一种求解半向量二层规划问题的基于KKT背离度量方程的粒子群优化算法

Solving Semivectorial Bilevel Programming Problem Using the Particle Swarm Optimization Based on KKT Violation Metric Function

下层多目标规划问题的Pareto最优解的精确性对于成功求解半向量二层规划问题具有决定性作用.本文基于多目标规划问题的KKT背离度量方程,设计了具有确定性终止准则的半向量二层规划问题的粒子群算法.最后,利用线性半向量二层规划算例和非线性半向量二层规划算例进行数值仿真,仿真结果表明,算法中的KKT背离度量方程能有效控制下层问题Pareto最优解的精度,从而确保问题最优解的真实有效性.

The accuracy of the lower level Pareto optimal solution is very important for the semivectorial bilevel programming problem. Based on the KKT condition of the multiobjective programming problem, the KKT violation metric equation is constructed and the accuracy of the Pareto optimal solution of the lower level problem is controlled by the metric equation. Then, taking the precise control value of the lower level Pareto optimal solution as the termination condition, the particle swarm optimization algorithm is designed for semivectorial bilevel programming problem. Finally, two sets simulation examples are used to verify the effectiveness of the proposed algorithm.