EA-MSCA: An effective energy-aware multi-objective modified sine-cosine algorithm for real-time task scheduling in multiprocessor systems: Methods and analysis

Highlights

• A proposed multi-objective SCA to improve its performance when solving the TSMPS.

• To improve the performance of EA-M2SCA, the polynomial mutation was integrated.

• The proposed algorithms are referred to as EA-MHSCA and EA-M2SCA.

• EA-MHSCA and EA-M2SCA are compared with a number of known multi-objective algorithms.

Abstract

With the significant growth of multiprocessor systems (MPS) to deal with complex tasks and speed up their execution, the energy generated as a result of this growth becomes one of the significant limits to that growth. Although several traditional techniques are available to deal with this challenge, they don’t deal with this problem as multi-objective to optimize both energy and makespan metrics at the same time, in addition to expensive cost and memory usage. Therefore, this paper proposes a multi-objective approach to tackle the task scheduling for MPS based on the modified sine-cosine algorithm (MSCA) to optimize the makespan and energy using the Pareto dominance strategy; this version is abbreviated as energy-aware multi-objective MSCA (EA-M2SCA). The classical SCA is modified based on dividing the optimization process into three phases. The first phase explores the search space as much as possible at the start of the optimization process, the second phase searches around a solution selected randomly from the population to avoid becoming trapped into local minima within the optimization process, and the last searches around the best-so-far solution to accelerate the convergence. To further improve the performance of EA-M2SCA, it was hybridized with the polynomial mutation mechanism in two effective manners to accelerate the convergence toward the best-so-far solution with preserving the diversity of the solutions; this hybrid version is abbreviated as EA-MHSCA. Finally, the proposed algorithms were compared with a number of well-established multi-objective algorithms: EA-MHSCA is shown to be superior in most test cases.

Introduction

Until recently, all the computing devices were based on a single processor system-on-chip (SPS) which limited their computing capabilities to take a long time with low throughput which became a considerable obstacle to growth, especially for industry and technology applications (Hadizadeh and Tanghatari, 2017, Razian and MahvashMohammadi, 2017). The multiprocessor system-on-chip (MPS) alleviated many of those problems by building a number of small processors known as processing cores, or also called processing elements, on a single chip to allow processing in parallel for more than one task at a time to reduce the delay time and improve throughput. MPS platforms can be classified to heterogeneous and homogenous MPS. In a heterogeneous MPS platform, the processing cores have various instruction set architecture (ISA). On the contrary, the homogenous platform has processing cores with the same ISA. If the processing cores in the homogenous platform are totally identical with respect to performance and power, this platform is known as a symmetric MPS platform. Rather than, it is called an asymmetric MPS platform (Yun, Hwang, & Kim, 2019).

MPS is a great boon to real-time applications, such as control systems, radar tracking, and audio/video streaming (Mo, Kritikakou, & Sentieys, 2018) in providing timely responses in applications that cannot tolerate delay. Despite their advantages in speed and throughput, MPS consumes very large amounts of energy which increases the cost of their operation. Consequently, decreasing the energy consumption of MPS is highly desirable to save costs and battery lifetime, as well as to improve the performance MPS.

To reduce the energy consumed by MPS, the tasks assigned to them must be accurately scheduled; this process is known as task scheduling (TS) and the problem is known as the task scheduling MPS (TSMPS) problem. Unlike MPS, TS on SPS is straightforward because the tasks are executed sequentially and the dependency among tasks is respected if it is detected. MPS, however, must distribute and arrange the tasks while taking into consideration the dependency among processors. In addition, among the processors, there is a communication cost to exchange the data regarding the related tasks allocated to them. Although MPS can implement tasks in parallel at the same time to increase throughput and minimize the time taken, energy consumption would increase. To overcome this drawback, dynamic energy and frequency scaling (DVFS) can be used to reduce energy consumption (Wang, Qian, Yuan, & You, 2017).

The tasks assignment to the processing elements in MPS is considered a challenging problem that is NP-hard (Balin, 2011, Engin et al., 2011). The traditional methods, such as exhaustive search, proposed to overcome this problem suffer from time complexity and increased memory space, which motivates researchers to use meta-heuristic algorithms to overcome those disadvantages. In addition, in comparison with the heuristic algorithms, meta-heuristic algorithms could substantially avoid the local minima, in addition to alleviating using domain-specific knowledge and therefore they could be applied to solve several other problems. Meta-heuristic algorithms are ideal in that regard due to their ability to obtain the near-optimal solution for many optimization problems at a reasonable time (Abdelhafez et al., 2019, Jain et al., 2019, Mahato and Singh, 2018, Hashemi and Rahmani, 2018, Mafarja and Mirjalili, 2018, Mirjalili et al., 2018, Abdel-Basset et al., 2020, Abdel-Basset et al., 2020). Several meta-heuristic algorithms have been proposed to improve the performance in addressing TSMPS-the next section reviews the major work.

Some of the papers reviewed in the next section were applied to the task graphs with small task sizes up to 230 and this didn’t strengthen the motivation for using those algorithms with increasing the size of the tasks since their performance is unknown so-far. The remainder of the papers report approaches still suffer from becoming trapped in local minima that prevent them from reaching better outcomes.

Recently, a population-based algorithm called the sine-cosine algorithm (SCA) (Mirjalili, 2016) has been proposed for solving the uni-modal, multi-modal, and composite test functions (Digalakis and Margaritis, 2001, Yao et al., 1999). The advantages of the SCA that motivate this study are that it is simple, easy to implement, and easy to be modified to improve its performance. Despite the significant success of SCA in solving several real problems, it still suffers from the following main disadvantage in its optimization core: it searches for a better solution around the current solution with a step size located between the current solution and the best solution multiplied by a random number ranging of 0 and 2, which may make some regions intractable for SCA, or may reduce the convergence speed toward the optimal solution because of multiplying the best-so-far solution by a random number. This disadvantage therefore motivates the proposal of a multi-objective modified sine-cosine algorithm (EA-M2SCA) by dividing the SCA optimization process into three stages:

• The first stage utilizes the start of the optimization process to explore the regions of the search space of the problem as much as possible.

• The second utilizes some of the optimization processes to explore the regions around a solution selected randomly from the population.

• The last stage moves the current solution toward the best-so-far solution in order to accelerate the convergence toward the optimal solution.

The performance of EA-M2SCA was experimented on the TSMPS to reach better solutions. Additionally, to increase the convergence speed toward the best-so-far solution, based on a specific probability, the current solution will be replaced with the best-so-far solution mutated using the modified polynomial mutation, but this may reduce the solutions diversity and subsequently the probability of falling into local minima will significantly increase. Therefore, the current solutions based on a specific probability will be also mutated using the polynomial mutation to avoid stuck into local minima. This hybrid version of EM-M2SCA with polynomial mutation was abbreviated as EM-MHSCA. Those two proposed algorithms: EM-M2SCA and EM-MHSCA are validated using two kinds of task graphs: standard task graphs and the task graphs based on real applications: the tasks size at the range of [52, 1100] and a number of edges ranging of 127 and 2056 are the characteristics of the standard task graphs, while the formulated graph has three tasks with sizes of 90, 98, and 336. In addition, to observe the superiority of the proposed approach, it is compared with a number of the well-known multi-objective optimization algorithms. The experimental results show that EA-MHSCA are competitive for some datasets and superior for the others with all the other algorithms in terms of the make-span and energy consumption. Finally, the main contributions of this research are summarized as follows:

• A proposed modification to multi-objective SCA (EA-M2SCA) to improve its performance when solving the TSMPS.

• To improve the performance of EA-M2SCA, it was integrated with the polynomial mutation strategy in two effective manners to avoid stuck into local minima with increasing the convergence toward the best-so-far, this version was named as EA-MHSCA.

• EA-MHSCA and EA-M2SCA are compared with a number of well-known multi-objective algorithms to check its efficacy.

The remainder of this paper is organized as follows: Section 2 provides a review of relevant literature, Section 3 describes MPS and performance measures, Section 4 presents our proposed approach, Section 5 Experimental settings, 6 Results and discussion describe the experimental settings and the results and Section 7 provides conclusions about this work in addition to introducing a number of future works.