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Cold-chain logistics presents significant challenges to sustainable development in terms of economics, society, and the environment. To address this issue, this paper focuses on solving a real-world problem—the multipath location-routing problem-based cold-chain logistics (MPLRPCCL), which considers soft time windows and heterogeneous fleets. The mathematical model aims to optimize the total logistics costs, including fuel consumption, carbon emissions, cargo deterioration, penalties, operating depots, and renting fleets. To effectively solve this problem, the paper proposes three versions of a memetic algorithm (MA) that incorporate control modules for monitoring the MA's performance and improving its global optimization performance. Computational evaluations were conducted, and the results show that the proposed algorithms are effective and outperform the classic MA framework. Furthermore, the proposed model and algorithms were applied to real-world cases in Hangzhou city, China, demonstrating their practical applicability. Overall, this paper offers a promising approach to tackling the complex challenges posed by cold-chain logistics and contributes to the sustainable development of this important field. [ABSTRACT FROM AUTHOR]