A robust design optimization method with integrated evidence computation is proposed. The uncertainties are given in form of a multi-level BPA structure consists of statistical parameters and BPA values. Estimation of statistical parameters are given with associated BPA values. The optimization problem is reformulated as a multi-objective optimization problem with one objective is set to minimize the cost, while another one is to maximize the evidence. Monte-Carlo based interval operations are used to combine the information of the evidence. Number of the focal elements is set to equal to the population size. A Proper Orthogonal Decomposition (POD) technique based MOO algorithm with Tchebysheff decomposition is implemented to search the robust solutions. The algorithm computes function values and corresponding cumulative evidence in an integrated way. Experimental results of the test function show that amount of computational cost can be reduced. With proposed method, simulation of determining debris targets of a pulsed Laser Orbital Debris Removal(LODR) system under uncertainty is presented.