School of Mathematics and Physics, Qinghai University, Xining, China.
School of Mathematics and Statistics, Qinghai Normal University, Xining, China.
PLoS One. 2022 Aug 30;17(8):e0273564. doi: 10.1371/journal.pone.0273564. eCollection 2022.
In the engineering and economic management fields, optimisation models frequently involve different decision-making levels. These are known as multi-level optimisation problems. Because the decision-making process of such problems are hierarchical, they are also called a hierarchical optimisation problems. When the problem involves only two-level decision-making, the corresponding optimisation model is referred to as a bilevel programming problem(BLPP). To address the complex nonlinear bilevel programming problem, in this study, we design an evolutionary algorithm embedded with a surrogate model-that it is a approximation method and correlation coefficients. First, the isodata method is used to group the initial population, and the correlation coefficients of the individuals in each group are determined based on the rank of the leader and follower objective functions. Second, for the offspring individuals produced by the evolutionary operator, the surrogate model is used to approximate the solution of the follower's programming problem, during which the points in the population are screened by combining the correlation coefficients. Finally, a new crossover operator is designed by the spherical search method, which diversifies the generated offspring. The simulation experimental results demonstrate that the proposed algorithm can effectively obtain an optimal solution.
在工程与经济管理领域，优化模型经常涉及不同的决策层次，这些模型被称为多层优化问题。由于此类问题的决策过程具有层次性，因此它们也被称为分层优化问题。当问题仅涉及两级决策时，相应的优化模型被称为双层规划问题（Bilevel Programming Problem，BLPP）。为了解决复杂的非线性双层规划问题，本研究设计了一种嵌入代理模型的进化算法，即近似方法和相关系数。首先，使用 ISODATA 方法对初始种群进行分组，并根据领导者和追随者目标函数的等级确定每个组中个体的相关系数。其次，对于进化算子产生的后代个体，使用代理模型来近似跟随者规划问题的解，在此过程中，通过结合相关系数对种群中的点进行筛选。最后，通过球形搜索方法设计了一种新的交叉算子，以增加生成后代的多样性。仿真实验结果表明，所提出的算法可以有效地获得最优解。
