This study presents a comparative analysis of metaheuristic algorithms applied to the Asymmetric Capacitated Vehicle Routing Problem (ACVRP) within the context of municipal recycling waste management. The main goal is to optimize the collection routes for municipal waste collection vehicles to reduce operational costs, particularly in relation to the total distance traveled and the number of vehicles required. The problem was modeled as a graph in a case paradigm of a small municipality in Greece, namely Xanthi, where bins represent nodes and streets represent directed edges. A variety of initialization methods (Cheapest Arc, Most Constrained Arc, Savings Heuristic, etc.) and optimization algorithms (Greedy Descent, Guided Local Search, Simulated Annealing, and Tabu Search) were applied to the graph. Results show that by dynamically adjusting routes based on bin load data, the total distance traveled by waste vehicles was reduced by 65%, and the number of required vehicles was halved. Economic analysis demonstrated a 55% reduction in total costs when applying distance constraints, with further reductions possible under unconstrained scenarios. This research highlights the potential of advanced metaheuristic optimization to significantly improve the efficiency and sustainability of waste management operations.