Elsevier

Information Sciences

Volume 536, October 2020, Pages 372-390
Information Sciences

A coalition-structure’s generation method for solving cooperative computing problems in edge computing environments

https://doi.org/10.1016/j.ins.2020.05.061Get rights and content

Abstract

Coalition-structure’s generation methods are usually employed to solve team allocation optimization problems or cooperative computing scheduling problems in the case of multitasking concurrency. In edge computing environments, affected by such factors as a large number of edge nodes, weak computing power, multiple optimization objectives and multiple constraints, the traditional methods can hardly guarantee the optimization speed and the optimal solution’s quality when solving similar problems. Based on the advantages of cooperative game algorithms and heuristic algorithms, we propose a coalition-structure’s generation method suitable for edge computing environments in this paper. Firstly, we introduce the concept of bargaining set and remove the impossible coalition-structures by judging the no-bargain coalition to narrow the strategic space. Secondly, for increasing the optimization speed and the optimal solution’s quality, we improve the inertia weight computing method and the particle state determination method of the primary discrete particle swarm, propose M-ary discrete particle swarm optimization (MDPSO). Finally, we design a series of contrast experiments and verify that this method boasts obvious advantages in optimization speed, the optimal solution’s quality, stability, and other aspects.

Introduction

A coalition is a collection of agents established to complete a specific task [1]. As a dynamic concept, coalitions are generated with the arrival of new tasks and disintegrated with the completion of tasks [2]. In the case of multitasking concurrency, all agents available will generate multiple coalitions to complete all tasks. These coalitions are collectively known as the coalition-structure (CS) [3]. In other words, the CSs abstractly describe the strategy adopted by the agent to initiate cooperative behavior. For the shortest time and lowest cost, researchers are keen to study “how to generate an optimal CS”. The results have been widely used to solve cooperative scheduling of resources [4], design of robot configuration plans [5], optimization of project R&D team structure [6] and other practical issues.

With the rapid development of the edge computing technology, edge nodes gradually become intelligent. They can autonomously cooperate with other members to generate a CS to process concurrent large-scale scientific computing tasks [7]. This cooperative computing model “closer to the source” has significantly released the pressure of central computing power. However, affected by such factors as number of edge nodes, computing power, optimization objectives and constraints, the optimal CS’s generation problem in edge environments is more complicated. Therefore, it is also regarded as one of the significant challenges in the field of edge computing [8], [9]. Usually, researchers translate this problem into “how to search for the optimal solution in the strategic space,” and solve this problem using cooperative game algorithms or heuristic algorithms.

For solving similar problems, cooperative game algorithms introduce the concepts of Shapley value, nucleolus, kernel and bargaining set in the game theory [10]. Through the stability principle of time, utility, cost-performance [11] or the principle of reasonableness [12], it continuously removes the relatively unstable CS in the strategic space and finally retains one or more approximately optimal CSs. The methods based on the cooperative game algorithm are essential to strive for a relative equilibrium state [13]. Therefore, they are suitable for multi-objective scenarios, especially for solving the optimization problem with economical cost and time cost as objectives [14]. TZ Li [15] proposed a task scheduling method based on the potential game. It solved the cooperative work problem of the mobile edge computing based on AD-HOC, verified the conditions to avoid null solutions. Zhang [16] solved the real-time scheduling problem in the manufacturing workshop by using the cooperative game algorithm. He verified that strict determination conditions would generate a large number of operations, eventually resulting in a contradiction between the optimization speed and the optimal solution’s quality. Cooperative game algorithms can indeed obtain several “satisfactory solutions [17]”, but the computing time will increase sharply with the strategic space shrinks, even. At the same time, it is possible to produce null solutions. Therefore, completely relying on the cooperative game algorithm has some defects. For example, it takes too long computing time, and the optimal solution’s quality cannot be guaranteed.

Solving the similar problems with the heuristic algorithm usually follow these steps [18].

I. Transform the CSs into code that can be formally described.

II. Analyze multiple objectives, transforming the multi-objective problem into a single total objective function by specifying different weights.

III. Use a heuristic algorithm to search the optimal solution of the total objective function. The heuristic algorithm can be one of several types, including simulated annealing, genetic, tabu search, and particle swarm optimization algorithms, among others.

Musrrat [19] proposed an efficient differential evolution algorithm to solve the multi-objective optimal allocation problem. In spite of the fast optimization speed and the great convergence, it is too time-consuming in scenarios with a large number of tasks. Zhao and Zhang [20] studied the application of a discrete particle swarm optimization (PSO) algorithm in the process of team allocation optimization. They considered the local aggregation problem of discrete points to improve the optimal solution’s quality. Still, the algorithm has poor stability, and it is liable to fall into the optimal local solution. Zhang has made significant achievements in optimizing overlapping coalitions and maximum successful coalitions in recent years [21], [22]. Still, the optimal solution’s quality is not ideal in scenarios with a large number of edge nodes. Therefore, using the heuristic algorithm alone cannot fully solve the optimal CS’s generation problem in a large strategic space.

From the above, using the cooperative game algorithm or the heuristic algorithm alone can hardly satisfy the application scenarios with large strategic space, multiple optimization objectives and complex constraints. To this end, many researchers have attempted to mix a variety of algorithms. The results obtained have been able to better solve the practical problems such as network coverage optimization, multi-objective programming and scheduling [23]. Inspired by this idea, we combine the advantages of two kind algorithms and propose a hybrid CS’s generation method in this paper on the basis of our previous research [24]. Fig. 1 shows the work process of our method. Firstly, we introduce the concept of bargaining set and remove the impossible CSs by judging the no-bargain coalition to narrow the strategic space. Secondly, for increasing the optimization speed and the optimal solution’s quality, we improve the inertia weight computing method and the particle state determination method of the primary discrete particle swarm, propose the M-ary discrete particle swarm optimization (MDPSO). Finally, we demonstrate the effectiveness of the method by experiments and analyze the influence of different weight coefficients on the optimal solution’s quality.

The method proposed in this paper has a good application effect in many real-world scenarios. For example, while computing the heat resistance of the quasi polymer nanostructure with its edge computing system. The research institute of Daqing Oilfield Chemical Co., Ltd. chose this method to make the task assignment program. In the actual application, this method has a faster run time, and the expected completion time (ECT) and cost of the scheme are superior to the original plan. Thus, it saves considerable time and economic value for the scientific research institution and significantly contributes to the research and development of new materials in the oilfield.

For easy to follow, we structure our paper as follows. Section 2 sets the application scenarios, describes the basic concept and formula and generalizes the key problems. Section 3 expounds on how to remove the impossible CSs by judging the no-bargain coalition. In this section, we introduce the no-bargain coalition and its determination conditions. Section 4 elaborates on the operation mechanism and improvement points of MDPSO and analyzes the computation complexity and advantages. Section 5 presents our experiments to demonstrate the effectiveness of our method. Section 6 summarizes our results and gives directions for future work.

Section snippets

Fundamental work

We give the definition of the scenario and the basic concepts, described the key problems to be solved. For ease of understanding, Table 1 shows key notations used in our presentation.

Remove the impossible CSs

The cooperative game algorithms based on the concepts of the bargaining set, nucleoli and kernel can quantitatively evaluate the optimal solution’s quality [28]. The principle is to continuously narrow the strategic space through the “internal bargain” and finally delineate the optimal solution or the optimal solution set (multiple near-optimal solutions). Therefore, the average computing time of such algorithms rests with the number of strategies and the determination criteria for the optimal

Search for the optimal CS

For increasing the optimizing speed and the optimal solution’s quality, we establish the optimization model, give the fitness function and coding mode, and improve the discrete particle swarm optimization algorithm.

Experiment verification

In this part, we verify the effectiveness of our method by comparing it with other algorithms that solve similar problems. The brief description of the experimental design is shown as follows.

I Explain the experimental preparation work. Introduce the experimental environment, task information, environmental parameters and comparing algorithms.

II. Analyze the performance indicators’ changes of the algorithms in various conditions, to demonstrate that MDPSO has apparent advantages in optimization

Conclusion

In this paper, we proposed a CS’s generation method for solving the cooperative computing problem in edge computing environments. We divided this method into two stages. In the first stage, we adopt the concept of the bargaining set to narrow the strategic space. In the second stage, we improve DPSO to increase the optimization speed and the optimal solution’s quality. Finally, we summarize our results as follows.

I. MDPSO is more suitable for solving the optimal CS’s generation problem in edge

CRediT authorship contribution statement

Kejia Zhang: Conceptualization, Methodology, Software, Investigation, Writing - original draft. Yanan Hu: Validation, Formal analysis, Visualization, Software. Feng Tian: Validation, Formal analysis, Visualization. Chunsheng Li: Resources, Writing - review & editing, Supervision, Data curation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgments

This work was supported by the National Natural Science Foundation of China under Grants 51774090, by the Natural Science Foundation of Heilongjiang Province under Grant F2016002, and by the Fundamental Research Funds for the Northeast Petroleum University under Grants KYCXTD201903 and 2017PYQZL-11.

The authors would like to express their gratitude to the anonymous reviewers, whose helpful comments and suggestions improved the quality of this paper.

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