Bi-level programming with two layers of hierarchical structure usually is used to solve the problem of system optimization.As an important branch of operations research,it has been frequently applied to various fields,such as resource allocation,pricing,supply chain management,and environmental protection.At the same time,it is extremely difficult to solve the bi-level programming problem.Only when the structure of bi-level programming satisfies certain requirements can the solution efficiency be higher,otherwise the solution of bilevel programming problem will be very difficult.But for some models based on the actual design problems,such as non-linear,non-smooth bi-level programming model,it is difficult that the above methods obtain a global optimal solution.The global search ability of swarm intelligence optimization algorithm is strong,and there is no special requirement for the model to optimize the objective function.The intelligent optimization algorithm has become an effective algorithm for solving bi-level programming problems,such as GA,PSO and simulated annealing algorithm.In this paper,we propose an adaptive particle swarm optimization algorithm based on disturbances(ADPSO)to solve the bi-level programming model by summarizing the research results of related literatures.Firstly,the basic PSO algorithm is improved from three aspects,and then the optimized particle swarm algorithm is used to solve the bi-level programming model.Finally,the algorithm proposed in this paper is validated by comparing with other algorithms.The contents of this paper are as follows:(1)An adaptive particle swarm optimization algorithm based on disturbances(ADPSO)is proposed.The main improvement strategies are as follows:1)The disturbance factor is added to the velocity updating formula,so that the population search range is expanded;2)The adaptive inertia weight is exponentially decreasing in order to balance the global and local optimization;3)adding an adaptive Cauchy mutation on the best particle to expand the search space,reduce the possibility of local optimum and avoid premature convergence.The proposed algorithm can enhance global search capability,and has higher optimization performance,so that the convergence precision and convergence speed of the PSO are improved obviously.(2)An algorithm that uses the improved PSO for solving the bi-level programming problem is proposed.The interactive iteration between two improved particle swarm optimization algorithms reflects the decision-making process of bi-level programming problem.Compared with other examples,it is proved that this algorithm is an effective algorithm for bi-level programming problem.Finally,a bi-level programming model of urban rail passenger transport pricing is established and the proposed bilevel programming algorithm is used to solve the model,which verifies the feasibility of the model and algorithm.In the end,the research results and methods in this paper are summarized,and the future is forecasted. |