In this paper, we introduce a discrete variant of the MOA (DMOA) tailored specifically for tackling the automated guided vehicle (AGV) routing optimization problem. To ensure a high-quality initial population, we employ a random-roulette selection-based initialization method to generate the initial mayfly population. Moreover, we integrate combinatorial update operators and an enhanced 2-opt operator into the mayfly position update phase, allowing the algorithm to adapt seamlessly to discrete optimization problems while retaining the core MOA position update mechanism. Furthermore, a combinatorial mutation operator is devised to refine the solutions of offspring mayfly populations. Through comprehensive experimentation across 24 instances ranging from 16 to 1002 nodes from the TSPLIB dataset and a practical application scenario involving AGV routing optimization, we assess the efficacy of DMOA. The experimental results, supported by rigorous statistical analyses, demonstrate the feasibility of the proposed algorithm in tackling the TSP and AGV routing optimization and its superiority over traditional approaches, state-of-the-art algorithms, and novel methodologies, highlighting its potential utility in real-world optimization scenarios.