Each active edge server or VM consumes a baseline power even if underutilized. Thus, scheduling algorithms that consolidate workload (i.e., increase average CPU utilization) can reduce the total number of active servers or active time, lowering energy consumption Ahmed et al. (2021). Ullah works have shown that minimizing the number of VMs used and reducing task makespan leads to significant energy savings in fog and cloud environments Ullah et al. (2024). For example, Singh et al. achieved lower energy usage by scheduling workflows such that fewer VMs were active and tasks finished sooner Singh and Kumar (2023). Similarly, Saidi et al.demonstrated that improving VM CPU utilization (through better task allocation) directly reduces overall energy consumption in a cloud data center Saidi and Bardou (2023). These studies underscore that how tasks are matched to resources can markedly impact energy efficiency. Energy-aware scheduling has therefore become a prominent research topic in edge and cloud computing Kocot et al. (2023), with solutions ranging from heuristics to advanced machine learning.

Greedy heuristics like First-Fit Decreasing (FFD) are popular for task scheduling and bin packing due to their simplicity and speed. In FFD, tasks are sorted by decreasing size and then placed onto the first available resource (VM) that can accommodate them. This strategy is easy to implement and often yields an acceptable solution quicklyda da Costa et al. (2023). FFD and related heuristics have beenapplied to cloud/edge scheduling, for instance to allocate tasks to VMs based on workload sizes and VM capacities Chen et al. (2023). However, heuristic methods do not guarantee optimal or near-optimal solutions and can perform poorly for complex multi-dimensional scheduling constraints. Greedy FFD approaches may be less efficient for complex scenarios such as cloud and fog computing Juan et al. (2023). In dynamic edge environments with many variables, heuristics risk getting trapped in local optima and may not adapt well to changing conditions.

To improve upon static heuristics, researchers have turned to metaheuristic and evolutionary algorithms that explore the solution space more broadly. Differential Evolution (DE) is one such evolutionary optimization algorithm known for fast convergence and simplicity of operations Song et al. (2023). DE evolves a population of candidate solutions (scheduling assignments, in our context) by iteratively applying mutation and crossover, and selecting the fittest solutions. It has shown success in many scheduling and resource allocation problems, from cloud task scheduling to IoT edge clustering. Metaheuristics like DE can approach near-optimal solutions for NP-hard scheduling problems, though they involve more computation time than heuristics Ahmad et al. (2022), and Laili et al. (2023). Recent studies have hybridized heuristics with metaheuristics to get the best of both–using heuristics to guide or initialize the search, then applying global optimization to fine-tune the allocation. For example, Abdel-Basset et al. (2022) introduced a hybrid DE (HDE) algorithm with custom improvements to solve cloud task scheduling, achieving better results than both classical DE and simpler schedulers like first come first served algorithm and Round-Robin algorithmAbdel-Basset et al. (2022). Likewise, Chhabra et al. (2022) combined Whale Optimization with oppositional DE to minimize makespan and energy for scheduling independent cloud tasks, and reported 3%–19% reductions in energy use compared to baseline algorithms Chhabra et al. (2022). These works illustrate the promise of hybrid approaches in balancing exploration (global search for energy/timing optimization) with exploitation (greedy efficient packing of tasks). To clearly present and compare the current state of research in edge computing task scheduling, we have analyzed and summarized prominent related works in terms of their main contributions, methods, and limitations in Table 1.

This paper proposed a hybrid scheduling strategy—FFDDE—that integrates the traditional First-Fit Decreasing (FFD) heuristic into the Differential Evolution (DE) algorithm for task allocation in edge computing environments. The proposed FFDDE approach is evaluated in comparison to the conventional load-aware FFD (LLFFD) and GA (genetic algorithm), with a focus on energy consumption and task completion time. To the best of our knowledge, this work is among the first to explicitly combine heuristic control methods with evolutionary algorithms in edge computing and quantitatively assess their impact on energy efficiency. Simulations were conducted using Edge CloudSim Nandhakumar et al. (2024), a platform specifically designed for edge computing scenarios, incorporating realistic models of wireless latency, user mobility, and server energy consumption based on CPU utilization. This research demonstrates that embedding domain-specific heuristic knowledge into evolutionary algorithms can lead to more energy-efficient task scheduling without compromising system performance.

The proposed strategy is a hybrid algorithm that integrates the FFD heuristic into the evolutionary loop of Differential Evolution (DE). In our approach, a candidate solution to the scheduling problem is represented as a mapping of tasks to virtual machines (VMs), encoded as an integer vector of length N, where each element indicates the index of the VM assigned to a given task. For N tasks and M VMs, each candidate thus defines a complete assignment. Since standard DE operates on real-valued vectors, we adapt it to this discrete scheduling context by allowing mutation and crossover operators to generate intermediate (fractional) values, which are subsequently rounded or interpreted as discrete VM indices. To maintain solution feasibility—ensuring that no VM exceeds its task-handling capacity—we introduce a repair mechanism. If a VM ends up overloaded, we redistribute some of its tasks to less-loaded VMs using a strategy inspired by FFD, thereby preserving load balance.

The integration of FFD into DE occurs at two key stages:

(a) Population Initialization: The initial population of the DE algorithm is seeded with solutions generated using the FFD heuristic and some perturbed variants, providing DE with a strong starting point derived from domain-specific knowledge. (b) Heuristic Correction: After standard DE mutation and crossover, each newly generated candidate solution undergoes a heuristic refinement step. In this step, tasks are first sorted by length, and then reassigned to VMs using a first-fit approach that takes current VM loads into account. This leverages the FFD’s strength in fast and efficient task packing to guide the search process.

The fitness function for DE is defined as a weighted combination of total energy consumption and task makespan. Specifically, the fitness is calculated as:

Fitness = Total Energy Consumption+ λ × Makespan.

Where total energy consumption is the sum of energy used by all edge servers during scheduling, and makespan refers to the completion time of the last task. The weight λ is a positive constant introduced to penalize excessively long schedules, thereby encouraging energy-efficient solutions that also avoid severe task delays. This design favors strategies that consolidate tasks onto fewer servers—allowing others to remain idle or enter a low-power state—without causing unacceptable queuing delays on individual VMs.

The DE algorithm’s parameters were determined through a sensitivity analysis to ensure robust performance. The final configuration uses a population size of 50, a mutation factor F = 0.5, and a crossover rate CR = 0.9, as this combination was found to consistently provide an effective balance between convergence speed and solution quality in our experimental scenarios. The algorithm is executed for 100 generations or until the improvement in fitness falls below a predefined threshold.

By combining the global search capability of DE with the domain-specific efficiency of FFD, the hybrid algorithm aims to discover superior scheduling solutions compared to either method alone. It is worth noting that hybrid metaheuristics have shown strong potential in cloud and edge scheduling. For example, Yousif et al. (2024) demonstrated that seeding DE with heuristically generated solutions improved stability and execution time in IoT-edge task scheduling when compared with alternatives such as the Firefly Algorithm or Particle Swarm Optimization (PSO).

The definitations and descriptions are as follows:

In this study, we constructed an edge computing simulation environment using the EdgeCloudSim platform to evaluate the performance differences between the proposed hybrid Differential Evolution (DE) algorithm—incorporating traditional control heuristics—and the baseline LLFFD heuristic scheduling strategy. The experimental environment consists of a small-scale edge computing cluster comprising four physical edge servers, each configured with three virtual machines (VMs), totaling 12 VMs in the simulation.

Two task groups were simulated, with the primary focus on a lightweight workload composed of 160 tasks. These tasks were evenly distributed across four representative edge computing application categories, with 40 tasks per category:

Augmented Reality Applications (AUGMENTED_REALITY): Represent tasks related to image processing and rendering with high throughput demands. These tasks characterize compute-intensive requirements typical of edge-based augmented reality scenarios, such as object recognition or real-time scene rendering.

Health Monitoring Applications (HEALTH_APP): Encompass real-time physiological monitoring and analytical tasks. These are highly sensitive to latency and require high reliability, reflecting real-time analysis and alerting services in healthcare contexts.

Heavy Computational Applications (HEAVY_COMP_APP): Include tasks such as robotic path planning and complex model inference, which demand significant computational resources. These tasks are typically less sensitive to short-term latency fluctuations.

Infotainment Applications (INFOTAINMENT_APP): Comprise video streaming and content distribution workloads with moderate bandwidth requirements and a certain level of stability. These tasks are representative of mobile video services and media content delivery at the network edge. During simulation, all tasks are injected into the system at approximately the same time (around the 200-s mark), emulating a high-concurrency task submission scenario. This experimental configuration is designed to intensify the scheduling challenge and provide a rigorous environment for performance comparison. Under such conditions, the resource management capabilities of the two scheduling approaches—particularly in terms of task execution latency, energy consumption, and resource allocation efficiency—can be effectively evaluated and contrasted. The specific parameters are as follows:

Task end: To create a realistic and diverse workload, the characteristics of the 160 tasks were defined based on their application category. The computational demand and data size for each task type followed a normal distribution, with parameters detailed in Table 2.

To ensure the statistical robustness of the research results and mitigate the impact of random fluctuations, we independently repeated each set of simulation experiments for both FFDDE and GA (population size = 50, F = 0.5, and CR = 0.9) strategies 30 times. Note that the results of each LLFFD run were the same.

As illustrated in Figure 4, regarding the average task execution time, the traditional LLFFD algorithm recorded 5.86 s (standard deviation ± 3.85s). After incorporating the Genetic Algorithm (GA), the average time decreased to 4.43 s (SD ± 2.91s), and the FFDDE algorithm further reduced it to 3.95 s (SD ± 1.15s). Compared to LLFFD, GA and FFDDE shortened the average task execution time by approximately 24% and 33%, respectively. Moreover, FFDDE had the smallest standard deviation, indicating a significant reduction in the volatility of its task execution times and demonstrating a clear advantage in minimizing both task waiting and execution durations.

As shown in Figure 5, under the traditional LLFFD strategy, tasks were significantly concentrated on a limited subset of virtual machines, with several VMs operating at full capacity (four in the case of LLFFD, compared to only one under FFDDE and GA). In contrast, FFDDE and GA, the heuristic algorithms exhibited a more balanced load distribution across VMs. This indicates that LLFFD tends to produce load imbalance, leading to the formation of performance hotspots on specific virtual machines, which in turn results in noticeable task execution delays and increased energy consumption.

As illustrated in Figure 6, the three algorithms demonstrated distinct differences in total energy consumption. The traditional LLFFD algorithm consumed the most energy, totaling 16,189 J. In comparison, the GA algorithm used 14,809 J, while the FFDDE algorithm was the most efficient, consuming only 14,429 J. This translates to energy savings of approximately 8.5% for GA and a more significant 10.9% for FFDDE, relative to the LLFFD baseline. A further analysis of per-task energy consumption highlights the superiority of FFDDE. It reduced the average energy per task from 101.2 J (for LLFFD) to 90.2 J, while also lowering the standard deviation from 79.7 to 70.7. This indicates that the FFDDE algorithm utilizes computing resources more efficiently, thereby effectively mitigating high energy consumption peaks.

Virtual Machine Load Distribution Performance.

There are significant differences in the task virtual machine allocation methods among the three algorithms: The FFDDE algorithm achieves better load balancing, more even task distribution, and a more reasonable number of tasks executed by each virtual machine (ranging from 6 to 20 tasks), without obvious hotspots or resource idle situations. Correspondingly, the difference in average execution time and average energy consumption of each virtual machine has significantly reduced.