review. Brain Inf 7: 1–19.https://doi.org/10.1186/s40708-020-00109-x doi: 10.1186/s40708-020-0102-9
[88]	Reilly RG, Peelle JE (2021) The left inferior frontal gyrus is sensitive to individual differences in reading comprehension ability: An eye-tracking study. PLoS One 16: e0245897. https://doi.org/10.1371/journal.pone.0245897 doi: 10.1371/journal.pone.0245897
[89]	Savelli E, Gregory‐Smith D, Murmura F, et al. (2022) How to communicate typical–local foods to improve food tourism attractiveness. Psy. Mark 39: 1350–1369. https://doi.org/10.1002/mar.21668 doi: 10.1002/mar.21668
[90]	Shen F, Morris JD (2016) Decoding neural responses to emotion in television commercials: an integrative study of self-reporting and fMRI measures. J Adv Res 56: 193–204. https://doi.org/10.2501/JAR-2016-016 doi: 10.2501/JAR-2016-016
[91]	Singh J, Goyal G, Gill R (2020) Use of neurometrics to choose optimal advertisement method for omnichannel business. Ent Inf Sys 14: 243–265. https://doi.org/10.1080/17517575.2019.1640392 doi: 10.1080/17517575.2019.1640392
[92]	Silva M (2015) A systematic review of Foresight in Project Management literature. Proc Comp Sci 64: 792–799. https://doi.org/10.1016/j.procs.2015.08.630 doi: 10.1016/j.procs.2015.08.630
[93]	Smidts A, Hsu M, Sanfey AG, et al. (2014) Advancing consumer neuroscience. Mark Lett 25: 257–267. https://doi.org/10.1007/s11002-014-9306-1 doi: 10.1007/s11002-014-9306-1
[94]	Solnais C, Andreu-Perez J, Sánchez-Fernández J, et al. (2013) The contribution of neuroscience to consumer research: A conceptual framework and empirical review. J Econ Psy 36: 68–81. https://doi.org/10.1016/j.joep.2013.02.011 doi: 10.1016/j.joep.2013.02.011
[95]	Stanton SJ, Sinnott-Armstrong W, Huettel SA (2017) Neuromarketing: Ethical implications of its use and potential misuse. J Bus Eth 144: 799–811. https://doi.org/10.1007/s10551-016-3059-0 doi: 10.1007/s10551-016-3059-0
[96]	Stillman P, Lee H, Deng X, et al. (2020) Examining consumers' sensory experiences with color: A consumer neuroscience approach. Psy Mark 37: 995–1007. https://doi.org/10.1002/mar.21360 doi: 10.1002/mar.21360
[97]	Varan D, Lang A, Barwise P, et al. (2015) How reliable are neuromarketers' measures of advertising effectiveness? Data from ongoing research holds no common truth among vendors. J Adv Res 55: 176–191. https://doi.org/10.2501/JAR-55-2-176-191 doi: 10.2501/JAR-55-2-176-191
[98]	Vyas S, Seal A (2022) A deep convolution neural networks framework for analyzing electroencephalography signals in neuromarketing, In: Proceedings of International Conference on Frontiers in Computing and Systems: COMSYS 2021. Singapore: Springer Nature Singapore, 119–127. https://doi.org/10.1007/978-981-19-0105-8_12
[99]	Wajid A, Raziq MM, Ahmed QM, et al. (2021) Observing viewers' self-reported and neurophysiological responses to message appeal in social media advertisements. J Retail Cons Serv 59: 102373. https://doi.org/10.1016/j.jretconser.2020.102373 doi: 10.1016/j.jretconser.2020.102373
[100]	Wei Q, Lv D, Lin Y, et al. (2023) Influence of utilitarian and hedonic attributes on willingness to pay green product premiums and neural mechanisms in China: An ERP study. Sustainability 15: 2403. https://doi.org/10.3390/su15032403 doi: 10.3390/su15032403
[101]	WTO (2023) Available from: https://www.wto.org/english/forums_e/public_forum23_e/public_forum23_e.htm
[102]	Xu Z, Wang X, Wang X, et al. (2021) A comprehensive bibliometric analysis of entrepreneurship and crisis literature published from 1984 to 2020. J Bus Res 135: 304–318. https://doi.org/10.1016/j.jbusres.2021.06.051 doi: 10.1016/j.jbusres.2021.06.051
[103]	Yuan J, Zhang Y, Zhao Y, et al. (2023) The emotion-regulation benefits of implicit reappraisal in clinical depression: Behavioral and electrophysiological evidence. Neur Bull 39: 973–983. https://doi.org/10.1007/s12264-022-00973-z doi: 10.1007/s12264-022-00973-z
[104]	Zhang Y, Bian Y, Wu H, et al. (2023) Intuition or rationality: Impact of critical thinking dispositions on the cognitive processing of creative information. Thin Skills Create 48: 101278. https://doi.org/10.1016/j.tsc.2023.101278 doi: 10.1016/j.tsc.2023.101278
[105]	Zhao M (2022) The impact of cognitive conflict on product-service system value cocreation: An event-related potential perspective. J Clean Prod 331: 129987. https://doi.org/10.1016/j.jclepro.2021.129987 doi: 10.1016/j.jclepro.2021.129987
[106]	Zhu Z, Jin Y, Su Y, et al. (2022). Evaluation of the neuromarketing research trend: 2010–2021. Front Psyc 13: 872468. https://doi.org/10.3389/fpsyg.2022.872468 doi: 10.3389/fpsyg.2022.872468

This article has been cited by:

1.	Qinghua Li, Hu Shi, Wanting Zhao, Chunlu Ma, Enhanced Dung Beetle Optimization Algorithm for Practical Engineering Optimization, 2024, 12, 2227-7390, 1084, 10.3390/math12071084
2.	Kun Li, Hao Wu, Xinming Liu, Jianing Xu, Ying Han, Intelligent Diagnosis of Rolling Bearing Based on ICEEMDAN-WTD of Noise Reduction and Multi-Strategy Fusion Optimization SCNs, 2024, 12, 2169-3536, 36908, 10.1109/ACCESS.2024.3373554
3.	Ya‐Kun Zhang, Jian‐Bo Tong, Ze‐Lei Chang, Jing Yan, Xiao‐Yu Xing, Yu‐Lu Yang, Zhan Xue, QSAR Modeling of Pyridone Derivatives as α‐amylase Inhibitors Using Chemical Descriptors and Machine Learning, 2025, 10, 2365-6549, 10.1002/slct.202404214
4.	Fengtao Wei, Yue Feng, Xin Shi, Kai Hou, Improved sparrow search algorithm with adaptive multi-strategy hierarchical mechanism for global optimization and engineering problems, 2025, 28, 1386-7857, 10.1007/s10586-024-04883-9

Reader Comments

Your name:*

Email:*
© 2023 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)