Algorithms And Applications For Solving A Class Of Distributionally Robust Optimization Problems

Distributionally robust optimization is an optimization model for solving uncertain problems.It has been widely used in many fields such as securities investment,management science,economics and so on.In recent years,many scholars have paid attention to it.In stochastic programming problems,uncertain variables usually obey certain probability distributions,but in realistic decision,these definite distributions are often unknown or we only know part of the distribution information.Distributionally robust optimization is an effective method to solve uncertain problems.It is noticed that sometimes the set of distributions is related to the decision variables in practical problems,so this paper mainly focuses on a distributionally robust optimization problem with the set of distributions dependent on the decision variables.We propose direct and indirect methods to solve such distributionally robust optimization problems.The convergence analysis and some numerical experiments are carried out to illustrate their effectiveness.The main contents of this paper are as follows:Firstly,the background and progress of distributionally robust optimization are introduced.Secondly,based on Benders decomposition,an alternative algorithm for solving a class of distributionally robust optimization problems with set-dependent decision variables is proposed,and the convergence theory of the algorithm is established.An improved model and algorithm with less conservativeness are proposed for this kind of distributionally robust model under special circumstances,and the corresponding convergence analysis theory is established.Thirdly,in view of the limitations of the direct method,we propose an indirect method to solve the distributionally robust optimization problem with distributionally set dependent decision variables.The problem of robust optimization can be easily solved by reconstruction way,and then the solution of robust optimization can be obtained by solving the problem.Finally,the algorithm is applied to the problem of newspaper suppliers.Some numerical experiments show that the direct algorithm is effective in some special cases and the indirect algorithm is easy to solve.