求解二层规划问题的萤火虫智能群优化算法

Using firefly algorithm to solve bilevel programming problem

针对二层规划问题,给出二层决策问题数学模型的一种新的解法,二层规划萤火虫智能群优化算法:首先采用以原问题的下层问题的Kuhn-Tucker条件代替下层问题的思想,将二层规划问题转化为单层规划问题.其次为避免求解目标函数的梯度信息以及算法过早的陷入局部最优,利用基于Pareto最优解集的萤火虫智能群优化算法对其进行求解,并利用Matlab予以实现.利用5个具有代表性的标准测试实例对该算法予以测试,并与其他算法进行比较.结果表明,结合Kuhn-Tucker条件的萤火虫智能群优化算法在5个测试函数中均能寻找到最优Pareto解,并且在求解的上层目标函数值上均优于对比算法,表明新算法可行有效.

In order to solve bilevel programming problem, this paper proposed a novel intelligent optimization algorithm named the firefly algorithm. The thought of this paper is using Kuhn-Tucker conditions of the underlying problem instead the underlying problem, so that the bilevel programming problem can be conversed into single programming. In order to avoid solving the gradient information of the objective function and algorithm premature into local optimum, use the firefly intelligent algorithms that based on the Pareto optimal solution to solve it, and by using Matlab. Testing through a series of numerical example and comparing with other algorithms, the results show that the fireflies intelligent algorithm that combinated Kuhn- Tucker conditions is feasible and effective.