Hybrid Optimization Method Based on Coupling Local Gradient Information and Global Evolution Mechanism

Caicheng Zhu, Xin Zhao, Xinlei He and Zhili Tang ()
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Caicheng Zhu: College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Xin Zhao: College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Xinlei He: College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
Zhili Tang: College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China

Mathematics, 2024, vol. 12, issue 8, 1-25

Abstract: Multi-objective evolutionary algorithms (MOEA) have attracted much attention because of their good global exploration ability; however, their local search ability near the optimal value is weak, and for large-scale decision-variable optimization problems the number of populations and iterations required by MOEA are very large, so the optimization efficiency is low. Gradient optimization algorithms can overcome these difficulties well, but gradient search methods are difficult to apply to multi-objective optimization problems (MOPs). To this end, this paper introduces a stochastic weighting function based on the weighted average gradient and proposes two multi-objective stochastic gradient operators. Further, two efficient evolutionary algorithms, MOGBA and HMOEA, are developed. Their local search capability has been greatly enhanced while retaining the good global exploration capability by using different offspring update strategies for different subpopulations. Numerical experiments show that HMOEA has excellent capture ability for various Pareto formations, and it can easily solve multi-objective optimization problems with many objectives, which improves the efficiency by a factor of 5–10 compared with typical multi-objective evolutionary algorithms. HMOEA is further applied to the multi-objective aerodynamic optimization design of the RAE2822 airfoil and the ideal Pareto front is obtained, which indicates that HMOEA is an efficient optimization algorithm with potential applications in aerodynamic optimization design.

Keywords: aerodynamic optimization; multi-objective optimization; evolutionary algorithm; gradient optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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