5.1 Hybrid Multi-Objective Artificial Bee Colony Algorithm

Li and Han [⁷] proposed an algorithm called , a hybrid and improved version of the artificial bee colony (ABC) algorithm. In this approach, the initial problem is modeled as a hybrid flow shop scheduling (HFS) problem, addressing both single and multiple objectives. In the context of multi-objective HFS problems, three objectives are simultaneously considered: minimizing the makespan, the maximum workload on the device, and the total workloads on all devices. The scope of the algorithm extends to two distinct types of HFS: those with identical parallel machines and those involving unrelated machines. The proposed approach incorporates three categories of artificial bees, namely employed, observer, and scout bees, similar to the classical ABC scheme.

Each solution is represented by a string of integers. To adapt to the particularities of the problem, various perturbation structures are explored, and designed to improve the search capabilities of the algorithm.

The inclusion of an improved version of the adaptive perturbation structure in the proposed algorithm stands out, which seeks to effectively balance the exploitation and exploration capacity during the optimization process. A simple but highly effective selection strategy, along with an updated approach, is implemented to enhance the exploitation process.

To further intensify mining capabilities, a deep mining operator is introduced. In addition, an improved version of the scout bee is introduced that uses various local search methods to find the best food source or abandoned solution. This approach significantly contributes to improving the convergence ability of the proposed algorithm.

The effectiveness of the algorithm is tested using widely recognized benchmark instance sets, and performance verification of the proposed algorithm is performed.

5.2 Many-Objective Intelligent Algorithm with Sine Function

Cai et al. [⁸] developed a multi-objective distributed programming model that covers six objectives: total time, cost, cloud performance, energy consumption, resource utilization, and load balancing.

Furthermore, they introduced an intelligent multi-objective algorithm with a sine function to implement this model, called MaOEA-SIN. This algorithm considers the variation trend of the diversity strategy in the population, modeling it in an analogous way to the sine function.

The experimental results show outstanding programming efficiency, which contributes to improving security. This work presents a new perspective to address the challenging problem of data processing in the Internet of Things.

5.3 Multi-Objective Optimization Method using Hybrid Antlion Optimizer Algorithm

Abualigah and Diabat [¹⁰] introduced an innovative algorithm, called MALO, that combines antlion optimization with elite-based differential evolution to solve multi-objective task scheduling problems in cloud computing environments. In this method, the multi-objective nature of the problem arises from the need to minimize the makespan and maximize the resource utilization simultaneously.

The antlion optimization algorithm was improved by incorporating elite-based differential evolution as a local search technique. This approach improves the exploitability of the algorithm and prevents the possibility of getting trapped in local optima. The obtained results revealed that MALO outperformed other well-known optimization algorithms.

Notably, MALO showed faster convergence compared to other approaches when applied to larger search spaces, positioning it as a suitable option to address large-scale programming problems. In addition, a statistical analysis was carried out using -tests, evidencing a significant improvement in the results obtained by MALO. The comprehensive evaluation of leading methods in cloud task scheduling reveals a diversity of innovative approaches and advanced strategies.

The three works examined have proven to be pioneers in the development of efficient and effective solutions to the challenges inherent in this dynamic field. Together, these works have not only contributed significantly to the current state of the art in cloud task scheduling but also provided valuable insights and foundations for future research in this dynamic and challenging field.

6.1 Performance Metrics

Performance metrics play an essential role in evaluating and improving algorithms. These measures quantify the effectiveness and efficiency of an algorithm by providing objective information about its performance on various tasks.

Using performance metrics, developers and data scientists can evaluate effectiveness, compare algorithms, optimize parameters, diagnose problems, and perform sensitivity analysis, among other actions [²⁹].

In the context of cloud computing, various performance metrics have been used to evaluate the efficiency and effectiveness of the algorithms used, offering detailed insight into system performance, and assisting developers in making informed decisions. Below, Table 1 presents some of the most used performance metrics in Cloud Task Scheduling.

6.2 Benchmarks

Test instances or benchmarks are collections of data created for the specific purpose of evaluating and testing algorithms. The use of instances in the evaluation of algorithms in Cloud Task Scheduling provides a structured and objective framework to analyze and improve the performance of solutions in a dynamic and distributed environment.

These instances provide an accurate representation of real-world challenges and scenarios, allowing developers to make informed decisions and refine their approaches.

There are different sets of instances widely used for the evaluation of Cloud Task Scheduling algorithms. Some notable examples include:

These instance sets are used by the research community to evaluate and compare Cloud Task Scheduling algorithms in various contexts. Each data set presents specific characteristics that allow different aspects of performance in cloud computing environments to be simulated and analyzed.

On the other hand, there is CloudSim [³⁴], which is a simulation framework that provides sets of simulated instances for the evaluation of cloud task scheduling algorithms. It allows you to create simulated cloud environments for performance evaluations. Programmers can generate tasks, virtual machines, and hosts randomly and with different characteristics.

CloudSim is widely used by researchers to evaluate their algorithms in different generated environments.

7.1 Study Cases

Li and Han Li and Han compared their proposed LABC [⁷] against three different algorithms from the literature: EDA (Wang et al. [³⁵]), AIS (Liu et al. [³⁶]), and SFLA (Xu et al. [³⁷]). For the experimentation, they used a computer with a 3.3 GHz Intel Core i5 processor and 4 GB memory.

To test the performance of the algorithms in a multi-objective environment, they selected as instances two unrelated real machine HFS problems from [³⁵] to make the problem more like reality in a cloud system.

The results obtained by LABC are presented in Table 2 and 3 revealing the following highlights:

The LABC algorithm according to Li and Han [⁷] stands out for its competitive performance against various efficient algorithms. This success is based on the introduction of eight meticulously designed disturbance structures to improve exploitation capacity, the use of an improved deep exploitation observer bee mechanism to intensify local search, the implementation of an adaptive perturbation that balances exploitation and exploration, and a specific approach for scout bees that boosts the convergence capacity of the algorithm.

Cai et al. [⁸] conducted their experiments through the simulation of three clouds with different characteristics, the main difference is the Mips execution speed and the cost. The execution cost of the first cloud is cheaper, but the execution speed is slower and takes longer, which is suitable for smaller tasks. The second cloud has a relatively medium execution speed and execution cost.

The third cloud has a faster execution speed, but the cost also becomes high, suitable for performing larger tasks. Table 4 presents the detailed parameter settings of the simulated clouds. The experimentation was carried out by generating 300 tasks with an initial length of 500 million instructions (MI), the file size is 200 KB and the output file size is 100 KB. Then each task gradually increases with a trend of 500 MI, 10 KB, and 10 KB respectively.

The comparison of the MaOEA-SIN algorithm was carried out against five algorithms from the literature: NSGA-III, VaEA, GrEA, Two_Arch2, and KnEA. The study evaluated the performance of the MaOEA-SIN algorithm in a multi-cloud model by comparing six objective values.

The best, worst, and average solutions were selected based on the performance of these values. Table 5 presents six objectives: Total time, cost, cloud throughput, load balancing, resource utilization (RU) and Energy consumption, for six different approaches.

The average results presented in Table 5, indicate that MaOEA-SIN outperforms GrEA in cost, although it shows inferior performance in the cloud throughput objective. MaOEA-SIN stands out for its excellent average performance, demonstrating strong convergence.

Figure 2 shows the distribution of the data in the form of a box plot. Looking at the upper quartile, the median, and the lower quartile, the MaOEA-SIN algorithm has better convergence and distribution for six objectives. Convergence is reflected in the fact that the midline values are all optimal values in each objective.

Fig. 2 Comparison of performance presented in [8] of different algorithms on six objectives 

The distribution is reflected in the fact that the MaOEA-SIN algorithm has more dispersed points. In summary, the performance of the MaOEA-SIN algorithm is superior to that of other algorithms. To validate the effectiveness of the MALO algorithm, Abualigah and Diabat [¹⁰] present two series of experiments using synthetic datasets and real trace datasets.

For the first set of instances, the Cloudsim environment was used, which is a set of tools to imitate cloud computing scenarios [³⁴], because the investigation of new procedures or approaches in the real cloud computing ecosystem is usually limited by solid foundations, such as protection, security, speed and the high cost of money if experiments are carried out.m Therefore, it is difficult to conduct such research in repeatable, reliable, and scalable ecosystems (environments) using real world cloud environments [¹⁰].

For experimentation, they built two data centers within CloudSim, each with two hosts. Each host has 20 GB of RAM (one host is a dual-core machine and the other is a quad-core machine) and one TB of memory storage.

Each host has a collective processing power of one million MIPS. Several virtual machines were designed with different distributions generated such as 100, 200, 300, 400, 500, 600, 700, 800, 900, 1000, and 2000 instances. The CloudSim configuration is presented in Table 6. The MALO algorithm is compared against seven approaches from the literature: (Genetic Algorithm (GA) [³⁸], Discrete Symbiotic Organism Search (DSOS) Algorithm [³⁹], Hybrid Moth Search Algorithm (MSDE) [⁴⁰], Particle Swarm Optimization (PSO) Algorithm [⁴¹], Whale Optimization Algorithm (WOA) [⁴²], Moth Search Algorithm (MSA) [⁴³], and Antlion Optimizer (ALO) Algorithm [⁴⁴]).

Figure 3 presents the results obtained by the algorithms in terms of the degree of imbalance (DI), this metric shows us how equitably the tasks are distributed in the different resources. A lower degree of imbalance translates to a better use of resources and here we can see that MALO obtains the best DI compared to the other algorithms.

Fig. 3 Degree of imbalance of scheduling algorithms presented in [10] 

On the other hand, Figure 4 shows the average makespan values obtained by the algorithms for small and large tasks. The MALO algorithm reduced the value of makespan in all task cases. It is concluded that the value of the makespan increases slowly as the size of the tasks increases.

Fig. 4 The average makespan values for executing small and large tasks [10] 

The average value of makespan when using the modified optimization algorithms is better than traditional optimization algorithms [¹⁰]. Meanwhile, the average time interval of the MALO algorithm is smaller than that of other comparative methods. Figure 5 displays the response times (CPU) achieved by different task scheduling algorithms (GA, DSOS, MSDE, PSO, WOA, MSA, ALO, and the proposed MALO).

Fig. 5 The CPU time(s) of the task scheduling algorithms for the synthetic datasets [10] 

It is highlighted that MALO achieved minimum response times to solve problems of various sizes compared to the other methods, indicating a significant improvement in the efficiency of the algorithm. Specifically, for a task size of 600, the PSO algorithm recorded the lowest response time compared to other methods. For evaluation results of real trace datasets Abualigah and Diabat used the NASA Ames dataset [³²] and the HPC2N Seth dataset [³³].

Figures 6 and 7 present the response times (CPU) of various task scheduling algorithms (GA, DSOS, MSDE, PSO, WOA, MSA, ALO, and MALO) when performing tasks with real trace data sets. In Figure 6, MALO manages to almost reach the minimum response time for solving tasks of all sizes compared to other methods, especially using the HPC2N Seth datasets.

Fig. 6 The CPU time(s) of the task scheduling algorithms for solving the HPC2N Seth datasets [10] 

Fig. 7 The CPU time(s) of the task scheduling algorithms for solving the NASA Ames datasets [10] 

Similarly, in Figure 7, MALO stands out in approaching the minimum response time for tasks of all sizes, especially with the NASA Ames datasets. The difference in algorithm response times is evident across all task sizes, particularly with the HPC2N Seth datasets, standing out over other methods. Although the difference in response times of the MALO algorithm across all task sizes is not as clear compared to DSOS, an overall improvement is observed that contributes to the reduction in the time needed to find optimal solutions.

The degree of imbalance results between the MALO algorithm and other benchmark algorithms are presented in Figures 8 and 9 for the HPC2N Seth and NASA Ames datasets. MALO achieved a higher load balance (lower degree of imbalance) compared to the other methods. In almost all cases of data sets (100-2000), MALO exhibited the lowest degree of imbalance, highlighting its superior performance compared to comparative optimization algorithms.

Fig. 8 The degree of imbalance of the tasks scheduling optimization algorithms using the HPC2N Seth datasets [10] 

Fig. 9 The degree of imbalance of the tasks scheduling optimization algorithms using the NASA Ames datasets [10] 

This is reflected in a better balance between virtual machines in all problem instances. bMALO converged faster than the other approaches for larger search spaces, making it suitable for large scheduling problems.

7.2 Future Directions

Based on insights gained from case studies of three prominent algorithms in Cloud Task Scheduling [⁷,⁸,¹⁰], we identify promising directions for future research and development.

These future directions aim to guide researchers and practitioners in advancing the field of Cloud Task Scheduling, addressing emerging challenges, and ensuring the continued evolution of efficient and adaptive scheduling algorithms.