This paper presents the Alpine Marmot Optimization Algorithm (AMOA), a novel metaheuristic algorithm inspired by the foraging behavior of Alpine Marmots. AMOA utilizes a combination of exploration and exploitation strategies mimicking the marmot's characteristic movement patterns – searching for food in a territory, marking favored locations, and strategically relocating based on food availability and perceived risk. The algorithm incorporates three key components: a territory division mechanism, a marking strategy based on fitness values, and a relocation mechanism influenced by both food density and distance to previously marked locations. Mathematical formulations are provided to describe each component, including the territory division probability, the marking intensity, and the relocation probability. The performance of AMOA is evaluated through numerical experiments on benchmark optimization problems, demonstrating its effectiveness in finding near-optimal solutions within reasonable computational time. The algorithm's adaptability and potential for application in various complex optimization scenarios are discussed. Keywords: Metaheuristic, Optimization Algorithm, Artificial Bee Colony, Alpine Marmot, Territory Division, Marking Strategy, Relocation Mechanism.