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There are several important factors to consider in edge computing systems including latency, reliability, power consumption, and queue load. Task replication requires additional energy costs in mobile edge offloading scenarios based on master-slave replication for fault tolerance. Excessive task offloading may lead to a sharp increase in the total energy consumption of the system including replication costs. Conversely, new tasks cannot enter the waiting queue and are lost, resulting in reliability issues. This paper proposes an adaptive task offloading strategy for balancing the edge node queue load and offloading cost (Lyapunov and Differential Evolution based Offloading schedule strategy, LDEO). The LDEO strategy innovatively customizes the Lyapunov drift-plus-penalty function by incorporating replication redundancy offloading costs to establish a balance model between the queue load and offloading cost. The LDEO strategy computes the optimal offloading decisions with dynamic adjustment characteristics by integrating a low-complexity differential evolution method, aiming to find the optimal balance point that minimizes the offloading cost while maintaining reliability performance. The experimental results show that compared with the existing strategies, LDEO strategy effectively reduces the redundancy of fault tolerance cost and the waiting time under the condition of ensuring that the task will not be discarded over time. It stabilizes the queue length in a reasonable range, controls the waiting time and loss rate of tasks, reduces the extra energy consumption paid by replication redundancy, and effectively realizes the optimal balance under multiple conditions. [ABSTRACT FROM AUTHOR]