This paper presents a novel optimization algorithm called the Phototropic Growth Algorithm (PGA), which takes its inspiration from the growth patterns of plant cells in response to sunlight. The proposed algorithm has been evaluated on two benchmark test function suites, the CEC 2017 and CEC 2020, and compared to other established metaheuristic-optimization algorithms based on the quality of the solutions obtained. The effectiveness of PGA is further demonstrated by testing it on six challenging engineering design problems with constraints, showcasing its robustness in solving real-world problems with unknown search spaces. Simulation results show that PGA outperforms other competitive algorithms by consistently generating superior solutions and demonstrates strong potential for solving complex optimization tasks using a nature-inspired approach.