Applied Mathematics and Mechanics >
Solving high-dimensional global optimization problems via solution space restructuring with neural network
Received date: 2026-01-08
Revised date: 2026-03-30
Online published: 2026-06-18
Supported by
Project supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF), funded by the Ministry of Science and ICT (No.?RS-2024-00337001)
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It is well-known that appropriately determining the solution space and initializations is crucial for obtaining high-quality optimal solutions for optimization problems, considering both gradient-based and gradient-free techniques. However, the general framework for adaptively dealing with a particular optimization problem is commonly overlooked and thus still hidden in the literature. To overcome this limitation, a new approach assisted by the neural network (NN) is proposed for solving high-dimensional optimization issues. By restructuring the search space to optimize the objective function via a nonlinear mapping constructed by an autoencoder (AE), the surrogate solution space is constructed by a network training process and dynamically oriented to the optimal solution of the optimization issue. To enhance the optimization efficiency and address non-smooth problems, the classical metaheuristic grey wolf optimizer (GWO) and the adaptive moment estimation (Adam) are sequentially employed to complement the disadvantages of the constituted models. The effectiveness of the proposed approach is validated by solving a set of mathematical functions with 1 000-dimensional and three large-scale truss design optimization problems. Several numerical experiments show that the solution space is reduced in terms of both size and complexity based on the restructuring procedure, in which the global optimal solution is still conserved, leading to better optimization efficiency when solving optimization problems with complex search domains with large dimensions. In addition, the hybrid optimizer has also been proven to be more effective when combined with the restructuring technique owing to the use of the Adam algorithm in the second phase.
N. VO , T. LE-DUC , H. TANG , H. NGUYEN-XUAN , S. H. LEE , J. H. LEE . Solving high-dimensional global optimization problems via solution space restructuring with neural network[J]. Applied Mathematics and Mechanics, 2026 , 47(6) : 1383 -1400 . DOI: 10.1007/s10483-026-3393-7
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