| There are lots of bi-level programming (BLP) problems with leader-followerhierarchical structure in the realistic decision-making environment. And because of aseries of disturbance factors, the parameters of the models are often uncertain. Inorder to describe uncertain optimization problems, some mathematic models such asstochastic BLP, fuzzy BLP and interval linear BLP are widely used. But the robustoptimization becomes a new research topic instead of the methods above in theuncertain optimization, which needs not describe the distribution assumption of theuncertain parameters and possesses immunity against the uncertainty of the datum.Based on the theory and methodology of one-level robust programming and BLP, therobust solution and the transformation theorems of uncertain BLP are proposed underthe specific decision-making background. The corresponding algorithms are designedto solve the deterministic programming transformed for the robust solution.The main work and innovation points of this thesis include:Firstly, the definition of robust solution is influenced by the dependent degree ofthe upper and lower levels in the decision-making process for the uncertain BLP.Under the way of the decentralized decision-making, the robust solutions are definedfor the BLP with the coefficients under the different disturbance in objective functionsand constraint conditions. The disturbance modality about the box set and ellipsoidalset are given for the linear BLP, while the disturbance modality about the convex hullfor several discrete points and polyhedron set are given for the convex quadratic BLP.Then these corresponding original uncertain BLPs are converted to the deterministicBLP constrained with second-order cone in the lower level, and the mixed geneticalgorithm is proposed to obtain the robust solution.Secondly, under the way of the centralized decision-making, the linear andconvex quadratic BLP with the coefficients under the box disturbance is studied.Correspondingly, the definitions of robust solution and the transformation theorem aregiven. Meanwhile, the intersection form of two different decisions above is discussed.Finally, the algorithms are designed for the certain models transformed.Thirdly, several robust BLPs reducing conservation are studied for the linear,discrete linear and the mixed0-1polynomial BLPs. Also according to the new robustmetric constraint constructed by the robust index, the robustness of linear BLP with the probability distribution of the stochastic parameters independent and bounded isconsidered. As above, the algorithms are designed for the certain models transformed.Fourthly, the hierarchical decision problem exists in the product familyarchitecture design, so the robust BLP models are applied to the two differentoptimization design problems of the product family architecture in uncertain productdesign environment. And two practical examples are given to demonstrate thecorresponding methods. |
