The high computational cost of population based optimization methods has been preventing applications of these methods to realistic engineering design problems. The main challenge is to devise approaches that can significantly reduce the number of function (or simulation) calls required in such optimization methods. This dissertation presents some new online and offline approximation approaches for design optimization. In particular, it presents new DOE and metamodeling techniques for Genetic Algorithm (GA) based multi-objective optimization methods along four research thrusts. The first research thrust is called: Online Metamodeling Assisted Fitness Evaluation. In this thrust, a new online metamodeling assisted fitness evaluation approach is developed that aims at significantly reducing the number of function calls in each generation of a Multi- Objective Genetic Algorithm (MOGA) for design optimization. The second research thrust is called: DOE in Online Metamodeling. This research thrust introduces a new DOE method that aims at reducing the number of generations in a MOGA. It is shown that the method developed under the second research thrust can, compared to the method in the first thrust, further reduce the number of function calls in the MOGA. The third research thrust is called: DOE in Offline Metamodeling. In this thrust, a new DOE method is presented for sampling points in the non-smooth regions of a design space in order to improve the accuracy of a metamodel. The method under the third thrust is useful in approximation assisted optimization when the number of available function calls is limited. Finally, the fourth research thrust is called: Dependent Metamodeling for Multi- Response Simulations. This research thrust presents a new metamodeling technique for an engineering simulation that has multiple responses. Numerous numerical and engineering examples are used to demonstrate the applicability and performance of the proposed online and offline approximation techniques. In particular, it is shown that in situations where the application of population based optimization techniques requires numerous simulation evaluations (or function calls), the proposed online metamodeling assisted fitness evaluation approach, the DOE assisted online metamodeling approach, and the DOE assisted offline metamodeling approach can be employed to construct a global approximation to the simulation model and significantly reduce the number of function calls. Moreover, for simulations with multiple responses, the proposed dependent metamodeling approach can be used to construct reasonably accurate metamodels and thus facilitate optimization.