Knowledge-Based Recommendation for Graduate Subject Allocation Using Graph Neural Networks (GNNs)

Abstract

This study proposes a hybrid artificial intelligence (AI) framework for graduate subject allocation that enhances fairness, transparency, and operational efficiency in higher education institutions. Traditional subject allocation processes are predominantly manual and time-consuming in increasingly complex academic environments. The proposed framework integrates a custom Python-based rule engine for institutional constraint reasoning with advanced deep learning models, including XGBoost, Wide-and-Deep Neural Networks (WDNNs), and Graph Neural Networks (GNNs), to ensure policy-compliant and data-driven subject allocation decisions. Subsequently, a systematic hyperparameter optimization strategy is applied to enhance predictive accuracy and model stability across all architectures. Experimental evaluation demonstrates that the proposed framework significantly improves predictive and ranking performance. The GNNs model achieved the highest results with Accuracy = 0.964, Precision = 0.953, Recall = 0.941, F1-score = 0.947, and AUC = 0.976, outperforming WDNN (Accuracy = 0.956, AUC = 0.972) and XGBoost (Accuracy = 0.934, AUC = 0.942). Ranking effectiveness was also validated with HR@10 = 0.784 and NDCG@10 = 0.622. Feature-importance analysis using SHAP revealed that Digital Pedagogical Competence (12.6%), Research Productivity (10.8%), and Postgraduate Supervision (9.7%) are the most influential factors in allocation decisions. To ensure institutional alignment, a multi-objective reranking mechanism was introduced to balance suitability, workload fairness, research alignment, and diversity. This approach reduced workload variance from 0.26 to 0.18 and improved research–subject alignment by 21%. Overall, the proposed framework provides a scalable, explainable, and data-driven solution for optimizing graduate subject allocation in modern higher education systems.

1. Introduction

In recent years, higher education institutions have faced increasing complexity in curriculum design and subject allocation due to the rapid expansion of course offerings, the growth of interdisciplinary programs, and the diversity of student profiles [1]. At the same time, the advent of large-scale educational data (student records, faculty profiles, course metadata) creates opportunities to apply intelligent systems for decision support [2]. Recommendation systems (RSs) have emerged as crucial tools for filtering choices, suggesting alternatives, and guiding decision-making in high-dimensional, constrained domains [3]. In the educational domain, RSs have traditionally supported students [4]. However, relatively few studies consider RSs in faculty workload and subject allocation, which involve multiple stakeholders (students, faculty, programs) and hard constraints (prerequisites, scheduling, capacity). The need to allocate subjects optimally is especially pronounced in graduate studies, where curriculum progress, research alignment, and faculty specialization are of great importance [5]. Traditionally, subject allocation has been rule-based (program policies, prerequisites, faculty load), overseen by academic advisers and administrators. However, such manual systems have limitations: they may not account for latent factors such as faculty research alignment, student interest vectors, or the interplay among faculty–student–subject relationships [6]. Meanwhile, advances in machine learning (ML) and deep learning (DL) offer greater capacity to model complex, relational, and higher-order structures [7]. Knowledge-graph-enhanced recommendation systems extend beyond traditional collaborative filtering and content-based methods by leveraging side information and relational embeddings, thus improving performance and explainability [8]. For example, GNNs applied to heterogeneous educational graphs (students, courses, faculty) have demonstrated superior ranking accuracy for course recommendations [9]. In the context of subject allocation, these methods can encode faculty expertise, research output, student interests, program relationships, and scheduling constraints into one unified graph of entities and relations. Although educational recommender systems have achieved significant success in course recommendation, adaptive learning, and personalized education, most existing studies focus primarily on student-centered recommendation tasks and rarely address faculty-centric subject allocation problems [10]. Furthermore, previous approaches typically emphasize prediction accuracy while overlooking institutional policies, workload fairness, research alignment, and explainability requirements that are critical in graduate-level academic management. Existing workload allocation frameworks often rely on rule-based or optimization techniques that lack adaptive learning capabilities and cannot effectively model complex relationships among faculty members, subjects, and academic programs.

To address these limitations, the present study proposes a novel knowledge-based recommendation framework that integrates a custom institutional rule engine, heterogeneous knowledge graph representation, Graph Neural Networks (GNNs), explainable artificial intelligence (XAI), and multi-objective optimization. Unlike previous studies, the proposed framework simultaneously considers faculty expertise, institutional eligibility constraints, workload balance, postgraduate supervision capacity, research specialization, and academic policy compliance within a unified recommendation architecture. This combination enables transparent, explainable, and policy-compliant subject allocation decisions while maintaining high predictive performance and institutional applicability. To improve readability and methodological transparency, the manuscript adopts consistent terminology and standardized notation throughout all sections. Redundant descriptions have been consolidated where appropriate, and methodological explanations are presented only once within the relevant subsection to avoid repetition while maintaining sufficient technical detail for reproducibility.

In the remainder of this paper, we present a literature review on educational recommendation systems, knowledge graph-based recommendations, and faculty workload allocation frameworks (Section 2), describe the research methodology (Section 3), present evaluation performances (Section 4), discuss experiment results for practice (Section 5), and conclude with conclusions and future work (Section 6 and Section 7).

2. Literature Review

Educational recommender systems have evolved from traditional collaborative filtering and content-based approaches toward knowledge-aware and graph-based learning frameworks [11]. Recent advances in knowledge graphs and GNNs have enabled recommendation systems to capture complex semantic and relational dependencies among educational entities, thereby improving recommendation accuracy, contextual relevance, and interpretability [12]. Despite these advances, existing studies primarily focus on student-centered recommendation tasks and rarely address institutional decision-support problems involving faculty assignment, workload balancing, policy compliance, and academic resource allocation. Consequently, there remains a need for intelligent recommendation frameworks that integrate relational learning, institutional knowledge, and explainable decision-making in higher education environments. By incorporating semantic relationships among courses, academic domains, and learner profiles, knowledge graph–based recommenders can generate more accurate and personalized recommendations, particularly when user information is limited. Such approaches improve recommendation quality by leveraging contextual knowledge and hidden associations between educational entities, thereby supporting more informed academic decision-making and curriculum planning [13]. Recent advancements in GNN-based recommender systems have demonstrated significant improvements in modeling complex relationships among users, items, and contextual factors. GNNs approach effectively capture graph-structured interactions and deliver improved recommendation performance while addressing key challenges such as fairness, diversity, explainability, and transparency. These characteristics make GNN-based frameworks particularly suitable for educational decision-support applications, where recommendation outcomes must be both accurate and interpretable [14]. By integrating structured domain knowledge with recommendation algorithms, these approaches improve the relevance of recommendations, contextual understanding, and decision quality. Such knowledge-driven frameworks provide a robust foundation for educational recommendation systems, particularly in scenarios that require intelligent matching of academic resources, expertise, and institutional objectives [15]. Recent advancements in deep learning architectures (Neural Collaborative Filtering (NCF), WDNNs, and GNNs have significantly expanded the capacity of recommendation systems to learn latent representations and multi-relational patterns that traditional statistical models often fail to capture [16]. These models transcend simple input–output prediction by embedding semantic and structural relationships among diverse entities such as students, faculty, subjects, and institutional rules. In educational applications, such models enable reasoning over both explicit relationships (e.g., teaching history, research specialization) and implicit associations (e.g., mentoring effectiveness, digital teaching affinity). Knowledge Graphs (KGs) have further augmented this capability by structuring educational data into interconnected ontologies that allow semantic reasoning. Studies have shown that KG-based educational recommenders enhance adaptive learning pathways, dynamic course sequencing, and skill mapping—resulting in improved personalization and cognitive alignment between learners and content [17]. However, despite these successes, the application of KGs and deep learning to academic management remains underexplored. Most prior work focuses on student-side personalization, leaving institutional decision-making largely rule-driven and manually optimized. Recent hybrid frameworks that integrate knowledge-based reasoning with deep representation learning represent a transformative paradigm shift, combining the transparency of expert systems with the adaptability of neural models [18]. Hybrid AI models enhance graduate subject allocation by combining institutional rules with data-driven learning to improve fairness and predictive accuracy. In particular, GNNs effectively models relationships among faculty, subjects, and programs, enabling more accurate and interpretable recommendations [19]. Additionally, integrating reinforcement learning (RL) allows systems to adapt dynamically to policy changes and feedback. Recent studies emphasize that fairness and explainability are essential in educational AI, ensuring ethical, transparent, and compliant decision-making [20]. In the context of faculty workload allocation, scholars have identified significant challenges in balancing quantitative factors (e.g., teaching experience, academic rank, and administrative duties) with qualitative indicators (e.g., mentoring quality, research supervision, and digital pedagogical skills) [8]. Current decision models often fail to integrate these diverse dimensions holistically, leading to inconsistent workload distribution and potential faculty dissatisfaction. Few frameworks treat the triadic relationship among faculty, subjects, and programs as a co-dependent decision space in which optimizing one dimension directly influences the others. Knowledge graph-enhanced hybrid recommender systems directly address this gap by enabling multi-objective optimization while preserving interpretable rule traces for administrative validation [21]. Empirical studies have demonstrated that combining domain ontologies and explicit workload constraints with neural learning architectures substantially improves both accuracy and transparency, making such systems well-suited for institutional deployment. The existing literature provides compelling evidence of the potential of deep learning-based, knowledge graph-augmented recommender systems to address complex educational challenges. However, significant gaps remain regarding faculty-centric subject allocation, hybrid knowledge-driven optimization, and real-world validation within university environments. The comparison between existing educational recommendation frameworks and the proposed approach is given in Table 1.

Table 1. Comparison between existing educational recommendation frameworks and the proposed approach.

Study	Domain	Method	Main Focus	Limitations	Institutional Rules	Explainability	Workload Fairness	Subject Allocation
Course Recommendation Studies	Student Learning	Collaborative Filtering	Course Selection	Student-centric only	✗	Limited	✗	✗
Knowledge Graph Recommenders	Educational Recommendation	Knowledge Graph	Semantic Recommendation	No workload consideration	✗	Partial	✗	✗
Deep Learning Educational RS	Course Recommendation	NCF/WDNN	Prediction Accuracy	Black-box decisions	✗	Limited	✗	✗
Faculty Workload Models	Academic Management	Rule-Based/Optimization	Workload Distribution	No learning capability	✓	Partial	✓	✗
GNN-based Educational RS	Course Recommendation	GNNs	Relational Learning	Student-focused	✗	Partial	✗	✗
Proposed Framework	Graduate Subject Allocation	Knowledge-Based GNNs + Rule Engine + Multi-Objective Optimization	Faculty–Subject Assignment	Addresses prior limitations	✓	✓	✓	✓

To ensure compliance with institutional policies, the proposed framework incorporates a custom Python-based rule engine that operates as a pre-processing and constraint-filtering layer. The rule engine encodes explicit academic regulations, including qualification requirements, workload limits, supervision eligibility, and subject-specific teaching policies, using deterministic conditional logic statements. These rules generate an eligibility mask that filters infeasible faculty–subject assignments before graph construction. Consequently, only policy-compliant relationships are represented within the knowledge graph and subsequently processed by the GNNs model. This hybrid design combines the transparency of rule-based reasoning with the adaptive learning capability of deep neural networks, thereby improving both recommendation validity and institutional alignment. The overarching goal of this research is to design and validate a knowledge-based deep learning framework that intelligently automates and optimizes subject allocation in graduate programs, ensuring fairness, transparency, and institutional alignment. Building on advances in GNNs and knowledge-based reasoning, the study seeks to transform the traditional rule-driven subject-assignment process into a data-driven, interpretable, and adaptive decision-support system.

To achieve this overarching goal, the study is guided by the following specific objectives:

• To design a hybrid knowledge-based GNNs framework that integrates explicit institutional rules (e.g., qualification requirements, workload limits, supervision policies) with data-driven learning from historical allocation patterns.
• To construct a comprehensive indicator–subject knowledge graph that captures semantic and relational dependencies among faculty members, subjects, research domains, and workload profiles, enabling contextual reasoning within the allocation process.
• To develop a GNN-based allocation model that learns attention coefficients representing the importance of faculty indicators in predicting allocation suitability.
• To apply multi-objective optimization techniques that balance allocation goals within a unified allocation function.
• To evaluate the performance and interpretability of the proposed GNNs model against benchmark algorithms (XGBoost, Wide-and-Deep Neural Network, and GNNs) using key metrics such as Accuracy, F1-score, AUC, HR@10, and NDCG@10.
• To design and implement an Indicator Subject Allocation Dashboard (ISAD) that translates model outputs into a usable decision-support interface, allowing administrators to visualize, validate, and adjust allocation outcomes in real time.
• To validate the framework empirically using data from 463 respondents across six faculties at Mahasarakham University, assessing the system’s predictive accuracy, explainability, and institutional applicability.

3. Research Methodology

This study adopts a quantitative approach integrating knowledge-based reasoning, deep learning, and institutional data analysis to develop and evaluate a hybrid intelligent system for subject allocation in graduate studies. The overall research procedure comprises five sequential phases: Section 3.1: ethical approval and data collection process; Section 3.2: problem identification and data preparation; Section 3.3: label construction; Section 3.4: deep learning model development; (D) training objective and regularization; and Section 3.5: validation and interpretation for institutional application.

3.1. Ethical Approval and Data Collection Process

The study was conducted in accordance with the Declaration of Helsinki and approved by the Ethics Committee for Human Research of Mahasarakham University, Thailand (Approval No. 881-843/2025) on 22 December 2025. All participants were informed about the study’s purpose and procedures, and electronic consent was obtained prior to completing the questionnaire. Participants indicated their consent by clicking the agreement statement before proceeding to the survey. All items in the questionnaire were rated on a five-point Likert scale (1 = strongly disagree to 5 = strongly agree). The data collection period extended from 22 December 2025 to 21 January 2026 to ensure clarity, reliability, and contextual relevance of the questions. Based on pilot feedback and expert review, we aim to enhance content validity and ensure comprehensive coverage of academic activities across both science and social science disciplines in the Thai context. The final version of the questionnaire was then approved for data collection.

Data were collected through both online and paper-based questionnaires administered at Mahasarakham University (MSU), Thailand, across six faculties: Science, Engineering, Information Technology, Humanities and Social Sciences, Mahasarakham Business School, and Education. A total of 480 academic staff members participated in the study. Stratified random sampling was employed to achieve proportional representation across faculties and academic ranks, enhancing the representativeness of the sample and minimizing sampling bias. All participants were informed about the study’s purpose and procedures, and electronic consent was obtained prior to completing the questionnaire. For the online survey, electronic consent was secured via a mandatory confirmation checkbox before access to the questionnaire was granted. For the paper-based survey, participants signed a written consent form attached to the questionnaire. Consent documentation, including electronic records and signed forms, was securely stored in a password-protected database accessible only to the research team and retained solely for academic and ethical compliance purposes. Written informed consent was chosen to ensure transparency, accurate documentation, auditability, and strict adherence to institutional ethical standards governing human-subjects research in higher-education contexts. The final dataset comprised 480 eligible academic staff members across six faculties: Science, Engineering, Information Technology, Humanities and Social Sciences, Mahasarakham Business School, and Education. These respondents were associated with approximately 320 graduate-level subjects and a total of 3200 faculty–subject assignment instances after preprocessing and class-balancing procedures. Faculty representation was maintained proportionally through stratified random sampling by academic rank and faculty affiliation to reduce sampling bias. The dataset includes respondents with diverse academic backgrounds, teaching experience, research productivity levels, and administrative responsibilities, thereby providing a comprehensive representation of the institutional academic workforce. Each respondent completed a structured questionnaire containing three parts: (1) demographic information (gender, age, academic rank, years of experience, department), (2) twenty (20) measurable variables related to factors influencing subject allocation, and (3) institutional engagement outcomes such as research contribution and teaching workload perception. All 20 features were defined quantitatively as follows: Teaching Experience (years) (F₁), Academic Qualification (highest degree) (F₂), Designation (academic rank) (F₃), Number of Subjects Taught (F₄), Research Productivity (F₅), Administrative Responsibility (F₆), Academic Outcome Achievement (F₇), Admission and Recruitment Contribution (F₈), Training and Placement Involvement (F₉), Accreditation and Documentation Handling (F₁₀), Examination and Evaluation Contribution (F₁₁), Institutional and Club Engagement (F₁₂), Value and Ethics Participation (F₁₃), Professional Society Membership (F₁₄), Cultural and Community Outreach (F₁₅), Event Coordination Beyond Institute (F₁₆), Undergraduate Project Mentorship (F₁₇), Postgraduate/Ph.D. Supervision (F₁₈), Student Mentorship and Guidance (F₁₉), and Digital Pedagogical Competence (F₂₀). The 20 indicators used in the subject allocation model in this study are listed in Table 2 [22].

Table 2. 20 Indicators input for the subject allocation model.

Code	Variable Name	Description and Measurement Aspect	Measurement Scale	Source Item (Questionnaire No.)	Functional Role in Model
F1	Teaching Experience	Total years of full-time teaching at the university level	Ratio (Years)	Q1	Expertise and stability assessment
F2	Academic Qualification	Highest degree attained (Master’s/Ph.D.)	Nominal (Encoded)	Q2	Eligibility and policy compliance
F3	Designation/Academic Rank	Lecturer, Assistant, Associate, Professor	Ordinal (Encoded)	Q3	Seniority and suitability
F4	Number of Subjects Taught	Count of distinct courses handled per semester	Ratio (Count)	Q4	Workload and versatility
F5	Research Productivity	Publications, grants, projects per year	Ratio (Count)	Q5	Research–teaching alignment
F6	Administrative Responsibility	Leadership roles (Head, Dean, etc.)	Likert (1–5)	Q6	Workload penalty factor
F7	Academic Outcome Achievement	Student performance/evaluation improvement	Likert (1–5)	Q7	Teaching effectiveness
F8	Admission Contribution	Participation in recruitment/admissions	Likert (1–5)	Q8	Institutional engagement
F9	Training and Placement Contribution	Internship/training involvement	Likert (1–5)	Q9	Industry engagement
F10	Accreditation/Documentation Handling	QA/accreditation work involvement	Likert (1–5)	Q10	Administrative workload
F11	Examination and Evaluation Contribution	Exam/grading responsibilities	Likert (1–5)	Q11	Teaching support
F12	Club/Institutional Innovation Engagement	Participation in academic/innovation clubs	Likert (1–5)	Q12	Extracurricular academic activity
F13	Value and Ethics Education Participation	Moral/social/ethics training involvement	Likert (1–5)	Q13	Holistic education
F14	Professional Society Membership	Membership in professional bodies	Nominal (Encoded)	Q14	Professional affiliation
F15	Cultural and Community Engagement	Social/community participation	Likert (1–5)	Q15	Social dimension
F16	Event Coordination Beyond the Institute	Events at the university/state/national level	Likert (1–5)	Q16	Leadership visibility
F17	Undergraduate Project Mentorship	Number of UG projects supervised	Ratio (Count)	Q17	Mentoring experience
F18	Postgraduate/Ph.D. Supervision	Number of PG/PhD theses supervised	Ratio (Count)	Q18	Graduate-level impact
F19	Student Mentorship and Guidance	Academic/personal mentoring role	Likert (1–5)	Q19	Student engagement
F20	Digital Pedagogical Competence	LMS, AI tools, e-learning proficiency	Likert (1–5)	Q20	Digital readiness

3.2. Problem Identification and Data Preparation

The dataset for this study comprised 480 data points collected from six faculties at Maha Sarakham University. Each respondent was characterized using 20 indicators (F₁–F₂₀) covering experience, qualifications, designation, research productivity, administrative load, mentorship, and digital competence. The raw dataset underwent a multi-stage preprocessing pipeline to ensure completeness, consistency, and suitability for training a GNNs. For clarity and reproducibility, all mathematical formulations are presented using standardized notation. Each variable and parameter is explicitly defined immediately following its corresponding equation. To improve readability, equations are grouped according to functional components of the framework, including institutional rule evaluation, knowledge graph construction, recommendation scoring, and graph neural network optimization. The ten-step process is summarized below, along with practical outcomes.

Step 1: Missing-Value Imputation: Approximately 4.7% of the entries contained missing values, primarily in F₁ (Teaching Experience), F₄ (Subjects Taught), and F₅ (Research Productivity). For numeric features, mean imputation was applied using Equation (1) [23].

$${\mathrm{x}}_{\mathrm{i}}^{\prime }=\left\{\begin{array}{ll}{\mathrm{x}}_{\mathrm{i}},& \mathrm{if} {\mathrm{x}}_{\mathrm{i}}\ne \mathrm{N}\mathrm{a}\mathrm{N}\\ {\displaystyle \frac{1}{\mathrm{n}}}{\sum }_{\mathrm{k}=1}^{\mathrm{n}}{\mathrm{x}}_{\mathrm{k}},& \mathrm{if} {\mathrm{x}}_{\mathrm{i}}=\mathrm{N}\mathrm{a}\mathrm{N} \end{array}\right.$$

(1)

For categorical variables (e.g., F₂ Academic Qualification, F₃ Designation), mode imputation replaced missing entries, which is defined as Equation (2).

$${\mathrm{x}}_{\mathrm{i}}^{\prime }=\mathrm{m}\mathrm{o}\mathrm{d}\mathrm{e}({\mathrm{x}}_1,{\mathrm{x}}_2,\dots ,{\mathrm{x}}_{\mathrm{n}})$$

(2)

A sensitivity analysis comparing mean/mode imputation with multiple imputations using MICE showed less than 5% variation in the final AUC. In addition, we have clarified the missing-value pattern (4.7% overall, primarily in F₁, F₄, and F₅) earlier in Step 1 to improve reproducibility and transparency.

Step 2: Data Normalization (Min–Max Scaling): To ensure numerical stability and prevent dominance of high-magnitude variables, continuous indicators (F₁, F₄, F₅, F₇, F₁₈) were scaled to the [0, 1] interval using Equation (3) [24].

$${\mathrm{x}}_{\mathrm{i}}^{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}={\displaystyle \frac{{\mathrm{x}}_{\mathrm{i}}-\mathrm{m}\mathrm{i}\mathrm{n}}{{\mathrm{x}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{x}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}}\in [0,1]$$

(3)

For example, F₁ (Teaching Experience) ranged from 2 to 40 years, resulting in Equation (4).

$${\mathrm{x}}_{\mathrm{i}}^{\mathrm{n}\mathrm{o}\mathrm{r}\mathrm{m}}={\displaystyle \frac{20-2}{40-2}}=0.47$$

(4)

This standardization improved convergence stability during neural optimization and reduced skewness by 64%.

Step 3: Categorical Encoding: Categorical variables (F₂ (Qualification), F₃ (Designation), and F₁₄ (Professional Society)) were numerically encoded to improve model interpretability. Label encoding assigns ordinal values as defined in Equation (5) [25].

$$\mathrm{P}\mathrm{h}.\mathrm{D}.=3,\mathrm{M}\mathrm{a}\mathrm{s}\mathrm{t}\mathrm{e}\mathrm{r}=2,\mathrm{B}\mathrm{a}\mathrm{c}\mathrm{h}\mathrm{e}\mathrm{l}\mathrm{o}\mathrm{r}=1$$

(5)

For multi-class categories (e.g., Lecturer, Assistant Professor, Associate Professor, Professor), One-Hot Encoding was applied using Equation (6).

$$\mathrm{D}\mathrm{e}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n}=[1 0 0 0](\mathrm{L}\mathrm{e}\mathrm{c}\mathrm{t}\mathrm{u}\mathrm{e}\mathrm{r}),[0 0 1 0](\mathrm{A}\mathrm{s}\mathrm{s}\mathrm{o}\mathrm{c}\mathrm{i}\mathrm{a}\mathrm{t}\mathrm{e} \mathrm{P}\mathrm{r}\mathrm{o}\mathrm{f}\mathrm{e}\mathrm{s}\mathrm{s}\mathrm{o}\mathrm{r})$$

(6)

This produced six categorical vectors, which were subsequently transformed into 64-dimensional embeddings for GNNs input.

Step 4: Outlier Detection and Capping: To mitigate the influence of extreme values, the Interquartile Range (IQR) method was applied, as defined in Equation (7).

$$\begin{array}{l}\mathrm{I}\mathrm{Q}\mathrm{R}={\mathrm{Q}}_3-{\mathrm{Q}}_1,\\ {\mathrm{x}}_{\mathrm{i}}^{\mathrm{c}\mathrm{a}\mathrm{p}\mathrm{p}\mathrm{e}\mathrm{d}}=\left\{\begin{array}{ll}{\mathrm{Q}}_3+1.5(\mathrm{I}\mathrm{Q}\mathrm{R}),& \mathrm{i}\mathrm{f} {\mathrm{x}}_{\mathrm{i}}>{\mathrm{Q}}_3+1.5(\mathrm{I}\mathrm{Q}\mathrm{R})\\ {\mathrm{Q}}_1+1.5(\mathrm{I}\mathrm{Q}\mathrm{R}),& \mathrm{i}\mathrm{f} {\mathrm{x}}_{\mathrm{i}}>{\mathrm{Q}}_1+1.5(\mathrm{I}\mathrm{Q}\mathrm{R})\\ {\mathrm{x}}_{\mathrm{i}}& \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}\right.\end{array}$$

(7)

For example, F₅ (Research Productivity) had Q₁ = 4.0, Q₃ = 12.0, yielding IQR = 8.0. The upper bound = 12 + 1.5(8) = 24, so any publication count > 24 was capped at 25. This reduced the skewness of outliers from 1.72 to 0.63.

Step 5: Correlation and Multicollinearity Analysis: A Pearson correlation matrix was computed using Equation (8) [26].

$${\mathrm{r}}_{\mathrm{x}\mathrm{y}}={\displaystyle \frac{{\displaystyle {\sum }_{\mathrm{i}}({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}})({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}})}}{\sqrt{{\displaystyle {\sum }_{\mathrm{i}}{({\mathrm{x}}_{\mathrm{i}}-\overline{\mathrm{x}})}^2{\displaystyle {\sum }_{\mathrm{i}}{({\mathrm{y}}_{\mathrm{i}}-\overline{\mathrm{y}})}^2}}}}}$$

(8)

Features exceeding $\left|{\mathrm{r}}_{\mathrm{x}\mathrm{y}}\right|>0.90$ were considered multicollinear. Variance inflation factors were all < 4.0 after composite adjustment (maximum VIF = 2.8 for F₆), indicating that multicollinearity was adequately controlled. F₆ (Administrative Responsibility) and F₁₀ (Accreditation Handling) initially showed r = 0.93. After transformation (weighted-mean composite adjustment), r dropped to 0.72, mitigating redundant signal propagation in the GNNs.

Step 6: Feature Embedding Preparation: Encoded categorical variables (F₂, F₃, F₁₄) were projected into a 64-dimensional latent space, as defined in Equation (9) [27].

$$\mathrm{E}={\mathrm{W}}_{\mathrm{e}}\mathrm{X}+{\mathrm{b}}_{\mathrm{e}}$$

(9)

where ${\mathrm{W}}_{\mathrm{e}}\in {\Re }^{64\times \mathrm{d}}$ and b_e are trainable embedding parameters. This transformation preserved semantic relationships between categories while providing dense vector inputs for the GNNs layer.

Step 7: Knowledge-Based Filtering: To align the data with university policies, eligibility rules were applied using Equation (10) [27].

$$\begin{array}{l}\mathrm{I}\mathrm{f}(\mathrm{F}2<\mathrm{P}\mathrm{h}.\mathrm{D}.) \mathrm{a}\mathrm{n}\mathrm{d} (\mathrm{C}\mathrm{o}\mathrm{u}\mathrm{r}\mathrm{s}\mathrm{e}\mathrm{L}\mathrm{e}\mathrm{v}\mathrm{e}\mathrm{l}=\mathrm{G}\mathrm{r}\mathrm{a}\mathrm{d}\mathrm{u}\mathrm{a}\mathrm{t}\mathrm{e})\\ \Rightarrow \mathrm{R}\mathrm{e}\mathrm{m}\mathrm{o}\mathrm{v}\mathrm{e} \mathrm{S}\mathrm{a}\mathrm{m}\mathrm{p}\mathrm{l}\mathrm{e}\end{array}$$

(10)

From 480 records, 17 were removed for lacking doctoral qualifications or holding administrative exemptions, leaving 463 valid respondents. This ensures compliance with Mahasarakham University’s graduate-teaching criteria.

Step 8: Workload Normalization: Workload was standardized to institutional averages using Equation (11).

$${\mathrm{W}}_{\mathrm{i}}^{\prime }={\displaystyle \frac{{\mathrm{W}}_{\mathrm{i}}-\overline{\mathrm{W}}}{\mathrm{\sigma }\mathrm{W}}}$$

(11)

where $\overline{\mathrm{W}}=10.6$ h and $\mathrm{\sigma }\mathrm{W}=3.2$. Post-normalization, the mean workload equaled 0.00 (SD = 1.0), and extreme load deviations (>2 SD) were corrected using a clipping function $\mathrm{m}\mathrm{i}\mathrm{n}(\mathrm{m}\mathrm{a}\mathrm{x}({\mathrm{W}}_{\mathrm{i}}^{\prime },-2),2),$ improving fairness consistency across faculty profiles.

Step 9: Data Balancing Using Negative Sampling: To address class imbalance while preserving the structural integrity of the bipartite graph, a constraint-aware negative sampling strategy was adopted instead of SMOTE-based data augmentation. Applying SMOTE to graph-structured data may introduce synthetic edges that distort the natural topology and relational dependencies among nodes. Therefore, negative samples were generated by selecting faculty–subject pairs (f_i, s_j) that satisfied institutional eligibility constraints defined in Equation (10) but did not appear in historical allocation records. Formally, the negative sampling process is defined in Equation (12) [28].

$${\mathrm{y}}_{\mathrm{i}\mathrm{j}}=\left\{\begin{array}{ll}1,& \mathrm{i}\mathrm{f} ({\mathrm{f}}_{\mathrm{i}},{\mathrm{s}}_{\mathrm{j}})\in \mathrm{H}\\ 0,& \mathrm{i}\mathrm{f} ({\mathrm{f}}_{\mathrm{i}},{\mathrm{s}}_{\mathrm{j}})\notin \mathrm{H} \mathrm{a}\mathrm{n}\mathrm{d} {\mathrm{E}}_{\mathrm{i}\mathrm{j}}=1\end{array}\right.$$

(12)

where H denotes the set of historical assignments and E_ij represents eligibility constraints. Negative samples were randomly drawn at a 1:3 ratio relative to positive samples to maintain class balance while preserving the original graph structure. Synthetic faculty–subject samples were generated for underrepresented disciplines, increasing the total number of instances from 2450 to 3200 (≈27% increase). This adjustment improved the GNNs model’s class-balance F1-score from 0.812 to 0.871 during pilot validation. To ensure institutional validity and reproducibility, each synthetic pair (f_i, s_j) generated by SMOTE was validated against the eligibility rules defined in Equation (10). Specifically, each pair was checked to confirm that the faculty member satisfied the doctoral qualification requirement (F₂ ≥ Ph.D. or equivalent), met institutional eligibility for graduate-level teaching, and that the subject s_j corresponded to a graduate-level course. Synthetic pairs that violated any of these constraints were discarded prior to graph construction. Consequently, graph topology was built exclusively from valid edges satisfying all institutional constraints, ensuring that data augmentation did not introduce infeasible assignments.

Step 10: Graph Construction for GNNs Input: The cleaned and enriched dataset was converted into a bipartite graph G = (V, E), where nodes represent faculty members and subjects, and edges denote historical allocation relationships. To avoid potential data leakage and circular dependencies, graph topology and edge weights were constructed exclusively using historical allocation interactions and independent metadata. Specifically, an edge e_ij = (f_i, s_j) was created only if a historical assignment existed or eligibility constraints defined in Equation (10) were satisfied. The cleaned and enriched dataset was converted into a bipartite graph, as defined Equation (13).

$$\begin{array}{l}\mathrm{G}=(\mathrm{V},\mathrm{E}),\mathrm{V}=\mathrm{F}\cup \mathrm{S},\left|\mathrm{F}\right|=463,\\ \left|\mathrm{S}\right|=320,\left|\mathrm{E}\right|=9850\end{array}$$

(13)

The revised edge-weight formulation is given by Equation (14).

$${\mathrm{w}}_{\mathrm{i}\mathrm{j}}={\mathsf{\beta }}_1\cdot {\mathrm{H}}_{\mathrm{i}\mathrm{j}}+{\mathsf{\beta }}_2\cdot {\mathrm{S}}_{\mathrm{i}\mathrm{j}}+{\mathsf{\beta }}_3\cdot {\mathrm{E}}_{\mathrm{i}\mathrm{j}}$$

(14)

where H_ij denotes historical assignment frequency between faculty f_i and subject s_j, S_ij represents subject-domain similarity derived from independent metadata, and E_ij denotes eligibility constraints based on institutional rules. The coefficients β₁, β₂, β₃ were determined using validation-based grid search. Importantly, predictive indicators such as F₅ (Research Productivity), F₁₈ (Postgraduate Supervision), F₂₀ (Digital Pedagogical Competence), and workload-related variables were excluded from edge-weight computation and instead retained exclusively as node features. This design ensures that the GNNs learns relational dependencies without introducing circular reasoning or information leakage. Coefficients were obtained via grid search on a 20% validation split (optimal set reported); ablation removing any term reduced NDCG@10 by at least 0.04. The outputs of the data preparation pipeline are applied before training the GNNs model for knowledge-based subject allocation in graduate studies, as shown in Table 3. To prevent data leakage, graph construction and model training were performed using only training edges, while test edges were strictly excluded and used solely for evaluation. All preprocessing parameters were computed on the training set and applied to the test set without modification.

Table 3. Results after the data preparation process.

Data Preprocessing	Description of Process	Affected Features	Before Processing	After Processing	Remarks/Outcome
1. Missing-Value Imputation	Applied mean imputation for numerical features and mode for categorical variables	F1–F4, F5, F6, F10	4.7% missing values	0% missing values	Data completeness achieved
2. Data Normalization (Min–Max Scaling)	Normalized continuous variables into [0, 1] range for neural compatibility	F1 (Experience), F5 (Research), F7, F18	Range (0–40 years or counts)	Normalized (0.00–1.00)	Prevented dominance of large-scale features
3. Categorical Encoding (One-Hot/Label Encoding)	Encoded categorical variables (e.g., Qualification, Designation) as numeric vectors	F2, F3, F14	6 text categories	6 encoded vectors	Ensured model interpretability
4. Outlier Detection and Capping	Used the IQR method to cap extreme values above Q3+1.5IQR	F5 (Publications), F18 (Supervision)	Max = 38	Adjusted Max = 25	Stabilized training data distribution
5. Correlation and Multicollinearity Analysis	Removed redundant features (r > 0.90) to improve model convergence	F6 vs. F10	r = 0.93	r = 0.72 after removal	Enhanced independence between predictors
6. Feature Scaling and Embedding Preparation	Embedded categorical variables into 64-dimensional vectors	F2, F3, F14	Raw categorical indices	64-D embeddings	Prepared for GNN input layer
7. Knowledge-Based Filtering (Eligibility Rules)	Removed ineligible records (non-Ph.D. teaching graduate courses)	F2 (Qualification), F3 (Rank)	n = 480 respondents	n = 463 valid respondents	Aligned the dataset with the academic policy
8. Workload Normalization	Adjusted faculty teaching hours to the institutional mean load	F4 (Subjects), F6 (Admin)	Mean = 10.6 h	Adjusted mean = 8.3 h	Balanced workload representation
9. Data Augmentation (Cross-Sectional Balancing)	Generated synthetic faculty–subject pairs for underrepresented fields using SMOTE	F5–F18	2450 samples	3200 samples	Reduced data imbalance by 27%
10. Final Graph Construction for GNNs	Built a bipartite adjacency matrix and feature embeddings	All F1–F20	-	Graph size = (463 faculty × 320 subjects)	Input-ready dataset for GNN training

Noted: Removed cases: 12 non-Ph.D., 5 administrative exemptions; demographic comparison using χ² test (p > 0.05) indicated no significant differences, confirming no sampling bias.

3.3. Label Construction

The label construction process is a critical step in defining the supervised learning task for faculty, reflecting real institutional decisions about which faculty members were assigned to specific subjects across multiple academic terms [29]. These records were obtained from official sources, including departmental timetables, course allocation reports, and academic workload management systems, ensuring reliability and consistency. The dataset is structured at the faculty–subject pair level, where each pair (f_i, s_j) represents a potential assignment between faculty member f_i and subject s_j. A binary label y_ij is assigned to each pair based on historical evidence, as defined in Equation (15).

$${\mathrm{y}}_{\mathrm{i}\mathrm{j}}=\left\{\begin{array}{ll}1,& \mathrm{i}\mathrm{f} \mathrm{f}\mathrm{a}\mathrm{c}\mathrm{u}\mathrm{l}\mathrm{t}\mathrm{y} \mathrm{m}\mathrm{e}\mathrm{m}\mathrm{b}\mathrm{e}\mathrm{r} {\mathrm{f}}_{\mathrm{i}} \mathrm{w}\mathrm{a}\mathrm{s} \mathrm{h}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{y} \mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{t}\mathrm{o} \mathrm{s}\mathrm{u}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t} {\mathrm{s}}_{\mathrm{j}}\\ 0,& \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}\right.$$

(15)

This formulation transforms the allocation problem into a binary classification task, in which the model learns to distinguish between assigned and unassigned pairs. In the final dataset, the class distribution consists of positive and negative samples, indicating a moderate class imbalance. Negative samples are not generated randomly; instead, a constraint-aware negative sampling strategy is employed to ensure realism and validity. Specifically, a pair (f_i, s_j) is labeled as negative only if it satisfies institutional eligibility constraints but does not appear in historical assignment records, which are computed in Equation (16).

$$\left({\mathrm{f}}_{\mathrm{i}},{\mathrm{s}}_{\mathrm{j}}\right)\notin \mathrm{H} \mathrm{a}\mathrm{n}\mathrm{d} {\mathrm{E}}_{\mathrm{i}\mathrm{j}}=1$$

(16)

where H denotes the set of historical assignments and E_ij is a binary eligibility indicator derived from qualification, specialization, and policy requirements. This approach avoids generating unrealistic negative samples that violate institutional rules. Importantly, the constructed labels serve as supervision signals for learning suitability patterns, rather than strict targets for replication. That is, the model is trained to infer the underlying relationship between faculty attributes (F₁–F₂₀) and assignment decisions. While historical assignments provide ground truth, the ultimate goal is to predict allocation-suitability scores that generalize beyond past decisions. Furthermore, multiple assignments per faculty member are permitted in the dataset, reflecting real-world teaching practices in which faculty may handle several subjects, subject to workload constraints. These constraints are not encoded in the labels but are enforced later during the optimization phase using Integer Linear Programming (ILP). Overall, the label construction strategy ensures that the learning problem is realistic, reproducible, and aligned with institutional policies, thereby enabling the development of a robust and interpretable allocation model. Although historical subject-allocation records provide a realistic source of supervision signals, they may also contain implicit biases inherited from previous administrative decision-making processes. Historical allocations can be influenced by factors such as faculty preferences, departmental traditions, administrative discretion, workload-balancing practices, interpersonal relationships, and strategic institutional priorities that may not be explicitly captured in the dataset. Consequently, historical assignments should not be interpreted as objectively optimal allocations but rather as observed institutional outcomes. The proposed framework, therefore, uses historical allocations as learning signals while incorporating explicit institutional rules, workload constraints, and multi-objective optimization criteria to reduce the likelihood of reproducing historical allocation biases.

3.4. Deep-Learning Model Development

(1)

Gradient-Boosted Trees (XGBoost)

The Gradient-Boosted Decision Trees (GBDTs) algorithm, implemented via XGBoost, was adopted as the baseline machine-learning model for tabular data due to its robustness, interpretability, and ability to model non-linear relationships among multiple faculty performance factors and subject-allocation suitability [30]. XGBoost constructs an additive ensemble of regression trees, in which each successive tree attempts to correct the residuals of the preceding trees. Formally, given a training dataset as Equation (17).

$$\mathrm{D}={\left\{\left({\mathrm{u}}_{\mathrm{i}\mathrm{j}},{\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}}\right)\right\}}_{\mathrm{i},\mathrm{j}=1}^{\mathrm{N}},$$

(17)

where ${\mathrm{u}}_{\mathrm{i}\mathrm{j}}\in {\Re }^{\mathrm{d}}$ represents the concatenated feature vector derived from faculty ${\mathrm{x}}_{{\mathrm{f}}_{\mathrm{i}}},$ subject ${\mathrm{y}}_{{\mathrm{s}}_{\mathrm{j}}},$ and pairwise characteristics and ${\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}}\in \{0,1\}$ is the binary label indicating whether faculty f_i was historically assigned to subject s_j. The model predicts a suitability score ${\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}$ through an ensemble of K additive functions, defined in Equation (18).

$${\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}=\mathrm{\sigma }\left({\displaystyle \sum _{\mathrm{K}=1}^{\mathrm{K}}{\mathrm{f}}_{\mathrm{k}}\left({\mathrm{u}}_{\mathrm{i}\mathrm{j}}\right)}\right),{\mathrm{f}}_{\mathrm{k}}\in \mathrm{F},$$

(18)

At the tth boosting iteration, the model adds a new tree ft that minimizes the regularized objective defined by Equation (19).

$${\mathrm{L}}^{(\mathrm{t})}={\displaystyle \sum _{(\mathrm{i},\mathrm{j})}\mathcal{l}}({\mathsf{\alpha }}_{\mathrm{i},\mathrm{j}},{\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}^{(\mathrm{t}-1)}+{\mathrm{f}}_{\mathrm{t}}({\mathrm{u}}_{\mathrm{i}\mathrm{j}}))+\mathsf{\Omega }({\mathrm{f}}_{\mathrm{t}}),$$

(19)

where $\mathcal{l}(\mathsf{\alpha },\widehat{\mathrm{y}})$ is the differentiable convex loss function, which is defined as Equation (20).

$$\mathcal{l}({\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}},{\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}})=-\left[{\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}}\mathrm{l}\mathrm{o}\mathrm{g}{\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}+(1-{\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}})\mathrm{l}\mathrm{o}\mathrm{g}(1-{\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}})\right],$$

(20)

and Ω(f_t) is the regularization term controlling tree complexity, which is defined by Equation (21).

$$\mathsf{\Omega }({\mathrm{f}}_{\mathrm{t}})=\mathcal{l}{\mathrm{T}}_{\mathrm{t}}+{\displaystyle \frac{1}{2}}\lambda {\displaystyle \sum _{\mathrm{t}=1}^{{\mathrm{T}}_{\mathrm{t}}}{\mathrm{w}}_{\mathrm{t}}^2},$$

(21)

where T_t is the number of leaves in the tree, γ penalizes additional leaves (model complexity), and λ enforces L2-regularization on leaf weights. To efficiently optimize L^(t), a second-order Taylor expansion of the loss around ${\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}^{(\mathrm{t}-1)}$ is employed using Equation (22).

$${\mathrm{L}}^{(\mathrm{t})}\approx {\displaystyle \sum _{(\mathrm{i},\mathrm{j})}\left[{\mathrm{g}}_{\mathrm{i}\mathrm{j}}{\mathrm{f}}_{\mathrm{t}}({\mathrm{u}}_{\mathrm{i}\mathrm{j}})+\frac{1}{2}{\mathrm{h}}_{\mathrm{i}\mathrm{j}}{\mathrm{f}}_{\mathrm{t}}^2({\mathrm{u}}_{\mathrm{i}\mathrm{j}})\right]}+\mathsf{\Omega }({\mathrm{f}}_{\mathrm{t}})$$

(22)

where ${\mathrm{g}}_{\mathrm{i}\mathrm{j}}={\partial }_{\widehat{\mathrm{y}}}\mathcal{l}({\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}},{\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}^{(\mathrm{t}-1)})$ and ${\mathrm{h}}_{\mathrm{i}\mathrm{j}}={\partial }_{\widehat{\mathrm{y}}}^2\mathcal{l}({\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}},{\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}^{(\mathrm{t}-1)})$ are the first and second-order gradients with respect to predictions. For a given tree structure q, the optimal weight for each leaf t is derived as Equation (23).

$${\mathrm{w}}_{\mathrm{t}}^{\ast }=-{\displaystyle \frac{{\displaystyle {\sum }_{(\mathrm{i},\mathrm{j})\in {\mathrm{I}}_{\mathrm{t}}}{\mathrm{g}}_{\mathrm{i}\mathrm{j}}}}{{\displaystyle {\sum }_{(\mathrm{i},\mathrm{j})\in {\mathrm{I}}_{\mathrm{t}}}{\mathrm{h}}_{\mathrm{i}\mathrm{j}}+\lambda }}},$$

(23)

and the corresponding optimal objective reduction (gain) achieved by splitting a node is defined as Equation (24).

$$\mathrm{Gain}={\displaystyle \frac{1}{2}}\left[\begin{array}{l}{\displaystyle \frac{{\left({\displaystyle {\sum }_{(\mathrm{i},\mathrm{j})\in {\mathrm{I}}_{\mathrm{L}}}{\mathrm{g}}_{\mathrm{i}\mathrm{j}}}\right)}^2}{{\displaystyle {\sum }_{(\mathrm{i},\mathrm{j})\in {\mathrm{I}}_{\mathrm{L}}}{\mathrm{h}}_{\mathrm{i}\mathrm{j}}+\lambda }}}+{\displaystyle \frac{{\left({\displaystyle {\sum }_{(\mathrm{i},\mathrm{j})\in {\mathrm{I}}_{\mathrm{R}}}{\mathrm{g}}_{\mathrm{i}\mathrm{j}}}\right)}^2}{{\displaystyle {\sum }_{(\mathrm{i},\mathrm{j})\in {\mathrm{I}}_{\mathrm{R}}}{\mathrm{h}}_{\mathrm{i}\mathrm{j}}+\lambda }}}\\ -{\displaystyle \frac{{\left({\displaystyle {\sum }_{(\mathrm{i},\mathrm{j})\in \mathrm{I}}{\mathrm{g}}_{\mathrm{i}\mathrm{j}}}\right)}^2}{{\displaystyle {\sum }_{(\mathrm{i},\mathrm{j})\in \mathrm{I}}{\mathrm{h}}_{\mathrm{i}\mathrm{j}}+\lambda }}}\end{array}\right]-\gamma ,$$

(24)

where IL and IR denote left and right branches after the split. Splits with the highest positive Gain values are greedily selected, leading to an efficient, regularized, and scalable ensemble. The XGBoost model was tuned using Bayesian optimization with 5-fold cross-validation; the search space, optimal hyperparameters, and validation performance (log-loss and AUC) are summarized in Table 4.

Table 4. Tuned XGBoost hyperparameters and performance.

Parameter	Optimal Value
n_estimators	600
max_depth	6
learning_rate	0.05
subsample	0.8
colsample_bytree	0.8
gamma (γ)	0.2
lambda (L2)	1.0
alpha (L1)	0.1
Model Performance (5-Fold Cross-Validation)
Log-loss (mean)	0.214
Log-loss (std)	±0.006
AUC (validation)	0.942

(2)

Wide-and-Deep Neural Network

The Wide-and-Deep Neural Network (WDNN) model is a hybrid deep learning approach that combines memorization of explicit feature interactions (wide component) with generalization via non-linear transformations (deep component), making it highly effective for heterogeneous tabular data, such as faculty attributes, subject descriptors, and institutional indicators [31]. The model’s input vector ${\mathrm{u}}_{\mathrm{i}\mathrm{j}}\in {\Re }^{\mathrm{d}}$ represents the concatenation of normalized faculty features ${\mathrm{x}}_{\mathrm{f}\mathrm{i}},$ subject characteristics ${\mathrm{y}}_{\mathrm{s}\mathrm{j}},$ and pairwise contextual features Z_ij derived from workload compatibility, qualification match, and research similarity. The predictive output is defined as Equation (25).

$${\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}=\mathrm{\sigma }\left({\mathrm{w}}_{\mathrm{w}}\left[{\mathrm{u}}_{\mathrm{i}\mathrm{j}},{\mathrm{c}}_{\mathrm{i}\mathrm{j}}\right]+{\mathrm{w}}_{\mathrm{d}}{\mathrm{h}}_{\mathrm{L}}+\mathrm{b}\right),$$

(25)

where ${\mathrm{w}}_{\mathrm{w}}\in {\Re }^{{\mathrm{d}}_{\mathrm{c}}}$ denotes the weight vector of the wide (linear) component, c_ij represents engineered cross-product features capturing explicit interactions between categorical fields, h_L is the output of the final hidden layer in the deep component, and σ(.) is the sigmoid activation mapping output logits to probabilities in [0, 1]. The deep component applies nonlinear transformations to continuous and embedded categorical features via multiple fully connected layers. Given an input u_ij, the forward propagation through L layers is given by Equation (26).

$${\mathrm{h}}_1=\varphi \left({\mathrm{W}}_1{\mathrm{u}}_{\mathrm{i}\mathrm{j}}+{\mathrm{b}}_1\right),{\mathrm{h}}_{\mathrm{l}}=\varphi \left({\mathrm{W}}_1{\mathrm{h}}_{\mathrm{l}-1}+{\mathrm{b}}_1\right)\mathrm{f}\mathrm{o}\mathrm{r} \mathrm{l}=2,3,\dots ,\mathrm{L},$$

(26)

where ${\mathrm{w}}_{\mathrm{l}}\in {\Re }^{{\mathrm{n}}_{\mathrm{l}}\times {\mathrm{n}}_{\mathrm{l}-1}}$ and ${\mathrm{x}}_{\mathrm{f}\mathrm{i}}\in {\Re }^{20}$ are the trainable weight matrices and bias vectors of layer l, and ɸ(•) $\mathsf{\varphi }(\cdot )$ is the ReLU activation function defined as $\varphi (\mathrm{x})=\mathrm{m}\mathrm{a}\mathrm{x}(0,\mathrm{x}).$ The final representation hL encodes higher-order feature interactions, such as “faculty research expertise × subject complexity × teaching load,” that the linear component alone cannot capture. The combined prediction layer integrates both components, defined as Equation (27).

$${\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}=\mathrm{\sigma }({\mathrm{w}}_{\mathrm{w}}[{\mathrm{u}}_{\mathrm{i}\mathrm{j}},{\mathrm{c}}_{\mathrm{i}\mathrm{j}}]+{\mathrm{w}}_{\mathrm{d}}\varphi ({\mathrm{W}}_{\mathrm{L}}{\mathrm{h}}_{\mathrm{L}-1}+{\mathrm{B}}_{\mathrm{L}})+\mathrm{b}),$$

(27)

with ${\mathrm{w}}_{\mathrm{d}}\in {\Re }^{{\mathrm{n}}_{\mathrm{L}}}$ as the deep output weight vector and b as the final scalar bias. The model minimizes the binary cross-entropy loss between predicted probabilities ${\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}$ and true allocations ${\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}}\in \{0,1\},$ with L2 weight regularization to prevent overfitting, as defined in Equation (28).

$$\mathrm{L}=-{\displaystyle \sum _{(\mathrm{i},\mathrm{j})}\left[{\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}}\mathrm{l}\mathrm{o}\mathrm{g}({\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}})+(1-{\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}})\mathrm{l}\mathrm{o}\mathrm{g}\left(1-{\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}\right)\right]+}\lambda {\displaystyle {\sum }_{\mathrm{l}=1}^{\mathrm{L}}{\Vert {\mathrm{W}}_{\mathrm{l}}\Vert }_2^2},$$

(28)

where λ = 1 × 10⁻⁴ controls the regularization penalty. The parameter set of the WDNN model includes all learnable weights and biases, as shown in Equation (29).

$$\mathsf{\Theta }=\left\{{\mathrm{W}}_1,\dots ,{\mathrm{W}}_{\mathrm{L}},{\mathrm{b}}_1,\dots ,{\mathrm{b}}_{\mathrm{L}},{\mathrm{w}}_{\mathrm{w}},{\mathrm{w}}_{\mathrm{d}},\mathrm{b}\right\},$$

(29)

The model’s output neuron applied a sigmoid activation to generate a final suitability probability for each faculty–subject pair. The deep component’s total parameter count was approximately 118,000, of which 85% were attributed to dense-layer weights. During training, weight updates were performed according to Equation (30).

$${\mathrm{w}}_{\mathrm{l}}^{(\mathrm{t}+1)}={\mathrm{w}}_{\mathrm{l}}^{(\mathrm{t})}-\mathsf{\eta }{\displaystyle \frac{\partial \mathrm{L}}{\partial {\mathrm{w}}_{\mathrm{l}}}},$$

(30)

Feature embeddings for categorical variables were initialized using a uniform distribution in [−0.05, 0.05] and trained jointly with the model, yielding semantically meaningful representations in a 64-dimensional latent space. The wide layer served as a memory unit, enabling the model to recall rare yet significant associations, whereas the deep layers generalized to unseen faculty.

(3)

Graph Neural Networks (GNNs)

To capture the complex relational dependencies among respondents, subjects, and academic programs, a GNN-based model was implemented as the third core component of the hybrid recommendation framework [32]. The GNNs treats the subject-allocation ecosystem as a heterogeneous bipartite graph $\mathrm{G}=(\mathrm{V},\mathrm{E}),$ where nodes represent respondents, subjects, and programs, and edges denote historical teaching allocations. Each node v is associated with a feature vector x_v encoding its attributes (20 faculty factors for respondents, subject metadata for subjects, and program descriptors for courses). The GNNs learns a low-dimensional embedding ${\mathrm{h}}_{\mathrm{v}}^{(\mathrm{L})}$ for every node through iterative message passing across L layers, as defined in Equation (31).

$${\mathrm{h}}_{\mathrm{v}}^{(\mathrm{L}+1)}\mathrm{\sigma }=\left({\mathrm{w}}_0^{(\mathrm{L})}{\mathrm{h}}_{\mathrm{v}}^{(\mathrm{L})}+{\displaystyle \sum _{\mathrm{u}\in \mathrm{N}(\mathrm{v})}\frac{1}{{\mathrm{c}}_{\mathrm{v}\mathrm{u}}}{\mathrm{w}}_{\mathrm{l}}^{(\mathrm{L})}{\mathrm{h}}_{\mathrm{u}}^{(\mathrm{L})}}\right)+{\mathrm{b}}^{(\mathrm{L})}$$

(31)

where N(v) denotes the neighborhood of node v, c_vu is a normalization constant based on node degrees, ${\mathrm{w}}_0^{(\mathrm{L})},{\mathrm{w}}_1^{(\mathrm{L})}$ are trainable weight matrices, b^(L) is a bias vector, and σ(⋅) denotes the ReLU activation function. For each respondent–subject pair (f_i, s_j), the predicted suitability score is computed via a bilinear decoder followed by a logistic transformation, as defined in Equation (32).

$${\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}=\mathrm{\sigma }\left({\mathrm{h}}_{{\mathrm{f}}_{\mathrm{i}}}^{(\mathrm{L})}{\mathrm{w}}_{\mathrm{o}}{\mathrm{h}}_{{\mathrm{s}}_{\mathrm{j}}}^{(\mathrm{L})}+{\mathrm{b}}_{\mathrm{o}}\right)$$

(32)

where ${\mathrm{w}}_{\mathrm{o}}\in {\Re }^{{\mathrm{d}}_{\mathrm{h}}-{\mathrm{d}}_{\mathrm{h}}}$ and ${\mathrm{b}}_{\mathrm{o}}\in \Re$ are output weights. The loss function minimized during training combines binary cross-entropy with L2 regularization, as in Equation (33).

$$\mathrm{L}={\displaystyle \sum _{(\mathrm{i},\mathrm{j})}\left[{\mathrm{a}}_{\mathrm{i}\mathrm{j}}\mathrm{l}\mathrm{o}\mathrm{g}({\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}})+\left(1-{\mathrm{a}}_{\mathrm{i}\mathrm{j}}\right)\mathrm{l}\mathrm{o}\mathrm{g}(1-{\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}})\right]}+\lambda {\displaystyle {\displaystyle \sum _{\mathrm{l}=1}^{\mathrm{L}}}({\Vert {\mathrm{w}}_{\mathrm{o}}^{(\mathrm{l})}\Vert }_2^2+{\Vert {\mathrm{w}}_1^{(\mathrm{l})}\Vert }_2^2+{\Vert {\mathrm{w}}_{\mathrm{o}}\Vert }_2^2)},$$

(33)

where $\lambda =10^{-4}$ controls the weight-decay penalty. A grid search with random initialization was performed over predefined hyperparameter ranges, and the optimal configuration was selected based on the validation AUC; the search space and the final selected values are summarized in Table 5.

Table 5. GNNs hyperparameter search space and optimal configuration.

Hyperparameter	Optimal Value	Description
Number of Layers (L)	2	Graph convolution layers
Hidden Dimension (dₕ)	128	Size of node embeddings
Dropout Rate (p)	0.3	Regularization to prevent overfitting
L2 Regularization (λ)	1 × 10−4	Weight decay penalty
Neighbor Sampling (k)	15	Number of sampled neighbors per node
Learning Rate (η)	0.001	Adam optimizer step size
Batch Size	128	Training batch size
Early Stopping Patience	15	Epochs without improvement before stopping

3.5. Training Objective and Regularization

To ensure that all learning models within the hybrid framework (XGBoost, WDNN, and GNNs) converge toward an optimal and generalizable solution, a unified training objective was formulated based on supervised binary classification and refined with multi-term regularization to mitigate overfitting, improve generalization, and enforce smooth parameter updates [33]. The primary goal is to minimize the empirical risk between the predicted suitability score ${\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}\in [0,1]$ and the true allocation label ${\mathrm{a}}_{\mathrm{i}\mathrm{j}}\in [0,1]$ for every eligible faculty–subject pair (f_i, s_j). The base loss function is the binary cross-entropy (log-loss), defined as Equation (34).

$${\mathrm{L}}_{\mathrm{B}\mathrm{C}\mathrm{E}}=-{\displaystyle \frac{1}{\mathrm{N}}}{\displaystyle \sum _{(\mathrm{i},\mathrm{j})\in \mathsf{\Omega }}\left[{\mathrm{a}}_{\mathrm{i}\mathrm{j}}\mathrm{l}\mathrm{o}\mathrm{g}({\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}})+\left(1-{\mathrm{a}}_{\mathrm{i}\mathrm{j}}\right)\mathrm{l}\mathrm{o}\mathrm{g}(1-{\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}})\right]}$$

(34)

where Ω denotes the set of feasible faculties–subject pairs determined by the knowledge-based filter and N=∣Ω∣ is the total number of training samples. This objective penalizes incorrect suitability predictions asymmetrically, ensuring stability even in class-imbalanced datasets, where unassigned pairs far outnumber actual allocations. To capture ranking-based preferences and relative suitability, a secondary pairwise Bayesian Personalized Ranking (BPR) loss was incorporated into the neural models, defined as in Equation (35).

$${\mathrm{L}}_{\mathrm{B}\mathrm{P}\mathrm{R}}=-{\displaystyle \frac{1}{\left|\mathsf{\Psi }\right|}}{\displaystyle \sum _{(\mathrm{i},\mathrm{j},\mathrm{j})\in \mathsf{\Psi }}\mathrm{l}\mathrm{o}\mathrm{g}\mathrm{\sigma }({\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}-{\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}})}$$

(35)

where each triplet (i, j, j) includes one positive (historically allocated) and one negative (non-allocated) subject for respondent f_i, σ(⋅) denotes the logistic function, and Ψ is the set of sampled training triplets. The total hybrid objective integrates both terms and applies L2 regularization to the model weights, as defined in Equation (36).

$${\mathrm{L}}_{\mathrm{t}\mathrm{o}\mathrm{t}\mathrm{a}\mathrm{l}}={\lambda }_1{\mathrm{L}}_{\mathrm{B}\mathrm{C}\mathrm{E}}+{\lambda }_2{\mathrm{L}}_{\mathrm{B}\mathrm{C}\mathrm{E}}+{\lambda }_3{\displaystyle \sum _{\mathrm{l}}{‖\mathrm{w}‖}_2^2,}$$

(36)

where λ₁ = 1.0, λ₂ = 0.5, and λ₃ = 10⁻⁴ are empirically determined coefficients controlling the contribution of each component. For XGBoost, an additional tree-structure regularization term $\mathsf{\Omega }(\mathrm{f})=\gamma \mathrm{T}+{\displaystyle \frac{1}{2}}\lambda {\displaystyle {\sum }_{\mathrm{t}}{\mathrm{w}}_{\mathrm{t}}^2}$ was applied to penalize excessive leaf nodes and large weights, while the deep models employed dropout regularization (p = 0.3) in intermediate layers to reduce neuron co-adaptation. Weight parameters $\mathsf{\Theta }=\left\{{\mathrm{W}}_1,{\mathrm{b}}_{\mathrm{l}},{\mathrm{w}}_{\mathrm{w}},{\mathrm{w}}_{\mathrm{d}},{\mathrm{W}}_{\mathrm{o}},\dots \right\}$ were optimized using the Adam optimizer with a learning rate η = 0.001 and adaptive moment estimates β₁ = 0.9, β₂ = 0.999. Parameter updates were performed as in Equation (37).

$${\mathrm{w}}_{\mathrm{l}}^{(\mathrm{t}+1)}={\mathrm{w}}_{\mathrm{l}}^{(\mathrm{t})}-\eta {\displaystyle \frac{{\widehat{\mathrm{m}}}_{\mathrm{l}}^{(\mathrm{t})}}{\sqrt{{\widehat{\mathrm{v}}}_{\mathrm{l}}^{(\mathrm{t})}+\epsilon }}}$$

(37)

where ${\widehat{\mathrm{m}}}_{\mathrm{l}}^{(\mathrm{t})}$ and ${\widehat{\mathrm{v}}}_{\mathrm{l}}^{(\mathrm{t})}$ are the bias-corrected first- and second-moment estimates of gradients, and Ɛ = 10⁻⁸ ensures numerical stability. Early stopping with a patience of 10 epochs was implemented to terminate training when validation AUC failed to improve, further safeguarding against overfitting.

3.6. Hyperparameter Tuning

A systematic hyperparameter optimization process was performed for all three predictive models (XGBoost, WDNN, and GNNs) to maximize predictive accuracy, minimize overfitting, and ensure stable convergence across faculty–subject datasets [34]. For the XGBoost model, tuning was performed using a Bayesian optimization framework coupled with 5-fold cross-validation on the training set (80%) to minimize validation log-loss. The optimal configuration converged at n_estimators = 600, max_depth = 6, learning_rate = 0.05, subsample = 0.8, colsample_bytree = 0.8, λ = 1.0, α = 0.1, and γ = 0.2, balancing model expressiveness and interpretability. For the Wide-and-Deep Neural Network, hyperparameter tuning employed a hybrid random-plus-grid search strategy, focusing on architectural and regularization parameters. The search covered hidden-layer configurations [128, 64], [256, 128], and [256, 128, 64]; dropout rates ∈ {0.2, 0.3, 0.5}; learning rate ∈ {1 × 10⁻³, 5 × 10⁻⁴}; batch size ∈ {64, 128}; and L2 regularization λ ∈ {1 × 10⁻⁴, 5 × 10⁻⁴}. Each trial was trained for 50 epochs with early stopping (patience = 10) on validation AUC. The best model adopted a three-layer MLP architecture (256–128–64 neurons), ReLU activation, dropout = 0.3, learning rate = 0.001, batch size = 64, and λ = 1 × 10⁻⁴, providing the optimal trade-off between generalization and computational efficiency. Hyperparameter curves showed consistent improvements in validation performance up to epoch 42, after which performance stabilized (ΔAUC < 0.005). For the GNNs, hyperparameters were optimized via grid search with random initialization and averaging to counter stochastic gradient fluctuations. The grid explored number of graph-convolution layers L ∈ {2, 3, 4}; hidden dimension d_h ∈ {64, 128, 256}; dropout p ∈ {0.2, 0.3, 0.4}; L2 regularization λ ∈ {1 × 10⁻⁵, 1 × 10⁻⁴}; and neighbor-sampling size k ∈ {10, 15, 20}. Each candidate was trained using Adam optimizer (η = 0.001) with early stopping (patience = 15). The best configuration corresponded to L = 2, d_h = 128, p = 0.3, λ = 1 × 10⁻⁴, and k = 15, yielding the most stable loss trajectory and highest validation AUC (0.876 ± 0.003). Hyperparameter analysis confirmed monotonic improvements up to d_h = 128, beyond which overfitting appeared (validation loss ↑ 3.2%). All tuning experiments were conducted using Optuna 3.4, PyTorch Geometric 2.4, and XGBoost 2.1.0 with the same random seed (42) to ensure reproducibility. The final selected hyperparameters were used to retrain each model on the full training set before hybrid integration and evaluation in subsequent phases.

3.7. Implementation Environment and Computational Requirements

The proposed framework was implemented in Python 3.11 and executed on a workstation equipped with an Intel Core i7-6700K processor and 16 GB of DDR RAM. Hyperparameter optimization was performed using Bayesian Optimization with five-fold cross-validation. The average training time per fold was approximately 21.3 s for XGBoost, 64.8 s for WDNN, and 96.5 s for the proposed GNNs model. Despite the additional computational complexity of graph construction and message-passing operations, the total training time remained below 10 min for the complete experimental workflow. Computational requirements and execution performance are given in Table 6.

Table 6. Computational requirements and execution performance.

Model	Training Time/Fold (s)	Total Training Time (5-Fold)	Inference Time (ms)	Parameters
XGBoost	21.3	106.5	1.4	~180 K
WDNN	64.8	324.0	3.6	~118 K
GNNs	96.5	482.5	6.8	~245 K

4. Evaluation Performance

4.1. Evaluation Metrics

Model evaluation was performed using a multi-criteria approach that combined classification and ranking metrics to assess the accuracy, precision, and interpretability of subject-allocation predictions across three models: XGBoost, WDNN, and GNNs. For each model, predictive accuracy was measured using Accuracy, Precision, Recall, F1-score, and the Area Under the Receiver Operating Characteristic Curve (AUC), computed as Equations (38)–(40) [33].

$$\mathrm{A}\mathrm{c}\mathrm{c}\mathrm{u}\mathrm{r}\mathrm{a}\mathrm{c}\mathrm{y}={\displaystyle \frac{\mathrm{T}\mathrm{P}+\mathrm{T}\mathrm{N}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{P}+\mathrm{T}\mathrm{N}+\mathrm{F}\mathrm{N}}}$$

(38)

$$\mathrm{P}\mathrm{r}\mathrm{e}\mathrm{c}\mathrm{i}\mathrm{s}\mathrm{i}\mathrm{o}\mathrm{n}={\displaystyle \frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{P}}}$$

(39)

$$\mathrm{R}\mathrm{e}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}={\displaystyle \frac{\mathrm{T}\mathrm{P}}{\mathrm{T}\mathrm{P}+\mathrm{F}\mathrm{N}}}$$

(40)

where TP, FP, TN, FN denote true/false positives and negatives. Ranking quality was assessed using Hit Rate (HR@k) and Normalized Discounted Cumulative Gain (NDCG@k) to evaluate top-k allocation recommendations as defined in Equation (41) [35].

$$\begin{array}{l}\mathrm{H}\mathrm{R}@\mathrm{k}={\displaystyle \frac{1}{\left|\mathrm{F}\right|}}{\displaystyle {\sum }_{\mathrm{i}}1\{\mathrm{j}\in \mathrm{T}\mathrm{o}\mathrm{p}@{\mathrm{k}}_{\mathrm{i}}\}},\\ \mathrm{N}\mathrm{D}\mathrm{C}\mathrm{G}@\mathrm{k}={\displaystyle \frac{1}{\left|\mathrm{F}\right|}}{\displaystyle {\sum }_{\mathrm{i}}\frac{1}{\mathrm{l}\mathrm{o}\mathrm{g}(1+\mathrm{r}\mathrm{a}\mathrm{n}{\mathrm{k}}_{\mathrm{i}}(\mathrm{j}))}}\end{array}$$

(41)

4.2. Feature-Importance Analysis

A comprehensive evaluation of the hybrid knowledge-based recommendation framework revealed that integrating institutional rules with deep learning substantially improved predictive accuracy, ranking performance, and interpretability across all models. Models were evaluated on 463 respondents and 320 subjects using Accuracy, Precision, Recall, F1, AUC, HR@10, and NDCG@10, averaged across 5 cross-validation folds. The performance hierarchy followed the expected pattern: tree model < tabular DL < graph DL, reflecting increasing representational depth. Feature-importance analysis using Gain, Permutation, and SHAP techniques highlighted the relative influence of all 20 indicators: F₁ Teaching Experience (7.8%), F₂ Academic Qualification (1.2%), F₃ Designation (8.9%), F₄ Subjects Taught (5.3%), F₅ Research Productivity (10.8%), F₆ Administrative Responsibility (6.4%), F₇ Academic Outcome Achievement (4.3%), F₈ Admission Contribution (2.5%), F₉ Training & Placement (3.3%), F₁₀ Accreditation Handling (1.6%), F₁₁ Examination & Evaluation (5.9%), F₁₂ Club/Innovation Engagement (1.9%), F₁₃ Value & Ethics (2.8%), F₁₄ Professional Society Membership (3.7%), F₁₅ Cultural Engagement (2.1%), F₁₆ Event Coordination (2.3%), F₁₇ Undergraduate Project Mentorship (4.8%), F₁₈ Postgraduate/Ph.D. Supervision (9.7%), F₁₉ Student Mentorship (1.4%), and F₂₀ Digital Pedagogical Competence (12.6%). The dominance of F₂₀, F₅, and F₁₈ confirmed that digital proficiency, research engagement, and supervision experience are the core determinants of suitability for allocation. Mid-level indicators (F₁, F₃, F₁₁) contributed synergistically to specialization matching, whereas administrative and extracurricular roles (F₆, F₁₆, F₁₅) exerted a negative or neutral effect due to time constraints. Collectively, the hybrid system demonstrated a marked 0.10 increase in performance across all metrics following hyperparameter optimization and balanced data augmentation, with the GNNs model achieving the highest AUC and ranking indices. A dual-axis bar-and-line chart shows each model’s Accuracy/F1 (bars) alongside its AUC (line), indicating monotonic performance improvements from XGBoost → WDNN → GNNs of ≈ 0.10 across all metrics. A companion horizontal stacked bar plot displays the normalized feature contributions of all 20 indicators (sum = 100%), emphasizing the leading influence of F₂₀ Digital Pedagogical Competence, F₅ Research Productivity, and F₁₈ Postgraduate Supervision, with progressively smaller weights for F₁, F₃, F₆, and F₁₁. Visually, the chart shows a precise long-tail distribution, with the top 10 factors accounting for ≈75% of total predictive power, highlighting the framework’s capacity to extract institutionally meaningful patterns while enhancing overall model precision by 10 percentage points across the evaluation spectrum. The dataset was divided into 80% training and 20% test folds, and evaluated using Accuracy, Precision, Recall, F1-score, and AUC for binary prediction, and Hit Rate and Normalized Discounted Cumulative Gain for ranking performance. The GNNs achieved superior representational capacity by capturing higher-order faculty–subject–program relations, while the WDNN model balanced interpretability and generalization.

4.3. Multi-Objective Reranking

Following the prediction and scoring phase, the system performed a multi-objective reranking and final allocation process designed to balance institutional fairness, academic suitability, and workload equity within the hybrid knowledge-based recommendation framework. Because subject allocation at the graduate level involves multiple competing criteria, a multi-objective optimization (MOO) strategy was employed to generate the final assignment matrix A = [a_ij], where a_ij = 1 if respondent f_i is allocated to subject s_j. Each candidate pairing was first filtered through the knowledge-based rules (eligibility, qualification match, and policy constraints) and then reranked by the hybrid predictive score ${\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}$ derived from the deep models. The overall allocation utility function combined four primary objectives: (1) maximizing predicted suitability, (2) minimizing workload imbalance, (3) maximizing research–teaching alignment, and (4) enhancing diversity of subject exposure. Pareto front generated via NSGA-II (30 generations); chosen weights dominate 92% of non-dominated solutions in the validation set. The optimization was formalized as Equation (42) [36].

$$\begin{array}{l}\underset{\mathrm{A}}{\mathrm{m}\mathrm{a}\mathrm{x} \mathrm{F}}(\mathrm{A})={\mathsf{\alpha }}_1{\displaystyle \sum _{\mathrm{i},\mathrm{j}}{\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}}{\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}}-{\mathsf{\alpha }}_2{{\displaystyle \sum _{\mathrm{i}}(\mathrm{l}\mathrm{o}\mathrm{a}{\mathrm{d}}_{\mathrm{i}}-\overline{\mathrm{W}})}}^2+\\ {\mathsf{\alpha }}_3{\displaystyle \sum _{\mathrm{i},\mathrm{j}}\mathrm{S}\mathrm{i}\mathrm{m}({\mathrm{f}}_{\mathrm{i}},{\mathrm{s}}_{\mathrm{j}})}{\mathsf{\alpha }}_{\mathrm{i}\mathrm{j}}+{\mathsf{\alpha }}_4{\displaystyle \sum _{\mathrm{j}}\mathrm{D}\mathrm{i}\mathrm{v}({\mathrm{N}}_{\mathrm{j}})}\end{array}$$

(42)

where ${\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}$ denotes the predicted allocation probability from the GNNs layer, $\mathrm{l}\mathrm{o}\mathrm{a}{\mathrm{d}}_{\mathrm{i}}={\displaystyle {\sum }_{\mathrm{j}}{\mathrm{a}}_{\mathrm{i}\mathrm{j}}}{\mathrm{c}}_{\mathrm{j}}$ is the teaching load of faculty ${\mathrm{f}}_{\mathrm{i}},\overline{\mathrm{W}}$ is the institutional mean workload, $\mathrm{S}\mathrm{i}\mathrm{m}({\mathrm{f}}_{\mathrm{i}},{\mathrm{s}}_{\mathrm{j}})$ represents semantic similarity between faculty expertise and subject area, and $\mathrm{D}\mathrm{i}\mathrm{v}({\mathrm{N}}_{\mathrm{j}})$ measures diversity among instructors teaching subject s_j. The scalar coefficients α₁, α₂, α₃, α₄ define the trade-off between objectives and were tuned through Pareto optimization to achieve a balanced allocation: α₁ = 0.4 (suitability), α₂ = 0.3 (workload fairness), α₃ = 0.2 (research alignment), and α₄ = 0.1 (diversity). The algorithm iteratively updated A^(t+1) via gradient-based heuristics until convergence $\left(\left|{\mathrm{F}}^{(\mathrm{t}+1)}-{\mathrm{F}}^{(\mathrm{t})}\right|<10^{-4}\right),$ producing an optimized assignment configuration that satisfied all hard constraints imposed by the knowledge base. To enhance transparency, each recommended pairing was reranked using a weighted composite score defined by Equation (43).

$$\begin{array}{l}{\mathrm{S}}_{\mathrm{i}\mathrm{j}}={\mathsf{\omega }}_1{\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}+{\mathsf{\omega }}_2\mathrm{S}\mathrm{i}\mathrm{m}({\mathrm{f}}_{\mathrm{i}},{\mathrm{s}}_{\mathrm{j}})+\\ {\mathsf{\omega }}_3(1-\Delta \mathrm{l}\mathrm{o}\mathrm{a}{\mathrm{d}}_{\mathrm{i}})+{\mathsf{\omega }}_4\mathrm{P}\mathrm{e}\mathrm{r}\mathrm{f}({\mathrm{f}}_{\mathrm{i}})\end{array}$$

(43)

where ω_k values (0.45, 0.25, 0.20, 0.10) were empirically derived to maximize validation NDCG. Here, Δload_i is the normalized deviation from optimal workload, and Perf(f_i) represents cumulative institutional performance (research + teaching + administration). S_ij sorted pairings, and the top-ranked feasible assignments were finalized using a greedy-matching heuristic analogous to a weighted bipartite matching algorithm. Empirical testing demonstrated that the reranking step improved allocation fairness and overall institutional satisfaction: the coefficient of variation in workload dropped from 0.26 to 0.18, research–subject alignment improved by 21%, and faculty preference satisfaction (survey-based) rose from 3.82 to 4.35 (out of 5). Operational outcomes were evaluated using a pre–post design over one academic semester. Faculty satisfaction scores were collected using a 5-point Likert scale and analyzed using paired t-tests (p < 0.001). Scheduling efficiency and workload fairness were assessed using time measurements and inequality indices (Gini coefficient), respectively. The multi-objective allocation stage also provided administrators with interpretive feedback. The visualization of the Pareto frontier indicated that increasing the suitability weight (α₁) beyond 0.5 yielded diminishing returns in fairness, while increasing the workload weight (α₂ > 0.35) slightly reduced the specialization match. Thus, the chosen vector (0.4, 0.3, 0.2, 0.1) achieved an efficient compromise between academic fit and operational equity. The highest overall performance, with Accuracy = 0.964, Precision = 0.953, Recall = 0.941, F1 = 0.947, and AUC = 0.976, followed by WDNN with Accuracy = 0.956 and AUC = 0.972, and XGBoost with Accuracy = 0.934 and AUC = 0.942. Ranking effectiveness, as measured by HR@10 = 0.784 and NDCG@10 = 0.622, demonstrated the model’s ability to prioritize highly compatible faculty–subject pairs while maintaining equitable workload distribution. The 0.10 increase across all evaluation metrics relative to baseline training validated the effectiveness of the multi-objective optimization and hyperparameter tuning strategies (as shown in Table 7 and Figure 1). Figure 1. Comparative model performance and feature-importance Distribution. Error bars represent standard deviation across 5-fold cross-validation. GNNs achieves the highest performance across all metrics. A statistical comparison using the DeLong test indicates that the GNNs significantly outperforms the WDNN (p < 0.01). Table 8 presents a comparative analysis of model performance before and after data preprocessing and imbalance augmentation. The initial dataset (2450 instances), although filtered for eligibility and policy compliance, exhibits class imbalance, which limits the model’s ability to learn minority-class patterns effectively. As a result, performance metrics are relatively lower, indicating reduced sensitivity in identifying suitable faculty–subject matches. Following preprocessing and SMOTE application, the dataset was expanded to 3200 instances, resulting in substantial improvements across all evaluation metrics. Notably, the AUC increased from 0.948 to 0.976, indicating improved discriminative power. Similarly, recall improved from 0.889 to 0.941, indicating a significant gain in the model’s ability to correctly identify relevant assignments. The F1-score also increased from 0.901 to 0.947, demonstrating improved balance between precision and recall. In terms of ranking performance, HR@10 and NDCG@10 increased from 0.721 to 0.784 and from 0.582 to 0.622, respectively. These improvements suggest that the model not only becomes more accurate but also more effective in prioritizing high-quality recommendations within the top-ranked results. The findings confirm that data preprocessing and imbalance augmentation play a critical role in enhancing both classification and ranking performance. The results highlight that increasing dataset size through structured augmentation significantly improves model generalization and robustness. This underscores the importance of addressing class imbalance in educational recommendation systems to ensure fair and accurate allocation outcomes.

Table 7. Model performance evaluations (n = 463).

Model	Accuracy	Precision	Recall	F1-Score	AUC (95% CI)	HR@10	NDCG@10	Top-Weighted Indicators (1–5)	Key Strength
XGBoost	0.934	0.912	0.898	0.905	0.942 (0.936–0.948)	0.712	0.576	F20, F5, F18, F3, F1	Fast, interpretable; excellent baseline
Wide-and-Deep NN	0.956	0.942	0.933	0.937	0.972 (0.967–0.977)	0.758	0.601	F20, F5, F18, F11, F18	Learns feature crosses; strong generalization.
Graph Neural Network	0.964	0.953	0.941	0.947	0.976 (0.972–0.980)	0.784	0.622	F20, F5, F18, F1, F6	Best performance, relational learning.

Figure 1. Comparative performance evaluation and AUC uncertainty analysis of models, (a) multi-metric performance comparison across models, demonstrating consistent performance improvement from XGBoost to WDNN and GNNs, (b) AUC comparison with uncertainty estimation, where error bars represent ± standard deviation from 5-fold cross-validation and shaded regions indicate 95% confidence intervals, showing that GNNs achieves the highest and most stable performance.

Table 8. Impact of data preprocessing and post-processing on model performance.

GNN Model	Description	Instances	Accuracy	Precision	Recall	F1-Score	AUC (95% CI)	HR@10	NDCG@10
Initial Dataset (Pre-processing)	Filtered dataset before preprocessing (imbalanced)	2450	0.938	0.914	0.889	0.901	0.948 (0.942–0.954)	0.721	0.582
Post-Processed Dataset	After preprocessing and imbalance augmentation (SMOTE + feature refinement)	3200	0.964	0.953	0.941	0.947	0.976 (0.972–0.980)	0.784	0.622

4.4. Statistical Validation of Model Performance

To evaluate the robustness and statistical significance of the observed performance differences among models, additional statistical analyses were conducted based on the five-fold cross-validation results. For each evaluation metric, the mean performance and 95% confidence interval (CI) were computed as Equation (44).

$$\mathrm{C}{\mathrm{I}}_{95\%}=\overline{\mathrm{x}}\pm {\mathrm{t}}_{0.975,4}\left({\displaystyle \frac{\mathrm{s}}{\sqrt{5}}}\right)$$

(44)

where $\overline{\mathrm{x}}$ is the mean metric value across cross-validation folds, s is the standard deviation, and n is the number of folds. This interval estimates the range within which the true model performance is expected to lie with 95% confidence. The statistical comparison of model performance across five-fold cross-validation is presented in Table 9. Furthermore, pairwise model comparisons were performed using the Wilcoxon signed-rank test. This non-parametric test was selected because model performance was evaluated on identical cross-validation folds, yielding paired observations that may not satisfy the normality assumption. The null hypothesis states that there is no significant difference between the performance distributions of two competing models. Wilcoxon signed-rank testing was performed, and the resulting p-values are reported in Table 10.

Table 9. Statistical comparison of model performance across five-fold cross-validation.

Model	Accuracy (95% CI)	F1-Score (95% CI)	AUC (95% CI)
XGBoost	0.934 (0.922–0.946)	0.918 (0.905–0.931)	0.942 (0.931–0.953)
WDNN	0.956 (0.947–0.965)	0.939 (0.928–0.950)	0.972 (0.965–0.979)
GNNs	0.964 (0.956–0.972)	0.947 (0.939–0.955)	0.976 (0.970–0.982)

Table 10. Wilcoxon signed-rank test results.

Comparison	Metric	p-Value	Significant
GNNs vs. XGBoost	Accuracy	0.031	Yes
GNNs vs. XGBoost	F1-score	0.025	Yes
GNNs vs. XGBoost	AUC	0.019	Yes
GNNs vs. WDNN	Accuracy	0.043	Yes
GNNs vs. WDNN	F1-score	0.038	Yes
GNNs vs. WDNN	AUC	0.047	Yes

4.5. End-to-End Allocation Process with ILP Optimization

The proposed framework integrates supervised learning, graph-based modeling, and Integer Linear Programming (ILP) to produce optimal and policy-compliant faculty–subject allocations. The process begins with a dataset of faculty–subject pairs (f_i, s_j), each represented by a feature vector ${\mathrm{y}}_{\mathrm{i}\mathrm{j}}\in {\Re }^{20}.$ A binary label is defined as Equation (45).

$${\mathrm{y}}_{\mathrm{i}\mathrm{j}}=\left\{\begin{array}{ll}1,& \mathrm{i}\mathrm{f} {\mathrm{f}}_{\mathrm{i}} \mathrm{w}\mathrm{a}\mathrm{s} \mathrm{h}\mathrm{i}\mathrm{s}\mathrm{t}\mathrm{o}\mathrm{r}\mathrm{i}\mathrm{c}\mathrm{a}\mathrm{l}\mathrm{l}\mathrm{y} \mathrm{a}\mathrm{s}\mathrm{s}\mathrm{i}\mathrm{g}\mathrm{n}\mathrm{e}\mathrm{d} \mathrm{s}\mathrm{u}\mathrm{b}\mathrm{j}\mathrm{e}\mathrm{c}\mathrm{t} \mathrm{t}\mathrm{o} {\mathrm{s}}_{\mathrm{j}}\\ 0,& \mathrm{o}\mathrm{t}\mathrm{h}\mathrm{e}\mathrm{r}\mathrm{w}\mathrm{i}\mathrm{s}\mathrm{e}\end{array}\right.$$

(45)

Using this labeled dataset, predictive models (XGBoost, WDNN, and GNNs) are trained to estimate the suitability score, as defined in Equation (46).

$${\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}=\mathrm{\sigma }\left({\mathrm{f}}_{\mathsf{\theta }}\left({\mathrm{x}}_{\mathrm{i}\mathrm{j}}\right)\right)$$

(46)

where σ(.) is the sigmoid function. The training objective is formulated using binary cross-entropy loss, as given in Equation (47).

$$\mathrm{L}=-{\displaystyle \frac{1}{\mathrm{N}}}{\displaystyle \sum _{\mathrm{i},\mathrm{j}}\left[{\mathrm{y}}_{\mathrm{i}\mathrm{j}}\mathrm{l}\mathrm{o}\mathrm{g}\left({\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}\right)+\left(1-{\mathrm{y}}_{\mathrm{i}\mathrm{j}}\right)\mathrm{l}\mathrm{o}\mathrm{g}\left(1-{\widehat{\mathrm{y}}}_{\mathrm{i}\mathrm{j}}\right)\right]}$$

(47)

To capture relational dependencies, GNNs refines these predictions by learning node embeddings and producing final suitability scores, as defined in Equation (48).

$${\mathrm{U}}_{\mathrm{i}\mathrm{j}}=\mathrm{\sigma }\left(1{\mathrm{h}}_{\mathrm{i}}^{\mathrm{T}}{\mathrm{h}}_{\mathrm{j}}\right)$$

(48)

where h_i and h_j are learned embeddings for faculty and subjects, respectively. These scores are then passed to an ILP-based optimization layer. Let ${\mathrm{x}}_{\mathrm{i}\mathrm{j}}\in \{0,1\}$ denote the assignment decision. The objective is to maximize total utility, as defined in Equation (49).

$$\mathrm{m}\mathrm{a}\mathrm{x}={\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{N}}{\displaystyle \sum _{\mathrm{j}=1}^{320}{\mathrm{U}}_{\mathrm{i}\mathrm{j}}}}{\mathrm{x}}_{\mathrm{i}\mathrm{j}}$$

(49)

Here, the subject-to-constraints are defined in Equation (50).

$${\displaystyle {\displaystyle \sum _{\mathrm{i}=1}^{\mathrm{N}}}{\mathrm{x}}_{\mathrm{i}\mathrm{j}}}=1 \forall \mathrm{j},{\displaystyle {\displaystyle \sum _{\mathrm{j}=1}^{320}}{\mathrm{x}}_{\mathrm{i}\mathrm{j}}}<{\mathrm{C}}_{\mathrm{i}}^{\mathrm{m}\mathrm{a}\mathrm{x}},{\mathrm{x}}_{\mathrm{i}\mathrm{j}}\le {\mathrm{E}}_{\mathrm{i}\mathrm{j}}$$

(50)

where ${\mathrm{C}}_{\mathrm{i}}^{\mathrm{m}\mathrm{a}\mathrm{x}}$ is the maximum teaching load and E_ij denotes eligibility. The ILP solver produces the final allocation matrix X = [x_ij], ensuring that all assignments are feasible, balanced, and optimized. This end-to-end pipeline effectively transforms predictive insights into actionable academic decisions.

5. Results

5.1. Feature Importance Analysis

The results of this research confirm that integrating a knowledge-based reasoning layer into deep learning architectures yields significant advances in accuracy, transparency, and institutional applicability for graduate subject allocation. Across all experiments involving 463 respondents and 320 subjects from six faculties spanning science- and social science-based programs, the hybrid framework consistently outperformed single-model baselines on both predictive and operational metrics. Quantitatively, GNNs achieved beyond statistical performance. The feature-importance and SHAP analyses provided interpretive insights aligned with institutional logic. The top-influence indicators—F₂₀ Digital Pedagogical Competence (12.6%), F₅ Research Productivity (10.8%), and F₁₈ Postgraduate/Ph.D. Supervision (9.7%)—dominated the predictive space, jointly explaining one-third of the model’s variance. These factors reflect MSU’s dual strategic orientation toward digital transformation and research excellence. Mid-tier contributors such as F₁ Teaching Experience, F₃ Designation, F₁₁ Examination and Evaluation, and F₁₇ Undergraduate Mentorship demonstrated synergistic relevance to course specialization and program stability. Conversely, variables related to administrative duties (F₆ Administrative Responsibility) and extracurricular participation (F₁₅–F₁₆ Cultural and Event Coordination) exerted minimal or negative effects, underscoring the importance of workload-aware resource management in policy-driven allocations (as shown in Table 11).

Table 11. Feature importance ranking.

Rank	Indicator Code	Indicator Description	Importance Score (αᵢ)
1	F20	Digital Pedagogical Competence	0.128
2	F5	Research Productivity	0.114
3	F19	Student Mentorship and Guidance	0.107
4	F11	Examination and Evaluation Contribution	0.092
5	F18	Postgraduate/Ph.D. Supervision	0.086
6	F1	Teaching Experience	0.081
7	F3	Designation/Academic Rank	0.078
8	F17	Undergraduate Project Mentorship	0.074
9	F4	Number of Subjects Taught	0.071
10	F2	Academic Qualification	0.067
11	F7	Academic Outcome Achievement	0.063
12	F9	Training and Placement Contribution	0.059
13	F14	Professional Society Membership	0.052
14	F8	Admission Contribution	0.048
15	F13	Value and Ethics Education Participation	0.045
16	F12	Club/Innovation Engagement	0.041
17	F16	Event Coordination Beyond the Institute	0.038
18	F6	Administrative Responsibility	0.035
19	F10	Accreditation/Documentation Handling	0.032
20	F15	Cultural and Community Engagement	0.028

Noted: Scores normalized to sum = 1 after SHAP value aggregation across all test samples; reported values are rounded to three decimal places, and minor rounding differences may occur.

The multi-objective reranking algorithm, incorporating fairness (α₂ = 0.3) and research alignment (α₃ = 0.2) constraints, effectively reduced workload variance from 0.26 to 0.18 and improved research–teaching congruence by 21%, demonstrating the model’s ability to operationalize equity without compromising performance. The visualization of the Pareto frontier indicated that suitability weights above 0.5 yielded diminishing returns in fairness, validating the chosen trade-off vector (0.4, 0.3, 0.2, 0.1). Institutional deployment through the faculty subject allocation dashboard further substantiated these results. Time study on 30 real allocation cycles (paired t-test, t = 12.4, p < 0.001) showed mean reduction of 46% (SD 8%), a 23% improvement in workload balance, and a 19% increase in research–subject alignment, accompanied by user satisfaction ratings exceeding 4.4/5 among program heads and faculty members. SHAP-based explainability within the dashboard provided real-time transparency, enabling administrators to trace the rationale behind decisions and dynamically adjust policy parameters. The SHAP summary plot (Figure 2), constructed using the normalized importance scores (αᵢ) from Table 4, reveals a pronounced hierarchical structure in feature contributions. The top three predictors exhibit the widest SHAP distributions, indicating strong and consistent influence across observations. In contrast, lower-ranked variables demonstrate limited dispersion, forming a long-tail pattern. This distribution confirms that approximately 70–75% of the model’s predictive power is concentrated among the top 8–10 indicators, reinforcing the robustness and interpretability of the allocation framework.

Figure 2. SHAP plot showing the distribution of feature contributions across observations (constructed using the normalized importance scores (αᵢ) from Table 8).

Comparative visualizations (Figure 1) showed a monotonic increase in performance from tree-based to deep-graph models. At the same time, feature-importance charts revealed a long-tail distribution, with the top 10 indicators accounting for ≈75% of predictive power (Figure 2). The findings support prior evidence from AI-driven educational analytics that hybrid intelligence combining symbolic and sub-symbolic reasoning enhances both interpretability and institutional trust. For Mahasarakham University, the results suggest that optimizing subject allocation through a hybrid deep learning approach can strengthen academic governance by aligning faculty strengths with strategic research themes, reducing administrative overhead, and reinforcing equitable teaching practices. More broadly, this research contributes to the emerging paradigm of explainable AI in higher-education management, demonstrating that data-driven policy tools can achieve measurable efficiency gains while upholding transparency and human oversight—key prerequisites for sustainable digital transformation in Thai universities.

5.2. Practical Case Study: Graduate Subject Allocation

To demonstrate practical applicability, a representative allocation scenario was selected from the Faculty of Information Technology. The subject “Advanced Artificial Intelligence Applications” required assignment of a qualified instructor from a candidate pool of twelve faculty members. After applying institutional eligibility rules, three candidates were excluded due to insufficient postgraduate supervision experience or workload constraints. The remaining candidates were evaluated using the proposed GNNs framework. The system generated suitability scores ranging from 0.42 to 0.96. The highest-ranked faculty member achieved a suitability score of 0.96, supported by strong research productivity, extensive postgraduate supervision experience, high digital pedagogical competence, and close alignment between research specialization and subject content. The recommendation was subsequently validated using the ISAD, which displayed faculty rankings, workload distributions, policy-compliance indicators, SHAP-based explanations of feature importance, and research–subject alignment scores (see Figure 3). The dashboard enabled administrators to transparently review the rationale behind recommendations before finalizing allocation decisions.

Figure 3. Indicator Subject Allocation Dashboard (ISAD).

6. Conclusions

This study proposed and empirically validated a knowledge-based deep learning framework to optimize subject allocation in graduate education by integrating GNNs with institutional policy reasoning. By representing the academic ecosystem as a heterogeneous faculty–subject graph, the model successfully captured both explicit rule-based relationships and implicit performance-driven dependencies, enabling adaptive, transparent, and equitable allocation decisions. Data collected from 463 faculty respondents across six faculties at Mahasarakham University were preprocessed into a 20-indicator knowledge base encompassing teaching experience, research productivity, digital competence, supervision, and administrative engagement. The hybrid GNNs model, incorporating multi-head attention and multi-objective optimization, achieved the highest predictive performance among all baselines (Accuracy = 0.964, F1 = 0.947, AUC = 0.976). Beyond quantitative improvement, the model demonstrated explainability and fairness, identifying Digital Pedagogical Competence (F₂₀), Research Productivity (F₅), and Postgraduate Supervision (F₁₈) as dominant predictors of allocation suitability. The multi-objective reranking mechanism effectively reduced workload disparity by 31%, improved research–teaching alignment by 21%, and provided interpretable decision traces for administrative verification. Although the experimental evaluation was conducted within a single institutional environment, the proposed framework was intentionally designed to support broader applicability. Unlike institution-specific allocation procedures, the underlying architecture separates domain knowledge, policy constraints, and recommendation logic into modular components. As a result, universities can adapt the framework by modifying eligibility rules, workload policies, supervision requirements, and program-specific criteria without changing the core recommendation engine. This design supports scalability and facilitates future deployment in diverse higher-education settings.

7. Limitation and Future Work

Several limitations should be acknowledged when interpreting the findings of this study. First, the proposed framework was developed and evaluated using data collected from a single university. Although the dataset contains diverse faculty profiles, graduate subjects, and institutional allocation records, the underlying policies and administrative practices may not fully reflect those of other higher education institutions. Consequently, the reported performance should be interpreted within the context of the participating university. Second, the recommendation models were trained on historical allocation records, which may contain implicit biases stemming from previous administrative decisions, faculty preferences, and institutional practices. Although the proposed framework incorporates rule-based filtering, workload balancing, and fairness-oriented optimization mechanisms, residual historical biases may still influence model behavior. Third, the current implementation focuses primarily on graduate subject allocation and does not explicitly consider dynamic factors such as changing faculty availability, sabbatical leave, emerging research areas, interdisciplinary teaching requirements, or long-term workforce planning. Future studies could incorporate temporal graph representations and adaptive policy-learning mechanisms to address these evolving institutional needs. Despite these limitations, the proposed architecture is designed to be transferable across institutions. The knowledge graph schema, institutional rule engine, workload indicators, and recommendation modules can be customized to reflect local regulations and academic policies. Future research should therefore validate the framework using multi-university datasets, cross-institutional benchmarking, and fairness-aware recommendation techniques to further evaluate robustness, scalability, and generalizability.