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基于梯度搜索与进化机制的多目标混合算法

Multi-objective hybrid algorithm based on gradient search and evolution mechanism
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摘要 多目标进化算法(MOEA)因其良好的全局探索能力备受关注,但其在最优值附近的局部搜索能力却相对较弱,且对于具有大规模决策变量的优化问题,MOEA所需的种群数量与迭代次数都十分庞大,优化效率较低。基于梯度的优化算法能够很好地克服这些问题,但梯度搜索算法很难应用于多目标问题(MOPs)。在加权平均梯度的基础上引入随机权函数,发展多目标梯度算子,将其与基于参考点的第三代非支配排序遗传算法(NSGA-Ⅲ)结合,发展了多目标梯度优化算法(MOGBA)和多目标混合进化算法(HMOEA)。HMOEA在保留NSGA-Ⅲ良好的全局探索能力的同时,极大地增强了局部搜索能力。数值实验表明:HMOEA对于各种Pareto阵面都具有优秀的捕获能力,与典型的多目标算法相比效率提升了5~10倍。进一步将HMOEA应用于RAE2822翼型的多目标气动优化问题中,得到了理想的Pareto前沿,表明HMOEA是一种高效的优化算法,在气动优化设计中具有潜在的应用价值。 Because of its strong global exploration ability,the current multi-objective evolutionary algorithm(MOEA)has received a lot of attention.However,its local search ability close to the optimal value is relatively weak,and for optimization problems involving large-scale decision variables,MOEA requires a very large number of populations and iterations,which results in a low optimization efficiency.Gradient-based optimization algorithms can overcome these problems well,but they are difficult to be applied to multi-objective problems(MOPs).Therefore,this paper introduced a random weight function on the basis of a weighted average gradient,developed a multi-objective gradient operator,and combined it with a non-dominated sorting genetic algorithm-Ⅲ(NSGA-Ⅲ)based on reference points to develop multi-objective optimization algorithm(MOGBA)and multi-objective Hybrid Evolutionary algorithm(HMOEA).The latter greatly enhances the local search capability while retaining the good global exploration capability of NSGA-Ⅲ.Experiments with numbers demonstrate that HMOEA can effectively capture a wide range of Pareto forms,and that it is 5–10 times more efficient than standard multi-objective algorithms.And further,HMOEA is applied to the multi-objective aerodynamic optimization problem of the RAE2822 airfoil,and the ideal Pareto front is obtained,indicating that HMOEA is an efficient optimization algorithm with potential applications in aerodynamic optimization design.
作者 诸才承 唐智礼 赵鑫 曹凡 ZHU Caicheng;TANG Zhili;ZHAO Xin;CAO Fan(College of Aerospace Engineering,Nanjing University of Aeronautics and Astronautics,Nanjing 210016,China)
出处 《北京航空航天大学学报》 EI CAS CSCD 北大核心 2024年第6期1940-1951,共12页 Journal of Beijing University of Aeronautics and Astronautics
基金 国家自然科学基金(12032011)。
关键词 多目标优化 混合算法 进化算法 梯度方法 气动优化 multi-objective optimization hybrid algorithm evolutionary algorithms gradient method aerodynamic optimization
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