We present Design-by-Morphing (DbM), a novel design methodology applicable to creating a search space for topology optimization of 2D airfoils. Most design techniques impose geometric constraints and sometimes designers' bias on the design space itself, thus restricting the novelty of the designs created, and only allowing for small local changes. We show that DbM methodology does not impose any such restrictions on the design space and allows for extrapolation from the search space, thus granting truly radical and large search space with a few design parameters. In comparison to other shape design methodologies, we apply DbM to create a search space for 2D airfoils. We optimize this airfoil shape design space for maximizing the lift-over-drag ratio, $CLD_{max}$, and stall angle tolerance, $\Delta \alpha$. Using a bi-objective genetic algorithm to optimize the DbM space, it is found that we create a Pareto-front of radical airfoils exhibiting remarkable properties for both objectives.

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