一类非线性两级规划问题的模拟退火求解

Solving a Class of Nonlinear Bilevel Programming Problems by Simulated Annealing

提出一种基于模拟退火算法求解一类非线性两级规划问题的方法。为了提高模拟退火算法处理上级约束的能力，在模拟退火算法中引入一个辅助优化问题，通过求解该辅助优化问题产生满足上级约束的试探点，避免了使用罚函数处理上级约束。数值计算结果表明，与使用罚函数处理上级约束的模拟退火算法相比，本文提出的方法不仅可以提高求得全局最优解的可靠性，而且可以减少模拟退火算法的迭代次数。

A simulated annealing based method for solving a class of nonlinear bilevel programming problems is proposed in this paper.To improve the capacity of the simulated annealing algorithm to deal with the high level constraints,an auxiliary optimization problem is introduced in it.By solving this auxiliary optimization problem,the trial points satisfying the high level constraints can be generated, avoiding the use of the penalty function to deal with the high level constraints.The numerical computation results indicate that in comparison with the simulated annealing algorithm using the penalty function to deal with the high level constraints,the proposed method can not only improve the reliability for finding the global optimum but also reduce the iteration number of the simulated annealing algorithm and increase the computational efficiency.