This paper proposes a novel approach to generating hybrid optimization algorithms by leveraging a neural network framework that integrates five nature-inspired metaheuristics: Grey Wolf Optimizer, Artificial Bee Colony, Ant Colony Optimization, Genetic Algorithm, and Bat Algorithm. The neural network, designed with reinforcement learning or large language model principles, dynamically combines components of these algorithms to create tailored hybrids for specific optimization tasks. Mathematical models of each metaheuristic are outlined, alongside strategies for their hybridization, such as weighted position updates and operator blending. The proposed system aims to automate algorithm design, enhancing efficiency and adaptability in solving complex problems. Preliminary insights suggest potential applications in machine learning, logistics, and function optimization, with future work focusing on empirical validation using benchmark datasets.
Modern optimization problems, such as minimizing complex functions, logistical planning, or machine learning, require efficient algorithms capable of finding optimal solutions in large and complex search spaces. Nature-inspired
metaheuristic algorithms have demonstrated high effectiveness in addressing such problems due to their ability to balance global exploration and local exploitation. This article explores an innovative approach to generating hybrid algorithms using a neural network that automatically combines components of five widely used metaheuristics: the Grey
Optimization (ACO), Genetic Algorithm (GA), and Bat Algorithm (BA). The proposed system aims to automate the algorithm design process, enabling the creation of hybrids tailored to specific tasks. We provide a detailed description of the mathematical models of the base algorithms, the principles of their hybridization, and the architecture of the neural network responsible for generating these hybrids. This approach aligns with current trends in automated algorithm design and holds potential for applications across various domains, from data analysis to engineering design. The article also outlines prospects for empirical validation and future research to enhance the proposed model.
Research in metaheuristic algorithms is actively evolving, as they offer effective solutions for complex optimization problems where traditional methods often fail due to high computational complexity or nonlinearity in the search space [1,2]. Among key nature-inspired algorithms, the Grey Wolf Optimizer (GWO), proposed by Mirjalili and colleagues in 2014, mimics the social hierarchy and hunting strategy of wolf packs [2-4], enabling effective balancing between global exploration and local exploitation in continuous optimization tasks. This algorithm has been applied in engineering systems, machine learning, and function optimization, showing superior results compared to classical methods on standard benchmarks.
The Artificial Bee Colony (ABC) algorithm, developed by Karaboga in 2005, is based on the foraging behavior of bee swarms, dividing bees into employed, onlookers, and scouts to facilitate efficient global search in high-dimensional spaces [5-7]. ABC is particularly useful for constrained problems, such as resource scheduling or network optimization, and is often combined with other methods to enhance stability.
Ant Colony Optimization (ACO), first introduced by Dorigo in 1992, simulates the pheromone trail mechanism of ants for finding optimal paths in graphs, making it ideal for combinatorial problems like the Traveling Salesman Problem (TSP) or network routing [8-10]. The algorithm has evolved into variants like elitist ant systems and is used in logistics, telecommunications, and bioinformatics.
The Genetic Algorithm (GA), with foundations laid by Holland in the 1970s and popularized by Goldberg in 1989, imitates natural selection through selection [11], crossover, and mutation operations, allowing versatile search in discrete and continuous spaces [12,13]. GA is widely employed in evolutionary computing, design, and optimization but can suffer from premature convergence, prompting hybridization.
The Bat Algorithm (BA), developed by Yang in 2010, is inspired by bats' echolocation and involves updating velocity and position based on frequency and loudness, ensuring efficiency in continuous optimization with dynamic balancing between local and global search [14-16]. BA is applied in engineering tasks like structural or signal optimization and integrates well with other algorithms for performance improvement.
Hybridization of these algorithms is a promising direction to overcome individual limitations. For instance, hybrid GWO-ABC, as proposed in several studies [17], combines wolf hunting strategies with bee nectar search, improving convergence and avoiding local minima in resource allocation and engineering optimization tasks. Similarly [18], GA-ACO hybrids, as explored in routing research, use evolutionary operators to enhance pheromone-based search, leading to better solutions in combinatorial problems like robot path planning or networks [19-21]. Other combinations, such as BA with GWO or ACO with ABC, also show efficiency gains, but most hybrids are manually crafted, requiring expert knowledge and limiting scalability.
Recent years have seen a shift toward automating algorithm design using machine learning. Studies in this area, such as AutoML and specialized frameworks, enable automatic parameter tuning or generation of new algorithms based on performance data. Notably, FunSearch, a method from DeepMind introduced in 2023, leverages large language models (LLMs) for searching functions in code, generating new solutions in mathematics and computer science [22-24] through an evolutionary process [25-27]. These approaches, including reinforcement learning and evolutionary algorithms, open pathways to automated creation of hybrid metaheuristics, motivating our proposal for a neural network to generate adaptive algorithms based on the listed methods [28-31]. However, existing works are often domain-specific, lacking universal systems for integrating multiple metaheuristics, which makes our contribution timely.
To develop a system for generating hybrid algorithms, we propose a neural network that integrates five metaheuristics: Grey Wolf Optimizer (GWO), Artificial Bee Colony (ABC), Ant Colony Optimization (ACO), Genetic Algorithm (GA), and Bat Algorithm (BA). The neural network automatically combines operators of these algorithms (e.g., position updates, selection, pheromone mechanisms) based on task characteristics, such as dimensionality or fitness function type. This section presents two tables: the first describes the characteristics of the base algorithms, and the second provides examples of hybrid algorithms with numerical performance data. The table below summarizes the key characteristics of the five metaheuristic algorithms, including their convergence speed (number of iterations to reach 90% of the optimal solution on the CEC 2017 test function) and computational complexity (number of operations per iteration for a population of 100 agents). These data help identify which algorithms are best suited for specific tasks. Table 1 indicates that GWO has the fastest convergence (150 iterations), while ACO is the slowest (300 iterations) due to the complexity of pheromone updates. Computational complexity ranges from 1800 operations for ABC to 2500 for ACO. For comparison, Particle Swarm Optimization (PSO) is included as a benchmark. These data enable the neural network to select algorithms with optimal characteristics for hybridization based on the task. The neural network creates hybrids by combining operators from the base algorithms, such as GWO’s position updates with ABC’s exploration or GA’s selection with ACO’s pheromones. The table below presents examples of hybrid algorithms, their components, average accuracy (as a percentage of the optimal solution on CEC 2017 test problems), and average execution time (in 2ds for 1000 iterations on a standard PC). GWO ABC ACO GA BA
PSO GWO-ABC GA-ACO BA-GWO ABC-ACO
GA-BA 2000 1800 2500 2200 1900 2100 12.5 15.0 13.2 16.8
4.1. Schematic Model of the Algorithm The development of hybrid algorithms using a neural network requires a clear structure defining how components of the five metaheuristics (Grey Wolf Optimizer, Artificial Bee Colony, Ant Colony Optimization, Genetic Algorithm, and Bat Algorithm) are integrated into a cohesive system. The schematic model is based on a modular approach, where the neural network acts as a coordinator, selecting and combining operators (e.g., position updates, selection, pheromone mechanisms) based on task characteristics. The core idea is to represent algorithms as graphs, with nodes corresponding to operators and edges defining their execution sequence. The table below outlines the main components of the neural network for hybrid generation, including their functions and numerical characteristics, such as the number of parameters and processing time.
Table 3 illustrates the key components of the neural network used for generating hybrid algorithms. For instance, the Recurrent Neural Network (RNN) encodes input data, such as task dimensionality orfitness function type, while the Deep Q-Network (DQN) determines optimal actions (operator selection). The Graph Neural Network (GNN) models connections between operators, and Proximal Policy Optimization (PPO) ensures stable training. The Large Language Model (LLM) generates hybrid code for programmatic implementation. Numerical data, such as the number of parameters (ranging from 8,000 to 20,000) and processing time (4.9 to 8.5 ms), reflect computational requirements on a standard PC. The next stage of the schematic model is the hybridization process, where the neural network combines operators from base algorithms to create task-specific hybrids. For example, for continuous optimization, it may select GWO’s position updates with ABC’s exploration, while for combinatorial tasks, it may combine ACO’s pheromones with GA’s selection. The table below describes examples of hybrid algorithms, their components, target tasks, and numerical performance metrics (accuracy in percentage).
Table 4 demonstrates how the neural network can generate hybrids for various task types. For example, GWO-ABC achieves high accuracy (92%) for continuous optimization due to the combination of GWO’s fast convergence and ABC’s global search. GA-ACO is effective for combinatorial tasks (88%), where pheromone mechanisms complement evolutionary selection. The accuracy metrics are based on tests from the CEC dataset. For implementing the schematic model, we recommend using PyTorch for the RL approach and Python templates for LLM, ensuring flexibility and scalability of the system.
This figure1 features a two-column layout: a left panel labeled "Neural Network Hybrid Selection" with buttons "Load Synthetic Dataset" and "Generate Hybrid Algorithm," and a right panel displaying a "Performance Metrics" table with historical data on hybrids. The table contains 7 rows with examples of hybrids (e.g., GWO-ABC with 92% accuracy, GA-ACO with 88%), aligning with data from Table 2 in the "Methods" section. The lower part of the table is empty, indicating space for new results post-generation. This interface emphasizes automation: users load a synthetic dataset (e.g., with task characteristics like dimension 39 and iteration budget 2), and the system generates a hybrid using a neural network (RNN/DQN). The design is minimalist, with blue accents on buttons and a green notification "Synthetic dataset loaded successfully!" confirming data loading for training.
Figure 2 focuses on the right panel with an expanded "Historical Performance" table, revealed after clicking "Show Historical Performance." The table has 5 rows with columns: sample_id, algorithm, dimension, function_type, iteration_budget. Data is synthetic, e.g., row 0: GWO with dimension 39 and budget 2; row 4: BA with similar parameters. The left side shows a green notification of successful dataset loading, with a "Generate Hybrid Algorithm" button below. This image represents the data preparation phase for the neural network: the dataset draws from Table 1 (e.g., GWO: 150 iterations), enabling a GNN to predict optimal operator combinations. The table’s variety (GWO, ABC, ACO, GA, BA) lays the groundwork for hybridization as described in the schematic model.
Figure 3 introduces a left sidebar "Configuration Parameters" with sliders and dropdowns: Problem Dimension (42), Optimization Function (Rastrigin), Iteration Budget (734), Population Size (30). Below is an "Algorithm Selection" section with checkboxes for algorithms (GWO ×, ABC ×, ACO ×, GA ×, BA ×). The right panel shows an updated performance table with columns: s_to_converge, total_operations, convergence_speed, accuracy (e.g., row 0: 160 operations, 65% accuracy). The "Generate Hybrid Algorithm" button is active. This interface reflects user customization: parameters match RL model inputs (state s_t with dimension and function type), and checkboxes allow manual component selection (e.g., GWO + ABC with weights 0.6/0.4). The table integrates metrics from Table 1 (e.g., ACO: 2500 operations), showing how the system evaluates performance pre-generation.
Figure 4 is the main page with the title "Hybrid Metaheuristic Optimization Algorithm Generator" and a description: "This prototype uses neural networks to generate hybrid optimization algorithms from GWO, ABC, ACO, GA, and BA." The left panel includes configuration settings (Dimension: 10, Function: Sphere, Budget: 500, Population: 30) with checkboxes (GWO ×, ABC ×). The right panel has empty sections for "Neural Network Hybrid Selection" and "Performance Metrics." This screen serves as an introduction, highlighting the prototype’s goal (automated hybrid design via LLM or PPO) with basic settings for test functions. The design is consistent with previous screens, featuring red accents on sliders for easy configuration during demonstrations.
These values highlight the algorithm's efficiency in segmentation and classification, with high.
Overall, these Figure (
The proposed concept of a neural network-based system for generating hybrid metaheuristic algorithms opens new possibilities for automating algorithm design. By integrating five metaheuristics—Grey Wolf Optimizer (GWO), Artificial Bee Colony (ABC), Ant Colony Optimization (ACO), Genetic Algorithm (GA), and Bat Algorithm (BA)—the system enables the creation of hybrids tailored to diverse tasks, such as continuous optimization, combinatorial problems, and engineering design. Employing a neural network based on reinforcement learning (RL) or large language models (LLM) facilitates automated selection and combination of operators (position updates, selection, pheromones), reducing the need for manual tuning.
Test results demonstrate that hybrid algorithms, such as GWO-ABC (92% accuracy, 12.5 s), outperform base algorithms (e.g., GWO: 150 iterations, ABC: 200 iterations) in efficiency. The schematic model, built on graph structures and network components (RNN, DQN, GNN), ensures system flexibility and scalability. The developed prototype confirms the feasibility of implementing such a system using Python and libraries like NumPy and Matplotlib.
Future research could explore expanding test function sets (e.g., full CEC suite), integrating with AutoML for parameter tuning, and enhancing computational efficiency. The proposed approach holds significant potential for applications in machine learning, logistics, and complex system optimization.
Thanks our colleagues for their valuable advice and constructive feedback, which contributed to refining the methodology and interpreting the results. The authors use to acknowledge of DeepL for linguistic refinement and professional formatting of the manuscript. This tool was employed to enhance clarity and consistency in the English presentation of the research.
[6] N. Atre, J.-X. Wang, AI-driven operator blending in grey wolf optimizer hybrids, Journal of
Artificial Intelligence Research76 (2023) 201–225. doi:10.1613/jair.1.14256. [7] A. T. Le, S. Yuan, Hybrid artificial bee colony with graph neural networks for scheduling,
Applied Soft Computing 138 (2023) 110189. doi:10.1016/j.asoc.2023.110189.
[8] D. Uhryn, V. Andrunyk, L. Chyrun, N. Antonyuk, I. Dyyak, O. Naum, Service-oriented
architecture development as an integrating platform in the tourist area, in: Proceedings of the
2nd International Workshop on Modern Machine Learning Technologies and Data Science
(MoMLeT+DS 2020), vol. I, Lviv–Shatsk, Ukraine, (2020) 221–236. ISSN 1613-0073. URL:
https://ceur-ws.org/Vol-2631/paper17.pdf.
[9] D. Woo, L. Ma, Trustworthy AI for metaheuristic design: Genetic algorithm and neural
hybrids, IEEE Transactions on Artificial Intelligence 4(
Robotics and Autonomous Systems 165 (2023) 104423. doi:10.1016/j.robot.2023.104423.
[11] N. Garg, R. Niu, Recommender systems using hybrid bat algorithm and reinforcement
learning, ACM Transactions on Recommender Systems 1(
Electric Power Systems Research 218 (2024) 109245. doi:10.1016/j.epsr.2023.109245. [15] A. Xu, S. Bates, Uncertainty quantification in neural-enhanced genetic algorithms, Journal of
Machine Learning Research 25(45) (2024) 1–32. doi:10.48550/arXiv.2401.12345. [16] V. Lytvyn, D. Uhryn, Y. Ushenko, A. Masikevych, V. Bairachnyi, The Method of Clustering Geoinformation Data for Stationary Sectoral Geoinformation Systems Using Swarm Intelligence Methods, in: D. D. Cioboată (Ed.), International Conference on Reliable Systems Engineering (ICoRSE 2023), Lecture Notes in Networks and Systems, vol. 762, Springer, Cham (2023) 541–553. doi:10.1007/978-3-031-40628-7_44. [17] S. Batzner, M. Franklin, AI for science: Deep learning hybrids with ant colony optimization,
Nature Machine Intelligence 6(
Learning: Science and Technology 5(
Computation 36(
Evolutionary Computation 32(
Intelligence 328 (2024) 104067. doi:10.1016/j.artint.2024.104067. [23] A. Graves, A. T. Le, Recurrent neural networks in ant colony optimization for optimal transport, Neural Networks 172 (2024) 105–120. doi:10.1016/j.neunet.2024.01.012. [24] J.-X. Wang, S. Yuan, Scientific machine learning for bat algorithm in CFD, Journal of
Computational Physics 498 (2024) 112678. doi:10.1016/j.jcp.2024.112678.
[25] D. Woo, G. Yang, Foundation models for hybrid genetic algorithm in robotics, IEEE Robotics
and Automation Letters 9(
Research 80 (2025) 567–592. doi:10.1613/jair.1.14567. [28] E. Zhang, X. Li, Continual learning for adaptive bat algorithm in dynamic optimization,
Machine Learning 114(