Deep learning at the service of metaheuristics for solving numerical optimization problems

Integrating deep learning methods into metaheuristic algorithms has gained attention for addressing design-related issues and enhancing performance. The primary objective is to improve solution quality and convergence speed within solution search spaces. This study investigates the use of deep learning methods as a generative model to learn historical content, including global best and worst solutions, solution sequences, function evaluation patterns, solution space characteristics, population modification trajectories, and movement between local and global search processes. An LSTM-based architecture is trained on dynamic optimization data collected during the metaheuristic optimization process. The trained model generates an initial solution space and is integrated into the optimization algorithms to intelligently monitor the search process during exploration and exploitation phases. The proposed deep learning-based methods are evaluated on 55 benchmark functions of varying complexities, including CEC 2017 and compared with 13 biology-based, evolution-based, and swarm-based metaheuristic algorithms. Experimental results demonstrate that all the deep learning-based optimization algorithms achieve high-quality solutions, faster convergence rates, and significant performance improvements. These findings highlight the critical role of deep learning in addressing design issues, enhancing solution quality, trajectory, and performance speed in metaheuristic algorithms.