一种求解二层单目标规划问题的基于KKT背离度量方程的粒子群优化算法

An Algorithm of Solving Bilevel Programming Problem by Using the Particle Swarm Optimization Based on KKT Violation Metric Function

下层规划问题最优解的精确性对成功求解二层单目标规划问题具有决定性作用。基于单目标规划问题的KKT条件,引入KKT背离度量方程,利用该度量方程控制下层问题最优解的精度;然后以下层问题最优解的精度控制值为终止条件,设计求解二层单目标规划问题的粒子群算法;最后利用6组带箱式约束的经典算例对算法进行了评估,结果表明该算法能够提高计算效率并能加速算法收敛速度。

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