Through recent advances in modern production techniques, particularly in the field of additive manufacturing, new previously unthinkable geometries have become feasible. This vast realm of new possibilities cannot be adequately addressed by classical methods in engineering, which is why numerical design techniques are becoming more and more valuable. In this context, this work aims to present concepts that exploit the emerging possibilities and facilitate numerical optimization. The numerical optimization framework is based on a lattice structure, where the geometry is constructed through the functional composition of splines [1], resulting in a regular pattern of building blocks. In this approach, a macro-spline defines the outer contour, a micro-geometry specifies the individual tiles, and a parameter-spline governs the local parametrization of the microstructure. This parameter-spline enables control over features such as thickness or material density in specific regions [2]. This methodology creates a vast design space, allowing for the adaptivity of the microstructure to be easily expanded by increasing the number of control variables in the parameter-spline through h- or p-refinement. The geometric representation leverages volume splines, offering two key advantages: full compatibility with CAD/CAM systems and seamless integration with Isogeometric Analysis (IGA). To maximize the potential of this geometric parameterization, gradient-based optimization algorithms are employed, supported by analytical derivatives of the geometry and adjoint methods. This combination ensures efficient and precise exploration of the design space. We will present first results in two fields of application, namely a bone implant and a static mixer. The former is based on a linear elasticity model, whereas the latter requires to consider fluid-structure-interaction.