Many design problems are in fact optimization problems. The main emphasis in this project is on modeling some robust design problems, i.e. problems that deal with finding a robust optimal solution of an uncertain design problem. Our aim is to use the robust counterparts (RC) methodology of Ben-Tal and Nemirovskii. In this methodology, the robust counterpart represents a worst-case oriented approach: a solution is robust feasible only if the solution satisfies the technological constraints for all possible values of the uncertainty data. We assume that the data belongs to an ellipsoidal uncertainty set. In this case, the robust counterpart of a linear optimization problem leads to a conic quadratic optimization problem (which can be solved efficiently by using interior-point methods). In some specific problems such as the robust shortest path problem, the robust counterpart contains binary variables. In this case the robust counterpart is a binary conic optimization problem. The problem is in general not computationally traceable, since we need a branch and bound scheme to solve the problem. Therefore we need to develop a more efficient algorithm by exploiting the special structure. In this talk, we intend to solve the problem approximately via a semidefinite relaxation. We elaborate the semidefinite relaxation as proposed by Poljak et al. and by Ben-Tal Nemirovkii. A new semidefinite relaxation for conic quadratic problem with binary variables is presented.