基于SQP的双层单目标优化算法

Bilevel Single-Objective Optimization Algorithm Based on SQP

摘要: 近年来，进化算法已被证明是一种能有效处理双层优化问题的算法。在双层优化问题的嵌套结构中，下层优化的效率以及优化所需的大量计算资源，已经成为处理双层优化问题要面临的巨大挑战。因此，本文提出了一种基于SQP方法的双层优化算法(SQPEA)来处理双层单目标优化问题。在SQPEA算法中，我们引入了非线性优化算法SQP来对下层优化进行预优化处理，将预优化的最优解作为下层优化的初始解，并利用最优梯度向量来缩小下层搜索空间，提高下层优化效率，进而提高上层优化效率。最后，在12个标准测试问题上与成熟的双层优化算法进行对比实验，实验结果证明了所提算法在处理双层单目标问题上突出的性能表现。

Abstract: In recent years, evolutionary algorithm has been proved to be an efficient algorithm for solving bilevel optimization problems. In the nested structure of the bilevel optimization problem, the efficiency of the lower lower optimization and the large amount of computational resources required for the optimization have become a great challenge to deal with the bilevel optimization problem. Therefore, this paper proposes a bilevel optimization algorithm based on the SQP method (SQPEA) to deal with bilevel single-objective optimization problems. In the SQPEA algorithm, we introduce the nonlinear optimization algorithm SQP to pre-optimize the lower optimization, and take the optimal solution of the pre-optimization as the initial solution of the lower optimization, and use the optimal gradient vector to reduce the search space of the lower optimization and improve the efficiency of the lower level optimization, then improve the optimization efficiency of the upper level. Finally, comparing with a mature bilevel optimization algorithm on 12 standard test problems, the experimental results show that the proposed algorithm has outstanding performance in dealing with bilevel single-objective problems.