The uncertain problem in engineering can be solved by using interval

probabilistic or fuzzy theories. Interval analysis method is used to simulate the uncertainty in excavation and shoring of underground tunnels. By representing the uncertain parameters as interval numbers

the governed equations of structural system are obtained by means of the finite element method. These equations are complicated nonlinear interval equations which comprise uncertain geometric parameters. There are two optimization models which are discussed in this paper. Taking all the interval numbers in the equations as optimal design variables and representing the lower and upper bounds of each interval number as the boundary constrain of the variable respectively

the maximum and minimum of response components such as displacements and stresses are achieved by using the genetic and simulated annealing algorithms. The numerical results demonstrate the rationality and feasibility of the present method. As a contrast

the corresponding outputs of the boundary combination are analyzed.