Economic, environmental, and social effects are the most dominating issues in cold chain logistics. The goal of this paper is to propose a cost-saving, energy-saving, and emission-reducing bi-objective model for the cold chain-based low-carbon location-routing problem. In the proposed model, the first objective (economic and environmental effects) is to minimize the total logistics costs consisting of costs of depots to open, renting vehicles, fuel consumption, and carbon emission, and the second one (social effect) is to reduce the damage of cargos, which could improve the client satisfaction. In the proposed model, a strategy is developed to meet the requirements of clients as to the demands on the types of cargos, that is, general cargos, refrigerated cargos, and frozen cargos. Since the proposed problem is NP-hard, we proposed a simple and efficient framework combining seven well-known multiobjective evolutionary algorithms (MOEAs). Furthermore, in the experiments, we first examined the effectiveness of the proposed framework by assessing the performance of seven MOEAs, and also verified the efficiency of the proposed model. Extensive experiments were carried out to investigate the effects of the proposed strategy and variants on depot capacity, hard time windows, and fleet composition on the performance indicators of Pareto fronts and cold chain logistics networks, such as fuel consumption, carbon emission, travel distance, travel time, and the total waiting time of vehicles.