Feature Selection Based on Mud Ring Algorithm for Improving Survival Prediction of Children Undergoing Hematopoietic Stem-Cell Transplantation

Abstract

The survival prediction of children undergoing hematopoietic stem-cell transplantation is essential for successful transplantation. However, the performance of current algorithms for predicting mortality in this patient group has not improved over recent decades. This paper proposes a new feature selection technique for survival prediction problems using the Mud Ring Algorithm (MRA). Experiments and tests were initially performed on 13 real datasets with varying occurrences to compare the suggested algorithm with other algorithms. After that, the constructed model classification performance was compared to other techniques using the bone marrow transplant children’s dataset. Modern techniques were used to acquire their classification results, which were then compared to the suggested outcomes using a variety of well-known metrics, graphical tools, and diagnostic analysis. This investigation has demonstrated that our suggested approach is comparable and outperformed other methods in terms of results. In addition, the results showed that the constructed model enhanced prediction accuracy by up to 82.6% for test cases.

1. Introduction

Relapse to an underlying illness, which affects about 30% of the conditions on the rationale and stage of the disease, drastically reduces survival following heterologous hematopoietic stem-cell transplantation as a therapy for the blood malignancies hematopoietic system [1,2]. The graft-versus-leukemia (GvL) effect’s anti-neoplastic effectiveness of transplanted donor lymphocytes is constrained by tumor immune evasion and the restrictive preventive medicine required by the deadly graft-versus-host disease. Many germline-specific genes have also been shown to contribute to refusal and GvL, most notably minimal epitopes antigens, donor-recipient mismatches in common gene deletions, and donation polymorphisms outside the Haplotype in genes regulating, for example, immune response [3]. The alloimmunity capacity of the graft is primarily controlled by the genetic similarity of the human leukocyte antigen loci.

Mucosal inflammation brought on by cancer therapy can impact mucosa in the mouth, nose, and vagina. However, it is typically seen as inflammation and pain in the tongue, lips, and palate. Mucosal irritation brought on by treating cancer is caused by various pathobiology, dosage, medication, patient-related, and other unidentified variables [4,5]. One severe secondary effect of cancer therapy that necessitates hospitalization is severe oral mucositis, also known as ulcerative mucositis (UM). Reduced oral intake, bleeding, intense discomfort, and secondary dental problems are typical in cancer patients who develop UM; around half of them require adjustment of the cancer therapy, with a few resulting in treatment pauses. Up to 70% of people with cancer receiving high-dosage chemotherapy had an incidence of oral mucosal dermatitis, compared to 40% receiving a combination of conventional chemotherapy treatment therapy who are expected to experience this side effect. When receiving conditioning treatment before a bone marrow transplant, the UM incidence is abnormally high (70–80%). While concurrent chemotherapy and radiation to improve distant metastasis and central tumor control for head and neck malignancies, as well as continuous chemotherapy infusions for various cancers, result in severe UM in around 60–70% of patients [6,7].

Machine learning categorization enables decision-making in several facets of healthcare, including diagnosis, prediction, surveillance, treatment, and hospital administration. In classifiers for medical uses, accuracy is crucial [8,9]. The effectiveness of patients’ treatments may be improved by early illness diagnosis. Overcoming the curse of high dimensionality is one of the most crucial and essential challenges in any classifier, which serves as an incentive for utilizing an appropriate feature selection strategy. High dimensional datasets decrease the classification accuracy. The feature selection (FS) method is used to choose the most valuable characteristics from the provided medical datasets. It increases the predicted precision and decreases the calculation cost for illness diagnosis [10].

FS algorithms are data preprocessing techniques frequently used in classification or grouping tasks in data mining [11]. These techniques offer a condensed set of input attributes while maintaining the necessary discriminating data. High-dimensional datasets decrease the classification accuracy. The FS method chooses the most valuable characteristics from the medical datasets. It increases the predicted accuracy and decreases the calculation cost for illness diagnosis. FS algorithms are dimensionality reduction techniques frequently used in classification or clustering tasks in data mining. These techniques offer a condensed set of input attributes while maintaining the necessary discriminating data [12]. There are two types of FS: supervised and unsupervised. Unsupervised FS is suitable unless class labels for the data are given, in which case supervised feature selection is used. The filter, wrapper, and hybrid methods can be roughly grouped into three conventional FS methods [13].

Recently, there has been an emerging interest in finding a suitable alternative for patients with hematology where stem cells have been studied as a novel treatment. In addition, it has been shown that, in clinical application, it may be essential to identify patients suffering from unfavorable outcomes or who have a poor prognosis because they are genetically predisposed to developing acute graft-versus-host disease (GVHD) or transplant-related mortality. As part of an effort to promote the utilization of stem cells as a treatment for chronic and life-threatening diseases, in this paper, we proposed a new feature selection method using a new version of the Mud Ring Algorithm (MRA) for solving the survival prediction of children undergoing hematopoietic stem-cell transplantation. The proposed method used a modified MRA based on modifying the basic method’s exploration search ability. This paper proposes using the MRA as a feature selection method to select the optimal set of features from the bone marrow transplant; datasets have been collected from children to help improve the prediction models’ overall performance. MRA application for the feature selection problem was carried out by selecting the optimal subset of features from the training set, utilizing its improved optimization capability. The tests were initially carried out on 13 real datasets with varying occurrences and were allocated to evaluate the performance of the suggested approach categorization. The UCI machine learning repository provided the data that were chosen.

The rest of this paper is presented as follows. Section 2 presents the related work methods using optimization and machine learning techniques. Section 3 presents the proposed feature selection based on the Mud Ring Algorithm. Section 4 shows the experiments and results. Finally, the conclusions and future works are given in Section 5.

2. Related Work

A new meta-heuristic optimization technique called the Mud Ring Algorithm (MRA) is presented, which imitates the feeding behavior of bottlenose dolphins along Florida’s Atlantic coast [14]. MRA is primarily inspired by the mud ring feeding method and foraging behavior of bottlenose dolphins. By rapidly moving his tail in the sand and swimming around the school of fish, a single dolphin may use this technique to catch fish. When the fish gets lost, they jump above the surface and land in the dolphins’ waiting mouths. The MRA optimization method mimics this feeding approach physically and demonstrates the effectiveness of its optimization through a thorough comparison with other meta-heuristic methods. The statistical comparisons and outcomes demonstrated that the MRA outperforms previous meta-heuristic optimizers in handling various optimization problems and may produce the best solutions.

Due to its limited therapeutic range and considerable pharmacokinetic variability, Busulfan must be dosed correctly to minimize systemic toxicity from overexposure and graft failure from underexposure [15]. Biomarkers for predicting busulfan exposure are researched using global metagenomics. Fifty-nine pediatric patients were separated into three groups based on the area under the busulfan concentration-time curve (AUC), i.e., low-, medium-, and high-AUC groups [16]. They had urine samples collected prior to receiving busulfan. Deferoxamine metabolites were found in the high-AUC group. Compared to the low-AUC group, phenylacetylglutamine and two acylcarnitines were considerably lower in the high-AUC group. The high-AUC group had individuals with high ferritin levels because deferoxamine, an iron-chelating drug that reduces serum ferritin levels, was found in their blood. Therefore, they supported our theory that there is a significant negative relationship between serum ferritin level and busulfan absorption (dose/AUC) in a retrospective analysis of 130 pediatric patients.

This research [17] presents a new approach to feature selection and microarray data categorization. The initial step is to choose the essential genes (features) from the original collection of genes using a statistical filter called ANOVA. Then, a suggested evolutionary wrapper-based method to identify the ideal set of genes from the previously chosen genes uses the concepts of the improved Jaya (EJaya) method and forest optimization algorithm (FOA). Tuning the two crucial FOA parameters, mainly local seeding changes and global seeding adjustments, is the primary goal of utilizing EJaya. The suggested approach is examined on binary-class and multi-class microarray datasets to conduct extensive experimental research. It has been determined through a thorough review of the results that the suggested approach delivers more excellent classification performance with a fewer number of attributes than the benchmark system.

This work aims to collect information on DNA viruses and breast tumors to develop an accurate diagnosis model for fibroadenoma and breast cancer [17]. Research has consistently shown that the support vector machine (SVM) is more capable of making accurate diagnoses. In order to distinguish between breast cancer and fibroadenoma and to identify the critical risk factor for breast cancer, this study develops a hybrid SVM-based technique with feature selection. The SVM-based classifier’s categorical performance is marginally higher than LDA’s in terms of overall hit ratio, negative hit ratio, and positive hit ratio.

As a result of technological advancements in several industries, enormous amounts of data are produced. Medical datasets can have a high degree of complexity and small sample numbers. The classification of this high-dimensional data presents a challenge for researchers. In this study [18], they introduced a unique optimization strategy for better feature selection in the categorization of medical data. On 15 illness datasets with various feature sizes collected from UCI, the statistical findings of cmSAR were either the same or better than those of well-known metaheuristic algorithms and the original SAR method. All of the medical datasets were performed better by the suggested cmSAR.

This article presented an enhanced whale optimization algorithm, the Chaotic Multi-Squadron Whale Optimizer (CMWOA), which combines chaotic and multi-swarm techniques to conduct parameter optimization and feature selection concurrently for SVM [19]. The suggested SVM model was matched with numerous competitive SVM models based on other algorithms, using several clinical diagnosis issues of breast cancer, diabetes, and erythematous-squamous. The experimental findings show that the proposed method was considerably superior to all of its rivals in terms of classification accuracy and subset size.

The WOA is a well-known algorithm frequently used to resolve NP-hard issues, such as feature selection. However, it, and the majority of its versions, are plagued by a weak search technique and a population with little variety. Therefore, implementing effective tactics to address the feature selection issue and other fundamental WOA flaws is crucial. Because there are three efficient search strategies—migrating, selective picking, and enriched encircling prey—this study is devoted to developing an improved whale optimization algorithm called E-WOA [20]. To resolve global optimization issues, the effectiveness of E-WOA is assessed and contrasted with standard WOA versions. The data gathered demonstrated that the E-WOA performs better than the WOA versions. After E-WOA had shown comparable stability, a binary E-WOA called BE-WOA was proposed to pick beneficial characteristics, notably from medical datasets. In terms of fitness, accuracy, sensitivity, precision, and quantity of features, the BE-WOA is evaluated with the most recent high-performing optimization algorithms and verified using datasets related to medical conditions. The BE-WOA is also used to identify COVID-19 illness.

This study suggests a wrapper feature selection (FS) using an improved moth flame optimization (MFO) method. Its primary goal is to enhance the categorization tasks used in medical applications [21]. This study used a freshly created approach to find a nearly ideal feature subset for accurate illness detection. The moth movement style inspired the methodology. The two steps of enhancement are the foundation of the suggested modification technique. The proposed methods are validated using 23 medical datasets collected from UCI, Keel, and Kaggle data sources. The Levy flight operator and transfer functions have a striking impact on the functionality of MFO, as shown by the empirical results and numerous comparisons.

Table 1. An overview of the selected related works.

Ref	Method	Problem	Advantage	Disadvantage
[15]	‐ Improved Gradient-based optimizer	‐ Continuous feature selection	‐ Improved method ‐ Various datasets are used	‐ No real data have been used ‐ They did not tune the proposed method
[16]	‐ A comprehensive survey of various methods used in medical applications	‐ Feature selection problem in medical applications	‐ Review all the papers that have been used in the literature to solve various medical problems	‐ It can review other researchers from other applications
[17]	‐ Enhanced Jaya-based Forest optimization algorithm	‐ Cancer classification problems with high dimensional	‐ Improved method ‐ Various datasets are used	‐ No real data have been used ‐ They did not tune the proposed method
[18]	‐ Centroid mutation-based Rescue optimization algorithm	‐ Feature Section and classification problems	‐ Improved method ‐ Various datasets are used	‐ No real data have been used
[19]	‐ Chaotic multi-swarm whale optimizer	‐ Classification problem for medical diagnosis	‐ Improved approach ‐ Real datasets have been used	‐ The proposed method can be tested for other data and compared with other related methods

shows an overview of the selected related works.

3. Methodology

Dolphins use different strategies to hunt and feed on schools of fish, such as shrimp, squid, and mollusk. They work together to maximize their harvest of a large number of species. Group hunting includes a whacking strategy [22], strand feeding [23], and mud ring feeding [24]. Mud ring fishing is a unique hunting strategy used by dolphins to encircle a school of fish. In this process, the dolphins create circular waves with their tail, which disorientates the position of the school of fish, trapping them against a sandbar or reef, making them easier to pick up by mouth. This unique strategy used by bottlenose dolphins to search and trap prey inspired the Mud Ring Algorithm (MRA) optimizer technique. The Mud Ring Algorithm (MRA) is a simulation that recreates the hunting behavior of bottlenose dolphins and models their mud ring formation as they seek prey utilizing echolocation.

The Mud Ring Algorithm identifies the paths where the dolphins’ swarm gets closer to prey each time, shown with the K parameter. The K parameter shows that, as the hunting process progresses, the dolphin swarm draws closer and closer to its victim and the volume of the swarm’s sounds decreases as it gets closer to the target. Consequently, it regulates the transition between the exploration and exploitation stages of looking for prey (mud rings). The MRA algorithm explores worldwide and looks for better solutions in the exploitation process during the exploration phase. Exploration occurs in the search space when this parameter is large, while it tends to exploit when this value is low.

3.1. Exploration and Hunting for Prey Phase

Let us idealize some of the characteristics of dolphins’ echolocation; we operate under the following rules: Dolphins use a combination of velocities, $\overrightarrow{V}$, and positions, $\overrightarrow{D}$, as well as sound loudness, $\overrightarrow{K}$, to search for prey using echolocation. All dolphins are capable of automatically adjusting the volume of the sounds they produce in response to the proximity of their prey; even though the volume could change in a variety of ways, we hypothesize that the volume changes in response to the time step and the pulse rate, ‘r’, which can range from 0 to 1, where 0 indicates that there are no emission pulses and 1 indicates a highest pulse emission rate. The following are the computations for the vector $\overrightarrow{K}$:

$$\overrightarrow{K}=2\overrightarrow{a}\cdot \overrightarrow{r}-\overrightarrow{a}$$

(1)

where $\overrightarrow{r}$ is a random vector ranging from 0 to 1, and:

$$\overrightarrow{a}=2\left(1-\frac{\mathrm{t}}{\mathrm{T}\_\max }\right)$$

(2)

Virtual dolphins are organically employed as search agents to find prey (exploring). Dolphins search in a completely random position within a parameter space with d-dimensions. The dolphins’ relative positions define their position to one another. Therefore, in order to encourage the dolphins to part ways with one another and search for the fittest prey, we need a variable called $\overrightarrow{K}$ that either has a value greater than 1 or a value that is less than 1; thus, a dolphin chosen at random is selected rather than the best dolphin in the group. This selection mechanism, in conjunction with $\left|\overrightarrow{K}\right|\ge$ 1, encourages exploration and makes it possible for the MRA algorithm to conduct a global search. The mathematical derivation of the MRA algorithm is presented in the following.

It is essential to provide up-to-date criteria for periodically refreshing the positions and velocities. The following provides the workability (${\overrightarrow{D^{}}}^t$) depending on the velocity (${\overrightarrow{V^{}}}^t$) at time step t by:

$${\overrightarrow{D^{}}}^t={\overrightarrow{D^{}}}^{t-1}+{\overrightarrow{V^{}}}^t$$

(3)

where $V$ is a random velocity that is initialized. Each dolphin is initially assigned a random velocity in the range of $V_{min} to V_{max}$ based on the challenge size [14].

3.2. Feeding and Exploitation Phase of the Mud Ring

Dolphins can locate their prey and surroundings after they have detected them. However, the optimal design’s location in the search space is unknown a priori; hence, the MRA technique considers the target prey (optimal or a solution that is close to it) as the current best solution. As a result, once the best search agent has been identified, the other dolphins will seek to update their positions by the best dolphin position. These equations describe this behavior:

$$\overrightarrow{A}=\left|\overrightarrow{C}{\overrightarrow{D}}^{*}{}_{t-1}-{\overrightarrow{D}}_{t-1}\right|$$

(4)

$${\overrightarrow{D}}_t=\sin \left(2\pi .l\right)\times {\overrightarrow{D}}^{*}{}_{t-1}-\overrightarrow{K}\cdot \overrightarrow{A}$$

(5)

where $\overrightarrow{C}\mathrm{and}\overrightarrow{K}$ are coefficient vectors and $\overrightarrow{D}$ is the dolphin position vector, while ${\overrightarrow{D}}^{*}$ is the position vector of the best dolphin position thus far; t denotes the current time step and l is a random number.

Every time step, ${\overrightarrow{D}}^{*}$, positions should be adjusted if there is a better position available. To make a plume, the best dolphin circles its target while waving its tail quickly in the sand, creating a sine waveform, while the rest of the dolphins continue to circle the prey. The following formula is used to calculate the vector, $\overrightarrow{C}$:

$$\overrightarrow{C}=2\cdot \overrightarrow{r}$$

(6)

By finding the random vector $\overrightarrow{r}$, any position inside the search area can be located. Thus, Equation (5) acts as a simulation of the prey encircling, and it assists any dolphin in justifying its location as being near the current optimal position.

The MRA’s search process begins with a population of randomly selected solutions (dolphin positions). Dolphins justify their locations at each time step based on either the optimum site available so far or a randomly selected dolphin. As a result, the parameter depends on the time step taken to move from exploration to use. When $\left|\overrightarrow{K}\right|<1$, the optimal position for the dolphins is chosen, whereas at $\left|\overrightarrow{K}\right|\ge 1$, a dolphin is elected at random to justify dolphin positions. Finally, it is worth noting that the MRA algorithm has only two basic parameters that can be modified (C and K).

This paper proposes using the MRA as a feature selection method to select the optimal set of features from the bone marrow transplant; datasets have been collected from children to help improve the prediction models’ overall performance. MRA application for the feature selection problem is carried out by selecting the optimal subset of features from the training set, utilizing the improved optimization capability of the previously published MRA algorithm [14], which begins its search with randomly generated search individuals. The binary encoding type is used as the suggested algorithm’s representation scheme to pick the most optimal features. In this type of encoding (binarization), each search is represented as its distinct entry in a binary array, and the features are regarded as either being present (1) or absent (0). The 1s stand for the traits that were kept from the training set, whereas the zeroes denote eliminated elements. As a measure of an individual’s overall fitness, the F-Meas of search individuals in MRA is calculated and analyzed, as shown in Equation (11).

The MRA feature selection method is depicted in Pseudocode, as given in Algorithm 1, and its application to real-world datasets is discussed in the subsequent section. The initial dataset is then segmented into training, validation, and testing subsets. The proposed MRA looks for the best possible feature subset from the training set and then puts that subset through its paces on the validation set. The best search individual is presumed to have converged once the termination criteria have been met. Finally, this search individual with the highest possible fitness value is decoded to find the solution, which consists of a feature set with fewer elements.

Algorithm 1: MRA Algorithm

1. Initialize the population of dolphins randomly, Di, i ∈ [1, 2, ..., n] and velocity vi 2. Evaluate the fitness function of each dolphin 3. Find the best dolphin position (features set) D* 4. while ($\mathrm{t}$ < $\mathrm{T}\_\max$) 5. for i = 1 to n 6. Modify $\mathrm{K}$, $C$, $a$, and $l$ 7. if |K| >= 1 then                Generate new solutions by modifying velocity vi using Equation (3) 8. Else                /* Forming the mud ring*/                Update the current dolphin location using Equation (5) 9. end if 10. end for 11. Update the bounds for dolphins outside the search space 12. Attain the dolphin’s fitness functions 13. Update D* in case of a better position (features) 14. Set $\mathrm{t}$ $\to \mathrm{t}+1$ 15. end while Return D* (the best subset of features)

The flow diagram of the implication of the MRA method in the feature selection issue for the datasets of real-world is depicted in Figure 1. As the diagram shows, the initial dataset is first divided into three sub-sets: train, test, and validation. The proposed MRA aims basically to find the best sub-set of features from the set of training data, which is then tested using the set of validation data. After satisfying the termination criteria, the optimal search agent is considered as converged, and the search agent with the best fitness value is then decoded to be the solution that presents the reduced sub-set of features.

The experiments are performed to assess the MRA feature selection method performance, and the modern feature selection method results are used in comparison with the MRA results. In this experiment, the Support Vector Machine classifier (SVM) [25] is the classifier used to test the classification performance of the reduced sub-set of data. Various evaluation metrics are used, and all are defined in Equations (7)–(11).

For evaluation metrics, if $TN$, $TP, FN$, and $FP$ represent the true negatives, the true positives, the false negatives, and the false positives, respectively [26,27], then:

$$\mathrm{ACC}=\frac{TP+TN}{TP+FN+FP+TN}$$

(7)

$$TPR=\frac{TP}{TP+FN}$$

(8)

$$TNR=\frac{TN}{TN+FP}$$

(9)

$$\mathrm{G}-\mathrm{Mean}=\sqrt{TPR\times TNR}$$

(10)

$$\mathrm{F}-\mathrm{Meas}=2\times \frac{TPR\times TNR}{TPR+TNR}$$

(11)

4. Results and Discussion

Firstly, the experiments were performed on thirteen different real-world datasets with different numbers of instances and attributes to assess the proposed method’s performance. These data were chosen from the UCI machine learning repository [28]. Their results of classification were obtained from comparison between the modern methods (Archimedes optimization algorithm (AOA) [22], Jellyfish Search (JS) [29], Ant Lion Optimizer (ALO) [23], Whale Optimization Algorithm (WOA) [24,30], Heap-based Optimizer (HBO) [31], and Equilibrium Optimizer (EO) [32]) and the proposed method.

Table 2. Characteristics of the real-world datasets.

#	Dataset	Instances	Features	Positive	Negative
1	yeast-2_vs_4	514	8	51	463
2	wisconsin	683	9	239	444
3	Wdbc	569	31	212	357
4	Ionsphere	351	34	126	225
5	glass0	214	9	70	144
6	Parkinsons	195	22	28	147
7	Breast	277	9	81	196
8	Sonar	208	60	97	111
9	breastEW	569	30	212	357
10	Libra(123-others)	360	90	72	288
11	Vowel(2-others)	528	10	48	480
12	Ecoli (im-others)	336	7	77	259
13	Segment (BRICKFACE-others)	2310	19	330	1980

shows the characteristics of the real-world datasets.

Each dataset instance was randomly divided into three subsets in all experiments: train, validation, and test. For each dataset, the feature selection was performed using the proposed MRA feature selection method and the modern methods, while the SVM classifier was used as an evaluator for the selected features. To measure the performance of our proposal, 30 runs were performed independently, and the ACC, F-Meas, G-Mean, and Time metrics for each dataset were recorded for all used algorithms; then, each metric average was calculated. In addition, the selected feature number (# features) was recorded for each method.

Table 3. Performance measures for real-world datasets.

Dataset	Algorithm	ACC	F-Meas	G-Mean
yeast-2_vs_4	Or	92.97	47.06	55.47
	MRA	92.97	47.06	55.47
	AOA	89.84	NaN	0
	JS	89.84	NaN	0
	ALO	89.84	NaN	0
	WOA	92.97	47.06	55.47
	HBO	89.84	NaN	0
	EO	89.84	NaN	0
wisconsin	Or	94.12	91.53	93.49
	MRA	94.59	92.26	94.18
	AOA	94.82	92.47	94.16
	JS	92.35	88.7	90.86
	ALO	94.35	91.88	93.82
	WOA	94.24	91.68	93.65
	HBO	95.88	94.12	95.65
	EO	92.94	89.66	91.74
Wdbc	Or	94.37	92.86	95.08
	MRA	95.35	94.02	95.81
	AOA	94.65	93.18	95.23
	JS	94.37	92.86	95.08
	ALO	94.51	93.02	95.19
	WOA	94.79	93.36	95.42
	HBO	92.96	91.23	93.91
	EO	93.66	92.04	94.5
Ionsphere	Or	90.8	85.19	86.14
	MRA	90.8	85.71	87.2
	AOA	88.51	81.48	83.49
	JS	88.51	80.77	82.31
	ALO	89.66	83.02	84.24
	WOA	89.66	83.02	84.24
	HBO	93.1	89.29	89.8
	EO	88.51	80.77	82.31
glass0	Or	67.92	48.48	60.5
	MRA	69.81	50	61.57
	AOA	67.92	37.04	50.33
	JS	73.58	41.67	52.7
	ALO	69.81	50	61.57
	WOA	66.04	40	53.32
	HBO	69.81	50	61.57
	EO	69.81	50	61.57
Parkinsons	Or	85.42	63.16	69.72
	MRA	85.42	66.67	74.22
	AOA	85.42	63.16	69.72
	JS	85.42	63.16	69.72
	ALO	85.42	63.16	69.72
	WOA	85.42	63.16	69.72
	HBO	85.42	66.67	74.22
	EO	89.58	76.19	80.51
Breast	Or	73.91	35.71	48.45
	MRA	78.26	51.61	61.28
	AOA	72.46	42.42	55.42
	JS	72.46	42.42	55.42
	ALO	72.46	42.42	55.42
	WOA	72.46	42.42	55.42
	HBO	73.91	43.75	56.06
	EO	76.81	57.89	68.66
Sonar	Or	78.85	73.17	76.01
	MRA	82.69	78.05	80
	AOA	78.85	73.17	76.01
	JS	78.85	73.17	76.01
	ALO	78.85	73.17	76.01
	WOA	76.92	70	73.43
	HBO	78.85	71.79	74.83
	EO	80.77	77.27	79.35
breastEW	Or	94.37	92.86	95.08
	MRA	95.77	94.55	96.23
	AOA	94.37	92.86	95.08
	JS	94.37	92.86	95.08
	ALO	92.96	91.23	93.91
	WOA	95.07	93.58	95.3
	HBO	95.07	93.69	95.66
	EO	95.07	93.69	95.66
Libra(123-others)	Or	88.89	61.54	66.67
	MRA	90	66.67	70.71
	AOA	88.89	61.54	66.67
	JS	88.89	61.54	66.67
	ALO	88.89	61.54	66.67
	WOA	90	66.67	70.71
	HBO	90	66.67	70.71
	EO	90	66.67	70.71
Vowel(2-others)	Or	88.64	40	62.36
	MRA	90.91	NaN	0
	AOA	87.12	10.53	28.14
	JS	90.91	NaN	0
	ALO	88.64	40	62.36
	WOA	88.64	40	62.36
	HBO	90.91	NaN	0
	EO	90.91	NaN	0
Ecoli (im-others)	Or	94.05	87.18	90.74
	MRA	94.05	85.71	86.6
	AOA	94.05	85.71	86.6
	JS	92.86	84.21	88.03
	ALO	94.05	85.71	86.6
	WOA	94.05	85.71	86.6
	HBO	94.05	85.71	86.6
	EO	94.05	85.71	86.6
Segment (BRICKFACE-others)	Or	99.83	99.39	99.4
	MRA	99.83	99.39	99.4
	AOA	99.65	98.8	99.3
	JS	99.83	99.39	99.4
	ALO	99.83	99.39	99.4
	WOA	99.83	99.39	99.4
	HBO	99.83	99.39	99.4
	EO	99.65	98.8	99.3

shows the performances of all feature selection methods used in the comparison of real-world datasets. As reference, the first row is preserved for the original dataset (Or) results that consists of full features.

The results in Table 3 show that the MRA is better than the modern compared methods in terms of classification accuracy on nine datasets out of thirteen data, where the HBO method reaped the second-best order of ACC for six data only. Furthermore, for the G-Mean and F-Meas metrics, our proposal also occupies the best values for seven datasets out of the thirteen used data, which proves the MRA feature selection method’s stability against other modern methods. On the other hand, it can be noticed from Table 3 and Figure 2 that, although decreasing the number of features as in “yeast-2_vs_4” and “Segment (BRICKFACE-others) “data, the MRA method can keep the same level of performance gained by all feature sets, while for all other datasets, the MRA approach obtained an improved performance compared with the performance obtained by all of the feature sets. Based on these previous results, one can conclude that the proposed method for feature selection (MRA) can obtain a better performance in terms of computational complexity than the other algorithms because it has fewer features, which yields lower runtime and less space while guaranteeing the best performance.

The next step involved applying the proposed method to the bone marrow transplant children’s dataset to select the best feature (see

Table A1. Dataset attributes.

Attribute	Information
Donor_age	Age of the donor at the time of hematopoietic stem cells apheresis
donor_age_below_35	Is donor age less than 35 (yes, no)
donor_ABO	ABO blood group of the donor of hematopoietic stem cells (0, A, B, AB)
donor_CMV	Presence of cytomegalovirus infection in the donor of hematopoietic stem cells prior to transplantation (present, absent)
recipient_age	Age of the recipient of hematopoietic stem cells at the time of transplantation
recipient_age_below_10	Is recipient age below 10 (yes, no)
recipient_age_int	Age of the recipient discretized to intervals (0,5], (5, 10], (10, 20]
recipient_gender	Gender of the recipient (female, male)
recipient_body_mass	Body mass of the recipient of hematopoietic stem cells at the time of the transplantation
recipient_ABO	ABO blood group of the recipient of hematopoietic stem cells (0, A, B, AB)
recipient_rh	Presence of the Rh factor on recipient red blood cells (plus, minus)
recipient_CMV	Presence of cytomegalovirus infection in the donor of hematopoietic stem cells prior to transplantation (present, absent)
disease	Type of disease (ALL, AML, chronic, nonmalignant, lymphoma)
disease_group	Type of disease (malignant, nonmalignant)
gender_match	Compatibility of the donor and recipient according to their gender (female to male, other)
ABO_match	Compatibility of the donor and the recipient of hematopoietic stem cells according to ABO blood group (matched, mismatched)
CMV_status	Serological compatibility of the donor and the recipient of hematopoietic stem cells according to cytomegalovirus infection prior to transplantation (the higher the value, the lower the compatibility)
HLA_match	Compatibility of antigens of the main histocompatibility complex of the donor and the recipient of hematopoietic stem cells (10/10, 9/10, 8/10, 7/10)
HLA_mismatch	HLA matched or mismatched
antigen	In how many antigens there is a difference between the donor and the recipient (0–3)
allel	In how many allele there is a difference between the donor and the recipient (0–4)
HLA_group_1	The difference type between the donor and the recipient (HLA matched, one antigen, one allel, DRB1 cell, two allele or allel+antigen, two antigenes+allel, mismatched)
risk_group	Risk group (high, low)
stem_cell_source	Source of hematopoietic stem cells (peripheral blood, bone marrow)
tx_post_relapse	The second bone marrow transplantation after relapse (yes ,no)
CD34_x1e6_per_kg	CD34kgx10d6-CD34+ cell dose per kg of recipient body weight (106/kg)
CD3_x1e8_per_kg	CD3+ cell dose per kg of recipient body weight (108/kg)
CD3_to_CD34_ratio	CD3+ cell to CD34+ cell ratio
ANC_recovery	Neutrophils recovery defined as neutrophils count > 0.5 × 109/L (yes, no)
time_to_ANC_recovery	Time in days to neutrophils recovery
PLT_recovery	Platelet recovery defined as platelet count > 50,000/mm3 (yes, no)
time_to_PLT_recovery	Time in days to platelet recovery
acute_GvHD_II_III_IV	Development of acute graft versus host disease stage II or III or IV (yes, no)
acute_GvHD_III_IV	Development of acute graft versus host disease stage III or IV (yes, no)
time_to_acute_GvHD_III_IV	Time in days to development of acute graft versus host disease stage III or IV
extensive_chronic_GvHD	Development of extensive chronic graft versus host disease (yes, no)
relapse	Relapse of the disease (yes, no)
survival_time	Time of observation (if alive) or time to event (if dead) in days
survival_status	Survival status (0—alive, 1—dead)

), which helps improve the survival prediction performance of children undergoing hematopoietic stem-cell transplantation. The classification performance results of 30 independent runs on the bone marrow transplant children’s dataset are depicted in Figure 3, along with a comparison of the classification performance obtained using the AOA, JS, ALO, WOA, HBO, and EO methods. Malignant illnesses (such as acute lymphoblastic leukemia, acute myelogenous leukaemia, chronic myelogenous leukaemia, and myelodysplastic syndrome) and nonmalignant instances are all described in this dataset for children with hematologic diseases (i.e., severe aplastic anemia, Fanconi anemia, with X-linked adrenoleukodystrophy). Unrelated donor hematopoietic stem-cell transplantation was performed on all patients without any manipulation.

The violin plots illustrated in Figure 3 show the ACC, G-Mean, and F-Meas for the proposed MRA method and all compared methods. A violin plot is a hybrid of box and kernel density plots, which presents peaks in the data. These plots are commonly used to visualize the numerical data distribution and show summary statistics with the density of each variable. The distribution shape is extremely wide in the middle and skinny at the two ends for the MRA, ALO, HBO, and EO methods for the three used measures. In addition, ACC, G-Mean, and F-Meas for the MRA method are highly concentrated around the median, which directly indicates that the MRA algorithm occupies the first order in achieving the best performance in terms of ACC, G-Mean, and F-Meas and is then followed by HBO, EO, and ALO.

The violin plot elements in Figure 3 show that the median ACC, G-Mean, and F-Meas for the AOA method is lower than other compared methods. Additionally, the WOA method shows outlier points in ACC and G-Mean; the comparison leads us to remove both from the next comparison figure (Figure 4).

For more validation to our results, a statistical significance analysis is applied. A paired difference, two-sided signed-rank test “Wilcoxon signed-rank test”, which is a non-parametric statistical hypothesis [33] is used here for the thirteen real-world datasets beside the bone marrow transplant children’s dataset to fairly derive strong conclusions. The proposed MRA is compared with the three selected methods for each dataset. From the smallest, 1, to the largest, 14, all the ranked differences were recorded for each two compared methods; r and r− were assigned to the positive and the negative ranks after summing up separately. The significance level alpha “α” equals 0.05, used in comparison with the “T” value, has a critical value, which equals 21 for 14 datasets, while T = min {r, r−}. The null hypothesis—all differences in the performance between any two compared methods may be found by chance—was rejected only if the “T” value was less than or equal to 21 (critical value).

Table 4. Wilcoxon signed-rank for test ACC.

# Dataset	MRA:ALO		MRA:HBO		MRA:EO
	Dif	Rank	Dif	Rank	Dif	Rank
1	3.13	11	3.13	11	3.13	12
2	0.24	5	−1.29	−8	1.65	8
3	0.84	6	2.39	10	1.69	9
4	1.14	8	−2.3	−9	2.29	11
5	0	1	0	1	0	1
6	0	1	0	1	−4.16	−13
7	5.8	14	4.35	14	1.45	7
8	3.84	12	3.84	12	1.92	10
9	2.81	10	0.7	7	0.7	6
10	1.11	7	0	1	0	1
11	2.27	9	0	1	0	1
12	0	1	0	1	0	1
13	0	1	0	1	0.18	5
14	4.35	13	4.35	13	6.52	14
T	min{99, 0} = 0		min{73, 17} = 17		min{86, 13} = 13

,

Table 5. Wilcoxon signed-rank for test F-Meas.

# Dataset	MRA:ALO		MRA:HBO		MRA:EO
	Dif	Rank	Dif	Rank	Dif	Rank
1	48.06	14	48.06	14	48.06	14
2	0.38	4	−1.86	−8	2.6	9
3	1	5	2.79	9	1.98	8
4	2.69	6	−3.58	−11	4.94	10
5	0	1	0	1	0	1
6	3.51	9	0	1	−9.52	−13
7	9.19	12	7.86	13	−6.28	−12
8	4.88	10	6.26	12	0.78	6
9	3.32	7	0.86	7	0.86	7
10	5.13	11	0	1	0	1
11	−41	−13	0	1	0	1
12	0	1	0	1	0	1
13	0	1	0	1	0.59	5
14	3.33	8	3.33	10	5.78	11
T	min{89, 13} = 13		min{71, 19} = 19		min{74, 25} = 25

and

Table 6. Wilcoxon signed-rank for test G-mean.

# Dataset	MRA:ALO		MRA:HBO		MRA:EO
	Dif	Rank	Dif	Rank	Dif	Rank
1	55.47	13	55.47	14	55.47	14
2	0.36	4	−1.47	−8	2.44	9
3	0.62	5	1.9	9	1.31	8
4	2.96	7	−2.6	−10	4.89	10
5	0	1	0	1	0	1
6	4.5	10	0	1	−6.29	−11
7	5.86	12	5.22	13	−7.38	−13
8	3.99	8	5.17	12	0.65	7
9	2.32	6	0.57	7	0.57	6
10	4.04	9	0	1	0	1
11	−62.36	−14	0	1	0	1
12	0	1	0	1	0	1
13	0	1	0	1	0.1	5
14	4.74	11	4.74	11	6.71	12
T	min{88, 14} = 14		min{72, 18} = 18		min{75, 24} = 24

present the significance test results; note that the NaN values were replaced by the value −1 in the three tables, in order for them to be excluded by being at the bottom of the ranked list.

The results of the significance test of average ACC for MRA vs. ALO, WOA, HBO, and EO are presented in Table 4. In the case of MRA vs. EO, MRA has a positive difference for 13 datasets; hence, it is better than this algorithm, while EO has a negative difference and is better than MRA for only one dataset. The sum of all the positive ranks, R, is 86, and the sum of negative ranks, R−, is 18 for MRA vs. EO, respectively. Therefore, it can be concluded that MRA statistically outperforms EO. In addition, in the case of MRA vs. ALO and HBO, MRA statistically outperforms these algorithms where the values of T are 0 and 17. On the other hand, the results of the significance test of average F-Meas and G-mean for MRA vs. ALO, HBO, and EO are presented in Table 5 and Table 6. In the case of MRA vs. HBO and EO, MRA has a positive difference for 12 datasets; hence, it is better than these algorithms, while HBO and EO have a negative difference and are better than MRA for only two datasets. Based on the sum of all the positive and negative ranks (R and R−), it is clear that MRA performs better statistically than ALO and HBO, but not better than EO.

The feature selection distributions of the selected algorithms (MRA, ALO, HBO, and EO) are presented in Figure 4. MRA shows the most uniform distribution curve for the density of selected features than other compared algorithms while keeping the lower number of features (less than 30) through different iterations. The HBO algorithm shows the highest density of selected features with non-uniform curve, so it will be removed from the next comparison.

Figure 5 presents the bar chart for the selected feature numbers and time measures of the selected algorithms. Regarding the number of selected features, the proposed MRA shows the lowest number and is first in the order of the three selected algorithms. The ALO algorithm comes after the MRA in comparing the number of selected features, while the EO algorithm holds the last order in the comparison.

Regarding the run time, the MRA algorithm shows the lower run time and comes first in the order of the three selected algorithms. The EO algorithm comes after the MRA in comparing the run time, while the ALO algorithm keeps the last order in this comparison. The results and attributes chosen by the best three algorithms are displayed in

Table 7. The performance metrics and selected features by the selected algorithms.

Algorithm		MRA	ALO	EO
Classifiers performance	ACC	82.61	78.26	76.09
	F_Meas	83.33	80.00	77.55
	G-Mean	82.81	78.07	76.10
Selected features	Data-01
	Data-02			√
	Data-03
	Data-04		√	√
	Data-05		√	√
	Data-06		√	√
	Data-07
	Data-08		√
	Data-09			√
	Data-10			√
	Data-11	√	√	√
	Data-12	√
	Data-13	√	√	√
	Data-14	√	√
	Data-15	√	√	√
	Data-16
	Data-17			√
	Data-18		√	√
	Data-19			√
	Data-20	√
	Data-21	√	√	√
	Data-22	√		√
	Data-23	√	√
	Data-24			√
	Data-25	√	√	√
	Data-26		√	√
	Data-27		√
	Data-28	√	√	√
	Data-29	√	√
	Data-30	√	√
	Data-31	√		√
	Data-32
	Data-33
	Data-34
	Data-35
	Data-36	√	√	√

. It is clear that the suggested MRA is superior to the other compared algorithms, even though all three selected the same seven features (underlined for emphasis).

Finally, all the results of the preceding statistical tests prove that the MRA feature selection method can statistically outperform other algorithms and that it has strong competitiveness in terms of all the performance measures utilized. However, the proposed algorithm is plagued mostly by the drawback of having a randomized nature, because it is based on using an optimization algorithm that is performed by hundreds of iterations and is started with initial random solutions.

5. Conclusions

This research proposes the MRA algorithm applied to the SVM classifier as a feature selection algorithm to find the optimal features. Thirteen real-world datasets are taken into account to assess the performance of our proposal. The tested datasets were chosen from the UCI Machine Learning repository. Each investigated dataset is divided randomly into three training, validation, and testing sub-sets. To measure the performance of each dataset, the ACC, F-Meas, G-Mean, and the # features for each algorithm were recorded. As a result, the MRA shows superior and comparable results in term of feature selection and classification performance when compared to the AOA, JS, ALO, WOA, HBO, and EO algorithms. After proving its validity, the proposed MRA feature selection algorithm is applied to the bone marrow transplant children’s dataset to select the best features that can be used to achieve the best prediction performance.

Compared to the state-of-the-art methods, the MRA feature selection method showed superiority over other methods in the survival prediction of children undergoing hematopoietic stem-cell transplantation. The constructed model generated a higher numerical range of the significance test values, corresponding to maximum F-Meas values of 83.33 for bone marrow transplant data. Moreover, the accuracy of the results obtained using the constructed model for all test cases used in the present work exceeded 82%. It has been proven to be quicker than other algorithms, with high accuracy.

In future studies, multi-objective versions of MRA can be developed. Furthermore, it can address various issues in renewable energy and other disciplines. Another promising direction to explore is comparing various constraint-handling strategies for solving real-world constrained problems.