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Sustainable development is critical to cold chain logistics, including its economic, environmental, and social effects, especially in road transportation. To simultaneously address these issues, we propose a comprehensive cold-chain-based low-carbon location-routing-problem optimization model to minimize the total logistics costs and client and vehicle waiting time. The first objective comprises the fixed costs of depots to open and vehicles to rent, vehicle renting cost, driver salaries, fuel consumption cost, carbon emission costs, and damage costs of cargos that need to be refrigerated or frozen. The second objective consists of the waiting time of clients and vehicles to improve client satisfaction and the efficiency of the cold chain logistics network. In the proposed problem, we developed a strategy for improving the efficiency of the cold chain logistics network by mixing the types of cargos arranged in one vehicle. Aiming at efficiently solving the proposed model, six well-known multi-objective evolutionary algorithms (MOEAs) were used by combining an efficient framework, and first (FI) and best-improvement (BI) search mechanisms were considered. In the experiments, we examined the effectiveness of six MOEAs inserting the proposed framework and search mechanisms, and the result showed that NSGA-II/FI, SPEA2/FI, and NSGA-II/BI were the top three MOEAs. In the extensive experiments, the results showed that the delivery strategy, depot cost, depot capacity, crowding distance, and traveling speed have significant effects on the Pareto front, fuel consumption, carbon emission, vehicle and client waiting times, traveling distance, and traveling time. [ABSTRACT FROM AUTHOR]