Dual-rotor wind turbines (DRWT) may offer better energy efficiency over their single-rotor counterparts in isolated and in windfarm operation. The design and analysis of DRWT requires, among other, the use of computational fluid dynamics models. Depending on their formulation, these models can be computationally expensive. Numerous simulations are typically required during the design process, which may render the overall computational cost to be prohibitive. This thesis investigates and compares several optimization techniques for the design of DRWTs. In particular, the DRWT fluid flow is solved using the Reynolds-Averaged Navier-Stokes equations with a two-equation turbulence model on an axisymmetric mesh, while three design approaches are considered: (1) the traditional parametric sweep where the design variables are varied and the responses examined, (2) direct optimization with a derivative-free algorithm, and (3) surrogate-based optimization (SBO) using both data-driven and physics-based surrogates. The approaches are applied to test cases involving two, three, and 11 design variables. Two final cases utilize the physics-based SBO to carry out a parametric study of two of the design variables. The results show that the same optimized designs are obtained with all the approaches. However, going from the two-parameter case to the three-parameter case, the effort of setting up, running, and analyzing the results is significantly higher with the parametric sweep approach. The optimization techniques are more efficient because they require no assumptions of sampling discretization, and are much more likely to find the best design. In addition, they deliver the results with lower computational cost in comparison with the parametric sweep approach, while the SBO algorithms often outperform the direct approach in terms of computational expense.