Research On Bi-Level Programming Problem Based On Improved Particle Swarm Optimization Algorithm

Bi-level programming is a kind of system optimization problem with two layers of hierarchical structure. It gets vigorous development in the field of mathematical programming, and becomes a branch of operational research. Now bi-level programming has been widely applied to various fields, such as economics, management, finance and engineering application. At the same time, the bi-level programming model is very difficult to solve. Only in the two levels objective function and constraint conditions meet the requirements of the corresponding differentiable and convexity, the traditional optimization methods based on gradient solving efficiency is higher, but for complex bi-level programming (high dimension, non-linear, the objective function is slightly, the non-convex constraint space, etc), such methods are often difficult to obtain the global optimal solution. In recent years, Evolutionary algorithm, genetic algorithm, PSO algorithm and some other intelligent optimization algorithms, due to its lower requirements for function and has the advantages of strong global search ability, has been widely used in solving bi-level programming problem. By studying and absorbing the literature about the solving algorithm of bi-level programming problem, in this paper we proposed using the improved particle swarm optimization algorithm to solve the bi-level programming problem. Paper first made some improvements to the basic particle swarm optimization algorithm, and then the improved algorithm is used for solving bi-level programming model, next proposed a double iterative algorithm based on improved particle swarm optimization, finally verify the validity of the algorithm through experiments further. The main work of this paper is as follows:(1) A particle swarm optimization algorithm with adaptive mutation (PSO-AM) is proposed based on three aspects of improvement in standard PSO. First, adaptive adjustment inertia weight make the algorithm to reach optimum balance between the global search ability and local search ability. Second, the introduction of local convergence judgment mechanism can effectively determine whether the algorithm into local convergence. Third, if the algorithm into the local convergence, by adding random disturbance to the global extreme value, improves its ability to jump out of local optimal point. The proposed algorithm can effectively avoid premature convergence of the algorithm, the global convergence speed and convergence precision improved significantly.(2) A new algorithm that uses particle swarm optimization (PSO) method to solve the bi-level programming problem (BLPP) is presented. The algorithm uses the modified PSO to solve the bi-level programming model. In the proposed algorithm, the interactive iteration between the two PSO optimized synchronously the two levels of BLPP, and finally obtaining its optimal solution. To compare with other algorithms, this algorithm is effective for solving bi-level programming model.(3) Presents a bi-level programming application model-circular and economic production model. This thesis describes the background of the model, the present situation and need to solve problems, and then establishes the model of bi-level programming problem, finally the experimental results show that the new algorithm is effective.Finally, we summarize all the work we have done, and put forwards the research direction of future.