Municipal solid waste (MSW) management is known as one of the most crucial activities in municipalities that requires large amounts of fixed/variable and investment costs. The operational processes of collection, transportation and disposal include the major part of these costs. On the other hand, greenhouse gas (GHG) emission as environmental aspect and citizenship satisfaction as social aspect are also of particular importance, which are inevitable requirements for MSW management. This study tries to develop a novel mixed-integer linear programming (MILP) model to formulate the sustainable periodic capacitated arc routing problem (PCARP) for MSW management. The objectives are to simultaneously minimize the total cost, total environmental emission, maximize citizenship satisfaction and minimize the workload deviation. To treat the problem efficiently, a hybrid multi-objective optimization algorithm, namely, MOSA-MOIWOA is designed based on multi-objective simulated annealing algorithm (MOSA) and multi-objective invasive weed optimization algorithm (MOIWOA). To increase the algorithm performance, the Taguchi design technique is employed to set the parameters optimally. The validation of the proposed methodology is evaluated using several problem instances in the literature. Finally, the obtained results reveal the high efficiency of the suggested model and algorithm to solve the problem.