The Scientific Landscape of Hyper-Heuristics: A Bibliometric Analysis Based on Scopus

Abstract

Hyper-heuristics emerged as a broader metaheuristic framework to address the limitations of traditional optimization heuristics. By abstracting the design of low-level heuristics, hyper-heuristics offer a flexible and adaptable approach to solving complex problems. This study conducts a bibliometric analysis of the hyper-heuristic-algorithms-related literature indexed in the Scopus database to map its evolution, identify key research trends, and pinpoint influential authors and journals. The study encompasses document growth over time, predominant author keywords, high-impact journals, and prolific authors ranked by publication count and citation impact. A detailed examination of author keywords unveils the core research themes within the hyper-heuristic domain. The findings of this study provide valuable insights into the current literature in hyper-heuristic research and offer guidance for novice and experienced researchers.

1. Introduction

The relentless pursuit of optimal solutions to complex problems has driven researchers to explore innovative approaches. Among these, hyper-heuristics have emerged as a meta-level optimization paradigm that has garnered increasing attention across diverse scientific disciplines. Rooted in the need to efficiently manage the complexity inherent in real-world challenges, hyper-heuristics offer a flexible system for selecting and combining lower-level heuristics. With Burke and Kendal’s studies pioneering this field [1,2,3], hyper-heuristics have progressed from conceptual beginnings to practical tools utilized across diverse domains. From their initial theoretical conception, these methods have become sophisticated tools with applications spanning engineering, computer science, economics, and beyond [4].

Understanding its scholarly landscape is essential to grasp hyper-heuristic research’s full potential and trajectory. Bibliometric analysis provides a structured approach to examining the vast body of literature, enabling researchers to identify emerging trends, influential scholars, and knowledge gaps. By systematically mapping the evolution of hyper-heuristic research, it is possible to discern patterns of development, collaborations, and the impact of this field on other domains.

The Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) statement provides a robust methodology for conducting such bibliometric studies [5]. By adhering to PRISMA, researchers can enhance their findings’ transparency, rigor, and reproducibility. By applying the PRISMA statement, this study aims to illuminate the multi-faceted nature of hyper-heuristic research.

The article has been structured as follows: Section 2 briefly describes hyper-heuristics, introducing key concepts and definitions relevant to the study. Section 3 presents related studies, offering an overview of previous bibliometric analyses and reviews on the topic. Section 4 details the methods, techniques, and tools used in this analysis. Section 5 includes the main results, which are subdivided into six parts: publication trends per year, keyword analysis, topic classification, source distribution, country-level contributions, and leading authors in the field. Lastly, Section 6 presents a general discussion and the main conclusions drawn from the study.

2. Background

Heuristics and metaheuristics are essential in tackling complex optimization problems, particularly when exact models, such as branch-and-bound, integer programming, or dynamic programming, become computationally costly. While exact approaches are ideal in theory for delivering optimal solutions, they often break down in practice when confronted with large-scale combinatorial problems, dynamic inputs, or high numbers of constraints [6]. In such settings, heuristics, like the nearest neighbor algorithm for the traveling salesman problem or a greedy selection rule in scheduling, provide fast, domain-specific strategies to deliver good enough solutions with minimal computational cost.

When the problem is particularly complex (NP-complete or NP-hard) or has multiple objectives, uncertainty, or the need for global exploration, metaheuristics are used to enhance search performance and solution quality. These include widely used methods such as genetic algorithms for feature selection, simulated annealing for job shop scheduling, and particle swarm optimization for hyper-parameter tuning. Metaheuristics offer a more flexible and powerful alternative to simple heuristics, but they still require problem-specific encoding, parameter tuning, and often manual intervention, which limits their scalability across domains.

Metaheuristic algorithms represent an advancement over classical heuristics, prioritizing deep exploration of the solution space. They often integrate sophisticated neighborhood search rules and solution recombination techniques [7]. While metaheuristics typically yield higher-quality solutions than classical heuristics, this improvement often comes at the expense of increased computational cost. A key limitation of metaheuristics is their context-dependent nature and reliance on finely tuned parameters, which can hinder their generalizability to different problems. This limitation underscores the motivation for higher-level optimization approaches like hyper-heuristics.

Hyper-heuristic algorithms address the need for generalization and adaptability, especially when solving multiple instances of a problem class or operating in changing environments. Unlike metaheuristics, which directly search the solution space, hyper-heuristics operate by selecting or generating heuristics or metaheuristics to solve the problem. These approaches are particularly effective in domains like cloud resource management, educational timetabling, or software testing, where problem characteristics vary significantly over time or across institutions (see Section 5). By abstracting away from domain-specific algorithm design, hyper-heuristics enable the development of more adaptive, reusable, and scalable optimization frameworks.

Hyper-heuristics offer a higher-level abstraction for search and optimization than metaheuristics. Instead of operating directly on candidate solutions, hyper-heuristics manage a set of low-level heuristics (which can include metaheuristics). They are intended to select or generate the most appropriate heuristics for a given problem instance. Figure 1 shows the initial classification of hyper-heuristics based on their nature, resulting in four distinct categories: constructive selection, perturbative selection, constructive generation, and perturbative generation [8]. Constructive hyper-heuristics iteratively build solutions from scratch, while perturbative hyper-heuristics refine existing solutions. Generative hyper-heuristics represent a more advanced paradigm, automatically creating new heuristics from components of existing ones.

The integration of machine learning within hyper-heuristics is a significant and rapidly evolving area. This integration allows hyper-heuristics to learn from past experiences and adapt their behavior accordingly. Based on the timing of the learning process, hyper-heuristics are categorized into online and offline learning approaches. Offline learning hyper-heuristics derive knowledge from a training set of problem instances, aiming to generalize this knowledge to unseen instances. Online learning hyper-heuristics, in contrast, learn continuously during the problem-solving process, adapting to the specific characteristics of the current instance. This online learning capability is particularly valuable in dynamic environments.

It is crucial to distinguish between the hyper-heuristic methodologies and the specific problem domains they are applied to. While a hyper-heuristic can be designed to operate across various problems (e.g., scheduling, routing, packing), its underlying high-level heuristic for selecting or generating low-level heuristics remains independent of the problem instance. For example, a selection hyper-heuristic might employ a reinforcement learning strategy as the high-level heuristic to choose between different low-level heuristics. This reinforcement learning strategy is the core of the hyper-heuristic and is distinct from the specific scheduling or routing problem tackled by the low-level heuristics. Hyper-heuristics provide a general framework for managing and applying low-level heuristics that often deal with the problem domain, giving context and evaluation criteria. This separation allows for the development of versatile hyper-heuristics that can be readily adapted to new and diverse optimization contexts. Therefore, when analyzing hyper-heuristics research, it is essential to consider the performance of both high-level and low-level heuristics when applied to specific problem domains. This distinction allows for a more nuanced understanding of the strengths and weaknesses of different hyper-heuristic approaches.

The crucial distinction between metaheuristics and hyper-heuristics lies in their level of operation. Metaheuristics manipulate solutions directly, while hyper-heuristics operate on a higher plane, managing and selecting heuristics. This higher level of abstraction empowers hyper-heuristics with greater flexibility and adaptability across diverse problem domains, including vehicle routing, scheduling, and combinatorial optimization. Furthermore, the integration of machine learning with hyper-heuristics opens exciting new avenues for creating truly intelligent and adaptive optimization systems. This synergy is driving the current wave of innovation in the field and promises to deliver increasingly powerful and versatile optimization tools for the future.

3. Related Studies

The literature review encompasses several studies focused on hyper-heuristics. Most of these works delve into specific problem domains, illustrating how hyper-heuristics can be applied to solve particular challenges. For instance, Pillay [9] concentrated their review on the application of hyper-heuristics to educational timetabling. Their study comprehensively analyzes existing research in this area, including the seminal studies by Burke and Kendall [2,3]. Another recent contribution by Liu et al. [10] examined various heuristic methods (including hyper-heuristics) within the context of the vehicle routing problem. Vela et al. [11] concentrated on scheduling problems, examining hyper-heuristic applications in this field over the past decade. Their work categorized hyper-heuristic strategies and configurations used in diverse scheduling scenarios, highlighting the prevalence of evolutionary computation and identifying areas for future research, such as multi-objective optimization.

Burke et al. [12] provided a foundational classification of hyper-heuristic variants based on the heuristic search space and feedback mechanisms employed during the learning process. This study established a cornerstone for the field, aiming to automate the development of computational search methodologies for operational research problems. A later revision of this study [8] further refined the classification and definition of hyper-heuristics, distinguishing between heuristic selection and heuristic generation while also highlighting recent research trends and expanding applications into new domains such as bioinformatics, game strategies, and software engineering.

Li et al. [13] provided a review of reinforcement-learning-based hyper-heuristics. They categorize existing algorithms into value-based and policy-based approaches, describing typical algorithms in each category. The review also identifies current research gaps and suggests future directions for developing reinforcement-learning-based hyper-heuristics.

Sanchez et al. [14] analyzed hyper-heuristic research within the specific context of combinatorial optimization, investigating whether research efforts align with the most relevant problems in that domain. Their analysis identified key problem domains, such as shortest path and minimum spanning tree, suggesting areas for increased hyper-heuristic application.

Garate-Escamilla et al. [15] took a broader approach, employing text-mining techniques to analyze a large corpus of hyper-heuristic literature. Their study focused on identifying dominant research topics and visualizing relationships, revealing widespread manifestations of different hyper-heuristic areas.

While these studies provide valuable insights into specific applications and trends within hyper-heuristics, this article aims to provide a broader analysis, examining the publications of hyper-heuristics across all areas and analyzing the publications according to different dimensions.

To analyze this document set, we focused on the following research questions:

• How has the hyper-heuristics research landscape evolved over time, as reflected in publication trends?
• What key terms define the intellectual core of hyper-heuristics research?
• How have the thematic priorities within hyper-heuristics research shifted over the years?
• What are the dominant research themes and application areas within the hyper-heuristic domain?
• Which countries and regions are at the forefront of hyper-heuristics research?
• Who are the key thought leaders and influential researchers shaping the field of hyper-heuristics?
• Which journals serve as the main outlets for disseminating cutting-edge hyper-heuristics research?

How does this research contribute to existing bibliometric analyses?

Table 1. Comparative overview of the analytical approaches employed in previous studies and this research.

Article	POT	CtA	KA	TA	CA	AA	JA
Sanchez et al. [14]	☓	☓		☓		☓	☓
Gárate-Escamilla et al. [15]	☓		☓	☓			☓
Current work	☓	☓	☓	☓	☓	☓	☓

POT: Production over time. CtA: Citation analysis. KA: Keyword analysis. TA: Topic analysis. CA: Country analysis. AA: Author analysis. JA: Journal analysis.

presents a comparative overview of the analytical approaches employed in previous studies and this research. The comparison focuses on the following dimensions: production over time, citation analysis, keyword analysis, topic analysis, country analysis, author analysis, and journal analysis.

As Table 1 shows, Gárate-Escamilla et al. delved deep into topic analysis, providing valuable insights into current trends in hyper-heuristic research. However, their scope was limited to these dimensions (keywords and topics).

Sanchez et al. [14] conducted a broad analysis encompassing most dimensions, excluding keyword and country analysis. While their research focused on the application of hyper-heuristics to optimization problems, it is essential to note that, while initially designed for this purpose, their application has been expanded to further domains. Additionally, the field has evolved significantly in the last five years. In fact, more than 350 new articles involving hyper-heuristics have been published after 2020. This substantial growth highlights the need for a new analysis that not only updates the state of the art but also explores how hyper-heuristics are currently being applied across various domains.

In particular, it is worth investigating whether hyper-heuristics are expanding beyond traditional optimization problems, potentially being integrated into areas such as machine learning, automated reasoning, and real-time decision systems. Furthermore, analyzing recent trends over the past five years across multiple dimensions—including publication patterns, most cited works, key contributing countries, international collaborations, and keyword evolution—can provide valuable insights into how the field is maturing, diversifying, and gaining relevance in both academic and practical contexts.

This paper aims to complement previous research by offering a more holistic perspective. We seek to comprehensively understand the hyper-heuristics landscape in the literature, including its evolution, key themes, geographical distribution, and influential contributors.

4. Methods, Techniques, and Instruments

A bibliometric analysis was conducted adhering to the PRISMA statement [5]. PRISMA provides a comprehensive framework for conducting and reporting systematic reviews. Due to its clarity and specificity, PRISMA is widely adopted in bibliometric studies.

The analysis utilized data extracted from the Scopus database. A search was performed on 23 October 2024, using the keywords “hyper-heuristic” and “hyperheuristic” connected by the Boolean operator OR. The search encompassed article titles, abstracts, and keywords. To refine the results, the document type was restricted to articles. A report on results is presented in

Table 2. Data selection with Scopus.

Search Keywords (SK), Document Type (DT)	Result
SK = hyper-heuristic, DT = all	1740
SK = hyperheuristic, DT = all	606
SK = hyper-heuristic OR hyperheuristic, DT = all	1847
SK = hyper-heuristic OR hyperheuristic, DT = article	768
SK = hyper-heuristic OR hyperheuristic, DT = article, duplicates removed	767

.

The Scopus dataset was initially exported as a BibTeX file, which underwent subsequent modifications to enhance data accuracy. Specifically, the following preprocessing steps were applied:

• Removal of diacritics: All accented characters (e.g., á, é, í, ó, ú, ñ, ä, ë, ï, ö, ü) were replaced with their unaccented counterparts.
• Standardization of hyper-heuristic term: The terms “hyper-heuristic” and “hyper heuristic” were unified as “hyperheuristic” for consistency in the analysis. While the hyphenated form is grammatically correct, the unhyphenated version simplifies text processing for the Python (3.12.3) library.
• Plural form reduction: Plural forms of “heuristic” were converted to the singular form.
• Term unification for multi-objective and optimization: The terms “multi-objective” and “optimization” were standardized by removing hyphens and replacing “optimisation” with “optimization”.

The search results retrieved from the Scopus database were exported in BibTeX (.bib) format to ensure compatibility with bibliometric analysis tools. To process and analyze these data, we employed the PyBibX Python library, which provides efficient methods for parsing, extracting, and organizing bibliographic metadata [16]. This approach facilitated the construction of various visualizations and statistical summaries used throughout the study.

Table 3. Preliminary statistical report.

Metric	Value
Timespan	2003–2025
Total Number of Countries	68
Total Number of Sources	288
Total Number of Documents	767
Average Documents per Author	1.6
Average Documents per Source	2.66
Average Documents per Year	34.86
Total Number of Authors	1744
Total Number of Author Keywords	1797
Total Single-Authored Documents	17
Total Multi-Authored Documents	750
Average Collaboration Index	3.64
Max H-Index	23
Total Number of Citations	17,861
Average Citations per Author	10.24
Average Citations per Document	23.29
Average Citations per Source	62.02

presents a summary of key metrics from the bibliometric analysis. It provides a comprehensive overview of the research landscape, including information on publication volume, author activity, collaboration patterns, and citation impact. The data reveal a dynamic research community with a significant number of authors (1744) and publications (767). The average collaboration index (3.64) strongly emphasizes collaborative research within the hyper-heuristic field. The max H-index of 23 suggests the presence of highly cited researchers within the field. Also, the number of citations per document indicates that the research produced in this field is highly influential and impactful.

5. Results

This section provides the results of the bibliometric analysis, examining research trends, key topics, and influential publications in the area of hyper-heuristics. Through the following bibliometric analysis, we delve into the evolution of the field and identify emerging areas of interest.

5.1. Publications per Year

The first article was published in 2003 by Burke et al. [3]. Since then, the number of published articles on hyper-heuristics has steadily increased. The growth rate of publications has accelerated in recent years, suggesting a growing interest and research activity in this field. The year 2023 saw the highest number of publications, with almost 100 articles, indicating a significant surge in research activity.

Previous publications have shown that the growth of science can be approximated by exponential growth behavior [17]. As illustrated in Figure 2, the number of publications on hyper-heuristics appears to follow a similar trend. By fitting an exponential curve to the data, we obtained Equation (1), which closely approximates the observed growth (see Figure 3).

$$D(y)=4.603e^{0.1545\left(y-2003\right)}$$

(1)

5.2. Keywords Analysis

Figure 4 illustrates the prominent research areas within hyper-heuristics. The graph highlights optimization problems, particularly scheduling and routing. The range of keywords indicates ongoing exploration of optimization techniques and the potential for hybrid approaches.

Based on the frequency of these keywords in published works, we can identify the following thematic clusters:

• Optimization Problems (with a particular focus on scheduling and routing)
  • Job Shop Scheduling. A classic manufacturing problem involving multiple machines and jobs.
  • Flexible Job Shop. A variant of job shop scheduling where machines can be assigned to different tasks.
  • Vehicle Routing Problem. Optimizing routes for vehicles to serve multiple customers efficiently.
  • Location Routing Problem. Determining optimal locations for facilities and routes for vehicles.
  • Traveling Salesman Problem. Finding the shortest route that visits all cities exactly once.

These keywords collectively highlight the prevalent focus on optimization problems related to scheduling, routing, and logistics. Hyper-heuristics have proven their effectiveness in addressing the complexity and dynamism of these problems.

• Intelligent Optimization Algorithms

  6.

  Particle Swarm Optimization. A metaheuristic inspired by the behavior of bird flocks and fish schools.

  7.

  Genetic Programming. A genetic algorithm that evolves computer programs to solve problems.

  8.

  Ant Colony Optimization. A metaheuristic inspired by the behavior of ants searching for food.

These keywords emphasize the exploration and application of various optimization algorithms within the hyper-heuristic framework. Researchers have investigated the effectiveness of these algorithms as hyper-heuristics for specific problem domains.

Figure 5 shows the most frequently occurring author keywords related to hyper-heuristics from 2020 to 2024. The figure reveals several key trends in the field. A prominent association is observed between hyper-heuristics and genetic programming. The consistent presence of genetic programming in hyper-heuristic publications over the past five years is primarily due to its utility as a method within hyper-heuristic frameworks. Genetic programming is frequently used to automatically generate new, problem-specific heuristics, which is a core aspect of hyper-heuristic methodologies. Additionally, genetic programming can be employed to select or combine existing heuristics, essentially acting as the hyper-heuristic itself. Furthermore, genetic programming serves as a standard benchmark for comparing the performance of novel hyper-heuristic approaches, and it can also be used in developing and optimizing hyper-heuristic frameworks, highlighting its continued relevance and applicability in this field.

As expected, optimization topics dominate the landscape of hyper-heuristic algorithm applications. Figure 4 depicts the diversity and evolution of optimization-related research within this field. Over the years, hyper-heuristics have been employed to address a wide range of problems, including combinatorial optimization and multi-objective optimization.

The recurrent appearance of metaheuristic underlines its fundamental role in the development of hyper-heuristics. Hyper-heuristics often use metaheuristics as both high- and low-level heuristics. This dependency is reflected in the figure’s consistent representation of metaheuristic, reinforcement learning, and machine learning across different years.

While genetic programming and metaheuristics are core themes, Figure 4 also highlights the diversification of hyper-heuristics research. Most topics are closely tied to optimization. However, a few notable exceptions exist where hyper-heuristic is applied in non-optimization-specific domains, or at least areas where optimization is not the sole focus.

The term software testing indicates the application of hyper-heuristics in this stage of software engineering. This suggests hyper-heuristics are used to enhance testing strategies, possibly by evolving test cases or optimizing test coverage. This application aligns more with software engineering quality assurance than traditional optimization problems. Several recent studies reflect this trend. For instance, de Santiago Júnior et al. [18] integrate model-based and search-based testing to generate GUI test cases from a many-objective perspective. They employ hyper-heuristics alongside metaheuristics to optimize both functional and non-functional requirements. Similarly, Sulaiman et al. [19] propose a hyper-heuristic approach for test case generation in model-based testing for software product lines.

The inclusion of keywords such as deep reinforcement learning and cloud computing suggests the exploration of these novel technologies within hyper-heuristics. Deep reinforcement learning “incorporates both the advantages of the perception of deep learning and the decision-making of reinforcement learning” [20], enabling it to handle complex environments with high-dimensional inputs such as images, video, or raw sensor data. In the hyper-heuristic context, deep reinforcement learning is mainly used to solve combinatorial and multi-objective optimization problems [21,22].

The combination of hyper-heuristics and cloud computing is predominantly applied to scheduling tasks in the cloud, particularly in scientific workflows, resource allocation, and load balancing [23,24].

5.3. Topics

The Python library has been used to identify key topics and recurring themes within the existing literature to gain deeper insights into the evolving landscape of hyper-heuristic research.

Table 4. Topic Modeling Result and Suggested Group.

Suggested Group	Associated Words
Scheduling and Production Optimization	Scheduling, programming, genetic, rules, shop, job, time, results, manufacturing, production	Topic 0 (177)
Metaheuristic Optimization and Framework Development	Optimization, level, search, selection, framework, results, approach, performance, low, different	Topic 1 (127)
Vehicle Routing and Logistics	Cost, routing, vehicle, model, logistics, carbon, time, traffic, results, level	Topic 2 (61)
Cloud Computing and Resource Management	Resource, cloud, energy, computing, scheduling, network, sensor, performance, task, consumption	Topic 3 (51)
Machine Learning and Data Mining	Classification, data, feature, learning, SVM, accuracy, decision, tree, dataset, machine	Topic 4 (42)
Educational Timetabling	Timetabling, exam, approach, research, graph, course, table, educational, ITC, instances	Topic 5 (31)
Traveling Salesman Problem	City, salesman, approach, traveling, facility, tour, solution, instances, search, neighborhood	Topic 6 (15)
Evolutionary Computation for Routing Problems	Routing, uncertain, policies, arc, genetic, programming, capacitated, policy, vehicles	Topic 7 (14)
Healthcare Scheduling and Resource Allocation	Rostering, patient, nurse, pas, hospital, care, approach, scheduling, solutions, crowd	Topic 8 (14)
Unmanned Aerial Vehicle (UAV) Path Planning and Optimization	UAV, swarm, coverage, path, planning, optimal, optimization, DSO, environment, marine	Topic 9 (13)
Software Testing and Quality Assurance	Testing, software, strategies, generation, cases, SPL, coverage, pairwise, selection, approach	Topic 10 (13)

presents the results of the topic modeling analysis. It includes the number of documents assigned to each topic, the most relevant author keywords associated with the topic, and a suggested group title based on these keywords.

The resulting topics in Table 4 offer a comprehensive overview of the current state of hyper-heuristic research. By examining these topics and their relationships to the word groups in the graph, we can uncover valuable insights into the dominant research areas and emerging trends in this field. The topic descriptions, based on the resulting keywords and the representative articles listed in Table 5, are the following:

• Topic 0. Scheduling and Production Optimization
  This topic centers on applying hyper-heuristics for solving complex scheduling and production planning problems, particularly in manufacturing contexts such as job shop and flow shop scheduling. The most representative studies address the design of scheduling rules and dispatching strategies using multi-objective optimization, genetic programming, and Q-learning to enhance energy efficiency and throughput. The representative keywords listed above underscore the practical orientation of this research area toward industrial applications, with a notable emphasis on rules-based systems and simulation-based optimization frameworks.
• Topic 1.  Metaheuristic Optimization and Framework Development
  This topic focuses on designing and tuning generalized hyper-heuristic frameworks for combinatorial optimization problems. The dominant approach involves hybrid methods aimed at selecting or generating heuristics dynamically. Representative studies explore hyper-heuristic architectures adaptable across domains, emphasizing performance analysis, algorithm generality, and reusing heuristic components within flexible solution frameworks.
• Topic 2.  Vehicle Routing and Logistics
  This topic uses hyper-heuristics to tackle vehicle routing problems, focusing on environmental and operational constraints. Prominent subtopics include green vehicle routing, simultaneous pickup and delivery, and heterogeneous fleets. The literature emphasizes cost and carbon footprint reduction, traffic considerations, and real-world logistics constraints. Key studies propose hybrid metaheuristics and reinforcement learning strategies tailored to dynamic routing scenarios, suggesting a trend toward sustainable and adaptive transport logistics optimization.
• Topic 3.  Cloud Computing and Resource Management
  Research on this topic targets the optimization of cloud-based systems through hyper-heuristics that manage computing resources, energy consumption, and task scheduling. Articles highlight applications in scientific workflow scheduling and multi-objective cost management in cloud environments. The field increasingly integrates low-level scheduling heuristics with optimization methods to improve scalability and efficiency in distributed computing infrastructures.
• Topic 4.  Machine Learning and Data Mining
  This topic integrates hyper-heuristics with machine learning tasks, such as feature selection, classification, and cyber-security analytics. Techniques like support vector machines, decision trees, and ensemble learning are frequently used. Representative studies focus on optimizing algorithm selection or parameter tuning to improve model accuracy and robustness, particularly for large-scale datasets.
• Topic 5.  Educational Timetabling
  This topic encompasses the development of hyper-heuristics to solve educational timetabling problems. Key contributions include iterative local search strategies, hybrid methods combining add–delete mechanisms, and selection hyper-heuristics tuned for institutional constraints. The articles emphasize real-world applications, including school and university timetabling, incorporating hard and soft constraint handling, and addressing scalability and robustness in schedule generation.
• Topic 6.  Traveling Salesman Problem
  This topic explores hyper-heuristic approaches for solving variants of the traveling salesman problem, including multi-depot and modified cost functions. This line of research emphasizes generating adaptive heuristics for pathfinding tasks under various constraints and problem sizes.
• Topic 7.  Evolutionary Computation for Routing Problems
  This topic highlights the application of evolutionary algorithms, especially genetic programming and co-evolutionary strategies, to solve routing problems characterized by uncertainty and capacity constraints. Recent years have focused on capacitated arc routing problems and real-time path planning under uncertain demand or environmental conditions. Representative studies explore the interaction between reactive and predictive routing elements, indicating a shift toward hyper-heuristic systems that adapt to dynamic and stochastic problem instances.
• Topic 8.  Healthcare Scheduling and Resource Allocation
  This topic addresses the scheduling of healthcare personnel and resources, particularly nurse rostering and patient care coordination. Hyper-heuristics in this context aim to satisfy complex institutional requirements such as coverage, shift preferences, and workload balancing. The integration of domain-specific knowledge, such as multi-stage rostering models and hidden Markov models, shows how hyper-heuristics are tailored to the unique constraints of healthcare systems, emphasizing both efficiency and fairness.
• Topic 9.  Unmanned Aerial Vehicle (UAV) Path Planning and Optimization
  This emerging topic covers UAV mission planning through hyper-heuristic approaches, focusing on multi-objective optimization for coverage, surveillance, and communication tasks. Research emphasizes clustering, swarm intelligence, and real-time path adjustment in uncertain environments to optimize autonomous flight operations.
• Topic 10.  Software Testing and Quality Assurance
  This topic focuses on improving software testing processes through hyper-heuristics that guide test case selection, generation, and prioritization. Studies involve experimental comparisons of selection and acceptance mechanisms, often within combinatorial test generation frameworks. High-impact articles explore feature model variability testing and hyper-heuristics integration into automated quality assurance pipelines, reflecting a push toward intelligent software verification under resource constraints.

Table 5. Most representative articles per topic in the last 10 years.

Citations	Representative Articles	Topic
151	Zhao et al. [25]: A Hyperheuristic With Q-Learning for the Multiobjective Energy-Efficient Distributed Blocking Flow Shop Scheduling Problem	Topic 0
63	Nguyen et al. [26]: A Hybrid Genetic Programming Algorithm for Automated Design of Dispatching Rules
61	Freitag and Hildebrandt [27]: Automatic design of scheduling rules for complex manufacturing systems by multi-objective simulation-based optimization
110	Sabar et al. [28]: A dynamic multiarmed bandit-gene expression programming hyper-heuristic for combinatorial optimization problems	Topic 1
99	Sabar et al. [29]: Automatic design of a hyper-heuristic framework with gene expression programming for combinatorial optimization problems
92	Zhao et al. [30]: A Novel Cooperative Multi-Stage Hyper-Heuristic for Combination Optimization Problems
95	Olgun et al. [31]: A hyper-heuristic for the green vehicle routing problem with simultaneous pickup and delivery	Topic 2
91	Qin et al. [32]: A novel reinforcement learning-based hyper-heuristic for heterogeneous vehicle routing problem
42	Leng, L. et al. [33]: Decomposition-based hyperheuristic approaches for the bi-objective cold chain considering environmental effects
182	Tsai et al. [23]: A hyper-heuristic scheduling algorithm for cloud	Topic 3
63	Alkhanak and Lee [24]: A hyper-heuristic cost optimisation approach for Scientific Workflow Scheduling in cloud computing
35	Al-Khanak et al. [34]: A heuristics-based cost model for scientific workflow scheduling in cloud
64	Barros et al. [35]: Evolutionary Design of Decision-Tree Algorithms Tailored to Microarray Gene Expression Data Sets	Topic 4
41	Sabar et al. [36]: A Bi-objective Hyper-Heuristic Support Vector Machines for Big Data Cyber-Security
41	Asta and Özcan [37]: A tensor-based selection hyper-heuristic for cross-domain heuristic search
73	Soria-Alcaraz et al. [38]: Effective learning hyper-heuristics for the course timetabling problem	Topic 5
54	Soria-Alcaraz et al. [39]: Iterated local search using an add and delete hyper-heuristic for university course timetabling
38	Ahmed et al. [40]: Solving high school timetabling problems worldwide using selection hyper-heuristics
100	Choong et al. [41]: An artificial bee colony algorithm with a Modified Choice Function for the traveling salesman problem	Topic 6
59	Pandiri and Singh, A. [42]: A hyper-heuristic based artificial bee colony algorithm for k-Interconnected multi-depot multi-traveling salesman problem
41	Gharehchopogh et al. [43]: An Improved Farmland Fertility Algorithm with Hyper-Heuristic Approach for Solving Travelling Salesman Problem
40	Liu et al. [44]: A predictive-reactive approach with genetic programming and cooperative coevolution for the uncertain capacitated arc routing problem	Topic 7
37	Maclachlan et al. [45]: Genetic programming hyper-heuristics with vehicle collaboration for uncertain capacitated arc routing problems
29	Wang et al. [46]: Genetic programming with niching for uncertain capacitated arc routing problem
43	Smet et al. [47]: Modelling and evaluation issues in nurse rostering	Topic 8
37	Asta et al. [48]: A tensor-based hyper-heuristic for nurse rostering
28	Kheiri et al. [49]: A hyper-heuristic approach based upon a hidden Markov model for the multi-stage nurse rostering problem
22	Wei et al. [50]: Autonomous path planning of AUV in large-scale complex marine environment based on swarm hyper-heuristic algorithm	Topic 9
8	Bozorgi et al. [51]: A smart optimizer approach for clustering protocol in UAV-assisted IoT wireless networks
3	Zhao et al. [52]: Clustering-based hyper-heuristic algorithm for multi-region coverage path planning of heterogeneous UAVs
112	Zamli et al. [53]: A Tabu Search hyper-heuristic strategy for t-way test suite generation	Topic 10
77	Zamli et al. [54]: An experimental study of hyper-heuristic selection and acceptance mechanism for combinatorial t-way test suite generation
41	Strickler et al. [55]: Deriving products for variability test of Feature Models with a hyper-heuristic approach

Table 5. Most representative articles per topic in the last 10 years.

Citations	Representative Articles	Topic
151	Zhao et al. [25]: A Hyperheuristic With Q-Learning for the Multiobjective Energy-Efficient Distributed Blocking Flow Shop Scheduling Problem	Topic 0
63	Nguyen et al. [26]: A Hybrid Genetic Programming Algorithm for Automated Design of Dispatching Rules
61	Freitag and Hildebrandt [27]: Automatic design of scheduling rules for complex manufacturing systems by multi-objective simulation-based optimization
110	Sabar et al. [28]: A dynamic multiarmed bandit-gene expression programming hyper-heuristic for combinatorial optimization problems	Topic 1
99	Sabar et al. [29]: Automatic design of a hyper-heuristic framework with gene expression programming for combinatorial optimization problems
92	Zhao et al. [30]: A Novel Cooperative Multi-Stage Hyper-Heuristic for Combination Optimization Problems
95	Olgun et al. [31]: A hyper-heuristic for the green vehicle routing problem with simultaneous pickup and delivery	Topic 2
91	Qin et al. [32]: A novel reinforcement learning-based hyper-heuristic for heterogeneous vehicle routing problem
42	Leng, L. et al. [33]: Decomposition-based hyperheuristic approaches for the bi-objective cold chain considering environmental effects
182	Tsai et al. [23]: A hyper-heuristic scheduling algorithm for cloud	Topic 3
63	Alkhanak and Lee [24]: A hyper-heuristic cost optimisation approach for Scientific Workflow Scheduling in cloud computing
35	Al-Khanak et al. [34]: A heuristics-based cost model for scientific workflow scheduling in cloud
64	Barros et al. [35]: Evolutionary Design of Decision-Tree Algorithms Tailored to Microarray Gene Expression Data Sets	Topic 4
41	Sabar et al. [36]: A Bi-objective Hyper-Heuristic Support Vector Machines for Big Data Cyber-Security
41	Asta and Özcan [37]: A tensor-based selection hyper-heuristic for cross-domain heuristic search
73	Soria-Alcaraz et al. [38]: Effective learning hyper-heuristics for the course timetabling problem	Topic 5
54	Soria-Alcaraz et al. [39]: Iterated local search using an add and delete hyper-heuristic for university course timetabling
38	Ahmed et al. [40]: Solving high school timetabling problems worldwide using selection hyper-heuristics
100	Choong et al. [41]: An artificial bee colony algorithm with a Modified Choice Function for the traveling salesman problem	Topic 6
59	Pandiri and Singh, A. [42]: A hyper-heuristic based artificial bee colony algorithm for k-Interconnected multi-depot multi-traveling salesman problem
41	Gharehchopogh et al. [43]: An Improved Farmland Fertility Algorithm with Hyper-Heuristic Approach for Solving Travelling Salesman Problem
40	Liu et al. [44]: A predictive-reactive approach with genetic programming and cooperative coevolution for the uncertain capacitated arc routing problem	Topic 7
37	Maclachlan et al. [45]: Genetic programming hyper-heuristics with vehicle collaboration for uncertain capacitated arc routing problems
29	Wang et al. [46]: Genetic programming with niching for uncertain capacitated arc routing problem
43	Smet et al. [47]: Modelling and evaluation issues in nurse rostering	Topic 8
37	Asta et al. [48]: A tensor-based hyper-heuristic for nurse rostering
28	Kheiri et al. [49]: A hyper-heuristic approach based upon a hidden Markov model for the multi-stage nurse rostering problem
22	Wei et al. [50]: Autonomous path planning of AUV in large-scale complex marine environment based on swarm hyper-heuristic algorithm	Topic 9
8	Bozorgi et al. [51]: A smart optimizer approach for clustering protocol in UAV-assisted IoT wireless networks
3	Zhao et al. [52]: Clustering-based hyper-heuristic algorithm for multi-region coverage path planning of heterogeneous UAVs
112	Zamli et al. [53]: A Tabu Search hyper-heuristic strategy for t-way test suite generation	Topic 10
77	Zamli et al. [54]: An experimental study of hyper-heuristic selection and acceptance mechanism for combinatorial t-way test suite generation
41	Strickler et al. [55]: Deriving products for variability test of Feature Models with a hyper-heuristic approach

Table 5 presents a selection of the most representative papers published in the last ten years, grouped according to the main topics described above. These articles were selected based on their number of citations, reflecting their impact and relevance within each thematic area. Focusing on the most recent decade allows us to capture current research trends, methodological innovations, and emerging applications in the field. This approach ensures that the analysis highlights the evolution of hyper-heuristic techniques in contemporary contexts.

5.4. Sources

Figure 6 illustrates the top 10 journals ranked by the number of published hyper-heuristics-related articles and the total citations received for these publications. As can be seen, in terms of published articles, the journals Applied Soft Computing and Expert Systems with Applications stand out. However, regarding the number of citations, the most relevant journals are Swarm and Evolutionary Computation and IEEE Transactions on Evolutionary Computation. Of special interest are the cases of Journal of Heuristics and IEEE Transactions on Cybernetics. Although they have fewer published articles on hyper-heuristics, their citation rate is high enough to stand out in the citation count.

5.5. Countries

Some countries and regions are driving innovation in the field of hyper-heuristics. Figure 7 visually represents the geographical distribution of hyper-heuristic research activity. The color intensity of each country reflects its relative contribution to the field, as measured by the number of published documents. While China currently holds a dominant position, the presence of other nations suggests a competitive research landscape.

Figure 8 illustrates the top 10 countries based on the number of publications on hyper-heuristics. The graph highlights the global nature of hyper-heuristic research, with contributions from a diverse range of countries.

Figure 7 and Figure 8 show that China has the largest number of publications, indicating a strong research presence and active engagement in hyper-heuristic research. China’s substantial lead in hyper-heuristic publications is likely due to a combination of factors, including significant national investment in science and technology, a large and growing research community, and a strong emphasis on applied research and technological advancement in areas like AI [56]. The scale and complexity of problems in China’s rapidly developing economy and collaborative research environment may also contribute to this high volume of publications.

The United Kingdom’s strong standing as the second-leading country in hyper-heuristic publications is likely due to its robust academic foundation in optimization and operations research, with numerous prestigious universities and research institutions actively involved in this field [57]. The UK’s research community demonstrates a balanced approach, focusing on both the theoretical underpinnings and practical applications of hyper-heuristics. This active and well-supported research environment, with historical strengths in related areas like metaheuristics, contributes significantly to the high publication output in hyper-heuristics.

On the other hand, India, Spain, and Mexico follow the United Kingdom, demonstrating significant contributions from Western and developing nations. Brazil, Malaysia, Australia, Iran, and Turkey also have a notable presence in the field, suggesting growing interest and research activity in these regions.

Figure 9 presents a Sankey diagram that illustrates the flow of research publications from various journals to different countries, with each country focusing on specific keywords related to hyper-heuristics. The thickness of the flows represents the relative volume of publications.

According to Figure 9, the UK’s research concentrates on optimization, connecting to Evolutionary Computation and the European Journal of Operational Research. Chinese and New Zealand’s research is primarily focused on genetic programming. China also has significant links to optimization and reinforcement learning.

Optimization, a fundamental principle in hyper-heuristics, is a common thread connecting diverse research areas across the United Kingdom and China. Meanwhile, China’s emphasis on genetic programming highlights its potential as a promising approach for addressing complex optimization challenges. Lastly, China’s focus on reinforcement learning underscores its growing importance in the field, particularly for dynamic and complex problems.

Figure 9 reveals that, while there are regional differences in research emphasis, optimization remains a central theme across all three countries. The decisive role of Q-learning and reinforcement learning highlights the underlying principle of hyper-heuristics as a way of machine learning.

Figure 9 also demonstrates overlapping areas of interest among different countries, suggesting potential for international collaborations. Figure 9 further illustrates these collaborative relationships between authors from various countries. We have chosen to represent the 10 most collaborative countries, which are listed in

Table 6. Top 10 most collaborative countries.

Country	Number of Collaborations
United Kingdom	26
China	23
Australia	14
United States of America	12
Canada	11
Malaysia	11
Mexico	10
Saudi Arabia	10
Singapore	10
Brazil	9
Egypt	9

.

Figure 10 visually represents international collaborations among the ten most collaborative countries. The lines indicate the frequency of co-authorship between researchers from different countries. The United Kingdom, China, Australia, and the United States of America are leading countries in international hyper-heuristic research collaboration, forming extensive networks with numerous other countries. Emerging nations like Mexico and Brazil are also increasing their global research connections. It is important to note how countries like the United States and Canada, which do not appear among the top 10 most productive countries, still rank among the most collaborative nations. This suggests these countries play a key role in fostering international cooperation rather than focusing on high document output. Their strong academic networks, well-established research institutions, and access to funding may enable them to contribute significantly to hyper-heuristic research through joint projects rather than sheer publication volume.

Furthermore, this trend highlights the distinction between research quantity and influence. While China dominates in terms of the number of publications, the United States, Canada, and the United Kingdom leverage collaboration as a means of impact and knowledge dissemination. This collaborative approach could lead to higher citation rates, broader interdisciplinary applications, and greater global adoption of hyper-heuristic techniques.

Ultimately, this pattern underscores the importance of international partnerships in scientific progress. Countries with fewer publications but extensive collaborations may act as bridges between research hubs, facilitating cross-border knowledge exchange and strengthening the global research ecosystem.

5.6. Authors

Figure 11 presents a comprehensive overview of the most influential authors in the field of hyper-heuristics based on the number of published documents and citations.

As Figure 11 shows, E. Ozcan and E. K. Burke have established themselves as leading figures in the field of hyper-heuristics, with a substantial number of published works and citations. Closely behind, M. Zhang, G. Kendall, and S. Nguyen have significantly contributed to advancing hyper-heuristic research. Additionally, Y. Mei, Y. Zhao, R. Qu, and H. Terashima-Marin occupy prominent positions, underlining their active research and global impact on the field.

Figure 12 illustrates the collaboration networks of the top 10 most prolific authors in hyper-heuristics. Each node represents an author, and the edges connecting the nodes signify co-authorship relationships. The networks reveal distinct clusters of authors who frequently collaborate, suggesting strong research communities within specific subfields of hyper-heuristics.

Figure 13 provides a visual representation of the research interests and contributions of the most prolific authors in hyper-heuristics (also shown in Figure 11). Each data point represents an author and their publication count within a specific research topic (see Table 4). Figure 13 reveals that some authors, like E. Ozcan, G. Kendall, and R. Qu, demonstrate a broader research interest, publishing across multiple topics. This diversity in research interests suggests a dynamic and multi-faceted research landscape, with authors contributing to the field in various ways.

The collaborative relationships observed in the author collaboration network are further reflected in Figure 13. We can identify co-authorship patterns and potential research collaborations by analyzing authors within each topic column.

The Sankey diagram in Figure 14 visually represents the interconnections between journals, countries, and authors. It allows us to identify key trends and patterns in the research landscape. The Sankey diagram confirms the prominence of specific journals and countries identified in previous analyses. Moreover, the diagram highlights the leading authors associated with each country.

Lastly, Figure 15 offers a visual representation of the interconnections between keywords, countries, and authors.

In contrast to the previous Sankey diagrams (Figure 9 and Figure 14), Figure 15 introduces two additional countries: Croatia and Mexico. This expanded analysis reveals a broader geographical scope of hyper-heuristic research. Moreover, the inclusion of the keyword “scheduling” as a primary research focus in the United Kingdom further enriches our understanding of the diverse areas of interest within this field.

6. Discussion and Conclusions

This study employed a bibliometric approach to analyze the literature on hyper-heuristic algorithms indexed in the Scopus database. The primary objectives are to map the evolution of the field, identify key research trends, and pinpoint influential authors and journals.

This bibliometric analysis provided a comprehensive overview of the evolving landscape of hyper-heuristic research. The findings revealed a dynamic and expanding field characterized by steady publication growth. Our analysis indicated an average annual growth rate of 0.15, demonstrating a consistent increase in research activity.

The analysis identified key research areas within the field, with genetic programming emerging as a prominent theme. Keywords related to optimization techniques, such as scheduling, production, and vehicle routing, were frequently encountered. While genetic programming has maintained a consistent presence throughout the analyzed period, other keywords and research areas have emerged and evolved.

China and the United Kingdom have emerged as leading countries in hyper-heuristic research, contributing significantly to the field’s growth. However, it is essential to note the emergence of other countries, such as Mexico, Brazil, and India, as active contributors.

While E. K. Burke, G. Kendall, M. Zhang, and E. Ozcan have established themselves as influential authors, it is crucial to acknowledge the contributions of emerging researchers and their potential impact on future research directions.

In contrast to previous literature reviews, such as the comprehensive work by Sánchez et al. [14], which primarily focused on the classification and application of hyper-heuristics to optimization problems, this study offers a broader and updated perspective. By not limiting the analysis to a specific application domain, this bibliometric study explores the entire spectrum of hyper-heuristic research, including emerging areas such as software testing and hybrid intelligent systems. Furthermore, it extends the temporal scope by incorporating publications up to 2024, thus capturing the most recent developments and research dynamics.

As a result, a compelling narrative of the evolving hyper-heuristics research landscape is painted by bibliometric data. A field ripe for disruption is observed, transitioning from simple combinations of existing heuristics to a future of intelligent adaptation and learning. The continued emphasis on established optimization problems such as scheduling and routing is anticipated, but the genuine excitement lies in the rapid growth witnessed in machine learning integration. This is not merely a fashionable addition but a fundamental shift towards truly autonomous and intelligent problem solving.

The potential of deep reinforcement learning within hyper-heuristics is particularly intriguing. A hyper-heuristic could be envisioned that not only selects the most appropriate low-level heuristic for a given scenario but also learns entirely new strategies for search space navigation. Unprecedented performance gains—especially for complex, dynamic problems that prove challenging for traditional optimization methods—could be unlocked by this.

While cloud computing is mentioned, its potential is believed to be vastly under-explored. The possibilities extend beyond faster processing to distributed hyper-heuristic search, where multiple instances collaborate and share learned knowledge in real time. The way large-scale optimization challenges are tackled could be revolutionized in this way.

The sustained focus on specific application domains like scheduling and routing is deemed crucial. Hyper-heuristics are not merely theoretical constructs; they are intended for real-world problem solving. However, greater exploration of emerging domains such as smart cities, personalized medicine, and artistic creation is encouraged. Due to their adaptability, hyper-heuristics are uniquely suited to addressing the complex and often ill-defined optimization problems in these areas.

The strong connections between China and its neighbors and the transatlantic collaborations between the US and Europe suggest that knowledge sharing and joint research efforts are already underway. However, the relative isolation of certain regions, particularly in Africa and South America, highlights a potential for untapped talent and unique perspectives. Bridging these geographical gaps could significantly enrich the field of hyper-heuristics. A truly global perspective, fostered by active collaboration across borders, will be essential to unlock the full potential of hyper-heuristics and address the complex challenges facing our world.

This study provides a foundation for future research. Future investigations could expand the scope of the analysis by incorporating data from additional databases, such as Google Scholar and Web of Science, to gain a more comprehensive understanding of the research landscape. Furthermore, future studies could consider expanding the scope of document types beyond journal articles to include conference papers, book chapters, and technical reports. This would provide a more complete picture of the research activity. Examining the role of institutions and funding agencies in driving hyper-heuristic research would also provide valuable insights into the factors that shape the field’s development. By addressing these future research directions, we can better understand the hyper-heuristic research landscape and inform future research endeavors in this evolving field.