E-commerce has become a crucial business model through the Internet around the world. Therefore, its transaction trend forecast can provide important information for the market planning and development in advance. For this purpose, the integrated model of enhanced whale optimization algorithm (EWOA) with support vector machine (SVM) is proposed for forecast of E-commerce transaction trend in this study. First, the global optimization ability of the whale optimization algorithm (WOA) is enhanced by the search updating strategy. Second, multiple factors that may affect the E-commerce transaction trend are analyzed and determined using the gray correlation mechanism. Third, the EWOA algorithm is employed to optimize the SVM random parameters. Finally, the EWOA-SVM model is established for forecasting E-commerce transaction trend. Two representative cases tests confirm that the EWOA-SVM model is superior to other existing methods in terms of fast convergence speed and high prediction accuracy.
The current digital economy is moving forward much faster than before in recent years. Therefore, E-commerce transactions have become an important core of the digital economy in the global market [
At present, the prediction methods applied for E-commerce transactions trend have been focused on machine learning models, regression models, and combination models [
Zhang et al. [
SVM model is suitable for small sample prediction, and it has strong generalization ability and less random parameters. Li et al. [
For SVM to be used for forecasting the E-commerce transaction trend, two main problems need to be resolved. The first task is to reduce the influence of random parameters of SVM model, which is an optimization point. The other is to choose crucial factors on E-commerce transaction trend. Consequently, this study proposes an integrated model using enhanced Whale Optimization Algorithm (EWOA) with SVM model on the basis of multiple factors analysis and machine learning. In this approach, EWOA algorithm was used to optimize the random parameters of SVM model. The modeling process is introduced in Section
SVM, which is a hot spot model in machine learning models, has the characteristics of simple structure, few adjustable parameters, and strong generalization ability. It is often used in pattern recognition, disease diagnosis, regression prediction, and other fields [
The optimization problem is transformed into solving the equation by Lagrange multiplier, then the derivation of each variable is performed, and finally the dual form of the optimal problem is obtained [
Finally, the SVM regression function is defined as follows:
Generally, in SVM model, the penalty coefficient
To date, a variety of intelligent algorithms have been developed and applied, such as PSO algorithm [
The coefficient matrices
The whales adopt enveloping and spiraling behaviors in the predation stage. To realize the contraction encirclement,
Assume that the probability of the whale taking the action of shrinking encirclement and spiral attack is 50%, and the position updating strategy is expressed as follows:
In addition, whales randomly searching for food can succeed through updating
In the WOA algorithm, most of the parameters are random, and only the maximum number of iterations and population size need to be set, which is one of the advantages of the algorithm.
Wolpert and Macready [
The value of dynamic attenuation coefficient over iterations is depicted in Figure
Dynamic attenuation coefficient over iterations.
Aiming at the deficiency of population diversity weakening in the later iteration, an area search updating strategy is proposed. The whales migrate to other regions to search for food by the regional update frequency
Similar to WOA algorithm, most parameters in EWOA algorithm are random, but the maximum number of iterations, population size, and migration frequency need to be set in advance.
The process flowchart of the EWOA algorithm for searching the global optima is shown in Figure
Flowchart of EWOA optimization process.
As shown in Figure Initialize EWOA algorithm parameters. Determine whether to implement area search updating strategy. If the area search updating strategy is implemented, the location is updated according to equation ( Update the optimal location of whale population [ Determine whether to terminate the iteration. If the iteration is terminated, the optimization is completed. Otherwise, return to step (2).
There are five standard test functions used to analyze the model convergence efficiency. The
Standard test functions and variable ranges [
Equations | Variable ranges | Global optima | dim |
---|---|---|---|
[−100, 100] | 0 | 30 | |
[−00, 100] | 0 | 30 | |
[−10, 10] | 0 | 30 | |
[−600, 600] | 0 | 30 | |
[−5.12, 5.12] | 0 | 30 |
Note: “dim” denotes the test dimension.
In addition to EWOA algorithm, PSO algorithm [
Optimization algorithm parameters.
Algorithms | Parameters |
---|---|
PSO | |
CSA | |
WOA | |
EWOA |
In PSO,
Achievement of convergence results.
Test function | Algorithm | Average result | Best result | Worst result |
---|---|---|---|---|
PSO | 0.1083 | 5.51 | 2.41 | |
CSA | 2.49 | 4.54 | 9.01 | |
WOA | 1.49 | 6.38 | 4.34 | |
EWOA | 1.51 | 8.82 | 4.52 | |
PSO | 24.66 | 2.38 | 373.84 | |
CSA | 0.16 | 2.70 | 1.75 | |
WOA | 3.98 | 3.95 | 4.72 | |
EWOA | 1.56 | 1.89 | 4.46 | |
PSO | 0.81 | 4.98 | 3.09 | |
CSA | 6.85 | 1.90 | 0.81 | |
WOA | 5.54 | 7.70 | 1.01 | |
EWOA | 1.50 | 2.38 | 4.49 | |
PSO | 0.31 | 6.74 | 0.75 | |
CSA | 0.17 | 4.79 | 0.47 | |
WOA | 5.8 | 0 | 0.17 | |
EWOA | 0 | 0 | 0 | |
PSO | 15.52 | 7.96 | 28.85 | |
CSA | 9.25 | 3.97 | 17.90 | |
WOA | 3.78 | 0 | 5.68 | |
EWOA | 0 | 0 | 0 |
As can be seen, the EWOA algorithm presents better search outcomes than others. Obviously, the results obtained from unimodal functions such as
The fitness function to evaluate the convergence process is defined as follows:
The iterative convergence curves (log (Fitness)) using WOA and EWOA algorithms in various test functions are shown in Figure
Convergence curves of WOA and EWOA algorithms. (a)
E-commerce transaction volume indicates the average value of E-commerce sales volume and E-commerce procurement volume. The E-commerce transactions sample set was collected from 2005 to 2019 in China, including the annual E-commerce transaction volume and the multiple influencing factors. The influencing factors in E-commerce transactions mainly consist of basic resource, transaction level, and economic development level. The basic resources include the Internet penetration rate (A1; unit: %), number of websites (A2; unit: ten thousand), number of CN domain names (A3, unit: ten thousand), and number of Internet users (A4; unit: 100 million). Indeed, the Internet penetration rate is to reflect the sharing degree of basic resources. Websites applied as a transaction platform are an important index on E-commerce transactions; the number of CN domain names can reflect the number of Internet service companies. The number of Internet users is to reflect the demand for shopping services via Internet.
In transaction level, the factors including express delivery business volume (A5; unit: 100 million) and express delivery business revenue (A6; unit: 100 million yuan) have a crucial impact on transactions level. Among them, express delivery business plays an important role in the E-commerce sales. On the other hand, the express delivery business revenue can reflect the level of E-commerce transactions in the express delivery industry. In economic development level, Gross Domestic Product (GDP) regarded as a macroeconomic factor is considered a key factor in the economic activity. It can reflect the situation of the E-commerce development. Therefore, GDP (A7; unit: trillion yuan) is used to evaluate the E-commerce transactions in this study.
The statistics on China’s E-commerce transactions volume and the influence factors from 2005 to 2019 are presented in Table
Statistics of E-commerce transactions.
Year | A1 | A2 | A3 | A4 | A5 | A6 | A7 | |
---|---|---|---|---|---|---|---|---|
2005 | 8.5 | 69.4 | 109 | 1.11 | 8.66 | 239.7 | 18.58 | 1.29 |
2006 | 10.5 | 84 | 180 | 1.37 | 10.6 | 299.7 | 21.76 | 1.54 |
2007 | 16 | 150 | 900 | 2.1 | 12.02 | 342.6 | 26.8 | 2.17 |
2008 | 22.6 | 287 | 1357 | 2.98 | 15.13 | 408.4 | 31.67 | 3.14 |
2009 | 28.9 | 323 | 1368 | 3.84 | 18.58 | 479 | 34.56 | 3.67 |
2010 | 34.3 | 191 | 435 | 4.57 | 23.39 | 574.6 | 40.89 | 4.55 |
2011 | 38.3 | 250 | 353 | 5.13 | 36.73 | 758 | 48.41 | 6.09 |
2012 | 42.1 | 255 | 751 | 5.64 | 56.85 | 1005.3 | 53.41 | 8.11 |
2013 | 45.8 | 320 | 1082 | 6.17 | 91.87 | 1441.7 | 58.8 | 10.4 |
2014 | 47.9 | 355 | 1129 | 6.48 | 139.59 | 2045.4 | 63.59 | 16.39 |
2015 | 50.3 | 425 | 1636 | 6.88 | 206.7 | 2760 | 68.9 | 21.79 |
2016 | 53.2 | 482 | 2061 | 7.51 | 313.5 | 4005 | 74.41 | 26.1 |
2017 | 55.8 | 533 | 2084 | 7.72 | 400.6 | 4957 | 82.07 | 29.16 |
2018 | 59.6 | 523 | 2124 | 8.29 | 507.1 | 6010 | 91.92 | 31.63 |
2019 | 61.2 | 518 | 2185 | 8.85 | 630 | 7450 | 99.08 | 34.81 |
Note: “
The gray correlation is employed to analyze the correlation degree between multiple influencing factors and E-commerce transaction volume. Initially, the dimensionless process in E-commerce transaction volume and influencing factors is implemented to reduce the difference between the numerical values. Then, the correlation coefficient is calculated. The E-commerce transaction volume is denoted as the reference sequence
The correlation coefficient
The correlation degree
The correlation degree between E-commerce transaction volume and multiple influencing factors is presented in Table
Gray correlation degree in various influencing factors.
Gray correlation degree | |||
---|---|---|---|
A1 | 0.81 | A5 | 0.79 |
A2 | 0.79 | A6 | 0.91 |
A3 | 0.85 | A7 | 0.77 |
A4 | 0.81 |
It reveals that the highest correlation degree in the express business revenue (A6) reaches 0.91; the correlation degrees in Internet penetration rate (A1), number of CN domain names (A3), and number of Internet users (A4) exceed 0.8; the correlation degrees in website number (A2), express delivery business volume (A5), and GDP (A7) are below 0.8. As above, the collected data from A1, A3, and A4, A6 are considered as the input variables for the forecasting models.
Based on the integration of EWOA and SVM models, the proposed EWOA-SVM model is established to forecast E-commerce transactions trend. The architecture of prediction process is depicted in Figure Analyze the impact of multiple influencing factors on E-commerce transaction volume Calculate the correlation degree between different influencing factors and E-commerce transactions through gray correlation using equation ( Select strongly related factors with E-commerce transactions as model input variables Classify the training set and test set, and normalize the data Construct E-commerce transaction trend prediction model using EWOA-SVM Set the parameters of EWOA algorithm and SVM model [ Train EWOA-SVM model using training set Use EWOA to optimize the random parameters of SVM Calculate the fitness values of EWOA algorithm through equation ( Output the optimal parameters of SVM after the training process is complete Verify EWOA-SVM model using test set Employ trained SVM to predict E-commerce transaction trends Evaluate the forecast results of E-commerce transaction
Flowchart of E-commerce transaction forecast.
The performance of all algorithms throughout this study was carried out using MATLAB software, and the code of core programs and datasets can be freely accessed on the web page
The root mean square error (rmse) [
Two cases were used to test the effectiveness of the proposed EWOA-SVM model, also including the SVM and WOA-SVM model for comparison. SVM model is selected to analyze the influence of random parameters on the prediction results, and WOA-SVM model is chosen to compare with the mining capability of the EWOA algorithm. The E-commerce transaction data collected from 2005 to 2014 was chosen as the training set, and the data collected between 2015 and 2019 was used as the test set. The training convergence curves in both WOA-SVM and EWOA-SVM models are presented in Figure
Training convergence curves of WOA and EWOA algorithms between 2005 and 2014.
The test results from the performance of SVM, WOA-SVM, and EWOA-SVM models are presented in Figure
Test results of E-commerce transactions between 2015 and 2019.
Results of E-commerce transactions forecast from 2015 to 2019.
Year | Actual | SVM | WOA-SVM | EWOA-SVM |
---|---|---|---|---|
2015 | 21.79 | 19.69616 | 21.94652 | 21.73803 |
2016 | 26.1 | 25.92237 | 26.24643 | 26.63792 |
2017 | 29.16 | 28.82402 | 28.35714 | 28.36315 |
2018 | 31.63 | 32.02076 | 32.57347 | 32.20004 |
2019 | 34.81 | 34.98426 | 34.36644 | 34.55087 |
The E-commerce transaction data collected between 2005 and 2010 was selected as the training set, and the data collected between 2011 and 2019 was used as the test set. The training convergence curves of the WOA-SVM and EWOA-SVM models are presented in Figure
Training convergence curves of WOA and EWOA algorithms between 2005 and 2010.
Test results of E-commerce transactions from 2011 to 2019.
Results of E-commerce transactions forecast from 2011 to 2019.
Year | Actual | SVM | WOA-SVM | EWOA-SVM |
---|---|---|---|---|
2011 | 6.09 | 5.923791 | 6.09362 | 6.322908 |
2012 | 8.11 | 8.275549 | 7.878242 | 6.545946 |
2013 | 10.4 | 11.43486 | 13.30829 | 13.27391 |
2014 | 16.39 | 14.07154 | 15.8526 | 16.24195 |
2015 | 21.79 | 18.59799 | 20.41689 | 21.19814 |
2016 | 26.1 | 24.75947 | 24.83894 | 25.52773 |
2017 | 29.16 | 27.97686 | 27.22712 | 27.7213 |
2018 | 31.63 | 31.79973 | 32.85884 | 32.54913 |
2019 | 34.81 | 35.85496 | 36.01635 | 35.09898 |
The SVM, WOA-SVM, and EWOA-SVM models were used to predict the trend of E-commerce transactions in Cases 1 and 2. The prediction results of the model were evaluated in this section. For Cases 1 and 2, the relative error (Re%) curves from SVM, WOA-SVM, and EWOA-SVM models are shown in Figure
Prediction error curves. (a) Prediction relative errors in Case 1. (b) Prediction relative errors in Case 2.
Forecast error values.
Case | Year | Re (%) | ||
---|---|---|---|---|
SVM | WOA-SVM | EWOA-SVM | ||
Case 1 | 2015 | −9.61 | 0.71 | −0.23 |
2016 | −0.68 | 0.56 | 2.06 | |
2017 | −1.15 | −2.75 | −2.73 | |
2018 | 1.23 | 2.98 | 1.80 | |
2019 | 0.50 | −1.27 | −0.74 | |
Case 2 | 2011 | −2.72 | 0.10 | 3.82 |
2012 | 2.04 | −2.85 | −19.28 | |
2013 | 9.95 | 27.96 | 27.63 | |
2014 | −14.14 | −3.27 | −0.90 | |
2015 | −14.64 | −6.30 | −2.71 | |
2016 | −5.13 | −4.83 | −2.19 | |
2017 | −4.05 | −6.62 | −4.93 | |
2018 | 0.53 | 3.88 | 2.91 | |
2019 | 3.01 | 3.46 | 0.83 |
For Case 1, the Re interval of the SVM model was [−9.61%, 1.23%]; the Re interval of the WOA-SVM model was [−2.75%, −2.98%]; the Re interval of the EWOA-SVM model was [−2.73%, 2.06%]. The fluctuation range of the EWOA-SVM model was the smallest, and the Re error of the model was significantly smaller than the other two models. For Case 2, the maximum Re value for WOA-SVM and EWOA-SVM exceeded 27%. The prediction error of E-commerce in 2013 was relatively large, but the remaining errors were less than 20%. The overall prediction effects of WOA-SVM and EWOA-SVM models were better than that of SVM model.
The prediction evaluation results using the rmse and
Evaluation results of each model.
Cases | Models | rmse | |
---|---|---|---|
Case 1 | SVM | 0.97 | 99.27 |
WOA-SVM | 0.59 | 98.23 | |
EWOA-SVM | 0.51 | 98.69 | |
Case 2 | SVM | 1.53 | 97.79 |
WOA-SVM | 1.48 | 98.30 | |
EWOA-SVM | 1.26 | 98.42 |
At present, the global economy has entered a brand-new information network era. E-commerce is a new type of business operation model, which has been fast inspired with the impetus of the information technology. As E-commerce has the characteristics of wide transaction coverage, low cost, fast information circulation, and high work flow coordination, it has become a new engine for economic development. Accordingly, E-commerce transaction trend is becoming an important indicator to measure the business or economic activity level. To this end, this study proposes the EWOA-SVM model to predict the trend of E-commerce transactions, which provides a theoretical and effective tool for E-commerce development.
In real applications, a precise E-commerce transaction trend prediction can provide a decision-making basis for the governments or enterprises to formulate relevant development policies or plans in future business or industrial investments. The proposed model in this study can mine the crucial factors with high correlation degree in E-commerce transactions and construct E-commerce transaction trend correlation indexes. Importantly, it can be applied to logistics enterprises, Internet enterprises, and other information network companies in their business behavior.
In this study, the model training data was collected from E-commerce transactions volume and the influence factors, e.g., A1–A7, between 2005 and 2019. This sufficient data support and robust EWOA network structure can effectively alleviate the overfitting problem. The evaluation results of each model have been given more evidence with discussion to clarify this issue. The main contributions in this paper are concluded as follows: A dynamic search coefficient and search updating strategy are combined to solve WOA algorithm’s limitations. Accordingly, the EWOA algorithm can reach the global optima, i.e., 0, for multimodal functions, indicating a strong ability to escape from local minima. The express delivery, Internet penetration rate, number of CN domain names, and number of Internet users are confirmed as the most crucial factors in the E-commerce transactions trend. The evaluation results demonstrate that the EWOA-SVM model is superior to existing algorithms in the prediction of E-commerce transaction trend. For example, rmse of the EWOA-SVM model for Case 1 is 13.56% smaller than that of the WOA-SVM model and 47.42% smaller than that of SVM model. In Case 2, the rmse of the EWOA-SVM model is 14.86% smaller than that of the WOA-SVM and 17.64% smaller than that of the SVM model.
In the future work, it suggests that additional influencing factors in E-commerce transaction trend may be extended in practical circumstances. Besides, the generalization ability for various data prediction may be improved further.
The data used to support the findings of this study are included within the article.
The authors declare no conflicts of interest with respect to the research, authorship, and/or publication of this article.