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 the mobile edge offloading scenario based on master-slave replication for fault tolerance. Excessive task offloading may lead to sharp increase in the total energy consumption of the system including replication costs. On the contrary, new tasks cannot enter the waiting queue and are lost, resulting in unreliable problems. This paper proposes propose 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 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. By integrating a low-complexity differential evolution method, the LDEO strategy computes the optimal offloading decisions with dynamic adjustment characteristics, aiming to find the optimal balance point that minimizes the offloading cost while maintaining reliability performance. Experimental results show that compared with the existing strategies, the LDEO strategy effectively reduces the redundancy and the growth rate of task completion time, with similar task execution completion rate. By ensuring that the queue length remains stable within a reasonable range, controlling both task waiting time and loss rate, and reducing the additional energy consumption associated with replication redundancy, the LDEO strategy effectively achieves optimal balancing under multiple conditions.