Combined Approach for Treating Stochastic Vector Optimization Problem

Abstract

In this thesis, a study of stochastic vector optimization problem (SVOP) is made in a comprehensive manner. Several combined problems are developed and formulated as approaches for characterizing the efficient solutions of SVOP. One of these approaches is called a modified hybrid approach which combines the characteristics of both the generalized Tchebycheff norm and the stochastic constraint problems with random variable in the constraints. This approach is rather simpler than the other scalarization method, since its parameters can be included only in the constraints instead of being included in both the objective function and the constraints. In this work, the stochastic parameters is considered to be in the right hand of the constraints. This approach is deduced by combining the generalized Tchebycheff norm approach together with the constraint approach. The advantages of the suggested approach over the hybrid one lies in the fact that all its parameters can be included only in the constraints. In addition, it gathers the characteristics of both generalized Tchebycheff norm and constraint approaches.