Algorithms For Fuzzy Chance Constrained Programming Problem

Fuzzy chance constrained programming has been widely applied into supply chain inven-tory、portfolio selection、 logistics, engineering control and capital budgeting, etc. The key to solve such problems is to get equivalent form of the chance constraints. To the best knowledge of the author, for solving fuzzy chance constrained programming problems, the main methods are reforming method and fuzzy simulation method based on genetic algorithm. While reforming method can only be applied to the fuzzy chance constrained programming, in which the decision variables and fuzzy variables in the chance constraints can be separated or have a certain linear relationship. The main idea of the fuzzy simulation method based on genetic algorithm is using the fuzzy simulation to check the feasibility of solutions, then getting the optimal solution based on the fittest survival principle of the genetic algorithm. But the fuzzy simulation is an approx-imation process, which may cause the solution unstable. The size of the simples is not easy to determined, which may cause the approximate solution can not converged to the stationary points of the original problem.In this article, we put forward transforming the original problem into a bi-level program-ming(BLP)based on the probability distribution of fuzzy variables, then by solving the BP problem to get the optimal solution of the original problem. The main content is summarized as follows:Firstly, for nonlinear FCCP problem with single fuzzy variable, we based on the relationship between fuzzy possibility measure and fuzzy variable distribution to transformed the original problem into a BLP problem with convex second-stage programming. Then we substitute the second-stage programming with its KKT conditions to get a complementary constraint opti-mization problem. Finally, the complementary constraints are solved with smoothing method. The numerical experiments show that this algorithm is efficient, and this method speed up the calculation and convergence, which locally improve the accuracy of solution.Secondly, we introduced a new variable for solving the fuzzy chance constrained program-ming problems with several variables and chance conditions. Then using the above new method, the original problem is transformed to a general nonlinear programming. Finally, we proved the method is efficient through numerical experiments.