The study of sustainable management of municipal solid waste (MSW) collection has been increasing in recent years. However, the focus areas of research are mostly in the economics and environmental dimensions. This paper adds social aspects of MSW into considerations to accelerate more comprehensive decision making. The consideration on the capacity and fixed costs of vehicles, the distances from depot to the disposal facilities are determined in this paper. The environmental issues relating to fuel consumption, carbon emissions, and the evaluation of social impact from the penalty costs of imbalanced trip assignments are also determined to adopt a comprehensive solution to the capacitated vehicle routing problem (CVRP) model. Then, the optimization model of MSW collection is proposed to minimize management costs which compose of the fixed costs of vehicles, fuel consumption costs, carbon emissions costs, and penalty costs. In this paper, two metaheuristic techniques are used to optimization the CVRP model in the MSW collection system. A new metaheuristic algorithm, called an intelligence hybrid harmony search algorithm (IHHS), is proposed in comparison with the standard harmony search (SHS) algorithm. The result shows that the IHHS algorithm can obtain the global optimal solution and can minimize the total objective function for the CVRP model.