## 1 Introduction  
As the prevalence of smart devices, the rapid expansion of the Internet of Things (IoT), and the rise of 5G networks continue, increasingly complex and computationally demanding applications are becoming deeply integrated into our lives. While device processing capabilities have improved, there remains a significant gap compared to the resource demands of applications. To address these demands, data must be transmitted to the cloud for computation, leveraging its infinite computing power. However, this approach is constrained by limited bandwidth between devices and the cloud, exacerbated by the growing data volume due to application complexity, leading to noticeable increases in transmission latency. Thus, scholars propose deploying edge servers near smart devices or IoT devices for task computation, known as mobile edge computing (MEC). While MEC significantly reduces transmission-induced latency, latency between smart devices and edge servers remains a notable issue. However, executing all tasks locally on devices can reduce transmission-induced latency but may excessively deplete the limited energy of wireless devices, leading to device failure. Therefore, effectively allocating tasks to balance latency and energy consumption has become a crucial research problem [1]. [PERSON] et al. [2] established four models for computing energy consumption and latency in edge computing task offloading. To strike a balance between energy consumption and latency, researchers have formalized the problem as a multi-objective optimization challenge, employing an enhanced non-dominated sorting genetic algorithm (NSGA-II) to obtain the optimal solution. [PERSON] et al. [3] devised a computational sharing system model, offloading tasks to nearby smart devices or edge servers for computation. They proposed a multi-objective evolutionary algorithm (MOEA) to achieve the optimal trade-off between energy consumption and task processing delay, further optimizing the offloading quantity with NSGA-II to prolong network lifespan. [PERSON] et al. [4] also introduced RAMOS, which efficiently schedules tasks to edge devices by utilizing idle computing cycles in heterogeneous mobile IoT devices. The scheduling operates in two modes: latency minimization maximizes system throughput while adhering to energy constraints, and the energy-saving mode aims to minimize total energy consumption while meeting task deadlines. [PERSON] et al. [5] presented MOAPSO-DP, employing a non-preemptive priority algorithm, APSO, and dynamic programming to schedule tasks in edge computing to virtual machines on edge servers, significantly reducing computation time. In summary, latency and energy consumption are focal points in edge computing. However, prioritizing latency often leads to increased energy consumption. Many existing strategies optimize for a single objective and lack careful consideration of multiple goals, necessitating multi-objective optimization to find the best compromise between latency and energy consumption. [PERSON] et al. [6] proposed an advanced binary particle swarm optimization algorithm to refine content caching strategies in multi-objective optimization. Additionally, they employed a multi-objective bat algorithm to optimize task-offloading decisions, aiming for reduced latency and energy consumption. They integrated weighting to combine multiple objective functions, transforming the multi-objective problem into a single-objective one for streamlined optimization. However, this conversion to a single objective via weighting may result in unequal importance among objectives. In contrast, [PERSON] et al. 's ENsdBA method [7] enhanced the bat algorithm by integrating non-dominated sorting and crowding distance. While retaining all new solutions to prevent algorithm stagnation, this method might retain suboptimal solutions. The bat algorithm (BA), compared to genetic algorithms (GA) and particle swarm optimization (PSO), has demonstrated itself as a more contemporary, stable, and rapidly converging method [8].