EDA算法求解一类特殊的非线性双层规划问题

EDA Algorithm for Solving a Class of Special Nonlinear Bi-level Programming Problems

研究下层为线性规划上层为二次规划的非线性双层规划问题。利用单纯形最优性等价条件和基于正态分布的分布估计算法(EDA)求解该问题的全局最优解。为了提高算法效率,结合种群最优个体,给出了有效的交叉算子。设计算法时,用均匀设计产生初始种群,从而增加种群的多样性。为克服进化算法的弱局部收敛性,文中提出一种新的方法增加算法的局部收敛性。数值试验结果表明,文中提出的算法是有效且快速的。

This paper studies the nonlinear bi-level programming with the lower for linear programming and the upper for quadratic programming. The optimal simplex equivalent conditions and estimation of distribution algorithms （EDA） based on Gaussian distribution are employed to obtain the global optimal solution to the problem. The algo- rithm is combined with the optimal individual of the population for higher efficiency, and an effective crossover oper- ator is given. In designing an algorithm, uniform design is used to generate the initial population, which can in- crease the diversity of the population. To overcome the weak local convergence of evolutionary algorithm, this paper proposes a new approach to increasing the local convergence of the algorithm. Numerical test results show that the proposed algorithm is effective and fast.