Some Algorithms Of Bilevel Programming And Its Application In Oilfield Development

In real life, each department is inevitably influenced by the decisions from its superior departments, and its decisions also affect its subordinate departments. This kind of phenomenon reflects the hierarchy of a system. The simple one-level programming can’t solve these problems fully. Therefore, the study on bilevel programming problem (BLPP) has very important significant.The main contents of this paper are summarized as follows:Firstly, the background, the research status, the classification and the application of BLLP are introduced.Secondly, the continuous linear bilevel programming problem (L-BLPP) is introduced. It gives the model and related theories of L-BLPP, introduces three common methods which are image method, penalty function method and model transformation method for solving L-BLPP. Then a special kind of L-BLPP is studied, and a new algorithm basing on the model transformation method is also given to solve it. The feasibility of the algorithm is verified by a concrete example.Thirdly, the nonlinear bilevel programming problem is introduced. It gives the model and related theories of nonlinear bilevel programming problem, introduces four common methods which are the steepest descent algorithm, penalty function algorithm, trust region algorithm and simulated annealing algorithm.Finally, the application of BLPP under the background of the oil company is introduced. Basing on the actual situation of the company of oil, a multi-objective bilevel programming model is established. The relationship between subentry productions and their corresponding influencing factors is given by multiple quadratic regression analysis. Then by the method of linear weighted sum, the multi-objective model is changed to a single-objective model. And the lower decision variables of the single-objective model are changed to the factors of subentry productions. Simulated annealing algorithm is given to solve the model. At last, the historical data of an oilfield company is simulated and the trial is given. The result is good.