An Enhanced Tunicate Swarm Algorithm with Symmetric Cooperative Swarms for Training Feedforward Neural Networks (2024)

1. Introduction

Feedforward neural networks (FNNs) are fundamental brain networks and formidable mathematical constructs regulating nonlinear regression and categorization challenges. FNNs exhibit outstanding simultaneous processing, nonlinear universal repercussions, flexible adaptability, a simplistic network layout, substantial assessment precision, collaborative storage tolerating errors, fantastic self-regulation, and self-organization. Their overarching objective is integrating external signals and pre-established networks to renew weights and thresholds and recognize the most appropriate solution. FNNs have been extensively trained using various tactics, such as triangulation topology aggregation optimization (TTAO) [1], the propagation search algorithm (PSA) [2], subtraction average-based optimization (SABO) [3], snow ablation optimization (SAO) [4], the waterwheel plant algorithm (WWPA) [5], and Young’s double-slit experiment (YDSE) [6].

Gölcük et al. assembled an augmented arithmetic optimization technology to instruct FNNs, and this tactic showcased attractive resilience and long-term stability to yield an extensive computational solution and lessen the transmission error [7]. Bilski et al. adopted a fast computational method to instruct FNNs. This tactic exhibited tremendous superiority and adaptability to acquire greater evaluation predictability and superior categorization precision [8]. Weber et al. deployed a physically enhanced training method to instruct FNNs. This tactic demonstrated excellent sustainability and practicality to maintain less dissemination errors and a superior deviation threshold [9]. Konar et al. crafted a noise-robust image classification to instruct FNNs, and this tactic exhibited considerable adaptability and self-management in acquiring the most suitable identification variables [10]. Elansari et al. crafted a genetic method to instruct radial FNNs, and this tactic manifested fantastic generalization and comprehension to transmit a higher-quality estimated solution [11]. Chai et al. described a genetic method with a mutation strategy to instruct FNNs, and this tactic received sufficient engagement and sustainability to inhibit preordained convergence and to achieve the most suitable precision [12]. Pan et al. deployed an integrated bat technology with the tabu search technique to instruct FNNs, and this tactic depicted abundant functionality and practicality to cultivate a better integration solution [13]. Lai et al. pursued metaheuristic algorithms to instruct FNNs. This tactic established considerable adaptability and competitiveness to recognize the appropriate computational component solution and upgraded the categorization integrity [14]. Bemporad et al. pursued a sequential least-squares and alternating direction approach to instruct FNNs. This tactic demonstrated instructive competitiveness and functionality in attaining superior connection weights and deviation thresholds [15]. Wang et al. explored an ameliorated back-propagation technology to instruct FNNs, and this tactic showed excellent sustainability and practicality to accomplish the desirable connection weight and deviation threshold [16]. Bülbül et al. implemented a genetic algorithm to instruct FNNs. This tactic exhibited extremely high sustainability and accessibility in delivering the most desirable operational solution [17]. Javanshir et al. attempted metaheuristic approaches to instruct FNNs. These tactics required a consolidated network layout to mitigate the transmission error and maximize the attraction precision [18]. Schreuder et al. implemented Bayesian hyper-heuristics to instruct FNNs. This tactic depicted sustainability and accessibility in maintaining assessment errors and accurate predictions [19]. Özden et al. presented a CCOT optimization approach to instruct FFNs, and this tactic highlighted remarkable adaptability and productivity to accomplish high classification precision and greater collaboration efficiency [20].

Maddaiah et al. integrated a modified cuckoo search method to instruct FNNs, and this tactic exhibited outstanding superiority and consistency in generating the lowest transmission deviation [21]. Arthur et al. integrated a recursive least-squares approach to instruct FNNs, and this tactic was trustworthy and stable for gathering appropriate solutions and training variables [22]. Liu et al. employed an adaptive momental bound method to instruct FNNs, and this tactic maintained remarkable durability and adaptability to deliver better assessment metrics and greater categorization accuracy [23]. Atta et al. employed a modified weighted chimp optimization methodology to instruct FNNs, and this tactic showed desirable feasibility and reliability in distinguishing the most suitable weight and bias [24]. Baştemur et al. crafted a marine predator approach to instruct FNNs, and this tactic maintained influential mining and extraction to generate the most advantageous theoretical solution [25]. Li et al. introduced a coevolutionary learning algorithm to instruct FNNs, and this tactic featured a minimal material distribution, strong practicality, and adequate contraction productivity [26]. Yang et al. constructed a pelican optimization algorithm to instruct FNNs, and this tactic featured a profound, broad investigation and comprehension to recognize the most appropriate measured solution and integration precision [27]. Zhang et al. evolved a genetic algorithm with the feature selection method to instruct FNNs, and this tactic was claimed to be more desirable and adaptable in accomplishing an acceptable transmission error and appropriate quantum connectivity [28]. Wang et al. discovered an alternative gradient compression algorithm to instruct FNNs, and this tactic exhibited substantial population variation and expansive recognition to acquire outstanding evaluation efficiency and convergence acceleration [29]. To summarize, the traditional techniques exhibit insufficient resolution efficiency, substantial resource waste, frequent unanticipated convergence, and multidimensional proliferation. Metaheuristic algorithms have the advantages of upward utilization productivity, superb adaptability, high stabilization, potent self-regulation, flexible extension, simplicity, robust parallelism, and an accessible algorithmic combination. Adding advanced search strategies, adopting different encoding forms, and combining them with other algorithms can enhance the convergence speed and calculation accuracy.

The TSA is based on gradient-free optimization technology that mimics the jet motorization and swarm scavenging of tunicates to recognize food resources and acquire a universal desirable solution [30]. The differential sequencing alteration operator is incorporated into the TSA to enhance the availability and practicability, which can remedy the marginalized estimated precision, sluggish cooperation efficiency, and stagnation of intuitive anticipation. The ETSA, with symmetric cooperative swarms, is deployed to instruct FNNs, aiming to customize the deviation thresholds between neurons and the connection weights between various layers according to the transmission error between the anticipated input and the authentic output, which accomplishes the lowest dissemination error and desired neural layout. The ETSA exhibits the sustainability and reproducibility of a straightforward algorithm architecture, excellent control parameters, great traversal efficiency, strong stability, and easy implementation to avoid unanticipated convergence and to identify a consistent solution. The ETSA integrates exploration or exploitation to determine the best solution. The experimental results show that the ETSA integrates exploration and exploitation to enhance stability and robustness alongside exhibiting effectiveness and feasibility to obtain a faster convergence speed, superior calculation accuracy, and greater categorization accuracy.

The main contributions are summarized as follows: (1) An enhanced tunicate swarm algorithm (TSA) is utilized to train FNNs. (2) The differential sequencing alteration operator can broaden the identification scope, enrich population creativity, expedite computational productivity, and avoid search stagnation. (3) The ETSA integrates utilization and extraction to generate the most advantageous transmission error and has strong stability and robustness to accelerate optimized efficiency. (4) The experimental results confirm that the ETSA exhibits remarkable feasibility and superiority in obtaining a faster convergence speed, superior calculation accuracy, greater categorization accuracy, higher categorization precision, and less transmission errors.

This article is separated into the following sections: Section 2 summarizes the conceptual description of FNNs. Section 3 details the TSA. Section 4 measures the ETSA. Section 5 illustrates ETSA-based FNNs. The experimental results and analysis are presented in Section 6. The conclusions and future research are mentioned in Section 7.

2. Conceptual Description of Feedforward Neural Networks

FNNs are constructed from numerous neurons distributed in the input, hidden, and output layers, using any activation function. The node connections are one-way transmissions. Figure 1 establishes three-layer FNNs.

The net input of node $j$ is estimated as

$s_{j} = \sum_{i = 1}^{n} (W_{i, j} \cdot X_{i}) - θ_{j}, j = 1, 2, \dots, h$

(1)

where $n$ is the node size, $W_{i j}$ is the connection weight, $X_{i}$ is the $i t h$ input node, and $θ_{j}$ is the $j t h$ hidden node’s deviation threshold.

The hidden layer’s output value is estimated as

$S_{j} = s i g m o i d (s_{j}) = \frac{1}{(1 + e x p (- s_{j}))}, j = 1, 2, \dots, h$

(2)

The net input of node $k$ is estimated as

$o_{k} = \sum_{j = 1}^{h} (w_{j, k} \cdot S_{j}) - θ_{k}^{'}, k = 1, 2, \dots, m$

(3)

$O_{k} = s i g m o i d (o_{k}) = \frac{1}{(1 + e x p (- o_{k}))}, k = 1, 2, \dots, m$

(4)

where $h$ is the number of hidden nodes, $w_{j k}$ is the connection weight from the $j t h$ hidden node to the $k t h$ output node, $S_{j}$ is the output of the hidden node $j$ , and $θ_{k}^{'}$ is the $k t h$ output node’s deviation threshold.

3. Tunicate Swarm Algorithm

The TSA simulates the jet motorization and swarm scavenging of tunicates to enhance computational efficiency and determine the globally accurate solution. Jet motorization utilizes its gravity, the advection of deep ocean currents, and interaction forces to avoid individuals’ search conflicts, which have muscular mobility to achieve the best location. Jet propulsion contains three components: avoiding searching for individual conflicts, moving toward the best individual area, and remaining close to the best individual. Swarm scavenging utilizes the tunicate’s neural perception of water flow changes and individual luminescence to determine the companions’ location and move closer to the target food source, thereby achieving the group’s goal of successfully finding food. Figure 2 emphasizes the tunicate’s swarm foraging.

3.1. Avoiding Searching for Individual Conflicts

To avoid conflicts and overlaps between individuals, $A$ is utilized to enhance the computational efficiency, accelerate the convergence accuracy, and calculate each tunicate’s new location, which is estimated as

$A = \frac{G}{M}$

(5)

$G = c_{2} + c_{3} - F$

(6)

$F = 2 \cdot c_{1}$

(7)

where $G$ is the gravitational force; $F$ is the turbulent ocean currents’ advection; and $c_{1}$ , $c_{2}$ , and $c_{3}$ are random variables in [0, 1].

The vector $M$ denotes the interaction force, which is estimated as

$M = ⌊ P_{\min} + c_{1} \cdot (P_{\max} - P_{\min}) ⌋$

(8)

where $P_{\min} = 1$ is the minimum speed, and $P_{\max} = 4$ is the maximum speed.

3.2. Movement toward the Direction of the Best Neighbor

To avoid neighborhood conflicts, the search individual moves toward the optimal tunicate position, improving the search efficiency and accuracy. The separation between the food resources and the predator must be assessed to locate the most appropriate direction, which is estimated as

$\vec{P D} = | \vec{F S} - r_{a n d} \cdot \vec{P_{P}} (t) |$

(9)

where $\vec{P D}$ is the distance, $\vec{F S}$ is the food source, $t$ symbolizes the iteration, $\vec{P_{P} (t)}$ is the search individual, and $r_{a n d}$ is a random variable in [0, 1].

3.3. Convergence toward the Best Individual

Each tunicate moves toward the best individual to optimize the search efficiency. The ideal tunicate has a higher fitness solution and represents a better candidate value, accelerating the search process and increasing the accuracy of the solution’s probability.

$\vec{P_{P}} (t) = {\begin{array}{l} \vec{F S} + A \cdot \vec{P D}, & i f r_{a n d} \geq 0.5 \\ \vec{F S} - A \cdot \vec{P D}, & i f r_{a n d} < 0.5 \end{array}$

(10)

where $\vec{P_{P}} (t)$ is the corresponding movement’s location.

3.4. Swarm Behavior

The search individual adopts swarm behavior to gather around the food source and to adjust their position, which retains optimal and suboptimal solutions to improve the search efficiency and to determine the best location.

$\vec{P_{P}} (t + 1) = \frac{\vec{P_{P}} (t)}{2 + c_{1} - 1}$

(11)

where $\vec{P_{P}} (t + 1)$ is the reorganized location of the tunicate’s next generation relative to the food supply.

Algorithm 1 portrays the pseudocode of the TSA.

Algorithm 1: TSA

Input: Tunicate population

\vec{P_{P}}

Output: The most satisfactory solution

\vec{F S}

Procedure: TSA

Initializing the parameters

A

G

F

M

, and

T

Set

P_{\min} \leftarrow 1

P_{\max} \leftarrow 4

, and

S w a r m \leftarrow 0

while

t < T

for

i \leftarrow 1

to 2 do /Estimating swarm scavenging behavior via looping/

\vec{F S} \leftarrow C o m p u t e F i t n e s s (\vec{P_{P}})

/Estimating the fitness value/

/Jet motorization behavior/

c_{1}, c_{2}, c_{3}, r_{a n d} \leftarrow R a n d ()

R a n d ()

symbolizes a random variable in [0, 1]/

M \leftarrow ⌊ P_{\min} + c_{1} \cdot (P_{\max} - P_{\min}) ⌋

F \leftarrow 2 \cdot c_{1}

G \leftarrow c_{2} + c_{3} - F

A \leftarrow G / M

\vec{P D} \leftarrow | \vec{F S} - r_{a n d} \cdot \vec{P_{P}} (t) |

/Swarm scavenging behavior/

(r_{a n d} \geq 0.5)

then

S w a r m \leftarrow S w a r m + \vec{F S} + A \cdot \vec{P D}

else

S w a r m \leftarrow S w a r m + \vec{F S} - A \cdot \vec{P D}

end if

end for

\vec{P_{P}} (t) \leftarrow S w a r m / (2 + c_{1})

S w a r m \leftarrow 0

Amending the parameters

A

G

F

and

M

t \leftarrow t + 1

end while

return

\vec{F S}

end procedure

procedure

C o m p u t e F i t n e s s (\vec{P_{P}})

for

i \leftarrow 1

n

do /

n

symbolizes the dimension/

F I T_{P} [i] \leftarrow F i t n e s s F u n c t i o n (\vec{P_{P}} (i, :))

/Estimating the fitness value of predator/

end for

F I T_{P b e s t} \leftarrow B E S T (F I T_{P} [])

/Estimating the best fitness value via Best function/

return

F I T_{P b e s t}

end procedure

procedure

B E S T (F I T_{P})

B e s t \leftarrow F I T_{P} [0]

for

i \leftarrow 1

n

(F I T_{P} [i] < B e s t)

then

B e s t \leftarrow F I T_{P} [i]

end if

end for

return

B e s t

/Return the best fitness value/

end procedure

4. Enhanced Tunicate Swarm Algorithm

The differential sequencing alteration operator exhibits magnificent sustainability and dependability to mitigate slow anticipation, strengthen acquainted extraction, and screen out top-performing tunicates [31]. The optimal selected search agents are sorted according to the fitness value of each tunicate, i.e., the population is sorted in ascending order (i.e., from best to worst) based on the fitness value of each search agent, which is estimated as

$R_{i} = N - i, i = 1, 2, \dots, N$

(12)

where $N$ is the population size. The higher the ranking, the better the search agent. Each tunicate is sorted, and the selection probability $P_{i}$ is estimated as

$p_{i} = \frac{R_{i}}{N}, i = 1, 2, \dots, N$

(13)

Algorithm 2 portrays the differential sequencing alteration operator “DE/rand/1”. Individuals with a higher ranking have a greater probability of being selected as the basis vector or terminal vector in the mutation operator, and the purpose is to spread good information about the population to future generations. The differential sequencing alteration operator is not based on the selection probability to select the starting vector. If the two vectors of the differential vector are both selected from the higher-ranked vectors, the search step size of the differential vector may rapidly decrease and lead to a local optimum.

Symmetry is a remarkable property in algorithms and applications, which reveals patterns within data, simplifies complex issues, and enhances computational efficiency. In this paper, we draw inspiration from symmetric cooperative swarms. During the optimization process, the entire tunicate swarm is divided based on the fitness values, and the population is sorted in ascending order (i.e., from best to worst), which enables the search agent to undertake different responsibilities and tasks and to promote the exploration and exploitation of the global solution.

Algorithm 2: Differential sequencing alteration operator of “DE/rand/1”

Sorting population, estimating fitness value, and furnishing screening probability

P_{i}

Arbitrarily extracting

r_{1} \in {1, N}

{base vector index}

while

r a n d > p_{r_{1}} (p_{r_{1}} = 0.5) o r r_{1} = = i

Arbitrarily extracting

r_{1} \in {1, N}

end

Arbitrarily extracting

r_{2} \in {1, N}

{terminal vector index}

while

r a n d > p_{r_{2}} (p_{r_{2}} = 0.5) o r r_{2} = = r_{1} o r r_{2} = = i

Arbitrarily extracting

r_{2} \in {1, N}

end

Arbitrarily extracting

r_{3} \in {1, N}

{commencing vector index}

while

r_{3} = = r_{2} o r r_{3} = = r_{1} o r r_{3} = = i

Arbitrarily extracting

r_{3} \in {1, N}

end

5. Enhanced Tunicate Swarm Algorithm-Based Feedforward Neural Networks

The overarching objective is to acquire the most realistic solution and the highest categorization of retraining test samples. The transmission error is to estimate the disparity between the anticipated input and the authentic output. The first step is the metaheuristic algorithm variables. There are three ways to represent weights and biases: vector, matrix, and binary. The mathematical models considering the ETSA algorithm are all represented by vectors, so we use a vector representation. The vector $\vec{V}$ symbolizes the connection weight and deviation threshold, which is estimated as

$\vec{V} = {\vec{W}, \vec{θ}} = {W_{1, 1}, W_{1, 2}, \dots, W_{n, n}, h, θ_{1}, θ_{2}, \dots, θ_{h}}$

(14)

where $n$ is the input nodes, $W_{i, j}$ is the connection weight, and $θ_{j}$ is the deviation threshold.

After expressing the weights and biases of the FNN as vectors, the objective function of the neural network needs to be used to define the fitness value of the ETSA. Training an FNN aims to achieve the highest classification, approximation, or prediction accuracy for the training and test samples. Generally, performance is calculated as the difference between a network’s desired and actual outputs. The mean squared error (MSE) is estimated as

$M S E = \sum_{i = 1}^{m} {(o_{i}^{k} - d_{i}^{k})}^{2}$

(15)

where $m$ is the output nodes, $d_{i}^{k}$ is the desired output, and $o_{i}^{k}$ is the actual solution.

FNNs require more sample datasets for training and evaluation. The average MSE value is estimated as

$\bar{M S E} = \sum_{k = 1}^{s} \frac{\sum_{i = 1}^{m} {(o_{i}^{k} - d_{i}^{k})}^{2}}{s}$

(16)

where $s$ is the sample dataset.

The objective fitness of retraining FNNs is estimated as

$M i n i m i z e : F (\bar{V}) = \bar{M S E}$

(17)

Algorithm 3 portrays EMPA-based FNNs. Figure 3 emphasizes the flowchart of the ETSA for FNNs.

Algorithm 3: ETSA-based FNNs

Input: Tunicate population

\vec{P_{P}}

Output: The most satisfactory solution

\vec{F S}

Procedure: TSA

Initializing the parameters

A

G

F

M

, and

T

and the structure of FNNs, each tunicate symbolizes the connection weight and deviation threshold

Set

P_{\min} \leftarrow 1

P_{\max} \leftarrow 4

, and

S w a r m \leftarrow 0

Estimating the tunicate’s fitness value via Equation (17)

Identify the best tunicate

while

t < T

Sorting population, estimating fitness value, and furnishing screening probability

P_{i}

/differential sequencing alteration operator stage/

Arbitrarily extracting

r_{1} \in {1, N}

{base vector index}

while

r a n d > p_{r_{1}} (p_{r_{1}} = 0.5) o r r_{1} = = i

Arbitrarily extracting

r_{1} \in {1, N}

end

Arbitrarily extracting

r_{2} \in {1, N}

{terminal vector index}

while

r a n d > p_{r_{2}} (p_{r_{2}} = 0.5) o r r_{2} = = r_{1} o r r_{2} = = i

Arbitrarily extracting

r_{2} \in {1, N}

end

Arbitrarily extracting

r_{3} \in {1, N}

{commencing vector index}

while

r_{3} = = r_{2} o r r_{3} = = r_{1} o r r_{3} = = i

Arbitrarily extracting

r_{3} \in {1, N}

end /end of differential sequencing alteration operator stage/

for

i \leftarrow 1

to 2 do /Estimating swarm scavenging behavior via looping/

\vec{F S} \leftarrow C o m p u t e F i t n e s s (\vec{P_{P}})

/Estimating the fitness value/

/Jet motorization behavior/

c_{1}, c_{2}, c_{3}, r_{a n d} \leftarrow R a n d ()

R a n d ()

symbolizes a random variable in [0, 1]/

M \leftarrow ⌊ P_{\min} + c_{1} \cdot (P_{\max} - P_{\min}) ⌋

F \leftarrow 2 \cdot c_{1}

G \leftarrow c_{2} + c_{3} - F

A \leftarrow G / M

\vec{P D} \leftarrow | \vec{F S} - r_{a n d} \cdot \vec{P_{P}} (t) |

/Swarm scavenging behavior/

(r_{a n d} \geq 0.5)

then

S w a r m \leftarrow S w a r m + \vec{F S} + A \cdot \vec{P D}

else

S w a r m \leftarrow S w a r m + \vec{F S} - A \cdot \vec{P D}

end if

end for

\vec{P_{P}} (t) \leftarrow S w a r m / (2 + c_{1})

S w a r m \leftarrow 0

Amending the parameters

A

G

F

and

M

Estimating the tunicate’s fitness value via Equation (17)

t \leftarrow t + 1

end while

return

\vec{F S}

end procedure

procedure

C o m p u t e F i t n e s s (\vec{P_{P}})

for

i \leftarrow 1

n

do /

n

symbolizes the dimension/

F I T_{P} [i] \leftarrow F i t n e s s F u n c t i o n (\vec{P_{P}} (i, :))

/Estimating the fitness of predator/

end for

F I T_{P b e s t} \leftarrow B E S T (F I T_{P} [])

/Estimating the best fitness value via Best function/

return

F I T_{P b e s t}

end procedure

procedure

B E S T (F I T_{P})

B e s t \leftarrow F I T_{P} [0]

for

i \leftarrow 1

n

(F I T_{P} [i] < B e s t)

then

B e s t \leftarrow F I T_{P} [i]

end if

end for

return

B e s t

/Return the best fitness value/

end procedure

Computational Complexity

Time complexity: The population amount in the ETSA is symbolized by $N$ , the permitted repetition by $T$ , and the outcome dimension by $D$ . The initialization necessitates $O (N \times D)$ . Additionally, the ETSA measures each tunicate’s fitness that requires $O (N \times D \times T)$ . Ultimately, the ETSA administers fundamental operation-related procedures that necessitate $O (M)$ , where $M$ symbolizes the jet motorization and swarm scavenging of the tunicate for superior discovery and extraction. Hence, the ETSA’s cumulative time complexity is necessitated, $O (N \times D \times T \times M)$ .

Space complexity: This specifies the methodology’s comprehensive volume of space occupied. The ETSA’s cumulative space complexity necessitates $O (N \times D)$ . The ETSA maintains tremendous durability and adaptability to accomplish the most advantageous solution.

6. Experimental Results and Analysis

6.1. Experimental Setup

The numerical experiment was implemented on a computer with a LAPTOP-OAO85F38 device, a 12th Gen Intel(R) Core(TM) i9-12900HX 2.30 GHz processor, and 64 GB of memory with a Windows 11 system. All algorithms were programmed in MATLAB R2018b.

6.2. Test Samples

The test samples were extracted from the automated learning storage at the University of California, Irvine (UCI) to investigate the dependability and durability of the ETSA. Table 1 conveys the descriptions of the samples.

6.3. Parameter Configuration

The configured parameters remained exemplary empirical solutions extracted from the source publications. The ETSA was distinguished from ETTAO based on the differential sequencing alteration operator [31]; EPSA based on the simplex method [32]; and SABO, SAO, and EWWPA based on the Lévy flight strategy [31] and the elite opposition learning strategy [32], YDSE, and TSA. Table 2 conveys the configured parameters of each technique.

6.4. Results and Analysis

For each technique, the population amount was 30, the permitted repetition was 500, and the consecutive execution was 20. Best, Worst, Mean, and Std symbolize the optimal value, worst value, mean value, and standard deviation. The ranking was based on accuracy, where accuracy symbolizes the categorization quantification. These assessment metrics could completely convey the comprehensive superiority and predictability of each technique.

Table 3 conveys the experimental results of the extensive samples. The comparative techniques were regulated to instruct the FNNs, aiming to customize the deviation thresholds between neurons and the connection weights between various layers according to the transmission error between the anticipated input and the authentic output, which accomplishes the lowest dissemination error and desired neural layout. By retraining extensive samples, the ETSA was distinguished from alternative techniques to validate its scalability and profitability. For Scale, Seeds, Cancer, Diabetes, Parkinson, and Zoo, the Best, Worst, Mean, and Std of the ETSA were more productive than those of ETTAO, EPSA, SABO, SAO, EWWPA, YDSE, and TSA. The assessed solutions of the ETSA were substantially boosted, and in contrast with the TSA, the ETSA maintained outstanding sustainability and adaptability. The ETSA received the highest cumulative categorization accuracy and ranking. The ETSA exhibited substantial practicality and constructiveness in refraining from investigating stalemates and recognizing the most appropriate detection solution. For Balloon, the SAO, YDSE, and ETSA exhibited satisfactory trustworthiness and dependability in delivering international customized solutions. The other measured solutions of the ETSA were more productive than those of ETTAO, EPSA, SABO, EWWPA, and TSA. The ETSA maintained a distinguished ranking and the most remarkable categorization accuracy, which received a trustworthy investigation and extraction to maximize search productivity and promote estimated precision. For Blood, Survival, Liver, Iris, and Splice, the Best, Worst, and Mean of the ETSA were more productive than those of ETTAO, EPSA, SABO, SAO, EWWPA, YDSE, and TSA, and the estimated solutions of the ETSA were substantially strengthened compared with the TSA. For Wine and Statlog, the Best of the ETSA was weaker than those of SABO, but the Best, Worst, and Mean of the ETSA were more productive than those of ETTAO, EPSA, SAO, EWWPA, YDSE, and TSA. The Std of the ETSA was better than those of the other algorithms. The categorization accuracy and ranking of the ETSA were more productive than those of the other techniques. For Gene and WDBC, the Best, Std, Worst, Mean, and categorization accuracy of the ETSA were more accurate than those of the other techniques. For XOR, the ETSA guaranteed outstanding dependability and sustainability to recognize the most appropriate recognition solution. The Best, Worst, Mean, Std, and categorization accuracy of the ETSA were of higher quality than those of ETTAO, EPSA, SABO, SAO, EWWPA, YDSE, and TSA. The differential sequencing alteration operator demonstrates an adaptable localized extraction and search screening to broaden the identification scope, enrich population creativity, expedite computational productivity, and avoid search stagnation. The ETSA mimics jet motorization and swarm scavenging to mitigate directional collisions and to maintain an optimal solution that is customized and regional. The ETSA has a simplified-technique construction, higher-quality configured parameters, excellent extraction productivity, dependable stability, and intuitive implementation. The ETSA exhibits phenomenal sustainability and practicality to accelerate the estimation efficiency and to establish the transmission error. Moreover, it juxtaposes extraction and investigation to accomplish a faster convergence speed, greater measured precision, and superior categorization accuracy.

7. Conclusions and Future Research

In this paper, an enhanced TSA based on a differential sequencing alteration operator was characterized to instruct FNNs, aiming to determine the best combination of the connection weight and deviation value according to the transmission error between the anticipated input and the authentic output. The differential sequencing alteration operator has adaptable localized extraction and search screening to broaden the identification scope, enrich population creativity, expedite computational productivity, and avoid search stagnation, which enhances the selection probability to filter out the optimal search agent. The ETSA with symmetric cooperative swarms exhibits a simplified-technique construction, higher-quality configured parameters, excellent extraction productivity, dependable stability, and intuitive implementation. The ETSA integrates the jet motorization and swarm scavenging of tunicates to explore superior computational alternatives and more accurate categorization precision. The ETSA integrates utilization and extraction to discover the most advantageous transmission error and has strong stability and robustness to accelerate optimized efficiency. Most of the ETSA’s computational solutions were superior to those of ETTAO, EPSA, SABO, SAO, EWWPA, YDSE, and TSA. The experimental results confirm that the ETSA exhibits remarkable feasibility and superiority in cultivating a faster convergence speed, superior calculation accuracy, higher categorization precision, and less transmission errors and is a productive and adequate technique for instructing FNNs.

In future research, the TSA will be studied regarding the following aspects: First, the convergence speed and calculation accuracy of the TSA will be enhanced by introducing innovative search strategies, employing unique coding methods, and integrating it with other algorithms. Second, the ETSA will be investigated for its sustainability and dependability by retraining multiple neural network layouts, such as convolutional neural networks, recurrent neural networks, generative adversarial networks, graph neural networks, long short-term memory, Hopfield networks, deconvolutional networks, and recurrent neural networks. Third, the modified TSA will be used for the intelligent detection and intelligent control of distinctive understory crops. We will utilize under-forest crop harvesting and planting machinery and intelligence, precision plant-protection equipment, and intelligence to achieve under-forest crop intelligent and portable machinery and equipment. This research will allow us to fine-tune extractions and exploration to deliver the most advantageous universal measured solution.

Author Contributions

Conceptualization, J.Z. and C.D.; methodology, J.Z.; software, C.D.; validation, J.Z. and C.D.; formal analysis, J.Z.; investigation, C.D.; resources, C.D.; data curation, J.Z.; writing—original draft preparation, J.Z.; writing—review and editing, C.D.; visualization, C.D.; supervision, J.Z.; project administration, J.Z.; funding acquisition, J.Z. and C.D. All authors have read and agreed to the published version of the manuscript.

Funding

This research was funded by the Start-up Fund for Distinguished Scholars of West Anhui University under grant no. WGKQ2022052, School-level Quality Engineering (School-enterprise Cooperation Development Curriculum Resource Construction) under grant no. wxxy2022101, School-level Quality Engineering (Teaching and Research Project) under grant no. wxxy2023079, and PWMDIC design and application under grant no. WXCHX0045023110.

Data Availability Statement

All data used to support the findings of this study are included within the article.

Acknowledgments

The authors would like to thank everyone involved for their contributions to this article. They would also like to thank the editors and anonymous reviewers for their helpful comments and suggestions.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. Three-layer FNNs.

Figure 2. Tunicate’s swarm foraging.

Figure 3. Flowchart of ETSA for FNNs.

Figure 4. Interaction lines of Blood.

Figure 5. Interaction lines of Scale.

Figure 6. Interaction lines of Survival.

Figure 7. Interaction lines of Liver.

Figure 8. Interaction lines of Seeds.

Figure 9. Interaction lines of Wine.

Figure 10. Interaction lines of Iris.

Figure 11. Interaction lines of Statlog.

Figure 12. Interaction lines of XOR.

Figure 13. Interaction lines of Balloon.

Figure 14. Interaction lines of Cancer.

Figure 15. Interaction lines of Diabetes.

Figure 16. Interaction lines of Gene.

Figure 17. Interaction lines of Parkinson.

Figure 18. Interaction lines of Splice.

Figure 19. Interaction lines of WDBC.

Figure 20. Interaction lines of Zoo.

Figure 21. ANOVA evaluation of Blood.

Figure 22. ANOVA evaluation of Scale.

Figure 23. ANOVA evaluation of Survival.

Figure 24. ANOVA evaluation of Liver.

Figure 25. ANOVA evaluation of Seeds.

Figure 26. ANOVA evaluation of Wine.

Figure 27. ANOVA evaluation of Iris.

Figure 28. ANOVA evaluation of Statlog.

Figure 29. ANOVA evaluation of XOR.

Figure 30. ANOVA evaluation of Balloon.

Figure 31. ANOVA evaluation of Cancer.

Figure 32. ANOVA evaluation of Diabetes.

Figure 33. ANOVA evaluation of Gene.

Figure 34. ANOVA evaluation of Parkinson.

Figure 35. ANOVA evaluation of Splice.

Figure 36. ANOVA evaluation of WDBC.

Figure 37. ANOVA evaluation of Zoo.

Table 1. The descriptions of the samples.

Samples	Attribute	Class	Training	Testing	Input	Hidden	Output
Blood	4	2	493	255	4	9	2
Scale	4	3	412	213	4	9	3
Survival	3	2	202	104	3	7	2
Liver	6	2	227	118	6	13	2
Seeds	7	3	139	71	7	15	3
Wine	13	3	117	61	13	27	3
Iris	4	3	99	51	4	9	3
Statlog	13	2	178	92	13	27	2
XOR	3	2	4	4	3	7	2
Balloon	4	2	10	10	4	9	2
Cancer	9	2	599	100	9	19	2
Diabetes	8	2	507	261	8	17	2
Gene	57	2	70	36	57	115	2
Parkinson	22	2	129	66	22	45	2
Splice	60	2	660	340	60	121	2
WDBC	30	2	394	165	30	61	2
Zoo	16	7	67	34	16	33	7

Table 2. Configured parameters of each technique.

Technique	Configured Parameter	Value
ETTAO	Random variable $r_{0}$	[0, 1]
	Random variable $θ$	$[0, π]$
	Random variable $r_{1}$	[0, 1]
	Random variable $r_{2}$	[0, 1]
	Random variable $r_{3}$	[0, 1]
	Random variable $r_{4}$	[0, 1]
	Scaling factor $F$	0.7
EPSA	Random variable $l$	[0, 1]
	Random variable $k$	[0, 1]
	Reflectivity $α$	1
	Expansion coefficient $γ$	1.5
	Compression coefficient $β$	0.5
SABO	Random variable $r$	[0, 1]
SAO	Degree-day factor $D D F$	[0.35, 0.6]
	Random variable $θ$	[−1, 1]
EWWPA	Random variable $r_{1}$	[0, 2]
	Random variable $r_{2}$	[0, 1]
	Random variable $r_{3}$	[0, 2]
	Exponential number $K$	[0, 1]
	Random variable $F$	[−5, 5]
	Random variable $C$	[−5, 5]
YDSE	Random variable $r a n d 1$	[−1, 1]
	Random variable $r a n d 2$	[−1, 1]
	Constant equal $δ$	0.38
	Random variable $r_{1}$	[0, 1]
	Random variable $r_{2}$	[0, 1]
	Random variable $r_{3}$	[0, 1]
	Random variable $H$	[−1, 1]
	Random variable $g$	[−1, 1]
	Constant value $C$	$10^{- 20}$
TSA	Random variable $c_{1}$	[0, 1]
	Random variable $c_{2}$	[0, 1]
	Random variable $c_{3}$	[0, 1]
	Initial speed $P_{\min}$	1
	Subordinate velocity $P_{\max}$	4
	Random variable $r_{a n d}$	[0, 1]
ETSA	Random variable $c_{1}$	[0, 1]
	Random variable $c_{2}$	[0, 1]
	Random variable $c_{3}$	[0, 1]
	Initial speed $P_{\min}$	1
	Subordinate velocity $P_{\max}$	4
	Random variable $r_{a n d}$	[0, 1]
	Scaling factor $F$	0.7

Table 3. Experimental results of extensive samples.

Datasets	Result	ETTAO	EPSA	SABO	SAO	EWWPA	YDSE	TSA	ETSA
Blood	Best	0.316889	0.317249	0.310636	0.336686	0.320688	0.323835	0.319381	0.310442
	Worst	0.347076	0.3498	0.340483	0.360053	0.36186	0.363015	0.418541	0.340643
	Mean	0.329963	0.327813	0.324835	0.348525	0.338287	0.342114	0.359617	0.323607
	Std	0.008784	0.007876	0.007238	0.006777	0.013991	0.011051	0.039013	0.009500
	Accuracy	77.65	75.82	75.59	75.12	75.39	75.51	75.10	78.82
	Rank	2	3	4	7	6	5	8	1
Scale	Best	0.182407	0.189806	0.172261	0.192530	0.245989	0.179612	0.173735	0.171205
	Worst	0.35483	0.447578	0.310832	0.430892	0.526096	0.449029	0.632089	0.282578
	Mean	0.252972	0.292112	0.239007	0.308002	0.34715	0.262735	0.427023	0.214141
	Std	0.045064	0.060025	0.042564	0.065262	0.06342	0.077169	0.120217	0.031758
	Accuracy	77.91	75.42	80.12	74.55	63.99	83.26	44.84	87.79
	Rank	4	5	3	6	7	2	8	1
Survival	Best	0.367473	0.357848	0.368378	0.389332	0.37657	0.371807	0.397835	0.355298
	Worst	0.394822	0.395185	0.425968	0.419753	0.4137	0.458642	0.459638	0.404498
	Mean	0.383053	0.376636	0.395945	0.405153	0.401543	0.400975	0.408877	0.382667
	Std	0.007578	0.010251	0.015060	0.009175	0.009251	0.020896	0.019368	0.011602
	Accuracy	78.08	78.13	77.55	78.17	79.43	76.44	75.00	80.77
	Rank	5	4	6	3	2	7	8	1
Liver	Best	0.428964	0.415928	0.412947	0.465486	0.455195	0.451656	0.436205	0.424381
	Worst	0.469874	0.475434	0.478378	0.485210	0.483358	0.485116	0.483295	0.462536
	Mean	0.455258	0.446192	0.452827	0.476293	0.473401	0.472646	0.459743	0.445463
	Std	0.012054	0.015585	0.014434	0.004854	0.008757	0.009367	0.012871	0.010707
	Accuracy	49.87	52.33	50.17	46.65	52.12	46.39	47.88	61.02
	Rank	5	2	4	7	3	8	6	1
Seeds	Best	0.085245	0.166826	0.058547	0.100719	0.123138	0.071942	0.071920	0.069260
	Worst	0.177658	0.599621	0.359525	0.244604	0.467159	0.187050	0.558932	0.218142
	Mean	0.123783	0.335809	0.110513	0.183878	0.285071	0.128777	0.312577	0.106494
	Std	0.020289	0.122721	0.075121	0.038772	0.09158	0.029973	0.127991	0.034834
	Accuracy	79.37	60.07	81.34	75.35	60.70	79.79	32.25	91.55
	Rank	4	7	2	5	6	3	8	1
Wine	Best	0.068164	0.190324	0.031128	0.170940	0.319797	0.094017	0.026969	0.044282
	Worst	0.34188	0.384862	0.236198	0.478632	0.64613	0.299145	0.475471	0.143103
	Mean	0.155598	0.291944	0.089794	0.286180	0.462896	0.172222	0.231765	0.072509
	Std	0.065642	0.059593	0.050365	0.073876	0.084683	0.047326	0.118520	0.025277
	Accuracy	80.66	68.19	84.02	71.23	68.85	78.69	46.97	93.44
	Rank	3	7	2	5	6	4	8	1
Iris	Best	0.058682	0.060606	0.038514	0.090909	0.05618	0.040404	0.245448	0.040404
	Worst	0.269259	0.413874	0.283007	0.461786	0.487202	0.474747	0.589213	0.268810
	Mean	0.128795	0.20602	0.106206	0.228221	0.328889	0.117677	0.357722	0.112052
	Std	0.060784	0.096333	0.056131	0.105334	0.108598	0.096122	0.116241	0.069511
	Accuracy	82.84	60.29	72.06	70.00	57.98	78.73	55.33	98.04
	Rank	2	6	4	5	7	3	8	1
Statlog	Best	0.234784	0.249537	0.180338	0.286014	0.286166	0.264045	0.211078	0.216368
	Worst	0.288495	0.301754	0.275562	0.421348	0.394453	0.376404	0.350271	0.273629
	Mean	0.265886	0.281697	0.212137	0.359834	0.327289	0.330609	0.294522	0.235184
	Std	0.014557	0.015801	0.022756	0.033623	0.031451	0.033907	0.048660	0.016115
	Accuracy	76.25	73.48	79.13	64.89	77.17	74.02	67.63	84.78
	Rank	4	6	2	8	3	5	7	1
XOR	Best	0	0	0	$6.0 \times 10^{- 180}$	0	0	0	0
	Worst	0.5	0.5	0.500000	0.333463	0.424648	0.250000	0.416680	0.500000
	Mean	0.196727	0.2	0.171365	0.112394	0.168183	0.087376	0.174735	0.030541
	Std	0.237589	0.191943	0.231167	0.125022	0.140049	0.122168	0.156624	0.113236
	Accuracy	31.25	50.00	26.25	31.25	50.00	26.25	25.52	75
	Rank	4	3	5	4	2	5	6	1
Balloon	Best	0	0	0	0	0	0	0	0
	Worst	0.2	0.287952	0.100000	0	0.261272	0	0.240000	0
	Mean	0.01	0.044607	0.005000	0	0.100872	0	0.058667	0
	Std	0.044721	0.086795	0.022361	0	0.084157	0	0.089798	0
	Accuracy	56.00	49.50	70	100	54.00	100	82.00	100
	Rank	4	5	3	1		1	2	1
Cancer	Best	0.052101	0.085435	0.046745	0.055092	0.057527	0.051753	0.048368	0.043406
	Worst	0.268777	0.265122	0.258809	0.117259	0.265255	0.080134	0.384836	0.061780
	Mean	0.076507	0.153148	0.095172	0.087726	0.135837	0.065609	0.178133	0.052799
	Std	0.04648	0.054871	0.059243	0.015037	0.07758	0.008885	0.101541	0.004563
	Accuracy	90.35	69.05	84.25	86.80	60.00	90.65	79.35	99
	Rank	3	7	5	4	8	2	6	1
Diabetes	Best	0.328746	0.335416	0.327375	0.383635	0.351005	0.400417	0.331844	0.331600
	Worst	0.368271	0.398871	0.382611	0.463778	0.441733	0.491124	0.470493	0.368422
	Mean	0.349953	0.36666	0.351470	0.424394	0.398097	0.459869	0.400600	0.346061
	Std	0.011186	0.01839	0.016199	0.020728	0.027286	0.024276	0.029280	0.010700
	Accuracy	74.46	75.09	73.60	61.59	63.64	70.50	60.92	79.69
	Rank	3	2	4	7	6	5	8	1
Gene	Best	0.158431	0.228571	0.526805	0.285714	0.335118	0.242857	0.270041	0.053199
	Worst	0.357143	0.362285	0.830130	0.400000	0.865535	0.357143	0.376766	0.300327
	Mean	0.259137	0.297735	0.779026	0.351833	0.386544	0.310714	0.318861	0.157217
	Std	0.065732	0.037348	0.066641	0.031232	0.114128	0.027761	0.032738	0.057520
	Accuracy	13.89	13.89	0	4.02	8.33	3.33	5.56	22.22
	Rank	2	2	7	5	3	6	4	1
Parkinson	Best	0.081809	0.155039	0.114286	0.124031	0.15024	0.085271	0.076804	0.048982
	Worst	0.358967	0.27907	0.330902	0.232558	0.329904	0.224806	0.313069	0.128458
	Mean	0.158529	0.225688	0.247639	0.173051	0.204651	0.131432	0.146357	0.091221
	Std	0.070283	0.034611	0.089362	0.030517	0.040259	0.030430	0.063948	0.021407
	Accuracy	64.32	60.30	56.82	63.94	62.95	63.94	59.92	75.76
	Rank	2	5	7	3	4	3	6	1
Splice	Best	0.305403	0.421545	0.878960	0.451515	0.4688	0.398485	0.371956	0.253672
	Worst	0.389753	0.49544	0.909569	0.650000	0.817532	0.601515	0.946633	0.356823
	Mean	0.356072	0.455426	0.896545	0.538283	0.525668	0.499394	0.728602	0.321266
	Std	0.026076	0.016927	0.007243	0.052382	0.096066	0.047601	0.182258	0.027700
	Accuracy	62.50	50.59	9.89	61.06	37.94	62.99	41.47	75
	Rank	3	5	8	4	7	2	6	1
WDBC	Best	0.060753	0.113178	0.068487	0.114213	0.104215	0.083756	0.036240	0.042878
	Worst	0.187882	0.303816	0.501979	0.294786	0.301424	0.177665	0.399487	0.083286
	Mean	0.09893	0.220109	0.154498	0.172528	0.212006	0.117390	0.144009	0.064770
	Std	0.02861	0.045492	0.121842	0.038787	0.054668	0.023614	0.121344	0.010727
	Accuracy	89.36	83.94	89.67	86.64	80.79	87.70	79.18	95.15
	Rank	3	6	2	5	7	4	8	1
Zoo	Best	0.164179	0.358209	0.108685	0.238806	0.471358	0.179104	0.082274	0.029851
	Worst	0.492537	0.722198	0.388060	0.506355	0.701371	0.432836	1.216725	0.194411
	Mean	0.287703	0.535868	0.195615	0.382816	0.58655	0.300746	0.572167	0.098595
	Std	0.081806	0.077119	0.075681	0.087923	0.062165	0.071543	0.318021	0.047253
	Accuracy	54.12	41.18	63.68	52.35	41.18	56.03	57.95	82.35
	Rank	5	7	2	6	7	4	3	1

Table 4. Results of the p-value Wilcoxon rank-sum test.

Datasets	ETTAO	EPSA	SABO	SAO	EWWPA	YDSE	TSA
Blood	$2.23 \times 10^{- 2}$	$9.62 \times 10^{- 6}$	$4.47 \times 10^{- 5}$	$1.43 \times 10^{- 7}$	$9.21 \times 10^{- 4}$	$3.29 \times 10^{- 5}$	$1.61 \times 10^{- 4}$
Scale	$4.32 \times 10^{- 3}$	$1.81 \times 10^{- 5}$	$3.85 \times 10^{- 2}$	$1.60 \times 10^{- 5}$	$1.43 \times 10^{- 7}$	$2.07 \times 10^{- 2}$	$1.38 \times 10^{- 6}$
Survival	$6.55 \times 10^{- 3}$	$1.08 \times 10^{- 2}$	$7.11 \times 10^{- 3}$	$3.50 \times 10^{- 6}$	$2.04 \times 10^{- 5}$	$1.23 \times 10^{- 3}$	$5.87 \times 10^{- 6}$
Liver	$1.23 \times 10^{- 2}$	$7.35 \times 10^{- 5}$	$4.67 \times 10^{- 2}$	$6.80 \times 10^{- 8}$	$2.56 \times 10^{- 7}$	$4.54 \times 10^{- 7}$	$9.21 \times 10^{- 4}$
Seeds	$8.36 \times 10^{- 3}$	$1.06 \times 10^{- 7}$	$1.98 \times 10^{- 2}$	$2.04 \times 10^{- 5}$	$2.22 \times 10^{- 7}$	$1.79 \times 10^{- 2}$	$9.75 \times 10^{- 6}$
Wine	$4.54 \times 10^{- 6}$	$6.80 \times 10^{- 8}$	$4.40 \times 10^{- 5}$	$6.80 \times 10^{- 8}$	$6.80 \times 10^{- 8}$	$2.18 \times 10^{- 7}$	$1.29 \times 10^{- 4}$
Iris	$1.81 \times 10^{- 2}$	$1.35 \times 10^{- 3}$	$9.46 \times 10^{- 8}$	$1.61 \times 10^{- 4}$	$3.07 \times 10^{- 6}$	$9.02 \times 10^{- 9}$	$2.21 \times 10^{- 7}$
Statlog	$5.87 \times 10^{- 6}$	$3.42 \times 10^{- 7}$	$1.79 \times 10^{- 4}$	$6.80 \times 10^{- 8}$	$6.80 \times 10^{- 8}$	$9.10 \times 10^{- 8}$	$1.22 \times 10^{- 3}$
XOR	$2.74 \times 10^{- 2}$	$2.45 \times 10^{- 3}$	$7.64 \times 10^{- 4}$	$2.78 \times 10^{- 6}$	$3.55 \times 10^{- 5}$	$2.16 \times 10^{- 2}$	$5.65 \times 10^{- 6}$
Balloon	$3.42 \times 10^{- 2}$	$2.08 \times 10^{- 3}$	$3.42 \times 10^{- 2}$	$N / A$	$2.99 \times 10^{- 8}$	$N / A$	$2.09 \times 10^{- 3}$
Cancer	$2.36 \times 10^{- 6}$	$6.80 \times 10^{- 8}$	$1.60 \times 10^{- 5}$	$2.96 \times 10^{- 7}$	$1.06 \times 10^{- 7}$	$9.67 \times 10^{- 6}$	$4.68 \times 10^{- 5}$
Diabetes	$3.23 \times 10^{- 2}$	$4.16 \times 10^{- 4}$	$3.94 \times 10^{- 3}$	$6.80 \times 10^{- 8}$	$2.22 \times 10^{- 7}$	$6.78 \times 10^{- 8}$	$1.05 \times 10^{- 6}$
Gene	$5.25 \times 10^{- 5}$	$4.54 \times 10^{- 7}$	$6.61 \times 10^{- 8}$	$8.89 \times 10^{- 8}$	$6.80 \times 10^{- 8}$	$2.40 \times 10^{- 7}$	$1.92 \times 10^{- 7}$
Parkinson	$9.28 \times 10^{- 5}$	$6.80 \times 10^{- 8}$	$1.66 \times 10^{- 7}$	$1.22 \times 10^{- 7}$	$6.80 \times 10^{- 8}$	$2.00 \times 10^{- 5}$	$6.87 \times 10^{- 4}$
Splice	$4.16 \times 10^{- 4}$	$6.80 \times 10^{- 8}$	$6.80 \times 10^{- 8}$	$6.80 \times 10^{- 8}$	$6.80 \times 10^{- 8}$	$6.79 \times 10^{- 8}$	$6.80 \times 10^{- 8}$
WDBC	$7.58 \times 10^{- 6}$	$6.80 \times 10^{- 8}$	$3.42 \times 10^{- 7}$	$6.76 \times 10^{- 8}$	$6.80 \times 10^{- 8}$	$6.78 \times 10^{- 8}$	$7.76 \times 10^{- 8}$
Zoo	$9.10 \times 10^{- 8}$	$6.75 \times 10^{- 8}$	$1.41 \times 10^{- 5}$	$6.75 \times 10^{- 8}$	$6.79 \times 10^{- 8}$	$9.68 \times 10^{- 8}$	$1.20 \times 10^{- 6}$

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