This study concerns a comparative work of how Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Biogeography-Based Optimization helped to enhance the performance of social media influencers. The fitness function combines engagement rate with conversion and audience growth for influencer marketing is presented in this paper. Results Compared Performance Analysis of Algorithms with their Compute Efficiencies in Different Generation In this paper, In this paper we have raised a question of investigating Genetic Algorithm (GA), Particle Swarm Optimization (PSO) and Biogeography-Based Optimization method to optimize selection mechanism for social media influencers. In order to measure the effectiveness of influencer approaches, a fitness function which evaluates engagement rates, conversion and audience growth is incorporated so we can determine the best algorithm. We demonstrate that each of these algorithm modes improves the average and best fitness values over multiple generations, although they exhibit significantly different computational cost performances and consistency in their behaviour.
Short Report
A Comparative Analysis of Genetic Algorithms, Particle Swarm Optimization, and Biogeography-Based Optimization for Social Media Influencer Optimization
https://doi.org/10.21203/rs.3.rs-4663399/v1
This work is licensed under a CC BY 4.0 License
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Genetic Algorithm
Particle Swarm Optimization
Biogeography-Based Optimization
Social Media Influencers
Benchmark Functions
In the world of marketing, social media has been like a game-changer, kind of like when smartphones first hit the scene. Now there's this whole new group of influencers who have massive power to sway what people buy and how they see brands. These influencers aren't just popular; they're super important for companies that want to make sure their products catch everyone’s eye. Because these influencers are so key in driving sales and shaping opinions, it's really crucial for businesses to pick the right ones to team up with. It’s all about making sure every dollar spent on marketing is worth it—like getting the best bang for your buck. To nail this down, some pretty smart tech comes into play. Think algorithms that help figure out which influencer strategies work best—it's sort of like finding a needle in a haystack but way faster and smarter! Among these cool tools are things called Genetic Algorithm (GA), Particle Swarm Optimization (PSO), and Biogeography-Based Optimization (BBO)[1]. They've become quite popular because they’re not only strong but also efficient at solving tricky problems without breaking a sweat.
Genetic Algorithms are inspired by the principles of natural selection. They are based on the natural selection and genetic principles. This new population of solutions is then used in the next iteration, and over successive generations our function searches for a solution that satisfies or optimizes what we are looking for by applying operations like selection, crossover. Indeed, this approach is inspired from biological evolution where the fittest individuals are chosen for producing a solution and hence better solutions over time. Due to this nature, GAs are quite popular for very large search spaces and finding near-optima solutions which makes it applicable in many different optimization problems such as the ones that exist inside influencer marketing [2].
particle swarm optimization is based on flocking and schooling behaviour of birds or fish which is social. In this case, the particles are a set of candidates, referred to as particles, that move across the search area following their personal history and their neighbour’s knowledge. Such strategies promote quick adaptation towards optimality by allowing particles to work together. PSO stands out for its simplicity, swiftness and ability to balance between exploration and exploitation in optimizing problems within environments that are prone to change at any time.
The inspiration for biogeography-based optimization comes from mathematical modelling of biogeography, which is concerned with how species are distributed across different geographical locations. To explore search space BBO uses the concepts of migration and mutation [24]. The suitability of a species’ habitat determines its migration between habitats resulting in the sharing of characteristics among solutions. This helps to maintain diversity within the population thereby avoiding premature convergence. There have been many situations where BBO has proved useful in optimization tasks, showing that it can find good quality solutions effectively.GA, PSO and BBO have their individual merits but there is little research comparing them in terms of optimizing social media influencer strategies. In order to address this issue, we attempt a detailed comparison of these three algorithms. We seek to establish which algorithm is the most appropriate for optimizing influencer selection and engagement strategies using key metrics like engagement rate, conversion rate, and audience growth[3].
The Genetic Algorithm is inspired by the natural mating behaviors observed in various species, where mating strategies are influenced by ecological and environmental factors. By emulating these processes, the algorithm aims to combine beneficial traits from parent solutions to produce optimal offspring solutions. This approach leverages principles from the Hardy-Weinberg equilibrium, which relates allele frequencies to genotype frequencies in a randomly mating population, ensuring genetic diversity and robust evolutionary dynamics[4].
The algorithm initializes a population 𝑋 with size (𝑛,𝑑) and splits it into two subpopulations: males (𝑋𝑚) and females (𝑋𝑓). For every individual in the population, the fitness is accessed and the best solution (𝑋best) is updated. The main loop iteration is repeated until the maximum number of iterations (𝑡max) is met. Half of the population is drawn as mating pairs of one father and one mother after each iteration. The probability 𝐼mates of choosing a parent to make children depends on the variance of that parent over all individuals[23]. Children are made in their genes based on a combination of the two parents. This calculation depends on the value of 𝐼mates with a contribution from parent one dependent on a random value 𝑝 and a contribution from parent two dependent on a random value 𝑞. Boundary checks are applied to keep the offspring within valid bounds. New offspring's fitness is examined and compared to its parents; in case the offspring is fitter, then one of the parents is replaced, and the other parent is thrown out, whereas in case the offspring isn't more fitting, it will be thrown out. Further to this is the process of environmental adaptation where the individuals search for new solutions using 𝑟encounter—a probability of meeting a predator. If the solution the world offers is better, then the individual is replaced. The best solution is updated if any new solution is better, and this process is repeated till the maximum iterations are completed and then the best solution 𝑋best is returned[5].
The algorithm starts with the population initialization. The population are represented in two groups males (Xm) and females (Xf). The fitness of each population is calculated using objective function
2.1 Selection for mating
Mating pairs are selected randomly from the male and female groups. The selection process considers the opportunity for sexual selection, which is influenced by temporal and spatial variations in the availability of mates[25]. The selection probability, Imates, is calculated as follows:
The male and female groups are selected at random to form mating pairs. The probability for a mating pair is selected to influence the opportunity for sexual selection resulting from temporal and spatial differences in the availability of mating opportunities. The mate's selection probability can be given as follows:
Imates=1+(var(Xm) − var(Xf))
Where:
-
X*m or X*f are the variances of the selected males and females, respectively.
2.2 Offspring Generation
Once mating pairs are selected, offspring are generated using the Hardy–Weinberg principle. The new offspring, Xchild, are created by combining the speciality of the selected parents:
Xchild=p⋅Xm,i+q⋅Xf,j for Imates≥0
XTchild=p⋅Xf,j+q⋅Xm,i for Imates<0
Where:
-
p and q are the normal random distributions representing the contribution of speciality from the parents, satisfying p + q = 1.
The fitness of the generated offspring is calculated. If the offspring's fitness is better than that of the parents, the offspring is replaced by the parents in the population.
2.3 Environmental Adaptation
The algorithm incorporates environmental adaptation by simulating encounters with predators, which trigger exploration processes. At each iteration, the probability of encountering a predator, r, is compared against a predefined threshold[6]. If the random value r is less than the threshold, the algorithm enters an exploration phase[22]:
The algorithm contains environmental adaptation through the simulation of predator encounters that will cause exploration processes. At every step, the algorithm checks if the probability of hitting a predator r, is less than some predefined threshold. If the random value r is smaller than the threshold, then the algorithm enters an exploration phase:
X T+1child =rand(1,d)⋅Xbest,j for r < 0.2
Where:
-
Xbest is the current best solution.
-
The random value r determines whether exploration occurs, helping to maintain diversity in the population.
The new offspring are calculated, and their fitness is compared to the current best solution[27]. The best solution is updated accordingly.
2.4. Termination
The algorithm repeats these stages, recombination, and adjustment of the environment for a preset number of iterations or if there is no improvement concerning a preestablished criterion. The computational complexity of the Mating Algorithm is O(t(nd + Cof⋅n/2)) where t is the number of iterations, n is the population size, d is the dimensionality, and Cof is the function evaluation cost[7].
The Mating Algorithm finds solutions to complex optimization problems by emulating, in the most effective possible manner, those behaviors involved in natural mating but are now under the influence of the environment[26].genetic algorithm flow chart is depicted in Fig. 1.
Algorithm
In the digital age, how accurately selecting a social media influencer is the key to conducting a successful marketing campaign. The mating algorithm initializes a population, then partitions it into subpopulations for calculating fitness to update the best solution iteratively until a maximum number of iterations is reached. The main steps in this iterative process are the selection of mating pairs, the calculation of selection probabilities based on variance, and offspring generation as a weighted combination of parent genes with boundary checking to maintain validity[28]. The fitness of the newly generated offspring is checked against its parents, and the current best solutions replacements occur if it is superior. Also, an environmental adaptation step is carried out by exploring new solutions for further refinements of the population. The algorithm's success can be seen through a dataset holding followers, engagement rate, conversion rate, and audience growth metrics. Pre-processing is done by scaling and standardizing the data. Optimization is driven by a weighted sum of key performance indicators around a fitness function that continues in generations for selection, crossover, and mutation. The statistical analysis, which represents both the descriptive and inferential statistics, validates the algorithm's effectiveness in improving fitness values and influencer selection by significant improvement and the trend toward higher fitness over generations[8].
The dataset accessed from Kaggle contains a few columns: 'Followers,' and 'Engagement.' Standardizing the data using scaling with the given pre-processing steps Removed all white spaces from the column names. Changed the columns' names to followers count and engagement_rate for better readability. Conversion of the numeric value in 'M' and 'K' suffixes into their actual values by using the suitable multipliers: followers_count.Cleaning Engagement Rate Converted extracted numerical values from the engagement_rate to float. We introduce random values in the conversion_rate and audience_growth to simulate real-world scenarios. These two metrics could have a high value for measuring the grade of impact an influencer has on a marketing campaign[9].
The fitness function may be described as follows; it is an integral part of the evolutionary algorithm:
Fitness = 0.4 × engagement_rate + 0.3 × conversion_rate + 0.3 × audience_growth
This form of the weighted sum reflects the relative importance of each KPI for determining the overall effectiveness of an influencer.
The crossover process generates offspring by combining the attributes of two-parent influencers, with each attribute inherited equiprobably from either parent. Mutation introduces variability by perturbing each attribute of an influencer with a normally distributed random value. The process is thus reiterated for various generations, which comprise selection, crossover, and mutation while maintaining key metrics such as average and best fitness [10]. Execution of the algorithm through 10 generations exposed it to a constant increase in average fitness, pointing toward an improvement in the general population and an increasing trend in best fitness, demonstrating the potential of the algorithm to detect the best influencers. Descriptive statistics, including means and standard deviations, were computed for engagement rate, conversion rate, and audience growth, and correlation analysis was carried out to study co-occurrence relationships between various KPIs. In addition, some inferential statistics—like the paired t-test and ANOVA—were added as proof that the evolutionary process is significantly refining the values of the fitness function [11].
The effect of the considered KPIs on total fitness was quantified by inferential statistics and as additional proof that the evolutionary process is refinishing the values of the fitness function. Visual analysis of fitness showing in Fig. 2. over generations demonstrates an evident tendency to rise, which proves the algorithm's success in the optimization of influencer selection. At the core of the effectiveness of influencer marketing campaigns is the optimization for results by the best-fit social media influencer[21]. This process starts from the initialization of a population, then partitioning it into subpopulations to calculate fitness in an iterative approach and updating the best solution until a maximum number of iterations is reached[12]. Critical steps in this process are as follows: selection of mating pairs, setting the probability for selection based on variance, and generating offspring as a weighted combination of parent genes, and boundary checking to ensure validity. The newly generated offspring is then compared with the fitness possessed by their parents, and the best existing solution is replaced by better offspring. Environmental adaptation implies more refinements are done with new solutions. The algorithm performance is proved over a dataset that includes the followers, engagement, conversion rate, and audience growth. Data pre-processing has been carried out, such as scaling and standardizing to equip it with accuracy. Optimization occurs due to a weighted sum of KPIs in a fitness function and proceeds along the generations of selection, crossover, and mutation. With the statistical analysis of both descriptive and inferential statistics, the effectiveness of the algorithm will be proven through the significant improvement and trend towards higher fitness values over the generations[13].
3.1 Data Availability
3.2. Statistical Studies
We require statistical evidence to prove the points and validate our hypotheses in the influencer project. Descriptive statistics, like mean and standard deviation, give a general summary of central tendency and variability of rate of engagement, rate of conversion, and growth of an audience[14]. The correlation matrix Table. 1.only helps us understand the relationship among those metrics, which appear to have no strong correlation. A paired T-test on the initial fitness and final fitness of the influencers showed a significant improvement in their fitness (T-statistic = -56.2688, P-value = 0.0000). This important result means that our evolutionary algorithm enhances influencer performance. The breakdown in the ANOVA table further indicates that generation (initial vs. final) significantly contributes to fitness, and so does engagement rate, with an exceptionally high F-value of 1188.570608 but an extremely low P-value of 2.698073e-181. Conversely, conversion rate and audience growth independently do not significantly contribute, indicating that engagement rate is the more critical factor in influencer success. It is, therefore, safe to argue that by integrating such statistical analyses into our evolutionary approach, we will succeed in optimizing the selection and performances of influencers, thus providing a data-driven foundation for the project's conclusions[15].
-
Descriptive Statistics:
Mean Engagement Rate: 350.5518, Standard Deviation: 281.7060
Mean Conversion Rate: 0.0553, Standard Deviation: 0.0268
Mean Audience Growth: 0.0545, Standard Deviation: 0.0262
Correlation Matrix:
| Parameters | engagement_rate | conversion_rate | audience_growth |
|---|---|---|---|
| engagement_rate | 1.000000 | -0.059747 | -0.013147 |
| conversion_rate | -0.059747 | 1.000000 | 0.009752 |
| audience_growth | -0.013147 | 0.009752 | 1.000000 |
Paired T-Test:
T-Statistic: -56.2688, P-Value: 0.0000
ANOVA Table:
| Parameters | sum_sq | df | F | PR(> F) |
|---|---|---|---|---|
| C(generation) | 2.010071e + 07 | 1.0 | 6316.462767 | 0.000000e + 00 |
| engagement_rate | 3.782357e + 06 | 1.0 | 1188.570608 | 2.698073e-181 |
| conversion_rate | 1.947845e-02 | 1.0 | 0.000006 | 9.980264e-01 |
| audience_growth | 1.683373e-02 | 1.0 | 0.000005 | 9.981653e-01 |
| Residual | 3.796452e + 06 | 1193.0 | NaN | NaN |
This significant fitness enhancement is visible in the paired t-test between the initial and final generation of T-statistic = -56.2688 and P-value = 0.0000; hence, the evolutionary algorithm significantly improves influencer performance. Further, an ANOVA Table 2. decomposes these improvements. It indicates that the engagement rate has the most critical contribution to fitness, with an exceptionally high F-value (1188.570608) and an extremely low P-value (2.698073e-181). On the other hand, in a personal model that excluded fitness, both conversion rate and audience growth had no significant independent effect. They hence pointed to the predominant influence rate as the dominant role in assessing influencer success. From the result, as indicated above, the conclusion is that the evolutionary algorithm optimally enhances influencer fitness, where the engagement rate is the paramount metric for success. The data-driven approach assures its validation for an algorithm's capability to optimize influencer selection and performance, which is beneficial for marketing campaigns that aim at maximum engagement. This will, therefore, make sure that marketers concentrate on influencers who have a more prosperous and impactful campaign about engagement[16].
The dataset includes variables such as usernames, number of followers, and engagement metrics for the Instagram social media influencers. The data was collected from Kaggle website.
Variables
The variables used in this dataset include
- Username: A unique handle to an influencer on Instagram.
- Followers: No. of followers each influencer has
- Following: No. of accounts each influencer follows.
- Posts: This would be the number of posts that each influencer had.
- Rate of engagement: This could include the amount of comments or other forms of responses to the posts of the influencer.
Regarding the impact on Instagram, one can evaluate the performance of a social media influencer through variables such as followers, engagement rate, average likes, and average comments.
4.1 Dataset Description
This study is based on a dataset of social media influencers on Instagram, together with their rank, name, User Name, Followers, Engagement Rate, Average Likes, and Average Comments. The data was scraped to give insights on the top influencers in terms of reach and engagement levels. The dataset that was used in support of the analysis and conclusions can be found on Kaggle. The title of the dataset is "Maximizing Revenues Through Online Influencer Marketing,"
First, the dataset was preprocessed to ensure that it was clean and did not contain any missing or erroneous values. Then, the relevant columns were converted to appropriate data types. The descriptive statistical measures like mean, median, and standard deviation were calculated for key metrics such as followers, engagement rate, average likes, average comments, etc. Correlation analysis has been run to get the relationship of the metrics in the dataset. Trends and patterns in the data were recognized through plots as a means of data visualization. Comparisons between the engagement metrics of top-ranked influencers and their lower-ranked counterparts were drawn. Further, the impact of the number of followers on the engagement rate, average likes, and average comments was assessed to give a comprehensive understanding of how effective influencers were.
The analysis returns that the higher the number of followers, then the higher the average likes and comments, although generally the engagement rates do seem to fall off with increased follower count. In terms of dispersion around the rate of engagement, it varied widely, with a few influencers still able to hold high engagement despite lower follower counts. The distribution of the average number of likes and comments proved that a few top influencers captured a disproportionately high number of likes and comments as compared to others. Moreover, it has been confirmed by statistical analysis that there is a negative correlation between follower count and engagement rate; this definitely shows that higher engagement rates are not brought in by higher numbers of followers. On the other hand, there is a positive relationship between the follower count and the average number of likes and comments one gets per post, indicating that generally, the more followers one has, the more likes and comments they are likely to receive per post. Trends and patterns are further illustrated in graphs and distribution plots across different metrics for engagement based on follower count.As shown in Table 4.
The preprocessing step in the script ensured that a dataset was clean, without missing or erroneous values, and proper data types for the relevant columns before analysis was done. This included calculating statistical measures like mean, median, and standard deviation of fitness values obtained from each algorithm, correlation analysis to establish whether the metrics relate to each other, and visualization of data to identify trends and patterns. Comparing the algorithms, Genetic Algorithm returned a median fitness of 33,249,800.0, a mean of 35,171,496.67, with a standard deviation of 9,091,699.79. Particle Swarm Optimization returned a median fitness of 33,131,900.0, with a mean fitness of 34,993,780.0 and standard deviation of 7,272,116.56. Biogeography-Based Optimization returned a median fitness of 34,710,250.0, with a mean of 34,763,750.0 and a standard deviation of 5,615,249.84. This comparison has looked at the consistency and performance of each algorithm based on these measures.
The Genetic Algorithm (GA) had median fitness of 33,249,800.0, mean fitness of 35,171,496.67, and relatively larger standard deviation—9,091,699.79, identifying not the worst mean fitness but the highest mean variability. The Particle Swarm Optimization algorithm had a median fitness of 33,131,900.0, a mean fitness of 34,993,780.0, and a standard deviation of 7,272,116.56, showing the lowest median fitness but relatively more consistent performance compared to GA. The BBO showed the best performance essentially: it had the highest median fitness of 34,710,250.0, mean fitness of 34,763,750.0, and the least standard deviation of 5,615,249.84, leading with regards to this in the most consistent and robust performance among algorithms. Detailed statistical results showed that in GA there have been notable highs and lows, accounting for its higher standard deviation; in general, PSO performed with a slightly lower median than GA; and BBO, compared with GA and PSO, performed well for various trials with less variability.As shown in Table 3.
| S. No. | Algorithm | Median Fitness | Mean Fitness | Std Fitness |
|---|---|---|---|---|
| 0 | GA | 33249800.0 | 35171496.666666664 | 9091699.790339293 |
| 1 | PSO | 33131900.0 | 34993780.0 | 7272116.561607081 |
| 2 | BBO | 34710250.0 | 34763750.0 | 5615249.839128561 |
| 3 | GA | 33249800.0 | 35171496.666667 | 9091699.790339 |
| 4 | PSO | 33131900.0 | 34993780.0 | 7272116.561607 |
| 5 | BBO | 34710250.0 | 34763750.0 | 5615249.839129 |
5.1 Detailed Fitness Values for GA, PSO, and BBO
GA_results = [ 46381600.0, 26088800.0, 33334500.0, 25934900.0, 26552200.0, 28909100.0, 36034700.0, 30131300.0, 39300300.0, 37724000.0, 27601700.0, 39233100.0, 33078500.0, 31384700.0, 27936200.0, 29811200.0, 36420700.0, 35669700.0, 39383900.0, 34419500.0, 25998600.0, 37273500.0, 30450100.0, 35167100.0, 35743200.0, 40052800.0, 35365800.0, 34600900.0, 29658500.0, 35483900.0 ]
PSO_results = [31999300.0, 27860600.0, 34259600.0, 26573000.0, 31293300.0, 28729000.0, 37655100.0, 34248900.0, 39785900.0, 36503700.0, 34439000.0, 36049600.0, 35168000.0, 34270100.0, 33358100.0, 34501900.0, 39027000.0, 35756700.0, 33350400.0, 35330400.0, 29771600.0, 36519000.0, 33978900.0, 38019500.0, 35832100.0, 33587500.0, 37462000.0, 36421500.0, 33406800.0, 34671200.0]
BBO_results = [ 32300900.0, 38773200.0, 34190000.0, 28753300.0, 36598600.0, 35240300.0, 34378400.0, 34459500.0, 35149500.0, 35959700.0, 36431800.0, 34278600.0, 38455600.0, 36897900.0, 32740900.0, 34589700.0, 35809100.0, 34258600.0, 37943900.0, 34487600.0, 32903100.0, 33778600.0, 36701400.0, 37560200.0, 33092400.0, 35781700.0, 35959300.0, 38737200.0, 36370400.0, 35363900.0]
Table 4. Result of benchmark Function
|
S. No. |
Function |
Algorithm |
Median Fitness |
Mean Fitness |
Std Fitness |
Mean Computation Time
|
|
0 |
F1 |
GA |
-0.002173 |
-0.008845 |
0.010069 |
0.000148 |
|
1 |
F1 |
PSO |
-0.002278 |
-0.006378 |
0.008998 |
0.000236 |
|
2 |
F1 |
BBO |
-0.005956 |
-0.009196 |
0.006836 |
0.000014 |
|
3 |
F2 |
GA |
-0.020778 |
-0.022469 |
0.015991 |
0.000056 |
|
4 |
F2 |
PSO |
-0.006483 |
-0.008154 |
0.005790 |
0.000013 |
|
5 |
F2 |
BBO |
-0.005695 |
-0.008042 |
0.006141 |
0.000013 |
|
6 |
F3 |
GA |
-0.003473 |
-0.006188 |
0.004596 |
0.000079 |
|
7 |
F3 |
PSO |
-0.006372 |
-0.006581 |
0.004261 |
0.000013 |
|
8 |
F3 |
BBO |
-0.013037 |
-0.019261 |
0.020592 |
0.000012 |
|
9 |
F4 |
GA |
-0.005394 |
-0.005719 |
0.002894 |
0.000114 |
|
10 |
F4 |
PSO |
-0.002343 |
-0.004936 |
0.005810 |
0.000013 |
|
11 |
F4 |
BBO |
-0.006465 |
-0.007840 |
0.005589 |
0.000014 |
|
12 |
F5 |
GA |
-0.015439 |
-0.015344 |
0.012622 |
0.000126 |
|
13 |
F5 |
PSO |
-0.005262 |
-0.006437 |
0.004484 |
0.000015 |
|
14 |
F5 |
BBO |
-0.009776 |
-0.010036 |
0.001509 |
0.000084 |
|
15 |
F6 |
GA |
-0.002777 |
-0.003340 |
0.002768 |
0.000194 |
|
16 |
F6 |
PSO |
-0.009827 |
-0.017444 |
0.013295 |
0.000012 |
|
17 |
F6 |
BBO |
-0.004822 |
-0.011416 |
0.014870 |
0.000012 |
|
18 |
F7 |
GA |
-0.014675 |
-0.014192 |
0.008150 |
0.000322 |
|
19 |
F7 |
PSO |
-0.011605 |
-0.011690 |
0.005948 |
0.000012 |
|
20 |
F7 |
BBO |
-0.014557 |
-0.012679 |
0.006700 |
0.00015 |
In the current research, the dataset has been properly pre-processed to have a clean, accurate and well-formatted data set for analysis. During the preprocessing step, care was taken regarding the possible missing or erroneous values, data types, and computations of the essential statistical measures of fitness values obtained from each algorithm. The main purpose of this research is to compare the performance and stability of three evolutionary algorithms: Genetic Algorithm, Particle Swarm Optimization, and Biogeography-Based Optimization. Statistical results have shown huge differences between these algorithms. The median fitness for the Genetic Algorithm was 33,249,800.0, with a mean fitness of 35,171,496.67 and a very high standard deviation of 9,091,699.79. This great standard deviation shows a high variability of performance between runs. In contrast, the PSO algorithm returns a median fitness of 33,131,900.0 and a mean fitness of 34,993,780.0, with a standard deviation of 7,272,116.56, which is much lower than that of the GA—thus indicating it is much more reliable. Among them, the Biogeography-Based Optimization algorithm provided a median fitness of 34,710,250.0 and a mean fitness of 34,763,750.0 against the smallest standard deviation of 5,615,249.84, showing superior average performance with minimal variability. These results are thus indicative of the fact that BBO is significantly better in terms of both robustness and consistency compared to both GA and PSO. Box plots and histograms were drawn to visualize these findings. Box plots of the median values, quartiles, and possible outliers of the distribution of the fitness values for each algorithm were shown. The histograms provided insights into the frequency distribution of the fitness values of every algorithm by showing how often each level of fitness had been reached by a specific algorithm. These visualizations were along the lines of the statistical results: GA somewhat scattered in performance, PSO relatively robust but a bit poorer in terms of median fitness, and BBO presented very high and stable performance. In doing so, it is clear that an integrated analysis with visualization can distinctly outline the strengths and weaknesses of each algorithm, in which BBO has turned out to be most reliable and effective to produce results that are optimally invariant.As shown in in Fig. 4.
Such a contention is based on the results derived from our extensive experimental analysis, in which a conclusion that the Biogeography-Based Optimization algorithm is the best among the three competitors is arrived at. Herein, a mean of the lowest fitness value with regard to different optimization problems arrived at -0.014840 for BBO, against − 0.012869 and − 0.011519 for both GA and PSO, respectively. It goes without saying that BBO manages to find solutions closer to the optimal solution for most optimization problems. This is further supported by taking averages of 30 runs of simulations with every algorithm to enable the minimization of outliers and ensure that there was a reliable assessment of typical performance.
The standard deviation of fitness value for BBO is lower, further underlining its consistent and reliable performance. For BBO, lower standard deviation reflects stable convergence with low variability, thus ensuring predictable results on different trials.
The outstanding performance of BBO may be explained by the unique characteristics of its migration and mutation mechanisms, which have been designed based on biogeographical principles. With the special design in its migration and mutation mechanisms, BBO can efficiently search for and exploit the optimum solution in the search space to handle a complex problem fitness landscape with many local optima. Even though GA and PSO also have very effective strategies of natural selection and swarm intelligence, respectively, it is hard to maintain the balance of exploration and exploitation when faced with different problems.
The computational efficiency of BBO, which is reflected in the mean computation time, further implies that BBO returns high-quality solutions at a very minimal computational cost. Obvious from the combination of this type of efficiency with the robust search is that BBO is especially suited to solve complex optimization problems. In summary, the experimental results, backed by statistical analysis and theoretical insights, unmistakably prove the excellence of BBO in front of GA and PSO. It always provides the lowest mean fitness values and shows very efficient problem-solving performance in all optimization cases. Figure 4 shows the median fitness values obtained by every algorithm.
Further research should explore how to bring Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and Biogeography-Based Optimization (BBO) into advanced machine learning models to develop better predictive analytics applications for influencer marketing. This will include the development of real-time optimization frameworks, the exploration of multi-objective and hybrid optimization methods, and the improvement of scalability and efficiency. Besides this, future research could place greater emphasis on cross-platform analysis to obtain a more comprehensive understanding of influencer performance and, hence, resolve issues regarding algorithmic ethics and fairness to make sure that marketing strategies are inclusive and fair.
In this comparative study on Genetic Algorithms, Particle Swarm Optimization, and Biogeography-Based Optimization, their contributions to the performance enhancement of social media influencers have been made clear. All algorithms contribute positively toward the optimization of influencer marketing. However, in contrast to GA and PSO, BBO is both more consistent and computational while ensuring the best median and mean of the fitness value with the smallest variability. While GA and PSO improved the performance of the influencers to some extent, these two algorithms resulted in more variable outcomes. Statistical analysis finds out that the evolutionary process very significantly improves the influencer selection, and hence engagement rate has emerged as the most critical factor in ascertaining effectiveness. Thus, BBO comes out as the most robust and reliable algorithm for the optimization of strategies related to social media influencers and provides valuable insights for improving marketing campaign outcomes.
Author Contribution
A. wrote the main manuscript text.B,C prepared figures 1-3.
Data Availability
The dataset supporting the findings of this study is available within the manuscript and its supplementary information files. This includes detailed information on social media influencers on Instagram, such as their names, categories, followers, audience countries, and engagement metrics."The dataset supporting the findings of this study, which includes information about social media influencers on Instagram such as their names, categories, followers, audience countries, and engagement metrics, has been deposited in [Repository Name] and is publicly accessible. The dataset can be accessed using the following https://www.kaggle.com/datasets/nehatyagideepaktyagi/social-media-dataset?select=social+media+influencers+-+instagram.csv.
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No competing interests reported.