Using Firefly Algorithm To Solve Bilevel Programming Problem

In the field of economic management,military and other areas,hierarchical decisionmaking system is very prevalent,multi-level planning is the basic model to study such a system optimization problem.The second-level planning problem is the most basic form of multi-level planning problem,multi-level planning problems can be seen as a number of two-tier planning problems combined.This paper mainly studies some problems in the second-level planning.Artificial Glowworm Swarm Optimization Algorithm(GSO)is based on the natural phenomenon of simulating the clustering activities of nature fireflies at night.The algorithm has the advantages of fast capturing extremes,fast simplicity,robustness and so on.Has been successfully applied to find the location of dangerous sources,multi-polar function optimization,harmful gas leakage positioning and so on.With the deepening of the theory of artificial firefly intelligent group optimization algorithm,its practical application is more and more extensive,in the calculation of intelligent neighborhood gradually attracted people's attention.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.