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The computation offloading problem in mobile edge computing (MEC) has received a lot of attention, but service caching is also a research topic that cannot be ignored in MEC. Due to the limited resources available on the Edge Server (ES), a wise computation offloading and service caching policy must be formulated in order to maximize system offload efficiency. In this paper, a many-objective joint optimization computation offloading and service caching model (MaJOCOSC) is designed. The model takes into account the limited computing and storage resources of ES, the delay and energy consumption constraints of different types of tasks, and multiple processing modes of user tasks, and sets delay, energy consumption, task hit service rate, service cache balancing, and load balancing as the five optimization objectives of MaJOCOSC. Meanwhile, a non-dominated sorting genetic algorithm (NSGAIII-ASF&WD) based on achievement scalar function (ASF) and the k-nearest neighbor weighted distance mating selection strategy is proposed for better solving the model. The ASF ensures that the given strategy performs well for each objective value, and the k-nearest neighbor weighted distance provides the user with a diversity of strategies. Simulation results show that NSGAIII-ASF&WD can obtain better objective values when solving the model compared with other many-objective evolutionary algorithms, and a suitable computation offloading and service caching strategy is obtained. [ABSTRACT FROM AUTHOR]