Beyond Optimization: How Topology Synthesis Creates New Possibilities in Engineering?

First, let's discuss the concepts of optimization and topology synthesis. At present, engineering research is mainly concentrated in optimization, while topological synthesis research is relatively small. Optimization is the modification of an existing design to fulfill engineering requirements, while topology synthesis is the creation of new structural forms that may not occur in conventional designs. For example, optimization can refine the geometry of an existing object, such as refining a cube-like shape to a circular shape. However, topology synthesis can create structural concepts that are fundamentally different by altering the connectivity or arrangement of the material, e.g., a donut-like structure instead of a solid one. In short, optimization modifies existing designs, while topology synthesis generates new design possibilities.

The examples of topology synthesis listed above only address the reduction of weight, material usage, maximization of stiffness, and minimization of stress in existing objects, but they are not entirely innovative. Humans create initial design concepts based on fleeting imagination, often without a deep understanding of mathematics. Therefore, these concepts are not born from complex algorithms. The question arises: can topology algorithms truly create entirely new structural concepts that humans may never have imagined?

Topology optimization can enhance existing designs and discover better structures based on requirements and objectives at present, for example, removing unnecessary structures or materials. While topology synthesis can be used to generate new structural concepts based on design requirements, e.g., the user has to specify the required instructions to create a mobile wheel that can carry a load of 500 kg. The above examples obviously involve the intuitive description of the "object," and the existing topology synthesis algorithms are unable to generate valid structural solutions without specific design objectives and constraints.

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