Task scheduling plays a key role in effectively managing and allocating computing resources to meet various computing tasks in a cloud computing environment. Short execution time and low load imbalance may be the challenges for some algorithms in resource scheduling scenarios. In this work, the Hierarchical Particle Swarm Optimization-Evolutionary Artificial Bee Colony Algorithm (HPSO-EABC) has been proposed, which hybrids our presented Evolutionary Artificial Bee Colony (EABC), and Hierarchical Particle Swarm Optimization (HPSO) algorithm. The HPSO-EABC algorithm incorporates both the advantages of the HPSO and the EABC algorithm. Comprehensive testing including evaluations of algorithm convergence speed, resource execution time, load balancing, and operational costs has been done. The results indicate that the EABC algorithm exhibits greater parallelism compared to the Artificial Bee Colony algorithm. Compared with the Particle Swarm Optimization algorithm, the HPSO algorithm not only improves the global search capability but also effectively mitigates getting stuck in local optima. As a result, the hybrid HPSO-EABC algorithm demonstrates significant improvements in terms of stability and convergence speed. Moreover, it exhibits enhanced resource scheduling performance in both homogeneous and heterogeneous environments, effectively reducing execution time and cost, which also is verified by the ablation experimental.

Cloud computing resource scheduling refers to the process of efficiently allocating and managing computing resources, such as virtual machines, storage, and networking, within a cloud infrastructure. The primary objective of resource scheduling in cloud computing is to optimize resource utilization, ensure high availability, and meet the performance requirements of applications and services hosted in the cloud environment. This involves making dynamic decisions on how to allocate resources to various tasks, workloads, or users in a way that maximizes efficiency and minimizes costs while maintaining a balanced and responsive system [

Additionally, the cloud computing resources can be divided into homogeneous and heterogeneous. As for the homogeneous one, there is a set of resources with the same or similar nature components. When they are processed by virtual machines, there are few fluctuations in processing speed. The time cost is low, and the load is less. On the contrary, the heterogeneous resources are composed of different resources with different natures. Cloud computing usually needs to deal with various resources, such as the requirement of storage space, varied computational speed, accuracy of data processing, and so on. So far, the investigations on the resource-scheduling techniques in heterogeneous multi-cloud environments are mainly focused on resource scheduling, provisioning, and clustering, which are usually limited to a single cloud platform. Resource scheduling with better adaptability used in higher-level, large-scale, and heterogeneous multi-cloud scenarios is still a challenge. Moreover, although most metaheuristic algorithms on heterogeneous resources improve the comprehensive performance, the complexity is also increased. Additionally, they usually tend to fall into local ones during the iterative convergence phase of the algorithm to find the optimal solution. The scheduling time is prolonged, reducing efficiency.

Currently, there are many optimization algorithms, like the cuckoo-improved particle swarm optimization (PSO). In literature [

In addition, the artificial bee colony (ABC) algorithm, as an intelligent algorithm, is also a popular swarm intelligence algorithm [

In this work, an evolutionary artificial bee colony algorithm (EABC) has been proposed to make the solution more diverse to avoid falling into local optimum by adding random perturbation to ABC. The probability of onlooker bees choosing honey sources was introduced to improve the inertia weight decline of the particle swarm algorithm. The average of fitness was taken into the original equation to determine whether it was far from the optimal solution and to increase the accuracy of the selection of the solution. Considering that the improved algorithm cannot effectively improve the processing speed of heterogeneous resources, we proposed an improved hierarchical particle swarm optimization (HPSO) algorithm and incorporated it into the EABC to obtain a hybrid hierarchical particle swarm and evolutionary artificial bee colony algorithm (Hierarchical particle swarm optimization-evolutionary artificial bee colony, HPSO-EABC), which is more robust in improving load balancing, processing different resources faster, and reducing the cost in resource scheduling. However, this paper also has some defects, such as the performance of the improved algorithm (EABC, HPSO-EABC) highly depends on the algorithm and parameter settings. Choosing the appropriate parameter values is critical to the performance, but parameter selection is often a challenging task and may require trial and error and adjustment to obtain the best results. Introducing more mechanisms and additional steps also leads to an increase in the complexity of the algorithm.

The remaining sections of this paper are organized as follows:

The principle of cloud computing task scheduling involves dividing the problem to be executed into two parts Map and Reduce. The submitted task of the user is split into several smaller tasks by the Map program. Through cloud virtualization technology, these sub-tasks are assigned to virtual machine computing resources with a certain scheduling method. The Reduce step integrates the computation results and puts out the ultimate ones. Throughout this process, the virtual machines are independent of each other, and each sub-task only can run on one virtual machine resource. On the other hand, heterogeneous resources are composed of different components with diverse properties. Cloud computing encompasses a variety of resources. Some tasks require large storage space with minimal computing speed requirements, while others have the opposite characteristics [

In comparison to homogeneous resources, most heuristic algorithms designed for handling heterogeneous resources tend to increase overall performance at the expense of complexity. During the iterative convergence process of these algorithms, it is easy to get trapped in local solutions, resulting in longer scheduling time and lower efficiency. The EABC algorithm proposed here combines the advantages of global search, robustness, and high efficiency, which belongs to bee colony optimization. Compared to the ABC algorithm, the EABC algorithm effectively improves task completion time and algorithm convergence within different environments. Additionally, the HPSO-EABC algorithm integrates the rapid convergence and the strong global search capability from the HPSO algorithm on the base of the EABC algorithm. It addresses the deficiency of EABC in terms of heterogeneous resource scheduling speed and ensures a more balanced workload allocation for virtual machines during resource scheduling. The framework of the cloud computing resource scheduling used here is shown in

In detail, the scheduling process is abstracted as m subtasks executing on n VM nodes.

The artificial bee colony algorithm is an optimization method proposed by imitating the behavior of bees. It does not need to know the special information about the problem, but comparing the advantages and disadvantages of the problem is required. Based on the local optimization-seeking behavior of each bee, the global optimum value will be deduced, which has a fast convergence speed. Furthermore, the process of gathering honey is regarded as a task assignment. The bee species are roughly divided into employed and non-employed bees. The non-employed bees are further divided into onlooker and scouter bees. The employed bees can pass their honey-harvesting information to the onlooker ones through the “waggle dance”. The onlooker bees will select the nectar source based on the information passed from the employed ones and continue to exploit. When a nectar source reaches the threshold value and does not update its position, one of the employed bees will turn into a scouter to re-exploit a new nectar source. After the iteration, the optimal solution will be decided according to the predefined criteria [

At the initial stage of this algorithm, there is no prior experience for the bee. All the bees are scouters. The population number was set as N. That is, there are N initial solutions. The location of the i-th nectar source can be expressed as

This section discusses the improvements in the search strategy of onlooker bees, in the standard ABC algorithm, the employed bees conduct a neighborhood search first, then the onlooker bees collect nectar through the information transmitted by the “waggle dance” of the employed bees. If a nectar source has a higher fitness value, the probability of being selected by the onlooker bees is also higher, there will be more onlooker bees in the neighborhood to exploit it. When onlooker bees are in the neighborhood search phase, the location of the new nectar source can be generally calculated using the following

On the other hand, it is hard to derive the optimal solution quickly with the steps mentioned above. To overcome this lack, the learning factor in the particle swarm algorithm was introduced. As a result, the swarm can locate the better nectar source more precisely through the guidance of the current optimal solution during the neighborhood search. _{1} and r_{2} are the two random numbers with different values, and

For the traditional ABC algorithms, the selection probability is achieved by the roulette wheel. It will lead the poorer nectar sources to abandon, reducing the diversity of the population, and finally making the algorithm premature. Here, an improved selection strategy in the initial algorithm is carried out, which is described as

The flow chart of our EABC algorithm is shown in

For ease of reading, in the following steps, the employed bees had been defined as “Bee A,” the onlooker bees were labeled as “Bee B,” and the scouters were described as “Bee C”.

The maximum number of iterations is set as T, and the current number of iterations is t. Based on the above theory, the EABC algorithm is implemented below.

In fact, for our proposed EABC algorithm, there are still some shortcomings that need to be improved, including

Fortunately, PSO has a global search capability. It can find the global optimal solution in the multi-dimensional search space. Besides handling complex resource scheduling, it also can search for the optimal solution quickly, improving scheduling efficiency.

Therefore, to overcome the shortcomings of EABC, PSO is used to improve the velocity update formula of particles and to stratify the particles. That is HPSO, and it is also fused with the EABC algorithm, giving rise to the HPSO-EABC algorithm.

To improve our algorithm, we have done more in-depth research on PSO [

For PSO, the velocity and position update equations are exhibited in

As a result, the guidance of the global optimal solution can be obtained, when the particles perform cognitive term learning. The increase in value

Besides, the particles will be stratified according to the number of iterations, and are further labeled as the pre-particle, mid-particle, and post-particle, respectively. The particles in different layers will be given different Inertia weighting factors

The Particle Swarm Optimization algorithm with Inertia Weight Optimization demonstrates increased adaptability following inertia weight optimization. Combining it with EABC allows for the synergistic utilization of their respective advantages, further enhancing the robustness and ensuring the stability of resource scheduling solutions. It also increases scalability to meet resource scheduling requirements in various environments.

In this integrated algorithm, the HPSO is responsible for generating initial solutions after the initialization by the EABC. During the EABC initialization, the particle population transformed into a new type of bee species named “initial bees.” These initial bees inherit the learning attributes of particles in the EABC algorithm. As per

In contrast to

The HPSO-EABC is a two-stage optimization approach. First, the HPSO algorithm is initialized with specific parameters. Initial velocities and positions are assigned to each particle, and then the individual and global best solutions are updated. The particle velocities are updated iteratively, and such process continues until a specified number of iterations is reached. The best solution is recorded and named the “initial bee”. Next, the “initial bee” which represents the result from the previous HPSO, serves as the initial source position for the EABC algorithm and further is initialized with its parameters. After that, the population is divided into employed bees and onlooker bees. The employed bees perform neighborhood searches based on the “initial bee” position, and the results obtained are communicated to the onlooker bees. The onlooker bees then continue to explore When a honey source reaches its maximum exploitation limit, a randomly employed bee will be transformed into a scouter to reset the nectar source.

These processes mentioned above are repeated until the best solution is found. The HPSO-EABC algorithm initially leverages the HPSO optimization to benefit from its strong exploitation capabilities, improving efficiency and robustness. Then it combines the concurrency of the EABC algorithm to ensure stability in later-stage solutions. As a result, the merged algorithm exhibits higher scalability and can adapt to resource scheduling in different environments. The specific flowchart of the HPSO-EABC algorithm is shown in

Since the subsequent HPSO algorithm is similar to that of the EABC algorithm, it will not be repeated here. Even so, early on the HPSO algorithm is implemented below in detail.

The CloudSim platform [

Other parameter settings and values used in the simulation are listed in

Parameter name | Parameter value |
---|---|

Task type | Homogeneous |

Number of tasks | 200–1000 |

Task length | 1000–2000 |

Number of VMS | 10 |

Virtual machine policy | Space shared |

Number of CPUs | 2 |

mips | 1000–10000 |

Memory RAM | 1024 MB |

Bandwidth BW | 10 MB |

Virtual machine execution cost per unit price | 3 |

Virtual machine memory cost per unit price | 0.05 |

Virtual machine bandwidth cost per unit price | 0.1 |

ABC, EABC | Parameter value |
---|---|

Population size | 60 |

Employed bees | 30 |

Onlooker bees | 30 |

Scouter | When the nectar source reaches the extraction limit, it is transformed by an employed bee. |

The limit | 100 |

Population size | 40 |

Inertia weighting factor | 0.2–0.9 |

Cognitive term factor | 2 |

Social term factor | 2 |

Firstly, the convergence of each algorithm is tested. The initial number of scheduling tasks is set to 1000. There are 10 computing resources, and the number of iterations varies from 1000 to 10000. The completion time is calculated with

As shown in

However, for the heterogeneous resource scheduling, as shown in

Different task loads, typical 200, 400, 600, 800, and 1000 tasks are selected with a fixed number of iterations of 10000 and were used to demonstrate the performance time of each algorithm. The completion time of the ABC, PSO, EABC, HPSO, and HPSO-EABC is calculated with

Furthermore, as shown in

The DI value for each ABC, PSO, EABC, HPSO, and HPSO-EABC algorithm for typical tasks of 200, 400, 600, 800, and 1000 is calculated and plotted in

For the heterogeneous environment, as shown in

A statistical test on the runtime and the load balance is carried out further to exhibit the difference between our proposed algorithms and other ones. The task-dependent statistical analysis results of runtime and standard deviation for each algorithm within homogeneous and heterogeneous scheduling scenarios are shown in Tables S1 and S2, respectively. The completion time displayed in

Since the EABC algorithm proposed here mainly combines two kinds of improvements: the location update strategy of neighborhood search of the onlooker bee and the honey source selection strategy, the ablation experiments were carried out on the EABC algorithm to further verify its rigor. All the experimental contents and data analysis of this part are provided in the part of Supplementary Materials of the paper. In detail, all the results are shown in Tables S3-S8. In detail, the experiment was divided into three groups. For the first one, we only retain the improvement of the location update strategy in the EABC algorithm, which is recorded as the EABC-A algorithm and compared with the ABC algorithm. Detailed data are recorded in Tables S3 and S4. For the second group, we only retain the improvement of the selection strategy in the EABC algorithm, which is recorded as the EABC-B algorithm and compared with the ABC algorithm. Detailed data are recorded in Tables S5 and S6. For the last group, we compare the EABC-A and the EABC-B algorithms, which contain only one improved strategy, with the EABC algorithm in this paper. Detailed data are recorded in Tables S7 and S8. The comparison of the first two groups, as listed in lower values shown in Tables S3–S6, proves that the two improved methods used in the EABC algorithm proposed here are effective. The comparison results of the third group prove once again that the effect of our EABC algorithm is better than that of both the EABC-A and EABC-B algorithms, which contain only one improved strategy.

Furthermore, the operating cost of resource scheduling C with a unit of US dollars for each algorithm was calculated with

In summary, the HPSO-EABC algorithm, as a hybrid HPSO with the EABC algorithm, has been proposed and used for multi-objective task scheduling optimization in a cloud computing environment.

The EABC based on the ABC algorithm has been proposed to make the solution more diverse to avoid falling into local optimum. As a result of the sensitivity in the free search, the EABC algorithm has enhanced algorithm parallelism.

The HPSO has been proposed to accelerate the processing speed of heterogeneous resources on the base of the traditional PSO algorithm.

The HPSO-EABC that hybrid EABC and HPSO has been proposed to further improve the stability and convergence of the algorithm, which is not only robust and easy to develop, but also can effectively reduce resource scheduling completion time and make the virtual machine operating load more balanced with low virtual machine operating costs for both homogeneous and heterogeneous scenarios.

Considering the integration of other algorithms or modifying the optimization strategies of the EABC algorithm and the inertia weight strategies of the HPSO algorithm could be explored in future work. The algorithm proposed here may be expanded to and applied in other fields like path planning, cluster control, and so on.

The authors thank the anonymous referees for their careful readings and provisions of helpful suggestions to improve the presentation.

This work was jointly supported by the Jiangsu Postgraduate Research and Practice Innovation Project under Grant KYCX22_1030, SJCX22_0283 and SJCX23_0293, the NUPTSF under Grant NY220201.

The authors confirm their contribution to the paper as follows: study conception and design: S. Zhao, H. Yan; data collection: H. Yan, Q. Lin, X. Feng, H. Chen; analysis and interpretation of results: S. Zhao, H. Yan, D. Zhang; draft manuscript preparation: S. Zhao, H. Yan. All authors reviewed the results and approved the final version of the manuscript.

The data are available from the corresponding author upon reasonable request.

The authors declare that they have no conflicts of interest to report regarding the present study.

The supplementary material is available online at