Enhanced teaching team evaluation system for vocational colleges

Abstract

Constructing an evaluation system for teaching teams is very important to promote the reform of teaching evaluation in higher vocational colleges. However, there is no existing artificial intelligence−based evaluation system for teaching teams that can accurately predict the teaching evaluations in higher vocational colleges. The artemisinin optimization (AO) algorithm draws its core inspiration from the treatment process of malaria with artemisinin. It simulates the human body as a “closed space”, with the malaria parasites considered as hidden "solutions”. The algorithm mimics the ongoing process of artemisinin medicine eradicating the malaria parasites within the body. But AO tend to fall into local optima without finding the global optimum. Therefore, we propose an intelligent AO version to predict teaching team. AO has been enhanced by adding the comprehensive learning mechanism and the dispersed foraging mechanism, that is CLDMAO. The CLDMAO is benchmarked against various cutting-edge algorithms using the CEC 2017 test functions to validate its effectiveness and stability. The results indicate that CLDMAO ranks first in the majority of the test functions. What’s more, the binary CLDMAO-KNN model performs excellently for the evaluation system for teaching teams in terms of error rate, fitness, and the number of features. Through this model, factors for establishing an evaluation system can be identified within the dataset, enabling the construction of a complete evaluation system and further analysis of the potential correlations between various factors.

Introduction

High vocational education is a vital cornerstone for China in fostering high teaching quality as well as technical and skilled professionals. It has seen rapid development and garnered significant attention¹. Recently, accelerating the development of modern vocational education has been given heightened priority. It is suggested that we should adhere to the principle of moral education, closely align this with the demands of technological advancements and industrial upgrades, continuously enhance the quality of vocational education teaching, and nurture more technical and skilled talents who possess both political integrity and professional competence for the modernization drive. Evaluating teaching quality is a crucial aspect of classroom instruction management and plays an essential role in overall teaching administration². In October 2020, the Central Committee of the Communist Party of China and The State Council released the General Plan for Deepening Education Evaluation Reform in the New Era and pointed out the direction for the reform of teaching evaluation in higher vocational colleges. For the construction of teachers’ teaching innovation team, clear teaching quality evaluation objectives and standards should be established to ensure that the evaluation closely conforms to the teaching core and truly reflects the internal needs of education and teaching³.

As for the connotation of “teaching quality”, there is a view that teaching quality is mainly reflected in whether the knowledge taught by teachers and the learning results of students can achieve the preset teaching objectives⁴. Another perspective views teaching quality as the aggregation of various attributes and features of the teaching process and its outcomes, which can be used to assess whether the teaching meets established standards. The comprehensive evaluation of teachers’ teaching quality in higher vocational colleges is a method based on educational evaluation theory and technology, which aims to comprehensively evaluate whether teachers’ teaching process and its results meet the preset quality standards. Its core purpose is to promote the continuous improvement of teaching quality and provide some kind of qualification certification for the evaluated teachers⁵. This kind of comprehensive evaluation is characterized by its integrity, comprehensiveness and dynamic, it is not limited to the evaluation of teaching results, but from multiple dimensions, and multiple stages of teachers’ teaching activities for all-round consideration. Through this method, teachers’ teaching level can be more accurately understood, and then targeted improvement suggestions can be provided for them to optimize the teaching effect.

Some perspectives suggest that teaching quality is the comprehensive framework of talent cultivation standards, representing a system of ongoing development and enhancement⁶. Helms-Lorenz and Visscher explored various interpretations of developing a comprehensive framework for understanding it in the context of educational practice. Also, they discussed the advantages and disadvantages of four different methods for assessing teaching quality⁷. Song used particle swarm optimization-least square support vector machine (PSO-LSSVM) to evaluate the teaching quality⁸. Xiao et al. conducted a survey on the current state of teaching quality evaluation for university teachers, developed an evaluation index system for economics and management courses, and proposed strategies to enhance teaching quality assessments⁹. Hou introduced a method for evaluating online classroom teaching quality based on advanced data mining techniques¹⁰. By selecting evaluation indicators for teaching quality from three perspectives—experts, teachers, and students—a comprehensive evaluation system for flipped classroom teaching quality in higher education has been established. These indicators are used as inputs for the support vector machine (SVM) learning process to create an evaluation model¹¹. Li et al. proposed an artificial intelligencE−based model for the characteristics of college students’ teaching ability¹². Ai and Feng established a teaching quality evaluation of higher vocational education by BP neural network algorithm¹³. Lu et al. proposed an RBF neural network teaching evaluation model, using the genetic algorithm (GA) to optimize the initial weights of the RBF neural network¹⁴. Zhong analyzed the genetic algorithm (GA) and chose the SVM algorithm to evaluate teaching quality¹⁵. Chen et al. proposed a BP neural network model based on improved PSO (IPSO) to enhance the effectiveness and accuracy of teaching quality evaluation¹⁶. A deep belief network-based online teaching quality evaluation method was proposed by Liang, achieving a high accuracy rate¹⁷.

Our study presents a practical and transparent system that analyzes routinely collected tabular indicators to produce an easy‑to‑interpret score and a ranked list of contributing factors. The approach uses simple normalization and data‑driven weighting, and it reports variability across repeated runs to convey result stability. Practitioners can adapt the system by mapping their local indicators to the provided template; no programming or specialized hardware is required. The outputs are designed to support action planning and communication—helping educators, clinicians, and administrators prioritize resources, track progress over time, and explain decisions with clear evidence. Because the pipeline is domain-agnostic, it can be deployed in non-computer-science settings with minimal configuration.

Over the past few decades, meta-heuristic algorithms (MAs) have seen significant development. Typically, MAs are characterized by their simple structure, ease of implementation, strong optimization capabilities, and minimal dependency on the mathematical properties of the optimization problem¹⁸. Some MAs draw inspiration from natural phenomena, including artemisinin optimization (AO)¹⁹, parrot optimizer (PO)²⁰, Runge Kutta optimizer (RUN)²¹, Harris hawks optimization (HHO)²², fata morgana algorithm (FATA)²³, satus-based optimization , hunger games search (HGS)²⁴, polar lights optimizer (PLO)²⁵, moss growth optimization (MGO)²⁶, status-based optimization (SBO)¹⁸, slime mould algorithm (SMA)²⁷, colony predation algorithm (CPA)²⁸, human evolutionary optimization algorithm²⁹, love evolution algorithm (LEA)³⁰, the weighted mean of vectors (INFO)³¹ and modified teaching–learning-based optimization (MTLBO)³². These MAs have made significant progress in fields such as feature selection³³, image segmentation³⁴, wind fault diagnosis³⁵, clinical diagnosis³⁶, parameter optimization³⁷, and energy optimization³⁸.

Yuan et al. proposed a new AO algorithm which was inspired by his raw artemisinin-based medication for malaria in 2024¹². The original AO encounters challenges such as low convergence accuracy and a tendency to settle on locally optimal solutions. Research suggests that there is still room for enhancing the optimization performance of both AO and its improved variants. Therefore, our team collected a large amount of data through questionnaires in 2024 about teachers’ perspectives on constructing an evaluation system for teaching teams. By organizing and summarizing these data for exploration and analysis, we aim to establish an intelligent improved AO predictive algorithm, which is named CLDMAO. By introducing the comprehensive learning strategy and dispersed foraging strategy to the modified AO, a new balance between global and local search capabilities is achieved. As a supervised classification method, the K-Nearest Neighbors (KNN) algorithm is worth noting that operates based on a voting mechanism³⁹. In this study, we optimize the KNN classifier using the binary version of CLDMAO and build a teaching quality evaluation prediction model of bCLDMAO-KNN. This model allows us to identify the factors from the dataset that contribute to building an evaluation system, construct a complete evaluation system, and further analyze the potential correlations between various factors. The primary contribution of the research can be summarized as follows.

• A novel metaheuristic algorithm, CLDMAO, is proposed. This algorithm specifically enhances the original Artemisinin Optimization (AO) by integrating a comprehensive learning (CL) mechanism and a dispersed foraging (DF) mechanism. These two strategies work synergistically to mitigate the premature convergence of the standard AO by establishing a superior balance between global exploration and local exploitation.

• The proposed CLDMAO algorithm is comprehensively benchmarked against both conventional and advanced metaheuristic algorithms using the CEC 2017 test functions. The comparison included ten mainstream algorithms (SSA, SCA, GWO, MFO, BA, SMA, INFO, RUN, AOA, AO) and seven advanced variants (WLSSA, CLSGMFO, OBLGWO, WDE, IGWO, SCADE, CBA).

• A new hybrid intelligent model for feature selection, bCLDMAO-KNN, is introduced. This model leverages the optimization power of the binary version of CLDMAO within a wrapper-based approach with the K-Nearest Neighbors (KNN) classifier. It demonstrates the practical effectiveness of our proposed algorithm in solving complex, real-world optimization problems.

• The bCLDMAO-KNN model is successfully applied to create an advanced evaluation system for teaching teams.

This paper is divided into the following main sections. Data preparation, artemisinin optimization, the comprehensive learning mechanism and dispersed foraging mechanism are covered in Section "Background". The proposed CLDMAO, the KNN classifier, and the bCLDMAO-KNN model are presented in Section "The Proposed Methodology". The experimental setup is described in Section "Experimental methodology", followed by a discussion in Section "Discussion", and the paper’s conclusion in Section "Conclusion".

Background

Data preparation

This data discussed in the research primarily comes from various vocational colleges, with questionnaires collected from a total of 1162 teachers. From the perspective of teaching input, teaching process, and teaching effectiveness, how important do you think this item is in the "Teaching Quality Evaluation Index System for Teaching Innovation Team”? The score ranges from 1 to 5, with 1 being very important, 2 being quite important, 3 being average, 4 being relatively unimportant, and 5 being very unimportant. Table 1 provides a detailed description of the 73 attributes.All methods were carried out in accordance with relevant guidelines and regulations. All experimental protocols were approved by the Ethical and Welfare Committee of Wenzhou University. Informed consent was obtained from all subjects prior to their participation in the questionnaire.

Table 1.

A detailed description of the 73 attributes.

Attributes	Name	Attributes	Name
C1	Age Structure	C38	Classroom Discipline
C2	Teaching Experience Structure	C39	Teacher’s Control over Teaching Pace
C3	Educational Background Structure	C40	Student Participation
C4	Professional Title Structure	C41	Social Service Ability (e.g., number of student participation in horizontal projects)
C5	Dual-Teacher Structure	C42	Enterprise Social Practice Ability (evaluation of students’ practical abilities)
C6	Full-time and Part-time Structure	C43	Students Winning Awards in Professional Skills Competitions
C7	Smart Classroom Construction	C44	Students’ Ability to Obtain Professional Skills Certificates
C8	Professional Multimedia Classroom Construction	C45	Students’ Positive Attitude towards Creativity (students’ innovation consciousness in enterprise work)
C9	Professional Training Equipment	C46	Students’ Activeness in Creative Behavior (number of applied intellectual property and its conversion rate)
C10	Training Management	C47	Students’ Enthusiasm for Innovation and Entrepreneurship (number of participations in innovation and entrepreneurship activities)
C11	Teaching Management System	C48	Students Award Rate in Innovation and Entrepreneurship Competitions
C12	Construction of Information-Based Course Resources	C49	Students’ Entrepreneurial Rate within 3 Years after Graduation
C13	Teaching Materials	C50	Students Employment Rate
C14	Textbook Selection	C51	Students Employment Rate in Matching Majors
C15	Special Funding	C52	Employers’ Satisfaction with Students
C16	Training Base Construction Funding	C53	Students Employment Benefits
C17	Personnel Funding	C54	Personal Career Position Promotion
C18	Other Funding	C55	Teachers’ Self-Evaluation of Teaching
C19	Clarity of Teaching Objectives	C56	Students’ Satisfaction with Teachers’ Teaching Attitude
C20	Rationality of Teaching Design	C57	Students’ Satisfaction with Teachers’ Teaching Process
C21	Richness of Teaching Content	C58	Students’ Satisfaction with Teachers’ Teaching Resources
C22	Relevance of Theory to Practice	C59	Students’ Satisfaction with Teachers’ Teaching Effectiveness
C23	Teacher’s Explanation of Key Points	C60	Parents’ Satisfaction with Teachers’ Teaching
C24	Teacher’s Analysis of Difficult Points	C61	Students’ Organizational Communication and Other Professional Qualities
C25	Appropriateness of Training Arrangement	C62	Teachers’ Award-Winning Teaching Achievements
C26	Integration of Ideological and Political Education into Courses	C63	Teachers’ Ability to Promote Professional Titles
C27	Utilization of Information Technology Means	C64	Teachers’ Ability to Improve Educational Background
C28	Flexibility of Teaching Methods	C65	Teachers’ Ability in Textbook and Course Construction
C29	Teacher’s Clarity of Language Expression	C66	Teachers’ Guidance for Students Winning Competitions
C30	Teaching Attitude	C67	Teachers’ Research and Exploration Ability in Teaching Reform
C31	Teacher’s Proficiency in Practical Demonstrations	C68	Teachers’ Social Service Ability
C32	Reasonableness of Teacher’s Student Evaluation Methods	C69	Students’ Participation in Overseas Technical Services
C33	Teacher’s Transfer of Experience	C70	Team’s International Output of Teaching Standards and Resource Packages
C34	Differentiated Teaching	C71	Students/Teachers’ Participation in International Competitions and Winning International Awards
C35	Teacher-Student Interaction	C72	Serving the "Belt and Road" Initiative and Implementing Going Global
C36	Professional Atmosphere	C73	Other International Achievements, such as Joint Education Programs and Establishment of Luban Workshops
C37	Teacher’s Cultivation of Student Habits

Artemisinin optimization (AO)

As the foremost drug for combating malaria, artemisinin undergoes distinct metabolic and diffusion processes within the human body, leading to three unique strategies. The amalgamation of these strategies constitutes the core of the AO algorithm. This algorithm is broken down into four stages: the initialization stage, the comprehensive elimination phase, the local refinement phase, and the post-consolidation phase. Each of these stages is detailed as follows.

Initialization stage: During this phase, artemisinin is administered to the patient either orally or by injection. In the context of the AO algorithm, drug particles are conceptualized as search agents, and together these agents form the solution set of the algorithm. The initial population is initialized, comprising individuals, and is established as follows.

1

where denotes the upper bound and is the lower bound of the solution space, respectively, while is the dimensionality of the solution space. refers to the - dimension of the - individual.

Comprehensive elimination phase: In the early stage of malaria treatment, patients are given high doses of drugs to quickly control the disease. The spread of artemisinin in the body is influenced by factors such as blood flow, vascular permeability, and the protein-binding ability of the drug. The AO algorithm uses the following formula to model the drug diffusion search process.

2

3

4

5

where represents the current evaluation count and represents the maximum evaluation count of the algorithm, respectively. denotes the probability coefficient that dictates the length of the eradication process. indicates the exponential concentration of the artemisinin drug. represents a random number with values ranging from 0 to 1. and denote the - dimension of the - individual before and after the update, respectively.

Local clearance phase: The goal of this stage is to eradicate any remaining malaria parasites in the body to prevent relapse. The AO algorithm utilizes a local clearance strategy, with the specific calculation formula outlined below.

6

7

8

where provides a normalized fitness value, effectively converting fitness scores into probability distributions that can be used as individual relative weights. represents the original fitness value of the population. This process emulates the clearance of residual malaria parasites in the body at low doses of artemisinin. The parameter takes on a random value between 0.1 and 0.6. , , and represent different individuals randomly selected from the population.

Post-consolidation phase: Once the patient’s condition improves, there is still a risk of malaria recurrence if the treatment regimen is not strictly adhered to. To address this concern, the AO algorithm integrates a post-consolidation strategy. This strategy assumes the presence of residual parasites in the body, simulating a scenario where the patient neglects the persistent parasites, which could lead to a malaria relapse. The mathematical modeling of this phase can be expressed below.

9

where denotes the - dimension of the population’s best individual, is a random value in the range of [0,1].

The comprehensive learning mechanism

A comprehensive learning mechanism is introduced to improve the initial AO algorithm for searching global optima. This novel approach ensures that the diversity of the AO population is maintained, preventing premature convergence.

In this novel learning mechanism, denotes the best position of the - individual encountered during evolution. Decisions are guided by , the learning probability, which can differ between agents. Each dimension of agent is associated with randomly generated number. If this random number surpasses , the dimension learns from its own ; otherwise, it learns from another agent’s . When an agent’s dimension learns from that of another agent, the tournament selection mechanism(described below) is employed.

1. The process starts by randomly selecting two agents from the population, excluding the the agent whose position is currently being updated.

2. The fitness values at these two agents’ positions are compared, and and the agent with the superior fitness is chosen.

3. The of the chosen agent becomes the learning example for that dimension. If an agent’s is the best overall, a dimension is randomly selected to learn from the corresponding dimension of another agent’s .

All these positions have the potential to create new locations in the search space by leveraging information from the past best positions of various agents. The agent iteratively learns from these these value until its performance shows no improvement for a specified number of generations, known as the refreshing gap . Crucially, each dimension of an agent can independently learn from various positions across multiple generations, rather than solely relying on for all dimensions. To clarify, each dimension within an agent can learn from the equivalent dimension of another agent’s . In this test, the refreshing gap is equal to seven for all test functions.

Previous research indicated that applying a uniform value to all search agents in the population yielded varying results for the same problem when different were used. To address this issue generically, we propose assigning a unique value to each agent. Consequently, search agents demonstrate different levels of exploration and exploitation capabilities, enabling them to address a broad spectrum of problems. To ascertain a specific value for each search agent, we derived the following formulation empirically.

10

In addition, our approach employs a robust boundary constraint handling mechanism. An agent’s fitness is evaluated, and its and the global are updated, only if its position lies within the predefined search boundaries. The strategy ensures that all learning exemplars remain feasible, thereby guaranteeing that any agent that strays outside the search space is guided back into the valid domain in subsequent iterations. This method not only maintains the integrity of the search process but also prevents agents from drifting outside the permissible limits, thereby enhancing the overall effectiveness and stability of the algorithm.

Dispersed foraging mechanism

Despite the limitations and areas for enhancement highlighted by Yuan et al., there remains significant potential to advance the AO and mitigate its tendency to converge to local minima. An artificial bee colony (ABC) inspired work allocation technique can be used to solve the shortcomings found in AO. Instead of being limited to the best answer available at the moment, this approach enables a subset of people to continuously seek new optimal solutions⁴⁰. This method permits a subset of individuals to continuously pursue new optimal solutions rather than being restricted to the current best solution.

In scenarios where resources are scarce, a dispersed foraging mechanism encourages part of the population to spread out into uncharted regions in search of resources. This dispersion enables them to discover resourcE−rich areas, thus enhancing their overall effectiveness. To model this behavior mathematically, we propose an innovative approach for foraging through dispersion. As the search agents spread out and gather information, they update their positions in the manner described below.

11

Let denotes a current position and denotes an updated position. We assume that the proportional control factor, , is drawn from a normal distribution characterized by a mean of 0.5 and a standard deviation of 0.12. In the context, and , represent two unique integers, with both values falling between 1 and . We introduce an innovative adaptive parameter, the dispersal rate (), within the dispersed foraging strategy, as illustrated in Eq. (12). It is this parameter that governs which individual undertakes the search for new food sources. This control is facilitated by a consequence parameter, , which is compared to the . Rapid convergence is facilitated by designating individuals as foraging individuals if ≥ and as common individuals if r < . As the number of evaluations increases over time, the also gradually decrease.

During the evaluation’s final stages, if search agents fail to disperse when nearing the optimal value, they risk converging to a local optimum. Concurrently, the gradually decreases with an increasing number of evaluations, which, as shown in Eq. (12), helps the algorithm avoid local optima. Within this study, Eq. (11) has been reformulated as Eq. (13).

12

13

where is the current evaluation number and denotes the maximum number of evaluations. represnets randomly generated values between 0 and 1. As illustrated in Eqs. (11) and (13), the parameter promotes more random behavior among individuals during the process. The parameter regulates the number of individuals dispersed to new areas. At the beginning of the iteration, the individuals are repositioned during diffusion and have a high DR, which is conducive to rapid convergence. As iterations increases and the decreases, the likelihood of individuals dispersing rises, thereby helping the algorithm escape local optima.

The proposed methodology

This section presents the CLDMAO algorithm, which incorporates the comprehensive learning mechanism and the dispersed foraging mechanism into the enhanced AO algorithm to boost its performance. To adapt the continuous CLDMAO algorithm for discrete feature selection problems, we develop a binary version, termed bCLDMAO. This enables solution encoding as binary strings, where each position directly represents the inclusion or exclusion of a feature. The bCLDMAO is then coupled with a KNN classifier in wrapper mode to select the subset of features that optimizes prediction accuracy for the teaching team evaluation system. Further details are provided in the following section.

Proposed CLDMAO

In CLDMAO, each agent does its initialization independently. To enhance the exploratory searchability of the original AO, the agent integrates the foraging behavior of ABC to update its position. The mathematical formulation of the artificial bees’ foraging behavior is represented in Eqs. (12) and (13). The pseudo-code for the CLDMAO is presented in Algorithm 1, and its flowchart is depicted in Fig. 1.

Algorithm 1.

CLDMAO Pseudo-code.

Fig. 1.

Flowchart of CLDMAO.

KNN classification

The KNN classifier is a straightforward, non-parametric learning technique that has demonstrated significant effectiveness in tasks related to function classification and approximation. It is well-regarded for its high completion rates and precise classification performance, as highlighted in various research^41–43. In this investigation, the model employs an instancE−based learning strategy, where the classification of a new instance is determined by the majority vote of the class labels of its (K) nearest neighbors. This approach means that the classification of a new data point is based on its resemblance to the training points, with the class label of the nearest training point being selected. Academic literature extensively explores the concept of similarity, with Euclidean distance being a prevalent metric for its measurement. The Euclidean distance between two points and in -dimensional space can be computed as Eq. (14).

14

This research utilizes the KNN classifier to assess classification accuracy, taking advantage of its quick training speed, straightforward implementation, and high efficiency.

The bCLDMAO-KNN model

The binary version of CLDMAO and KNN classifiers are used in combination for feature selection, which in turn enhances the dataset’s classification. The approach generates results that are both easily understandable and interpretable within the realm of classification tasks. The procedure followed in this research is detailed below, with a corresponding flowchart presented in Fig. 2.

Fig. 2.

Flowchart of bCLDMAO-KNN model.

Step 1: Initialize the input parameters and generate a random binary population to create a subset of features. Each feature is marked with a value of 1 if it is selected, or 0 if it is not, according to the respective individual.

Step 2: Utilize the KNN classifier to assess the selected attributes.

Step 3: Employ the selected feature subset to calculate the fitness of each individual.

Step 4: Choose the individual with the lowest fitness as the optimal position.

Step 5: Apply the comprehensive learning and dispersed foraging operator to individuals other than the optimal position to generate a new population.

Step 6: Select the most suitable option to reconstitute the new population.

Step 7: Continue iterating from step 4 to step 8 as long as the termination condition is not met.

Step 8: Determine the population’s fittest individual.

Step 9: Assess the classification accuracy using the KNN classifier.

Step 10: Return the optimal subset.

Experimental methodology

Function optimization validation

In this study, ensuring the fairness and rationality of the experiment is crucial to accurately evaluate the effectiveness of the new method. To maintain these principles of impartiality and validity, the entire global optimization experiment of this study uses the IEEE CEC2017 function set as the test suite. This benchmark dataset is widely recognized as a tool that facilitates the evaluation of various methods’ performance against established standards. What’s more, to demonstrate that the improved algorithm performance is due to the new design structure and not just the stacking strategy, this paper uses the number of evaluations instead of the number of iterations. The research employs the IEEE CEC 2017 functions test as test sets to evaluate the performance of CLDMAO. These functions contain a variety of highly complex mathematical optimization tasks, making them frequently used to evaluate the overall efficacy of an algorithm.

This study shows a population size of 30 individuals and a maximum evaluation of 300,000. To reduce potential confusion, the algorithms are independently tested over 30 times on these benchmark functions. Numerical results of these methods are presented, with emphasis on the mean value (Avg) and standard deviation (Std) of the optimal function values. To analyze the experimental results, we employ two different mathematical-statistical methods: the Wilcoxon signed rank test (WSRT) and the Friedman test (FT). WSRT assesses whether there are significant differences between comparison methods based on P-values. We report the mean and standard deviation (Avg ± Std) of the final objective values over multiple independent runs for every CEC 2017 function and for all comparator algorithms. For each function, we also provide the per-algorithm rank; aggregated average ranks across all functions are summarized with a Friedman test, together with Wilcoxon signed-rank p-values.

A p-value less than 0.05 indicates that the difference between the two methods is statistically significant. Otherwise, the difference is not considered significant. In this paper, to clearly show the superiority of the method, " + " is used to indicate that CLDMAO is superior to the comparison method, "-" is used to indicate that CLDMAO has poor performance, and " = " is used to indicate that there is little difference between the two methods. Additionally, these tests are conducted in MATLAB R2018b on a Microsoft Windows 11 platform. The system features a 12th-generation Intel ® Core ™i7-12700H CPU with a clock speed of 2.30 GHz and 16.0 GB of RAM.

By integrating comprehensive learning and dispersed foraging strategies, we develop three distinct schemes. The specifics of these schemes are outlined in Table 2. “CL” denotes comprehensive learning strategy, while “DF” represents the dispersed foraging strategy. In the table, "1" signifies that the strategy is employed, and "0" indicates that the corresponding strategy is not utilized. For instance, AO refers to the original algorithm without any enhancement strategies, whereas DFAO signifies the AO enhanced with a dispersed foraging strategy. In this paper, for simplicity, we refer to the algorithm incorporating both enhancement strategies as CLDMAO.

Table 2.

The integrated scheme of the introduced mechanism.

Methods	CL	DF
CLDMAO	1	1
DFAO	0	1
AO	0	0

Tables 3 and 4 present the FT and the p-value results for the strategy combination schemes. When combining the findings from both tables, CLDMAO achieves an average ranking of 1.5 in FT, placing it first overall in both statistical methods. Bold highlights the result that achieved the lowest ARV and a first-place ranking in Table 3. Significant p-values (p < 0.05) are emphasized in bold in Table 4. Consequently, CLDMAO exhibits superior optimization performance over the other algorithms studied. In contrast, AO, which lacks any improvements, ranks last across all evaluations. This suggests that both strategies introduced in this paper significantly enhance AO’s performance.

Table 3.

FT results on CEC2017.

	+/−/=	ARV	Rank
CLDMAO	~	1.5	1
DFAO	12/5/13	1.9	2
AO	24/3/3	2.6	3

The top-ranked result (lowest ARV) is in bold.

Table 4.

The p-value of CLDMAO with different AO.

Function	DFAO	AO
F1	0.861213	1.7E−06
F2	0.010444	1.7E−06
F3	0.000955	1.7E−06
F4	6.9E−05	3.2E−06
F5	5.2E−06	0.040702
F6	0.016878	3.1E−05
F7	6.3E−05	0.075213
F8	0.000894	0.089718
F9	5.7E−06	1.7E−06
F10	8.5E−06	0.003379
F11	0.236936	3.2E−06
F12	0.628843	1.7E−06
F13	0.404835	1.7E−06
F14	0.059836	3.4E−05
F15	0.004682	0.000616
F16	0.688359	6.3E−05
F17	0.544006	0.00439
F18	0.001709	1.7E−06
F19	0.289477	0.000125
F20	0.393334	0.000332
F21	0.003379	0.007731
F22	3.2E−05	0.000261
F23	0.125438	0.031603
F24	0.011079	0.019569
F25	0.191522	0.004682
F26	0.177907	0.477947
F27	0.036826	8.2E−05
F28	0.013194	2.2E−05
F29	0.797098	5.2E−06
F30	0.001593	1.7E−06

Significant p-values (p < 0.05) are in bold.

Table 3 shows that CLDMAO outperforms AO in optimizing 24 functions. Additionally, CLDMAO surpasses DFAO in 12 functions. CLDFAO consistently ranks higher than any AO variant with only one enhancement strategy applied. This indicateds that employing both strategies simultaneously leads to the maximum performance improvements for the algorithm.

Figure 3 shows the convergence performance of the proposed CLDMAO method with DFAO and AO on F1, F2, F4, F11, F12, F13, F16, F18, F22 and F26. This figure reveals that CLDMAO not only achieves the lowest convergence value but also exhibits the highest convergence speed for these test functions. For F12, CLDMAO converges more slowly than DFAO in the early and middle stages, which is due to the comprehensive learning mechanism preserving diversity and encouraging exploration. This mechanism sometimes delays rapid exploitation but can help the algorithm avoid local optima and improve final accuracy. In the later stages, CLDMAO narrows the gap and ultimately approaches a similar or better solution after sufficient iterations. For F13, the sudden significant decrement in the CLDMAO convergence curve occurs because the dispersed foraging and comprehensive learning strategies enable the population to jump out of a local optimum and rapidly find a much better solution. This type of behavior demonstrates the strong exploration capability and adaptability of CLDMAO in complex search landscapes. Moreover, it is evident that the CLDMAO algorithm significantly enhances both population diversity and convergence accuracy.

Fig. 3.

The convergence curves of various AO.

Besides, there are several conventional MAs, such as salp swarm algorithm (SSA)⁴⁴, sine cosine algorithm (SCA)⁴⁵, grey wolf optimization (GWO)⁴⁶, bat algorithm (BA), moth-flame optimization (MFO)⁴⁷, SMA, INFO, RUN and AOA. Then, the proposed CLDMAO is compared with these several algorithms on CEC2017 functions. The use of population and individual operations within CLDMAO effectively mitigates the occurrence of converging to local optima. To select the numerical results for these approaches, we used the average (Avg) and standard deviation (Std) of the optimal function values as criteria. The Avg assesses overall search capability, while the Std evaluates the algorithm’s robustness. Furthermore, the best result for each problem is highlighted in bold to emphasize their significance. The optimization results of the CLDMAO and nine competitors are presented in Table 5. Bold formatting indicates the minimum mean and standard deviation values in Table 5. The CLDMAO clearly shows superior performance on F3, F5-F12, F16-18, F20-26 and F29. Therefore, CLDMAO outperforms the other algorithms across the whole benchmark function. It ranks first on the CEC2017 function test as is shown in Table 6. The result with the smallest ARV value ranked first is bolded in Table 6.

Table 5.

Comparative results for CLDMAO and conventional methods.

	Avg	Std	Avg	Std	Avg	Std
	F1		F2		F3
CLDMAO	3157.108	3201.905	215.1769	28.16807	300	4.46E−06
GWO	1.83E+09	1.17E+09	3.57E+32	1.88E+33	31,750.66	9151.27
SMA	7228.798	6856.532	200.2575	1.27989	300.0156	0.012149
RUN	6131.884	6297.156	200.0024	0.002298	300.2152	0.106267
SSA	5382.99	5708.427	200.0049	0.025709	300	1.09E−08
SCA	1.25E+10	2.06E+09	2.54E+33	5.9E+33	37,104.44	5855.158
MFO	1.29E+10	8.77E+09	3.22E+36	1.19E+37	115,859.9	79,869.43
BA	502,253.9	278,606.4	200.0001	7.2E−05	300.1223	0.171545
INFO	100	1.18E−05	200.0001	0.00011	300	4.42E−06
AOA	4.13E+10	6.45E+09	1.48E+41	6.12E+41	74,859.75	7924.635
	F4		F5		F6
CLDMAO	461.0761	36.57817	545.018	10.29908	600.0082	0.044651
GWO	582.1586	55.50844	599.2038	18.90811	607.6216	4.090805
SMA	490.0368	7.103762	587.2756	23.61223	600.9772	0.563133
RUN	491.4942	22.14883	703.6681	30.23919	643.1017	9.165286
SSA	492.3806	23.76951	621.8561	32.92254	627.5808	7.709928
SCA	1430.135	220.8856	773.214	18.89323	648.4856	5.945107
MFO	1368.686	801.7536	720.0391	51.23472	636.5094	9.63246
BA	473.7469	29.9354	814.6307	63.77311	672.1403	8.046178
INFO	445.194	32.09535	648.7483	36.11917	625.2682	8.06798
AOA	10,480.59	2411.175	818.204	28.52539	669.8127	4.953956
	F7		F8		F9
CLDMAO	781.4263	12.71155	851.4169	9.006603	900.0149	0.041284
GWO	861.6768	33.61991	888.3582	25.29811	1864.06	642.3243
SMA	826.3188	27.34574	892.9231	26.76948	2217.333	1324.305
RUN	1052.824	65.89644	948.4147	18.87968	3407.536	596.3625
SSA	865.824	47.71056	913.6058	31.89578	3081.159	1710.143
SCA	1122.91	24.48357	1048.435	17.14132	5140.933	974.7956
MFO	1222.636	248.9506	1014.126	52.00418	6790.213	2161.515
BA	1592.116	187.8803	1048.754	60.40785	13,795.03	5308.073
INFO	987.4789	58.77174	927.6858	29.76521	3181.924	807.8844
AOA	1314.044	48.77608	1044.124	36.29159	5826.717	909.4183
	F10		F11		F12
CLDMAO	3499.38	359.816	1140.703	25.39608	9034.998	7278.78
GWO	3974.595	446.6046	1789.676	609.7065	84,526,327	98,188,174
SMA	4262.122	526.8504	1232.702	38.68239	1,104,119	766,301.6
RUN	4501.768	686.7155	1195.15	29.10976	1,325,966	564,187.3
SSA	4582.434	618.1327	1288.579	64.62241	1,087,503	1,097,854
SCA	8134.874	371.7127	2130.189	255.2004	1.24E+09	3.75E+08
MFO	5343.709	852.7703	4712.866	3795.956	5.05E+08	8.39E+08
BA	5797.826	829.3549	1331.636	53.32337	1,168,797	780,826
INFO	5079.956	880.1456	1263.356	63.35226	18,186.81	13,916.78
AOA	6403.661	537.6624	3858.075	976.9562	7.39E+09	2.18E+09
	F13		F14		F15
CLDMAO	20,320.61	18,616.02	30,856.8	107,780.6	8829.741	8426.275
GWO	10,455,032	50,167,024	174,955.3	295,790.9	357,888.1	823,238.9
SMA	21,994.84	23,866.45	33,606.71	17,397.72	28,031.25	12,670.93
RUN	29,311.99	14,550.75	2649.395	1025.713	15,840.91	1775.168
SSA	93,444.75	63,993.37	6035.774	4357.316	60,618.29	53,758.99
SCA	3.48E+08	1.49E+08	138,068.4	109,470.3	14,230,442	11,384,674
MFO	2.02E+08	5.75E+08	124,431.3	133,703.7	55,986.27	37,911.06
BA	253,016.6	122,540.2	6789.496	4506.809	101,062.5	44,796.01
INFO	13,904.16	13,218.98	1681.445	113.3215	2186.891	812.8879
AOA	36,464.01	9547.588	55,409.42	59,106.5	21,793.37	9195.868
	F16		F17		F18
CLDMAO	1982.032	175.3997	1831.576	114.0175	1842.118	10.30148
GWO	2341.907	286.0268	1948.835	115.8749	1,392,481	2,364,083
SMA	2409.925	250.3127	2206.167	169.3094	306,102	266,454.8
RUN	2681.283	209.3815	2164.131	208.1316	48,655.09	23,431.44
SSA	2569.474	367.5646	2015.731	141.642	196,981.9	128,862.5
SCA	3583.788	219.793	2357.31	185.9271	3,361,708	2,375,666
MFO	3144.962	383.4683	2472.289	224.6275	7,780,313	12,198,309
BA	3477.633	523.75	2804.374	385.6504	222,351.7	178,734.7
INFO	2668.306	266.3695	2238.71	255.0171	7567.535	7653.14
AOA	4473.56	1045.456	2877.346	320.1308	972,163.7	1,022,713
	F19		F20		F21
CLDMAO	9256.965	12,623.82	2184.602	96.77223	2346.813	13.02046
GWO	2,559,310	8,306,149	2352.478	130.3416	2380.94	25.07528
SMA	30,180.88	20,130.91	2531.286	156.4285	2395.02	21.72006
RUN	8831.714	6441.786	2404.041	145.3891	2435.678	35.4567
SSA	290,788.8	108,640.3	2392.935	113.7636	2397.354	30.61231
SCA	22,405,783	11,512,934	2586.106	126.663	2547.923	15.82192
MFO	7,788,803	25,790,531	2743.434	250.126	2510.603	54.50142
BA	663,706.9	140,385.1	2951.783	223.6684	2624.249	72.36719
INFO	2059.007	105.9584	2524.481	200.2128	2427.83	42.2258
AOA	1,085,298	140,694.3	2736.801	187.7022	2604.282	31.08165
	F22		F23		F24
CLDMAO	2528.604	715.5228	2699.138	12.64913	2868.43	8.542111
GWO	4378.528	1414.201	2745.562	23.65218	2929.052	53.02701
SMA	5505.441	903.6487	2734.89	23.14651	2924.931	25.19719
RUN	2669.117	1124.838	2769.427	29.46668	2907.574	26.77111
SSA	4522.104	2151.999	2756.894	29.7419	2916.874	27.15614
SCA	8684.743	2019.041	2999.499	26.9211	3159.51	28.8665
MFO	6590.008	1407.265	2850.303	40.90961	2986.975	36.98909
BA	6841.291	1971.281	3356.318	129.7834	3371.008	127.3521
INFO	5201.663	2179.466	2838.604	55.09727	2987.749	54.19538
AOA	8250.565	634.8369	3400.399	151.3405	3831.225	206.6682
	F25		F26		F27
CLDMAO	2887.282	0.545173	3900.863	496.1774	3223.388	16.39014
GWO	3008.471	85.22918	4691.716	341.3833	3245.367	24.48582
SMA	2888.342	7.04927	4532.155	190.528	3222.91	16.29087
RUN	2901.287	15.47116	4887.56	1624.311	3249.244	17.0526
SSA	2893.341	14.2582	4606.13	870.4455	3236.327	16.56649
SCA	3188.796	64.38342	6944.779	265.3758	3398.174	35.93862
MFO	3385.982	616.067	5966.53	551.9546	3257.892	22.31932
BA	2902.261	21.20829	9346.236	1974.801	3490.527	164.374
INFO	2896.899	18.70322	5962.878	1030.339	3269.928	37.33978
AOA	4545.241	596.8243	9355.397	1008.248	4360.746	263.618
	F28		F29		F30
CLDMAO	3141.527	52.88989	3419.751	76.5304	7367.498	2713.976
GWO	3429.432	98.86661	3759.408	188.5917	4,287,190	4,804,678
SMA	3248.266	48.42572	3762.362	196.447	16,719.37	4891.551
RUN	3126.673	41.39732	4059.542	263.086	68,141.02	21,958.88
SSA	3184.445	41.26514	3859.026	177.5958	945,402.5	721,561.7
SCA	3788.85	136.9119	4688.585	239.7697	71,216,357	23,928,069
MFO	4412.468	1047.104	4167.467	239.4233	2,551,529	6,597,951
BA	3126.644	55.39862	4938.291	400.7846	1,221,073	875,624.4
INFO	3130.673	57.77188	4002.914	268.7648	6267.956	1367.575
AOA	5915.59	628.2444	6466.841	1233.978	1.79E+08	3.58E+08

The minimum mean and standard deviation are in bold.

Table 6.

FT results of the CLDMAO with other algorithms on CEC2017.

Algorithm	Friedman rank test
	+/−/=	ARV	Rank
CLDMAO	~	1.733333333	1
GWO	30/0/0	5.033333333	6
SMA	26/0/4	3.666666667	2
RUN	26/1/3	4.366666667	5
SSA	25/1/4	4.033333333	4
SCA	30/0/0	8.433333333	9
INFO	20/5/5	3.733333333	3
MFO	30/0/0	7.866666667	8
BA	26/0/4	7.233333333	7
AOA	30/0/0	8.9	10

The top-ranked result (lowest ARV) is in bold.

Table 7 displays the p-values obtained from the WRST. A p-value below 0.05 indicates statistical significance. p-values less than 0.05 are bolded in Table 7. The table illustrates that while there are several p-values equal to or greater than 0.05, the differences in optimization results between CLDMAO and the other methods are not statistically significant in those cases. However, most data points fall below 0.05. The main reason why some optimizations are not statistically significant is that the compared advanced algorithms also possess strong optimization capabilities, leading to similar performance on certain CEC2017 functions. In these cases, the gap between CLDMAO and its competitors is narrow, so the Wilcoxon signed-rank test produces p-values greater than 0.05. This highlights a limitation of our method: although CLDMAO generally achieves better average performance and robustness, it may not always significantly outperform all strong algorithms on every test problem. The effectiveness of the enhancements (comprehensive learning and dispersed foraging) can be more evident for complex or multimodal problems, but less significant for simpler or well-explored functions. Consequently, CLDMAO exhibits superior optimization performance, outperforming the other nine methods.

Table 7.

The p-value of the CLDMAO with other algorithms on CEC2017.

Function	SSA	SCA	GWO	MFO	BA	SMA	INFO	RUN	AOA
F1	0.177907	1.7E−06	1.7E−06	1.7E−06	1.7E−06	0.028486	1.9E−06	0.018519	1.7E−06
F2	0.382034	1.7E−06	1.7E−06	1.7E−06	0.382034	0.382034	0.253644	0.382034	1.7E−06
F3	2.9E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	0.031603	1.7E−06	1.7E−06
F4	0.000529	1.7E−06	1.7E−06	1.7E−06	0.106394	1.2E−05	0.007731	0.001593	1.7E−06
F5	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.9E−06	1.7E−06	1.7E−06	1.7E−06
F6	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06
F7	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	2.1E−06	1.7E−06	1.7E−06	1.7E−06
F8	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	4.7E−06	1.7E−06	1.7E−06	1.7E−06
F9	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06
F10	4.3E−06	1.7E−06	0.000453	2.1E−06	1.7E−06	1.9E−05	2.1E−06	2.6E−06	1.7E−06
F11	1.9E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	4.3E−06	1.7E−06	1.2E−05	1.7E−06
F12	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	0.000359	1.7E−06	1.7E−06
F13	1.9E−06	1.7E−06	2.4E−06	2.4E−06	1.7E−06	0.991795	0.14139	0.035009	0.001709
F14	0.057096	2.8E−05	0.000453	0.00016	0.057096	0.009271	0.057096	0.057096	0.001287
F15	3.9E−06	1.7E−06	2.6E−06	8.5E−06	1.7E−06	8.5E−06	0.000189	0.000453	2.8E−05
F16	2.1E−06	1.7E−06	1.0E−05	1.7E−06	1.7E−06	3.2E−06	1.7E−06	1.7E−06	1.7E−06
F17	2.4E−05	1.7E−06	0.00049	1.7E−06	1.7E−06	3.2E−06	1.2E−05	3.2E−06	1.7E−06
F18	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06
F19	1.7E−06	1.7E−06	1.7E−06	1.8E−05	1.7E−06	6.9E−05	0.000136	0.025637	1.7E−06
F20	5.8E−06	1.9E−06	0.00016	3.2E−06	1.7E−06	3.2E−06	3.2E−06	1.7E−06	1.7E−06
F21	2.9E−06	1.7E−06	3.5E−06	1.7E−06	1.7E−06	2.6E−06	1.7E−06	1.7E−06	1.7E−06
F22	6.9E−05	1.7E−06	1.9E−05	1.9E−06	1.7E−06	2.1E−06	1.4E−05	0.001484	1.7E−06
F23	1.9E−06	1.7E−06	2.6E−06	1.7E−06	1.7E−06	9.3E−06	1.7E−06	1.7E−06	1.7E−06
F24	1.9E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.9E−06	1.7E−06
F25	0.628843	1.7E−06	1.7E−06	1.7E−06	0.000106	0.165027	0.012453	8.9E−05	1.7E−06
F26	0.002585	1.7E−06	2.6E−06	1.7E−06	1.9E−06	1.7E−06	2.9E−06	0.010444	1.7E−06
F27	0.017518	1.7E−06	0.001036	3.2E−06	1.7E−06	0.926255	6.3E−06	4.1E−05	1.7E−06
F28	0.001036	1.7E−06	1.7E−06	1.7E−06	0.718888	3.5E−06	0.991795	0.349346	1.7E−06
F29	1.7E−06	1.7E−06	1.9E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06
F30	1.7E−06	1.7E−06	1.7E−06	1.7E−06	1.7E−06	6.3E−06	0.115608	1.7E−06	1.7E−06

Significant p-values (p < 0.05) are in bold.

Figure 4 depicts the convergence performance of the proposed CLDMAO method on various benchmark test functions, specifically F9, F10, F12, F16, F18, F20, F22, F24 and F26. The convergence curves, obtained from the evaluation process, are plotted as continuous lines. The figure illustrates that the CLDMAO algorithm attains both the best convergence value and the highest convergence rate of these functions. Furthermore, compared with basic MAs, the CLDMAO algorithm significantly improves population diversity and convergence accuracy.

Fig. 4.

Convergence curves of involved algorithms on 9 functions.

The effectiveness of CLDMAO is further validated by comparing it against seven high-performance algorithm variants, all of which have been proven to deliver effective performance. These seven advanced algorithms, including WLSSA, CLSGMFO, OBLGWO, WDE, IGWO, SCADE, and CBA. Table 8 presents the experimental results of the average value and standard deviation value among CLDMAO and these advanced algorithms. Bold formatting indicates the minimum mean and standard deviation values in Table 8. The best value for each function test is bolded to emphasize their significance. It is clear that the CLDMAO show excellent performance on F2, F3, F4, F5, F6, F7, F8, F9, F11, F12, F16, F18, F21, F23, F24, F25, F28 and F29. Therefore, CLDMAO ranks first in the Friedman rank test on the CEC2017 functions, as is shown in Table 9. Bold the top-ranked result with the minimum ARV in Table 9. Therefore, it can be inferred that CLDMAO has superior optimization performance compared to the seven advanced methods.

Table 8.

Comparative results for CLDMAO and advanced methods.

	Avg	Std	Avg	Std	Avg	Std
	F1		F2		F3
CLDMAO	4111.658	5078.199	207.591	16.68249	300	5.65E−06
WLSSA	4526.855	4140.677	26,738,064	1.15E+08	300.0086	0.047349
CLSGMFO	4827.391	6003.924	4.51E+12	1.26E+13	2941.513	1780.728
OBLGWO	14,471,114	8,893,667	1.4E+18	7.4E+18	18,827.64	4943.787
WDE	19,840.42	7154.439	1.24E+12	3.51E+12	16,644.94	4120.162
IGWO	1,511,973	675,427.2	1.67E+14	5.23E+14	1255.277	583.8246
SCADE	1.96E+10	3.57E+09	3.4E+36	6.73E+36	60,046.79	6819.501
CBA	3861.206	5594.938	10,883.53	13,732.14	321.5018	21.71969
	F4		F5		F6
CLDMAO	438.1991	36.54256	545.0724	9.741749	600	1.43E−05
WLSSA	492.7264	22.50695	636.8126	34.78635	628.6376	12.08193
CLSGMFO	496.6796	29.08814	653.8985	35.41066	619.8307	9.6184
OBLGWO	530.354	35.38052	665.8824	44.52894	620.7304	17.3072
WDE	459.1271	23.31248	590.6352	12.4898	603.4021	0.757614
IGWO	500.279	25.14026	607.4996	19.35124	625.4183	7.248136
SCADE	3831.765	1048.144	832.9541	20.55956	662.7411	8.069903
CBA	502.8209	23.42649	842.6961	74.86275	672.7715	9.682123
	F7		F8		F9
CLDMAO	782.201	11.3006	848.1524	8.866827	900.6968	3.698144
WLSSA	858.4032	34.69511	921.4176	33.44212	2692.743	1314.411
CLSGMFO	894.1017	44.30483	923.8267	26.30808	3612.575	1109.718
OBLGWO	916.7019	74.58113	948.1294	38.96288	2688.54	1332.042
WDE	860.8026	18.40011	895.6533	11.50464	2937.1	515.5406
IGWO	902.0625	34.03293	896.5746	22.63151	2986.975	711.71
SCADE	1167.112	40.61807	1083.865	12.60624	8315.218	1376.44
CBA	1755.323	270.2681	1036.864	50.33692	8170.847	3010.242
	F10		F11		F12
CLDMAO	3485.146	490.6292	1145.711	27.13286	14,877.62	9246.846
WLSSA	4553.407	607.3896	1248.354	48.24956	2,616,902	2,189,698
CLSGMFO	4886.928	610.4791	1244.379	54.73059	894,385.5	737,176.3
OBLGWO	5213.619	892.7715	1296.553	43.73522	21,997,259	19,143,653
WDE	3405.602	245.9026	1175.749	17.08943	16,966.42	4693.923
IGWO	4580.448	666.2083	1249.789	33.97661	17,050,153	11,305,800
SCADE	8116.337	343.0522	3331.512	621.4835	2.03E+09	5.19E+08
CBA	5688.248	704.5465	1358.891	104.7482	10,738,414	6,489,731
	F13		F14		F15
CLDMAO	18,247.47	14,359.2	54,349.1	169,812.1	11,262.51	13,954.79
WLSSA	84,071.23	56,866.39	10,574.06	11,039.62	33,803.95	48,804.41
CLSGMFO	210,157.8	830,963.5	40,671.26	40,202.11	9659.873	13,681.26
OBLGWO	237,988.3	191,718.4	63,356.6	55,488.53	80,671.96	65,406.47
WDE	1511.48	33.72512	1466.005	9.451323	1550.526	11.20384
IGWO	164,179.3	250,708.8	43,095.66	31,158.42	56,362.51	41,393.86
SCADE	5.97E+08	2.9E+08	298,424.6	196,449.5	7,908,666	7,554,402
CBA	173,207.4	147,147.4	10,658.34	7777.02	98,377.17	79,109.51
	F16		F17		F18
CLDMAO	2004.958	189.6211	1879.285	171.6565	1843.161	13.95116
WLSSA	2590.92	326.9767	2026.992	193.4379	111,123.9	65,766.99
CLSGMFO	2747.185	337.7772	2248.495	214.9578	324,220.1	404,255.1
OBLGWO	2783.611	266.5376	2207.638	205.5273	1,418,996	1,092,986
WDE	2084.529	141.0173	1832.692	48.95674	2125.46	139.6903
IGWO	2481.443	336.2313	2036.319	157.0646	544,937.6	395,323.2
SCADE	3869.531	215.1866	2502.359	188.2133	3,728,734	1,794,349
CBA	3706.879	474.5427	2967.201	357.8959	235,452.8	189,327.1
	F19		F20		F21
CLDMAO	8696.448	11,221.96	2246.345	168.0387	2345.984	6.648249
WLSSA	346,298.3	207,577.7	2387.976	107.5864	2395.631	46.2445
CLSGMFO	9969.947	12,838.94	2543.274	181.0431	2418.539	30.26349
OBLGWO	557,221.4	617,504.6	2516.663	186.9966	2446.063	25.13661
WDE	1921.792	3.636535	2179.992	57.77505	2377.811	44.64975
IGWO	301,857.2	521,431.5	2362.39	155.068	2397.48	26.55625
SCADE	27,292,104	10,796,220	2737.399	80.82971	2583.481	21.3871
CBA	1,120,284	537,788.8	3066.686	287.5073	2634.894	77.38204
	F22		F23		F24
CLDMAO	2571.041	839.4925	2695.707	11.03962	2871.309	11.67148
WLSSA	2300.479	1.243657	2778.016	38.10967	2923.978	34.49417
CLSGMFO	2300.958	1.681592	2795.004	28.74233	2962.955	43.40874
OBLGWO	2759.652	1383.028	2821.196	40.39056	2968.007	39.09625
WDE	2408.61	467.219	2737.785	14.8258	2927.216	64.41941
IGWO	2311.514	2.429594	2776.001	29.25451	2931.965	26.19958
SCADE	4545.651	373.6762	3009.265	27.02061	3176.462	36.09461
CBA	7312.366	1328.988	3348.594	179.8935	3382.363	140.2261
	F25		F26		F27
CLDMAO	2886.945	1.011017	4043.205	357.3787	3223.829	15.29134
WLSSA	2895.21	15.18552	4306.534	912.7295	3245.533	29.61688
CLSGMFO	2892.684	13.80031	4122.907	1345.871	3318.078	92.7414
OBLGWO	2914.714	25.52424	5302.5	761.1463	3242.241	22.09288
WDE	2886.995	1.30042	3011.226	193.3391	3219.957	7.420666
IGWO	2909.43	15.57119	4732.734	484.8357	3236.385	15.85188
SCADE	3395.494	101.127	7414.906	373.2789	3443.512	51.75773
CBA	2914.732	27.2779	9439.478	2133.314	3429.689	149.6377
	F28		F29		F30
CLDMAO	3164.528	55.40114	3437.234	82.74855	7734.403	2885.775
WLSSA	3208.2	29.96689	3886.901	250.1089	1,712,922	1,236,705
CLSGMFO	3210.151	20.41939	3954.035	245.5919	104,875.8	290,550
OBLGWO	3269.077	32.66603	4028.215	222.4338	2,705,969	1,425,497
WDE	3220.346	7.885137	3561.368	72.83299	7002.992	709.785
IGWO	3253.555	26.83466	3869.045	222.1468	3,855,339	2,571,083
SCADE	4264.419	167.3949	5064.507	243.4947	1.05E+08	33,971,921
CBA	3218.183	34.53822	5129.969	562.3772	2,398,182	1,072,946

The minimum mean and standard deviation are in bold.

Table 9.

FT results of the CLDMAO with advanced algorithms on CEC2017.

Algorithm	Friedman rank test
	+/−/=	ARV	Rank
CLDMAO	~	1.666666667	1
WLSSA	26/1/3	3.4	3
CLSGMFO	23/2/5	4.3	4
OBLGWO	30/0/0	5.966666667	6
WDE	17/5/8	2.266666667	2
IGWO	28/2/0	4.466666667	5
SCADE	30/0/0	7.633333333	8
CBA	28/0/2	6.3	7

The top-ranked result (lowest ARV) is in bold.

Figure 5 shows the convergence performance of the proposed CLDMAO and advanced MAs on various benchmark test functions, specifically F2, F5, F6, F7, F8, F9, F16, F21, F23, F24, F28, and F29. Continuous convergence curves are constructed by plotting 50 data points, sequentially extracted from the evaluation process. The figure shows that CLDMAO achieves both the best fitness value and the fastest convergence speed across these functions. Furthermore, it clearly shows that the CLDMAO algorithm significantly enhances population diversity and convergence accuracy when compared to other advanced MAs.

Fig. 5.

Convergence curves of CLDMAO and improved algorithms on 12 functions.

Feature selection on the collected dataset

The collected dataset comes from 22 vocational colleges, including 10 Double First-Class universities. Among the 1162 members surveyed, 584 are from Double First-Class universities. There are 73 features in the collected dataset. This paper explores the significance of these 73 attributes and their interrelationships and develops a decision-support prediction model. This paper utilizes the binary CLDMAO frameworks to select a good feature subset for training the model. Subsequently, the trained bCLDMAO-KNN model is validated to predict the teaching quality evaluation of higher vocational education, which is based on an analysis of both the planning and execution intentions. By combining the bCLDMAO-KNN method with various other machine learning methods, including bSMA-KNN, bRUN-KNN, bMVO-KNN, bALCPSO-KNN, bIGWO-KNN, bDFSMA-KNN⁴⁸, bISMA-KNN, bINFO-KNN, bGBO-KNN classification models to evaluate the efficiency of bCLDMAO-KNN method.

To ensure consistency, the parameters for the remaining classifiers are configured according to established conventions. To evaluate classification accuracy, we conduct an unbiased tenfold cross-validation (CV) test. This procedure reserves a portion of the dataset for testing and uses the remainder for training the classifier. Crucially, the number of validation instances in each subset mirrors the size of the test dataset. The KNN classifier successfully executes the classification task with a field size (k) set to 1.

All mentioned algorithms are executed within a single main function to guarantee fairness. Each method shares the same random initialization within this main function, ensuring equitable conditions for comparison. The experiment is conducted with 20 search agents, 10 folds, and a maximum of 50 evaluations under identical experimental settings. We conduct tenfold cross-validation and report, for each fold, the selected feature subset size, error (and accuracy), best fitness, and time cost for bCLDMAO-KNN. Aggregated mean ± std across folds are provided. We compare against wrapper baselines (bSMA, bRUN, bMVO, bALCPSO, bIGWO, bDFSMA) using the same protocol and report Avg ± Std, average rank, Wilcoxon p-values.

To assess the effectiveness of feature selection, we compare the proposed bCLDMAO-KNN model, which relies on the KNN classifier for this purpose. Detailed experimental results, shown in As indicated by Table 10, the bCLDMAO-KNN model exhibits superior performance, securing first place in terms of best fitness, error, and number of features. Although its time cost ranks sixth, it falls within an acceptable threshold. The experimental results demonstrate bCLDMAO-KNN’s efficacy in classifying the aforementioned dataset, suggesting its potential practical application for educators.

Table 10.

Wilcoxon signed-rank test results.

Method		bSMA	bRUN	bMVO	bALCPSO	bIGWO	bDFSMA	bISMA	bINFO	bGBO	bCLDMAO
Best fitness	Avg	0.084953	0.079199	0.077286	0.094297	0.077677	0.079737	0.06997	0.076422	0.074618	0.062072
	Rank	9	7	5	10	6	8	2	4	3	1
Error	Avg	0.07313	0.077537	0.067222	0.084264	0.067995	0.070596	0.0619	0.066241	0.065423	0.054163
	Rank	8	9	5	10	6	7	2	4	3	1
NumOfFeatures	Avg	22.6	29.9	19.6	18	19.1	18.5	16.3	19.7	18.2	15.5
	Rank	9	10	7	3	6	5	2	8	4	1
Time cost	Avg	3.7768	9.4545	5.1916	9.1713	7.3712	9.1744	31.6536	4.5796	4.2548	8.9312
	Rank	1	9	4	7	5	8	10	3	2	6

Table 11 presents the results of the bCLDMAO-KNN model, detailing fold, selected feature subset size, error, best fitness and time cost. The results show that the bCLDMAO-KNN model gains an average selected feature subset size of 15.5, an average error value of 0.054163, and an average best fitness value of 0.062072. Figure 6 shows the best score obtained so far with the iteration process. The best fitness value for the bCLDMAO-KNN model is the lowest, highlighting the robustness of its accuracy and demonstrating its effectiveness. These low standard deviation values support the robustness of the model’s superior convergence performance and effectiveness in achieving a lower fitness value. The statistical robustness of the bCLDMAO-KNN model is quantitatively demonstrated in Table 11, where the low standard deviation of the error rate (0.019381) and best fitness (0.017983) across the tenfold cross-validation confirms its stable and reliable performance.

Table 11.

The detailed results gained by bCLDMAO-KNN model.

Fold	Selected feature subset size	Error	Best fitness	Time cost
#1	14	0.051724	0.058727	9.8221
#2	17	0.034483	0.044402	9.3051
#3	16	0.086207	0.092855	9.1774
#4	10	0.076923	0.079926	8.98
#5	13	0.059829	0.065742	9.1435
#6	13	0.051724	0.058042	8.9415
#7	17	0.051724	0.060782	8.3665
#8	25	0.051282	0.065841	8.9961
#9	15	0.060345	0.067602	8.0957
#10	15	0.017391	0.026796	8.4844
Avg	15.5	0.054163	0.062072	8.9312
Std	3.9511	0.019381	0.017983	0.50138

Fig. 6.

The best score obtained so far by mentioned models.

Finally, to analyze the classification results, we calculate the features picked by the proposed bCLDMAO-KNN model through 10 times of tenfold CV. The number of selected features is shown in Fig. 7. From Fig. 7, it is evident that the most frequently selected features include the impact on F71 (student/teacher participation in and awards from international competitions), F4 (professional title structure), F6 (full-time and part-time teacher structure), and F51 (employment rate in related fields). Additional analysis underscores the significance of these four features. Accordingly, the bCLDMAO-KNN model provides a means for teachers to evaluate teaching quality in higher vocational education.

Fig. 7.

The feature selection frequency distribution of bCLDMAO-KNN model during 10 times tenfold CV process.

Discussion

Experiment analysis

We quantified the linkage between optimization quality and classification performance on the collected dataset. Across the 10 CV folds (Table 10), the best fitness attained by bCLDMAO in each fold is strongly associated with the KNN error. On average, bCLDMAO-KNN selects 15.5 of 73 features (78.8% reduction) with a mean error of 0.054 (SD = 0.019). The correlation between subset size and error is negative but non-significant, indicating that classification gains primarily arise from improved optimization of the objective rather than subset size alone. To clarify, our enhanced optimization algorithm (CLDMAO) directly improves feature selection and classification performance in the following ways:

Quantitative impact of enhancements

The integration of the comprehensive learning and dispersed foraging mechanisms in CLDMAO increases population diversity and global search capability. Experimentally, bCLDMAO-KNN achieves the lowest average error (0.054163) and the lowest average best fitness value (0.062072) among all compared methods (see Table 9). Additionally, bCLDMAO-KNN identifies the smallest average subset of features (15.5 out of 73), demonstrating efficient feature selection.

Direct link between enhancements and outcomes

The improved search ability of CLDMAO prevents premature convergence and enables better exploration of the search space, which, in the context of binary feature selection, results in finding more relevant and informative feature subsets for classification. This leads to higher prediction accuracy and reduced feature redundancy, as evidenced by the superior performance metrics.

Controlled comparisons

All compared algorithms were evaluated under identical conditions (number of agents, folds, evaluations, etc.). bCLDMAO-KNN outperforms other wrapper-based feature selection algorithms by both error rate and feature subset size, demonstrating the benefit of the proposed enhancements.

To sum up, the enhancements to the optimization algorithm are quantitatively shown to produce better feature subsets, resulting in improved classification accuracy and model simplicity.

Teaching quality is the key factor of higher education. Studying this topic often requires assessing the overall structure of teaching quality through self-reporting. However, these tools have been criticized for a lack of consistency in teachers’ and students’ reporting of teaching practices⁴⁹. Evaluating teaching quality is highly challenging. Each teacher brings their training, experience, style, and abilities to the classroom, making it extremely difficult to establish a fair indicator of teaching quality⁵⁰. To effectively extract multidimensional data for teaching quality evaluation and accurately evaluate college teaching quality, Chen et al. proposed an SVM classification algorithm for quality evaluation of network distance teaching³⁹.

In our study, the data comes from 22 vocational colleges, including 10 Double First-Class universities. Among the 1162 staff members surveyed, 584 are from Double First-Class universities. According to the binary version of bCLDMAO-KNN model, four features—F71 (student/teacher participation in and awards from international competitions), F4 (professional title structure), F6 (full-time and part-time teacher structure), and F51 (employment rate in related fields)—show significant differences between Double First-Class and non-Double First-Class universities. Double First-Class universities place greater importance on international competitions and awards for their teaching teams, the rationality of the professional title structure, the proportion of specialized teachers to enterprise part-time teachers, and the alignment of student employment with their fields of study.

One important output indicator in the Ministry of Education’s performance evaluation system for Double First-Class universities is “enhancing internationalization”. This indicator assesses the breadth and depth of international exchanges and cooperation within institutions. It is divided into scale indicators and quality indicators, with the latter including metrics such as the number of student and teacher awards in international skill competitions. Under the guidance of the Ministry of Education’s policies, Double First-Class universities have established policies for international competition construction and rewards, whereas non-Double First-Class universities do not have this assessment content. This leads to a significant difference in how Double First-Class universities’ teaching teams and non-Double First-Class universities’ teaching teams perceive the importance of F71 (student/teacher participation in and awards from international competitions).

Similarly, the performance evaluation output indicators for Double First-Class universities include "building high-level dual-qualified teams", focusing on assessing the effectiveness of building dual-qualified teaching teams. This also includes scale indicators and quality indicators, with scale indicators primarily covering the proportion of full-time teachers with senior professional titles and the internal class hours of part-time teachers. This shows that Double First-Class universities place more emphasis on the promotion of teachers’ professional titles and the role of enterprise part-time teachers in the teaching team. Consequently, there is a significant difference in how Double First-Class universities’ teaching teams and non-Double First-Class universities’ teaching teams perceive the importance of F4 (professional title structure) and F6 (full-time and part-time teacher structure).

While the performance evaluation output indicators for Double First-Class universities do not include an indicator for "student employment in related fields", they do include an indicator for "level of school-enterprise cooperation", which focuses on assessing the closeness and depth of school-enterprise cooperation. Scale indicators here include the number of order classes, industrial colleges, jointly developed courses, jointly developed textbooks, teacher enterprise practice bases, jointly built internal and external training bases, jointly built research institutes and R&D centers, and productive training bases. By meeting these indicators, Double First-Class universities emphasize cooperation with relevant enterprises in teaching, internships, and employment, which in turn promotes the employment rate in related fields. This is why there is a significant difference in how Double First-Class universities’ teaching teams and non-Double First-Class universities’ teaching teams perceive the importance of F51 (employment rate in related fields).

In a word, the impact of the Ministry of Education’s performance evaluation for Double First-Class universities has led to more investment and requirements in areas such as internationalization, teaching teams, and school-enterprise cooperation, influencing the focus and perceptions of the teaching teams.

Advantages of proposed model

High Accuracy and Effective Feature Selection: The system demonstrates superior performance in identifying a minimal yet highly discriminative subset of features (reducing 73 attributes to an average of 15.5) from a complex dataset, leading to high classification accuracy and low error rates as shown in Table 9.

Provides Actionable Insights: Beyond simple prediction, the system identifies key factors that differentiate teaching team evaluation priorities (e.g., F71, F4, F6, F51). As discussed, these factors align with policy drivers like the “Double First-Class” initiative, making the results interpretable and useful for institutional decision-making.

Robustness and Stability: The low standard deviation in error rates and fitness values across the tenfold cross-validation (Table 10) confirms the model’s stable and reliable performance, ensuring that the findings are not due to chance.

Limitations

Computational Complexity: As a wrapper-based metaheuristic approach, the bCLDMAO-KNN model is computationally more intensive than simpler filter methods or standalone classifiers. Its time cost, while acceptable for this offline analysis, may be a limitation for real-time applications.

Generalizability: The model was trained and validated on data from Chinese higher vocational colleges. Its performance and the relevance of the selected features may differ in other educational contexts (e.g., different countries or types of universities) and would require further validation on more diverse datasets.

Data Dependency: The system’s effectiveness is contingent on the quality and scope of the initial questionnaire data. Any biases or limitations in the data collection process will inevitably be reflected in the model’s output.

Conclusion

In summary, this study introduces a comprehensive learning and dispersed foraging modified AO, named CLDMAO, aimed at establishing a comprehensive evaluation framework. To enhance the model’s efficiency and robustness, a comprehensive learning strategy and dispersed foraging mechanism are integrated into the modified AO algorithm. The enhanced AO’s global optimality is assessed using IEEE CEC 2017 functions. The results indicate that the proposed algorithm outperforms several other optimization methods across various test. Then, the comparative analysis of bCLDMAO-KNN and the other 9 feature selection methods shows higher classification accuracy and stability in constructing a teacher-team evaluation system.

In the future, CLDMAO’s potential could stretch into various areas, including image segmentation, multi-objective optimizations, and route planning. It could also benefit from incorporating strategies like genetic algorithms, Levy flights, and opposition-based methods. Yet, its computational efficiency needs enhancement to be viable for real-time uses, such as cloud resource allocation or traffic management. Improving CLDMAO’s speed is key to unlocking its full potential across sectors and is a promising area for further teacher-team evaluation system research, allowing for its better real-world application.

Author contributions

Author1: Qiming Tian Contributions: Writing—Original Draft, Writing—Review and Editing, Software, Visualization, Investigation. Author 2: Wanle Chi Contributions: Conceptualization, Methodology, Formal Analysis, Investigation, Writing—Review and Editing, Funding Acquisition, Supervision. Author 3: Dafeng Gong Contributions: Writing—Original Draft, Writing—Review and Editing, Software, Visualization, Investigation. Author 4: Yuwen Shi Contributions: Writing—Original Draft, Writing—Review and Editing, Software, Visualization, Investigation. Author 5: Lili Shi Contributions: Writing—Original Draft, Writing—Review and Editing, Software, Visualization, Investigation. Author 6: Huiling Chen Contributions: Conceptualization, Methodology, Formal Analysis, Investigation, Writing—Review and Editing, Funding Acquisition, Supervision. Author 7: Sudan Yu Contributions: Conceptualization, Methodology, Formal Analysis, Investigation, Writing—Review and Editing, Funding Acquisition, Supervision.

Funding

This work is funded by the Research Project of the Second Batch of National Vocational Education Teacher Teaching Innovation Teams (No. ZL2021120106).

Data availability

The datasets used and/or analysed during the current study available from the corresponding author on reasonable request.

Declarations

Competing interests

The authors declare no competing interests.

Ethical statements

Authors reporting experiments on humans and must confirm that all experiments were performed in accordance with relevant guidelines and regulations. .