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

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.