Shape optimization is a mathematical and computational methodology focused on determining the optimal geometric shape of a system or component within a defined design space. This process seeks to identify the configuration that maximizes or minimizes a specified performance objective function, such as minimizing drag, maximizing stiffness, or controlling energy distribution, while satisfying various physical, manufacturing, or cost constraints. It is a fundamental area in computational design and engineering, critical for enhancing efficiency, performance, and reliability across numerous scientific and industrial applications.