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While gradient-based optimization methods are efficient, they rely on function smoothness and initial guesses, prompting the use of gradient-free metaheuristic algorithms (MAs). On the other hand, MAs face a great challenge as the problem dimensionality increases. In this work, a new approach for high-dimensional single-objective optimization based on unsupervised learning is proposed. By defining both the input and output of the network to be candidate solutions in the same solution space, and the objective function to be the loss, the original optimization problem is transformed into training the network. For representative purposes, the classical metaheuristic Grey Wolf Optimizer (GWO) and the adaptive moment estimation (Adam) are sequentially used in the training process to take their complementary features in solving the objective function within a low computation budget. Indifferentiable and multimodal functions with 100-dimensional solution spaces are used to test the efficacy of the proposed approach. It is revealed that after GWO training, the network outputs are structured distributions around the global optimum, indicating potential of more significant dimension reduction in higher dimensions and promises in efficiently solving higher-dimensional optimization problems.

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A Neural Network Approach for Domain Reduction in High-Dimensional Optimization Problem

  • 会议论文

  • 发表日期：

    2025年

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  • Nam Thanh Vo,
  • Huy L. N. G. Tang,
  • Linh Viet Tran,
  • Phat Thanh Nguyen,
  • Somin Kim,
  • Seunghye Lee,
  • Jaehong Lee

摘要

While gradient-based optimization methods are efficient, they rely on function smoothness and initial guesses, prompting the use of gradient-free metaheuristic algorithms (MAs). On the other hand, MAs face a great challenge as the problem dimensionality increases. In this work, a new approach for high-dimensional single-objective optimization based on unsupervised learning is proposed. By defining both the input and output of the network to be candidate solutions in the same solution space, and the objective function to be the loss, the original optimization problem is transformed into training the network. For representative purposes, the classical metaheuristic Grey Wolf Optimizer (GWO) and the adaptive moment estimation (Adam) are sequentially used in the training process to take their complementary features in solving the objective function within a low computation budget. Indifferentiable and multimodal functions with 100-dimensional solution spaces are used to test the efficacy of the proposed approach. It is revealed that after GWO training, the network outputs are structured distributions around the global optimum, indicating potential of more significant dimension reduction in higher dimensions and promises in efficiently solving higher-dimensional optimization problems.