This paper presents a novel meta-heuristic algorithm inspired by the visual capabilities of the mantis shrimp (Gonodactylus smithii), which can detect linearly and circularly polarized light signals to determine information regarding the polarized light source emitter. Inspired by these unique visual characteristics, the Mantis Shrimp Optimization Algorithm (MShOA) mathematically covers three visual strategies based on the detected signals: random navigation foraging, strike dynamics in prey engagement, and decision-making for defense or retreat from the burrow. These strategies balance exploitation and exploration procedures for local and global search over the solution space. MShOA’s performance was tested with 20 testbench functions and compared against 14 other optimization algorithms. Additionally, it was tested on 10 real-world optimization problems taken from the IEEE CEC2020 competition. Moreover, MShOA was applied to solve three studied cases related to the optimal power flow problem in an IEEE 30-bus system. Wilcoxon and Friedman’s statistical tests were performed to demonstrate that MShOA offered competitive, efficient solutions in benchmark tests and real-world applications.