My research focuses on developing specialized hardware solutions for solving combinatorial optimization problems, particularly through Ising and Potts machines. These machines are designed to identify optimal combinations of variables by optimizing the Hamiltonian energy function associated with quadratic unconstrained optimization problems. My research is divided into two main directions. The first focuses on the algorithmic development of Ising and Potts machines, including the design and selection of efficient update equations and nonlinear functions to achieve high-quality solutions in the shortest possible time. This also involves investigating the diversity of solutions explored by the algorithms during the optimization process. The second direction focuses on developing dedicated hardware architectures to implement these algorithms on photonic integrated circuits (PICs). By leveraging the inherent advantages of light, such as low power consumption, high processing speed, and high throughput, this approach aims to enable efficient and scalable hardware accelerators for combinatorial optimization.