The Electric Vehicle Population Data, maintained by the Washington State Department of Licensing (DOL), presents a thorough overview of currently registered Battery Electric Vehicles (BEVs) and Plug-in Hybrid Electric Vehicles (PHEVs) in the state (Data.wa.gov, 2024). Figure 1 shows the distribution of BEVs and PHEVs in the state according to year and company in the tested dataset. This dataset, publicly accessible and regularly updated, serves as a valuable resource for scrutinizing the evolving landscape of electric vehicles. It encompasses detailed information about BEVs and PHEVs, empowering researchers and analysts to explore diverse facets of sustainable transportation. With its last update on 16 December 2023, this dataset, covering the period from its creation on 10 November 2020, provides a dynamic and evolving portrayal of the electric vehicle population in Washington. Hosted on data.wa.gov and managed by the Department of Licensing, it not only aids in evaluating the current growth and adoption of electric vehicles but also furnishes indispensable data for policymakers, urban planners, and industry stakeholders committed to advancing sustainable mobility initiatives in the region.

Table 1 illustrates the distribution of BEVs and PHEVs across various counties. King County shows a significantly higher number of electric vehicles than other counties, with Snohomish, Pierce, and Clark counties following. The number of electric vehicles decreases progressively in the other countries, as shown. Table 2 presents the most common electric vehicles currently registered, grouped by model.

Within the scope of this investigation, various machine learning classification techniques were utilized, and the following components represent those algorithms. Long-short-term memory, also known as LSTM, is a form of neural network that was developed primarily to overcome the difficulties associated with capturing long-term dependencies inside sequential data collections (Alhussan et al., 2023b). LSTMs are adept at preserving and utilizing knowledge over extended periods of time, which, in turn, makes them useful for predicting patterns in time-series data. LSTMs are widely used in tasks that include sequences, such as natural language processing and speech recognition. LSTM is a type of recurrent neural network (RNN) suitable for sequence-based tasks, effectively capturing long-term dependencies in data. Each of these methods has its strengths and weaknesses, making them suitable for specific machine learning applications.

Random Forest is a classification system that is well-known for its capacity to generate reliable predictions while simultaneously minimizing the danger of overfitting. It is composed of numerous decision trees, each of which is trained on a random sample of the data. Random Forest Classifier aggregates predictions from multiple decision trees, providing robust performance and reducing overfitting. This is one of the reasons why it is such a popular choice for classification and regression problems because it can utilize the collective intelligence of a wide variety of trees (Khafaga et al., 2022b). The basic machine learning methods encompass a diverse set of algorithms used in this study. The SGD Classifier, based on Stochastic Gradient Descent, is particularly useful for large-scale optimization problems, often employed in linear classification tasks (El-Kenawy et al., 2022a). Decision Tree Classifier constructs a tree structure to make decisions based on input features, suitable for both classification and regression problems (Hassan et al., 2022). K Neighbors Classifier, part of the k-Nearest Neighbors algorithm, makes predictions by considering the majority class of its nearest neighbors, making it effective for both simple and complex datasets (El-Kenawy et al., 2022b). SVC (Support Vector Classifier) is a powerful classification algorithm that aims to find the optimal hyperplane separating different classes (Khafaga et al., 2022c). NN Classifier typically refers to a neural network-based classifier, offering the flexibility to model complex relationships in data (Abdelhamid et al., 2023b).

The accuracy, sensitivity, and specificity of the classification module are metrics used to evaluate its performance. Additional performance metrics consist of Precision (PPV), F-score, and Negative Predictive Value (NPV). The respective abbreviations for the true-positive (TP), true-negative (TN), false-negative (FN), and false-positive (FP) values are provided here. The value of TP signifies a successful prediction that an instance is a member of the positive class; FP signifies a false prediction that the predicted instance is in the positive class; and TN signifies a correct prediction that the instance is a member of the negative class. These measurements delineate the characteristics of each indicator.

• Accuracy: the model’s ability to recognize full cases, regardless of positive or negative cases and is formed as shown in Equation 1

The results presented in Table 4 showcase the performance metrics of various classification models across different evaluation criteria. The SGD Classifier demonstrates a commendable overall accuracy of 79.53%, with a high True Positive Rate (TRP) of 90.09% but a relatively low True Negative Rate (TNP) of 6.25%. The decision tree classifier exhibits an improved accuracy of 82.89%, with a higher TRP and TNP than the SGD classifier, resulting in a superior F1 Score of 90.58%. K-Neighbors Classifier further enhances the accuracy to 84.97%, with notable increases in TRP and TNP, contributing to an enhanced F1 Score of 91.77%. The Support Vector Classifier (SVC) exhibits a higher accuracy of 86.21%, with substantial improvements in TRP and TNP, leading to an elevated F1 Score of 92.02%. The NN Classifier demonstrates increased accuracy at 87.68%, with significant improvements in TRP and Positive Predictive Value (PPV), resulting in an F1 Score consistent with the SVC. The random forest classification achieves a noteworthy accuracy of 90.70%, with a high TRP and TNP, contributing to an impressive F1 score of 93.75%. The LSTM model surpasses all others with an accuracy of 92.86%, showcasing the highest TRP, TNP, and F1 Score among the presented models. These results provide a comprehensive evaluation of the models’ classification performance, highlighting strengths and weaknesses across various metrics. Figure 2 shows visualization of the basic classification models’ results applied to the tested dataset.

The presented results in Table 5 offer a detailed evaluation of various hybrid models combining optimization algorithms with Long Short-Term Memory (LSTM) networks, focusing on their performance across multiple metrics. The DGGO + LSTM model stands out with an exceptionally high accuracy of 98.88%. This model exhibits a remarkable True Positive Rate (TRP) of 98.36% and an impressive True Negative Rate (TNP) of 99.38%, resulting in a robust Precision (PPV) of 99.34% and a high Negative Predictive Value (NPV) of 98.46%. The F1 Score of 98.85% further underscores the overall excellence of DGGO + LSTM in classification tasks. The GGO + LSTM model also demonstrates strong performance, achieving an accuracy of 96.66%. It maintains a balanced True Positive Rate (TRP) of 97.40% and a high True Negative Rate (TNP) of 95.79%, contributing to a solid Precision (PPV) of 96.46% and an F1 Score of 96.93%.

The PSO + LSTM, GWO + LSTM, WOA + LSTM, and GA + LSTM models exhibit slightly lower but still commendable accuracies ranging from 95.24% to 93.07%. These models show variations in their True Positive Rates, True Negative Rates, and other metrics, reflecting nuanced differences in their abilities to correctly classify positive and negative instances. These results demonstrate the efficacy of the DGGO + LSTM model, surpassing others in terms of accuracy and overall classification performance. The GGO + LSTM model also performs well, and the other hybrid models, while achieving slightly lower accuracies, still showcase respectable performance across various evaluation metrics. These findings suggest the potential of combining optimization algorithms with LSTM networks to enhance the predictive capabilities of classification models, with DGGO + LSTM leading the pack in this set of experiments. Figure 3 shows the effectiveness of proposed (DGGO + LSTM) and compared optimization models to the tested dataset.

The presented statistics in Table 6 provide a comprehensive overview of the performance measures for six different models, each combining DGGO, GGO, PSO, GWO, WOA, or GA with LSTM. The models are assessed based on various statistical measures, including minimum and maximum values, percentiles, confidence intervals, mean, standard deviation, coefficient of variation, and measures of central tendency. The range of accuracy across the models is relatively narrow, with coefficients of variation ranging from 0.2827% to 0.7615%. DGGO + LSTM consistently exhibits the highest accuracy, with the narrowest range and standard deviation, while GWO + LSTM shows a slightly wider range and standard deviation. The confidence intervals at different percentiles provide insights into the precision of the estimated means, with DGGO + LSTM showing consistently narrow intervals. The skewness values indicate the asymmetry of the data distribution, and all models exhibit varying degrees of skewness. The kurtosis values suggest the tail heaviness of the distributions, with DGGO + LSTM and GA + LSTM showing higher kurtosis values. In terms of the geometric mean, harmonic mean, and quadratic mean, all models demonstrate similar patterns, reinforcing the stability and consistency of the results. The sum of the values across all models remains close to 10, indicating a relatively consistent overall performance. The statistical analysis provides a detailed characterization of the performance distribution for each model, offering valuable insights into the reliability and variability of their accuracy measures. DGGO + LSTM consistently emerges as a high-performing model with narrow confidence intervals and stable statistical properties. These results facilitate a nuanced understanding of the models’ performance and aid in making informed comparisons between the different optimization algorithm-LSTM combinations

Following the previous experiment, several different classifiers, including DGGO + LSTM, GGO + LSTM, PSO + LSTM, GWO + LSTM, and GA + LSTM, were examined by applying them to the dataset that had been specifically described earlier. The primary purpose was to evaluate and contrast the degree of accuracy exhibited by each solution. Figure 4 illustrates that the findings indicate that the DGGO + LSTM algorithm beats other solutions, demonstrating a much greater accuracy rate than the other alternatives.

In the following experiment, we will investigate how hybrid algorithms exhibit varying degrees of accuracy. Repeating the experiment ten times and displaying the results of each iteration in the form of a histogram is the method that is utilized to arrive at an average. The numbers that were collected from each iteration of the experiment are depicted in Figure 5, which provides a visual depiction of the accuracy distribution over several repetitions.

The computation of residual values and heat is included in the experiments, and the results are visually shown through a variety of charts and comparisons. During the first computation, the residual values are graphically displayed on a dispersed y-axis that is grouped within columns. A representation of the distribution of these residual values may be found in Figure 6. To determine the degree of similarity between the anticipated and actual residual values, a QQ plot is utilized. This plot illustrates that the two sets of values are in tight alignment with one another. To compare the variances of the various groups, the homoscedasticity plot shown in Figure 6 is utilized. This reveals the consistent variances that exist between the groups. In addition, the heatmap shown in Figure 6 is utilized to accurately assess the magnitude of the individual values contained within the dataset. These studies, when taken as a whole, provide a thorough insight into the characteristics of residual values, their distribution, and the variance among groups, which ultimately helps to improve the interpretation of the results of the experiment. The ROC curve of the proposed DGGO + LSTM versus the original GGO + LSTM is shown in Figure 7.

As shown in Table 7, the results of the Analysis of Variance (ANOVA) prove markedly distinguishable that there are notable disparities among treatment groups within the datasets. Through the application of the above-described statistical technique, different patterns have been identified that reveal the effectiveness of the applied treatments that lead to the variations. More specifically, the sum of squares distributed along the lines of treatment groups turns out to be 0.02092, which is in conjunction with 5 degrees of freedom linked to treatment variables. Moreover, the SS residuals are obtained, meaning the variability within each treatment group is 0.001281 degrees of freedom assigned to residuals. In order to compare within and between group variances, this analysis uses an F-statistic, presumed with 5 and 54 degrees of freedom, equal to the F-ratio of 176.4. The result of this test is a very small p-value (p < 0.0001), which is high enough to reject the null equal-means hypothesis across groups managed by different treatments being used. Those results are the robust ground of statistically correlated data, which showed that regarding the applied treatment, a clear forerunner/champion between groups is observed. The ANOVA results reveal the main influence of treatments used in creating the dataset, which implies the superiority of intentionally applied experimental interventions in setting a quite significant ground for variation of the different treatment groups.

A modified Wilcoxon Signed Rank Test was used on six models combining optimization algorithms with the LSTM network that were formulated to examine the ability of each to outperform the theoretical mid-point of 0, as given in Table 8. Based on actual media results, they differ from theoretical ones, revealing their respective efficiencies. The medians for DGGO + LSTM, GGO + LSTM(eps), PSO + LSTM, GWO + LSTM, WOA + LSTM, and GA + LSTM were obtained as 0.9888, 0.9666, 0.9524, 0.947, 0.9438, and 0.9. Strikingly, all the models provided similar results regarding the population of the signed-rank S = 55 and no negative ranks, while positive ones were solely present. Here, the uniformity, which serves as the cornerstone and the rock of the work, makes the whole literature review series trustworthy and further helps to secure the credibility of the coming conclusions. Secondly, these two-way p-values of 0.002 each, which noticeably deviate from the theoretical mean, clearly demonstrate the statistically significant divergence from the calculated mean. Indeed, the smoking gun effect of the null hypothesis shows this, as well as the actual medians, in comparison to the theoretical probability. These simulations show that they do inherit the idea of medians from the software, and their improvement over the baseline median is partly due to that characteristic. This outstanding improvement clearly reveals the capability of the mentioned techniques when it comes to analytical models and data prescriptive tasks. Specifically, LSTM, together with optimization approaches, proved to be useful.