Bilevel optimization has been recognized as one of the most difficult and challenging tasks to deal with because a solution to the upper level problem may be feasible only if it is also an optimal solution to the lower level problem. In recent years, evolutionary bilevel optimization has attracted increasing interest. In this paper, an efficient self-adaptive bilevel differential evolution (SABiLDE) with k-nearest neighbors (kNN) based interpolation is proposed to solve bilevel optimization problems. The kNN approximation is applied to estimate the optimal lower level variables for any newly generated upper candidates to improve the computational efficiency. A similarity based self-adaptive strategy for the dynamic control of lower level population size and search radius is introduced to further enhance the efficiency of the lower level function evaluations. A test set with 10 standard test problems and the SMD suite with controllable complexities are used to evaluate the performance of the proposed approach. Compared with four recent state-of-the-art methods, the numerical results produced by the proposed method are promising and show great potential for solving generic bilevel optimization problems.

双层优化已被认为是要处理的最困难和最具挑战性的任务之一，因为只有在上层问题的解决方案也是下层问题的最优解决方案时，它才是可行的。近年来，进化的双层优化吸引了越来越多的兴趣。本文提出了一种具有k的有效自适应双级微分进化（SABiLDE）提出了基于近邻（kNN）的插值算法来解决双层优化问题。kNN近似可用于估计任何新生成的上层候选对象的最佳下层变量，以提高计算效率。引入了基于相似度的自适应策略，用于动态控制下层人口规模和搜索半径，以进一步提高下层功能评估的效率。使用具有10个标准测试问题的测试集和具有可控复杂性的SMD套件来评估所提出方法的性能。与最近的四种最新方法相比，该方法产生的数值结果是有希望的，并显示出解决通用双层优化问题的巨大潜力。