This section focuses on the basic performance testing of the COWOA proposed in this paper in four aspects, including the comparison between the COWOA optimization mechanisms, the comparison between the COWOA and nine original algorithms, the comparison between the COWOA and seven WOA optimization variants, and the comparison between the COWOA and eight optimization variants of other algorithms. Specific details of the 30 benchmarking functions of IEEE CEC2014 are given in Table 1. The parameters of the involved algorithm are as shown in Table 2 in all function experiments (Table 3).

For the experimental data, we use the experimentally derived average value (AVG) to reflect the performance of the corresponding algorithm, and the lower the mean value indicates, the more outstanding performance of the algorithm; we use the variance (STG) to reflect the stability of the algorithm, and the lower the variance indicates the relatively more stable performance of the algorithm. Also, in order to further discuss the comprehensive performance of all the algorithms participating in the comparison experiments, the Wilcoxon signed-rank test (García et al., 2010) and Friedman test (García et al., 2010) were also used to analyze the experimental results, and in the paper, respectively, are given in the form of tables and bar charts. In the results of the Wilcoxon signed rank test, “+” in the corresponding table given below indicates that COWOA performs better overall than the other algorithms, “ = ” indicates that it performs almost exactly the same as the other algorithms, and “-” indicates that it performs relatively worse than the other algorithms. Finally, in order to visually discuss the convergence ability of the algorithms and the ability to escape local optima, the partial convergence images of the algorithms are also given in the paper.

We have recommendations in other papers for fair empirical comparison between two or more optimization methods, which demand assigning the same computational resources per approach (Li et al., 2017; Chen J. et al., 2021; Liu K. et al., 2021; Zheng et al., 2022). To ensure the fairness of the external factors, we unified all the experiments based on functions in this section in the same environment, with the parameters of the specific experimental environment, as shown in Table 4.

This section discusses the proposed process of COWOA, with the main purpose of providing a minimum practical basis for the COWOA proposed in this paper; it also explores the impact of the CMS and the OLM on the WOA during the experimental process and the advantages that the COWOA exhibits in the experiments, such as the superior convergence speed compared to the WOA. Therefore, this subsection sets up a comparison experiment between the COWOA and the CMS-based WOA variant (CMWOA), the OLM-based WOA variant (OWOA), and the original WOA based on the 30 benchmark test functions in IEEE CEC2014.

According to Supplementary Table 1, it is easy to see that among the 30 benchmark function test experiments, the COWOA is relatively more prominent in terms of the number of times it has a smaller mean and variance performance compared to the other three algorithms. Among them, the more the mean value of COWOA, it means that COWOA has more vital exploration and exploitation ability on the optimal problem and also means that it is easier to get a better solution; the more the number of times to get smaller mean value means that COWOA is more adaptable on the optimization problem. In addition, we can see that the variance of the COWOA is relatively small, and the number of performances is relatively high, which indicates that the COWOA proposed in this paper is relatively more stable on the preliminary benchmark function test. Therefore, we can conclude that the comprehensive performance of the COWOA is better when the benchmark functions are optimized using COWOA, CMWOA, OWOA, and WOA, which also tentatively indicates that the COWOA has the prerequisites to be proposed.

To further demonstrate the performance of the COWOA and to enhance the persuasiveness of the COWOA proposed in this paper, two more intuitive statistical methods, the Wilcoxon signed-rank test, and the Freedman test, are used below to analyze and evaluate the experimental data. Table 5 shows the results of the Wilcoxon signed-rank test, where the second column of Table 5 gives the comparative details of the experiments, from which we can see that the COWOA proposed in this paper is superior to the original WOA in as many as 25 out of 30 basis functions, with one having similar performance and only four being relatively poor, which also shows that there is still room for improvement in the COWOA, but does not negate the fact that the COWOA is superior to the original WOA. Similarly, we can see that the COWOA also outperforms the CMWOA and OWOA. Also, the table gives the Wilcoxon ranking, and COWOA is ranked first in the comparison.

Table 6 gives the P-values obtained for this experiment based on the Wilcoxon signed-rank test, and the bolded parts in the table represent the results of experiments with P-values less than 0.05. By looking at the P-values, it can be seen that only a few values are greater than 0.05, which indicates that the COWOA exhibits much better performance than the single mechanism improvement variant and the original WOA in this comparison experiment.

Figure 4 Shows the Friedman ranking results of this improvement experiment, from which it can be more intuitively seen that the COWOA can obtain a smaller Friedman average than the other three comparative algorithms in the improvement process under the dual effect of CMS and OLM, which indicates that the COWOA is ranked first in this test method. Therefore, we can tentatively determine that the performance of the COWOA is optimal in this improvement experiment.

Figure 5 gives some of the convergence curves of the four algorithms in the process of finding the optimal solution. The 30 benchmark test functions used in the experiments are divided into four categories: unimodal, simple multimodal, hybrid, and combinatorial functions. Therefore, in order to highlight the performance of the COWOA, we selected the convergence plots so that Figure 5 covers these four categories. It is relatively intuitive to see from the plots that the convergence ability of COWOA on functions F10, F11, and F16 performs very well relative to the other three algorithms. Their convergence curves explore the relatively optimal solutions early in the pre-convergence period, indicating that the COWOA also runs the risk of being unable to escape from the local optimum in some problems. However, the convergence ability it possesses in this experiment is also unmatched by the WOA and cannot be compared. On functions F1, F2, F12, and F17, the shapes of the convergence curves of the COWOA and the CMWOA are extremely similar, but in terms of the final convergence accuracy, except for the equal convergence accuracy on function F2, COWOA is superior; in addition, we can also see that the convergence curve of COWOA reaches a relatively better time earlier than that of CMWOA, which indicates that the COWOA has been strengthened after the introduction of the OLM based on the CMWOA. Not only the convergence accuracy has been improved, but also the convergence speed has been significantly enhanced. The convergence curves of COWOA on functions F1, F2, F11, F12, F16, and F17 all have inflection points in the middle and early stages of the whole experiment, which indicates that the optimization algorithm can escape the local optimum at that stage. In summary, through the comparative experiments and analysis of COWOA with CMWOA, OWOA, and WOA, we can conclude that COWOA is an excellent optimized swarm intelligence algorithm among the improved WOA variants under different combinations of the two optimization methods.

The balance analysis results are given in Figure 6 based on partial benchmark functions. The balance analysis results of COWOA are shown in Figure 6A. The balance analysis results of CMWOA are shown in Figure 6B. The balance analysis results of OWOA are shown in Figure 6C. The balance analysis results of WOA are shown in Figure 6D. Finally, Figure 6E gives the convergence curves obtained by the above four algorithms for the corresponding benchmark function experiments. According to the equilibrium analysis results shown in Figure 6, it can be seen from the functions F6, F12, F17, and F19 that the CMS can enhance the exploration ability of WOA to a certain extent. The OLM improves the development ability of WOA. Combining the results of the equilibrium analysis and the corresponding convergence curves, it can be easily seen that the combination of CMS and OLM can make COWOA reach a better balance point in exploration and exploitation, so that COWOA can obtain better convergence accuracy and convergence speed than CMWOA, OWOA, and WOA in the benchmark function experiments.

In this subsection, to demonstrate that the COWOA still has outstanding optimization performance in the improved WOA variants and to further enhance the persuasiveness of the COWOA proposed in this paper, seven optimization variants of WOA were purposely selected for comparative experiments and results analysis on 30 benchmark functions. There are CWOA (Patel et al., 2019), IWOA (Tubishat et al., 2019), BMWOA (Heidari et al., 2020), ACWOA (Elhosseini et al., 2019), LWOA (Ling et al., 2017), OBWOA (Abd Elaziz and Oliva, 2018), and EWOA (Tu et al., 2021a). In Supplementary Table 2 shows the AVG and STD of the eight improvement variants of the WOA, including the COWOA, obtained in this experiment. By looking at the table, we can see that the COWOA obtains not only the relatively smallest mean value but also the variance on 13 of the 30 benchmark functions, such as functions F1, F2, F3, F4, F5, F7, F17, F18, F19, F20, F21, F29, and F30. This indicates that the COWOA is able to obtain not only relatively optimal solutions, but also possesses a stability that is difficult to match with the other seven WOA optimization variants. Based on the table of 30 benchmark functions in the experimental setup section, we can find that the 13 listed optimization problems cover the four categories of benchmark functions in the table, which indicates that the COWOA is still more adaptable among the participating WOA variants. In summary, we can conclude that the COWOA is an improved variant of WOA that performs well.

In order to further verify the excellent performance of the COWOA, two test results that are statistically significant are presented next, which are the results of the Wilcoxon signed-rank test and the results of Friedman ranking, as shown in Table 7 and Figure 7, respectively. As can be seen from Table 7, the COWOA has a significant average ranking advantage and the final Wilcoxon signed-rank test ranks first among the algorithms involved in the comparison; the second column of Table 7 gives the strengths and weaknesses of the COWOA relative to the other WOA variants in the Wilcoxon signed-rank test. Although the relative strengths and weaknesses are mixed, the final results show that the COWOA is relatively the best.

Table 8 gives the P-values obtained for this experiment based on the Wilcoxon signed-rank test, and the bolded parts of the table represent the results of experiments with P-values greater than 0.05. According to the results in the table, the number of P-values greater than 0.05 is a much smaller proportion of the overall results than the proportion less than 0.05, which indicates that the COWOA is superior to the other 7 well-known WOA variants in this evaluation method.

As seen in Figure 7, the COWOA obtained a Friedman mean of 2.71 and the smallest compared to the seven well-known WOA improvement variants, indicating that the COWOA ranks first under this test method. For the other seven compared algorithms, the mean value obtained by COWOA is 0.48 smaller than the second-ranked EWOA and 3.56 smaller than the poorly ranked CWOA. In summary, we can prove through this experiment that the COWOA is an excellent new variant of WOA improvement.

To confirm the superiority of the COWOA, we next took the convergence curves obtained throughout the experiment and selected images of the optimization process for nine functions according to the principle of including four classes of benchmark functions, as shown in Figure 8. The convergence curves of the COWOA on the listed functions are significantly better than those of the other seven WOA variants, except for F9, which shows that the COWOA is relatively the strongest in these optimization problems. On functions F1, F2, F12, F17, F21, F29, and F30, the other seven WOA variants’ convergence curves are relatively smooth. In contrast, the convergence curves of the COWOA have one or two inflection points in the middle and early stages of the experiment, which indicates that the COWOA can escape the local optimum early in the process of finding the optimal solution and that the convergence achieved in the end is the accuracy is also relatively optimal. In summary, in the comparative experiments set up in this paper, the convergence ability of the COWOA proposed can achieve relatively better than the seven WOA variants of the algorithm. Therefore, this experiment proves that the COWOA is an excellent WOA variant.

The results of the experiments that compare the computational costs of COWOA and the 7 WOA variants are shown in Figure 9. To ensure the experiment’s fairness, the experiment uniformly uses the same experimental setup as the benchmark function validation experiments. In addition, the results of this experiment are counted in seconds. As seen in Figure 9, COWOA, IWOA, EWOA, and CWOA have similar time costs in optimizing the 30 basic problems, and all have relatively higher complexity than ACWOA, BMWOA, LWOA, and OBWOA. This is due to the different complexity of the optimization methods introduced in the WOA variants. For COWOA, the CMS and the OLM bring more computational overhead to it. The comprehensive analysis of the experimental results presented in this section concludes that COWOA is computationally acceptable in terms of the time cost spent.

In this subsection, we set up a comparison experiment between the COWOA and the well-known original algorithms of today, and there are SCA, MFO, PSO, WOA, BA, GWO, GOA, FA, ACOR, and CSA. The main purpose of this section is to provide a practical basis for the COWOA proposed in this paper and to further demonstrate that the COWOA also has relatively outstanding convergence capabilities among other original algorithms.

Supplementary Table 3 presents the corresponding experimental results in the form of AVG and STG in Supplementary Table. By comparing and looking at the mean values; we can see that the COWOA exhibits the smallest mean values for functions F1, F2, F3, F4, F7, F10, F12, F17, F18, F19, F20, F21, F23, F29, and F30 out of the 30 is benchmark functions. The COWOA excelled in this area with 15 benchmark functions compared to other algorithms, a capability that other algorithms participating in the comparison experiments did not have. In addition, the COWOA showed the smallest variance in functions F1, F2, F3, F4, F7, F12, F17, F18, F20, F21, F23, F29, and F30, indicating that the COWOA is relatively more stable in its optimization of these benchmark functions. In summary, the COWOA is not only highly adaptive to the optimization problem, but also achieves relatively better solutions in comparison with the nine well-known original algorithms; the relatively small variance of the optimal solution for most of the problems demonstrates that the COWOA is more stable most of the time. Therefore, the overall capability of the COWOA is worthy of recognition, and the COWOA is a very good improvement algorithm.

To make the experimental results more scientific, the Wilkerson signed-rank test was used to evaluate the experimental results below, as shown in Table 9. According to Table 9, we can see that the COWOA ranks first in the overall ranking of the comparison experiments in this setup. The two columns Mean-level and Rank give the final ranking data more intuitively. In addition, the second column of the table shows the details of the experimental results based on 30 benchmark functions, from which it is easy to see that the original algorithm performs better on at least 17 optimization problems and at most 28 optimization problems for the different original algorithms. Although the performance on some problems is not as outstanding as the other original algorithms, this does not affect the overall performance of the COWOA, which is relatively the best among them, but only shows that the COWOA still has much room for optimization in the future.

Further validation of the Wilcoxon signed-rank test is given in Table 10, where the bold data indicates a p-value greater than 0.05. The number of p-values greater than 0.05 in the overall results of the COWOA against the 9 well-known original algorithms is very small, which proves that the COWOA still performs very well in comparison with the well-known WOA variants.

The results of the Friedman test are given in Figure 10, from which it can be seen that the COWOA has the smallest mean value of the Friedman compared with the nine well-known original algorithms, which indicates that the COWOA is ranked first in this basis function experiment. If the difference between the second-ranked ACOR and the COWOA is defined as △, then the absolute value of △ is greater than 1, |△| > 1. As a result, it can be proven that the COWOA still has an obvious advantage under this evaluation method.

To further demonstrate the benefits of COWOA, this subsection also uses the same experimental structure set up in the performance testing section of COWOA to give convergence curves for the entire iterative process and the convergence curves for the nine functions selected by the four classes of benchmark functions, as shown in Figure 11. It can be seen from the convergence plots that the convergence speed of COWOA has an undeniable advantage over the entire iterative process. The ability to develop a global optimum is relatively the best relative to the nine original algorithms. In addition, the convergence curves of the COWOA on functions F1, F2, F17, F21, F29, and F30 all have obvious inflection points, and the inflection points are relatively forward, which indicates that the optimization algorithm has an undeniable ability to escape the local optimum in the early stage of finding the optimal solution, which is a convergence performance that the other nine original algorithms do not have. In summary, through the analysis of the comparative experiments in this setup, we can conclude that the COWOA proposed in this paper is an excellent variant of WOA.

In this section, we make a comparative experiment and analysis of COWOA with eight optimization variants of other algorithms, which will be the most powerful interpretation of COWOA performance in the experimental part of this paper on basis functions. They are CBA (Adarsh et al., 2016), OBLGWO (Heidari et al., 2019a), mSCA (Qu et al., 2018), RCBA (Liang et al., 2018), HGWO (Zhu et al., 2015), SCAPSO (Nenavath et al., 2018), CDLOB (Yong et al., 2018), and CAGWO (Lu et al., 2018). Supplementary Table 4 shows the AVG and STG of the benchmark experimental results of COWOA against the eight improved algorithms. By comparing and looking at the average values, we find that for most of the benchmark functions, COWOA has the smallest average value. This indicates that the COWOA has a relatively higher quality optimization capability in this experiment. Furthermore, the relatively smallest variance of the optimal solutions obtained is a strong indication of the better stability of the COWOA’s optimization capability on these benchmark functions. Therefore, we can tentatively conclude that the COWOA is a novel and excellent improvement algorithm.

Table 11 shows the final analysis and evaluation details of the Wilkerson signed-rank test, from which it can be seen that the mean of the COWOA has a significant advantage in this set-up of the comparison experiment and is ranked first among the compared algorithms. In addition, the second column of the table gives the degree of superiority of the COWOA compared to the other eight algorithms, from which we can see that the COWOA exhibits relatively more outstanding optimization capabilities for most of the optimization problems, which not only demonstrates the greater performance of the COWOA but also proves that it has better adaptability to many optimization problems.

Table 12 shows the p-values of the COWOA for the eight well-known variants, where the bolded data indicate p-values greater than 0.05. According to the table, the number of data less than 0.05 occupies the majority of the overall portion, indicating that the COWOA performs better than the well-known variant algorithms.

Figure 12 shows the result of the Friedman ranking, from which it can be seen that the COWOA has the smallest average, which indicates that it still has a very strong advantage under this testing method. Therefore, COWOA is still a relatively better swarm intelligence optimization algorithm for the experiments in this setup.

In order to enhance the conviction that the optimization capability of the COWOA is relatively better in the comparison experiments, nine convergence curves obtained during the experiments are given below, as shown in Figure 13. The convergence curves of the COWOA have a convergence advantage over the other eight algorithms, except for the optimization F26, which finally achieves a relatively optimal convergence accuracy. In addition, the convergence curves of the eight compared algorithms are relatively smooth throughout the convergence process. In contrast, the convergence curves of the COWOA have different numbers of inflection points, and there is a very obvious drop in the curve after the inflection point, which indicates that the COWOA not only jumps out of the local optimum but also has a faster convergence speed. In summary, we can conclude that the convergence ability of the COWOA proposed in this paper is relatively more excellent compared to the eight excellent variants of other algorithms. Therefore, this experiment proves that the COWOA is an excellent swarm intelligence algorithm.

To confirm the performance of the bCOWOA-KELM model in the direction of feature selection, this section conducts feature selection experiments based on six public datasets in the UCI and a medical dataset (HD) collected at the moment, respectively. To enhance the persuasiveness of the experimental results, this paper also uses nine binary swarm intelligence optimization algorithms in the feature selection experiments for comparison experiments with the bCOWOA, including bWOA, bGWO, bHHO, bMFO, bSCA, bSMA, bSSA, bCSO, and BBA. The experimental parameters of the corresponding algorithms are given in Table 13.

In the experimental section of the public datasets, we set up comparison experiments based on six public datasets from the UCI repository, which are used to validate the performance of the bCOWOA-KELM model on the feature selection problem. Since the medical data problem addressed in this paper is binary in nature, the public datasets selected for this section are all of the binary type. Details of the parameters of these six public datasets are presented in Table 14.

In the experimental section of the HD dataset, HD sessions were recorded from April 1, 2020, to April 18, 2020, in an outpatient HD unit at First Affiliated Hospital of Wenzhou Medical University. The inclusion criteria are as follows: (1) age ≥ 18 years; (2) maintenance HD ≥ 3 months; (3) the frequency of the treatment was three times per week, and the duration of the treatment was 4 hours. The exclusion criteria are as follows: (1) HD sessions with missing data; (2) HD therapy without using of heparin or low molecular heparin. A total of 156 patients with 1239 HD sessions were included. The dialysate temperature was 37^°C, sodium concentration was 140 mmol/L, and calcium concentration was 1.5 mmol/L at the beginning of the sessions. Patients were detected blood routine once a month. The fast serological specimens were collected from a peripheral vein in a sitting position before dialysis on April 1st or April 2nd (mid-week therapy). BP was measured five times in each treatment session: At 0-h, 1 h, 2 h, 3 h after drawing blood and at reinfusion. Extra measurements of BP were carried out when patients suffered discomforts. IDH was defined as a drop of SBP ≥ 20 mmHg or a drop of (mean arterial pressure) MAP ≥ 10 mmHg from pre-dialysis to nadir intradialytic levels plus ≥ 2 repetitive measures (K/Doqi Workgroup, 2005). The description of this dataset’s details is given below, as shown in Table 15.

IDH denotes intradialytic hypotension and IQR denotes interquartile range.

In addition, this paper analyses and compares the average value (Avg) and standard deviation (Std) of the experimental results and evaluates the comprehensive performance of each binary classification model by ranking them, thus demonstrating more intuitively that the bCOWOA-KELM model has relatively better feature selection performance.

Finally, to ensure the fairness of the experimental process of feature selection, we set the overall size of each algorithm population to 20 and the number of iterations to 100 times uniformly; to ensure the consistency of the experimental environment and to avoid the influence of environmental factors on the experimental results, the running environment of all experiments in this section is consistent with the experimental part of the basic function.

In this subsection, we present some of the analytical evaluation methods used to analyze the results of the feature selection experiments (Hu et al., 2022a,b; Liu et al., 2022a,c; Shan et al., 2022; Shi et al., 2022; Xia et al., 2022a; Yang et al., 2022b; Ye et al., 2022). The aim is to provide a valid theoretical basis for demonstrating that the bCOWOA-KELM model performs better in feature selection than other comparative models. In the following, each of the mentioned evaluation methods is described.

In experiments, we usually classify the truth of the data as true (T) and false (F). We would then predict and classify them by machine learning, and the resulting positive predictions are defined as Positive (P) and the negative results are defined as Native (N). Thus, throughout the feature classification experiments, we typically derive four performance evaluation metrics that are used to assess the performance of the binary classifier model, as shown in Table 16.

The following is a detailed description of Table 16.

In addition, in order to better facilitate the evaluation of the feature extraction capability and classification capability of the bCOWOA-KELM model and to enhance the persuasiveness of the model proposed in this paper, this paper uses four categories of evaluation criteria commonly used in the fields of machine learning and information retrieval, and there are Accuracy, Specificity, Precision, and F-measure. The following section describes the details of the 4 evaluation criteria for the classifier experiments are described as follows:

where α generally takes a value of 1; P denotes Precision as mentioned above; and R denotes Recall, which is an assessment criterion covering the range ability and describes the underreporting of positive class predictions and the degree of recall of positive class results.

In this section, we set up comparative experiments based on six public datasets from the UCI repository to verify that the comprehensive performance of the bCOWOA-KELM model is relatively optimal in this experiment and also demonstrate that the bCOWOA-KELM model is more adaptive. For the experimental analysis, three evaluation methods were selected. The results were analyzed and validated by the Avg and Std design in each evaluation method and the average ranking of the algorithms involved in the comparison experiment on the six public datasets. The experimental analysis is presented below.

The experimental results of the classification accuracy of the bCOWOA-KELM model compared with other feature selection methods are given in Supplementary Table 5. The table shows the average classification of the bCOWOA-KELM model on the Breast, Ionosphere, HeartEW, Congress, Breastcancer, and heart datasets. The accuracy was always the largest, and their average classification accuracies were all above 94.81%, indicating that the bCOWOA-KELM model has relatively optimal classification ability. To further enhance the convincing power, the average ranking of each algorithm on the six public datasets was counted in this experiment, as shown in Table 17. It can be seen that bCOWOA ranks first in terms of average classification accuracy, which indicates that bCOWOA has outstanding adaptability to different datasets; BBA has the worst average ranking, which indicates that BBA has the relatively worst adaptability.

The results of this experiment describing the precision are given in Supplementary Table 6. As seen from the table, the average of bCOWOA on the six public datasets is always relatively the largest and its average precision is above 93.36%, which indicates that the bCOWOA-KELM model has the relatively best rate of correct classification among the compared methods. In addition, we also present the average ranking of each algorithm on the six datasets, as shown in Table 18. In particular, the bCOWOA-KELM model ranked first in terms of accuracy, bSMA ranked second, and bSCA ranked last.

Supplementary Table 7 shows the mean F-measure and variance of the bCOWOA-KELM model and the nine comparison models participating in the experiment on six public datasets. The F-measure is known to be a comprehensive criterion for assessing the classification performance of an algorithm, and it provides a more comprehensive assessment of the classification capability of bCOWOA. As can be seen from the table, the average F-measure values of bCOWOA are consistently the largest and their average accuracy is above 95.39%. As shown in Table 19, we also give the average ranking of each classification method on the six datasets. It can be seen that the bCOWOA-KELM model ranks first on average in terms of F-measure.

In this section, in order to verify whether the bCOWOA-KELM model is effective, we collected information such as the clinical features, dialysis parameters and indexes of blood routine test from the dataset. We conducted prediction IDH comparison experiments on the bCOWOA-KELM model proposed in this paper. To analytically validate the performance of the proposed bCOWOA-KELM model, four different classifier evaluation metrics were used to assess the comprehensive performance of the model as far as possible, including Accuracy, Specificity, Precision and F-measure. To demonstrate that the bCOWOA-KELM model is superior, we compare bCOWOA-KELM with combinations of bCOWOA and four other classical classifiers, including bCOWOA-FKNN, bCOWOA -KNN, bCOWOA-MLP, and bCOWOA -SVM. To further compare the performance differences between the categorical prediction model based on swarm intelligence optimization algorithm and classical machine learning algorithms such as RandomF, AdaBoost, and CART, we set up a comparison experiment between the bCOWOA-KELM model and these methods. Furthermore, to demonstrate that the predictive performance of the combination of bCOWOA-KLEM in the swarm intelligence optimization algorithms is also relatively better, we selected nine well-known swarm intelligence algorithms to set up a comparison experiment of with bCOWOA in this section, such as bGWO, bHHO, bSMA and so on. Finally, in order to demonstrate that the bCOWOA-KELM model has practical application value in the prediction of IDH and to reduce the effect of random factors on the experiment, we set up a 10-fold cross-validation (CV) analysis experiment on it.

In general, the same binary algorithm combined with different classifier methods often produces different classification results. The comparison experiment of the bCOWOA-KELM model with four other classifier combinations, including bCOWOA-FKNN, bCOWOA -KNN, bCOWOA-MLP, and bCOWOA -SVM, the analysis of the results for the four evaluation methods is given in a box plot in Figure 14. The graph shows that the values of the four evaluation criteria for the bCOWOA-KELM model are relatively more concentrated and have the relatively highest mean values. This indicates that the combined approach has the relatively best classification prediction ability and the most stable classification performance. bCOWOA-MLP model is the worst in the four aspects. The bCOWOA-FKNN model and the bCOWOA-KELM model perform similarly. However, looking closely at the box diagram, it is not difficult to find that the bCOWOA-KELM classification combination model has better means on all evaluation criteria, and the evaluation data generated by the experiment is relatively more concentrated. This shows that the bCOWOA-KELM is not only better at the end result but also proves that it has stronger stability. Therefore, we can conclude that the bCOWOA-KELM model is the best classification prediction model among the five combined approaches.

In order to examine the effect of the swarm intelligence optimization algorithm on the classification performance of the classifier in terms of feature selection experiments, we compared the bCOWOA-KELM model with five machine learning methods that did not incorporate the bCOWOA, and the comparison results are shown in Figure 15. Compared with BP, the proposed bCOWOA-KELM model has better stability than BP, although it is less optimal. Compared with the other four classification methods, the proposed bCOWOA-KELM model is better in terms of Accuracy and specificity and has a more stable performance. In summary, the comprehensive performance of the bCOWOA-KELM model proposed in this paper is better than the original classification method without the swarm intelligence algorithm.

To demonstrate the practical relevance of the prediction model and to further verify that the performance of the bCOWOA-KELM model is relatively optimal on the IDH dataset, the proposed bCOWOA was compared with nine binary algorithms based on the KELM classification technique, including bWOA, bGWO, bHHO, bMFO, bSCA, bSMA, bSSA, Bcso, and BBA. Then, all combinations of the above binary algorithms and KELM were analyzed and evaluated in terms of six aspects: Accuracy, Specificity, Precision, F-measure, Error, and time spent.

The statistical results of this experiment on the HD dataset are given in Figure 16. According to the results, the combination of bCOWOA and KELM on the first five evaluation criteria have a relatively concentrated box plot distribution compared to the combination of the other nine algorithms, indicating that the bCOWOA-KELM model has very considerable stability compared to the other algorithms. Meanwhile, bCOWOA also has the highest average value, indicating that bCOWOA has better classification capability than all the algorithms compared. However, the bCOWOA’s average value is the highest in terms of time spent, which is one of the drawbacks that should be of concern for the future of the algorithm. In conclusion, this part of the experiment demonstrates that the bCOWOA-KELM model has the relatively best classification ability for the HD dataset.

Table 20 analyses the results of the bCOWOA-KELM model after completing 10 feature selection experiments. In rows 2–11 of Table 20, the Fold column indicates the number of experiments, the second column indicates the number of features selected in each feature selection experiment, the remaining four columns indicate the Accuracy, Specificity, Precision and F-measure obtained, and the last two rows of Table 20 give the average value and variance corresponding to the four evaluation criteria, respectively. As can be seen from the table, the average classification accuracy value of the bCOWOA-KELM is 0.9241, the average specificity value is 0.9492, the average accuracy value is 0.9415 and the average F-measure is 0.9180. According to Table 21, it is easy to find that bCOWOA obtains the better scores on the four metrics In addition, bCOWOA improves 0.32% in accuracy, 0.62% in specificity, 0.54% in Precision, and 0.29% in F-measure over the second-ranked bSCA. bCOWOA improved 3.63% in accuracy, 4.62% in specificity, 4.94% in Precision, and 3.70% in F-measure over the worst-ranked bGWO.

To further verify the predictive performance of the bCOWOA-KELM model, we conducted a 10 times 10-fold crossover experiments based on the HD dataset. To facilitate the selection of features and the analysis of experimental results, we present 36 features and their selection through a histogram, as shown in Figure 17. What’s more, the features selected by bCOWOA-KELM to predict IDH are illustrated in Table 22.

In Figure 17, the vertical axis represents the code name of the feature that appeared in this experiment and the abscissa axis represents the number of times each feature was selected in 100 experiments. The characteristics of the green color in the figure are the key features selected in this experiment, including F22, F11, F14, F13, F3, F1, F21, and F23. They, respectively, represent platelet to lymphocyte ratio (PLR), MAP, white blood cells (WBCs), gender, ultrafiltration volume, dialysis vintage, monocyte to lymphocyte ratio (MLR) and neutrophil to monocyte ratio (NMR). Finally, we concluded that the eight key features selected by the bCOWOA-KELM model in this experiment are in line with clinical practice. Therefore, we have once again demonstrated the effectiveness of the bCOWOA-KELM model in combination with the clinical experience of IDH.