Entropic simplified swarm optimization for the task assignment problem

doi:10.1016/j.asoc.2017.04.030

Applied Soft Computing

Volume 58, September 2017, Pages 115-127

https://doi.org/10.1016/j.asoc.2017.04.030 Get rights and content

Highlights

•
The first work to apply simplified swarm optimization to the task assignment problem.
•
Entropy is adopted to describe the uncertainty level of assigned tasks; the task with higher uncertainty then has more chance to be reassigned.
•
ELS encourages solutions to exploit more promising neighbors since the search is not only arbitrary.
•
Statistical results indicate the proposed method is better than other algorithms.
•
ELS: Entropic Local Search.

Abstract

The task assignment problem (TAP) aims to assign application tasks to a number of distributed processors in a computation system in order to increase the efficiency and effectiveness of the system for minimizing or maximizing a certain cost. The problem is NP-hard; thus, finding the exact solutions is computationally intractable for larger size problems.

In this paper, a novel entropic simplified swarm optimization, known as ESSO, is proposed for solving this problem. In this method, an entropic local search (ELS) inspired by information theory is proposed to enhance the exploitation capability of SSO. Entropy is adopted to describe the uncertainty level of assigned tasks; the task with higher uncertainty then has more chance to be reassigned. Furthermore, for each reassigned task, the corresponding list of potential processors can be constructed using information theory; this enhances the probability of finding promising solutions in ELS.

To empirically evaluate the performance of the proposed method, experiments are conducted using twenty-four randomly generated problems ranging from small to large scale, and the corresponding results are compared with existing works. The experiment results indicate that ESSO is better than its competitors in both solution quality and efficiency.

Introduction

The task assignment problem (TAP) aims to assign application tasks to a number of distributed processors in a computation system to increase the efficiency and effectiveness of the system for minimizing or maximizing a certain cost [1]. A distributed computing system without proper task assignment often incurs higher cost. Therefore, many varied TAPs have been proposed in recent decades in order to obtain more effective assignments in a more efficient way. Most focus on minimizing the total system cost [2], [3], [4], [5], [6], [7], minimizing the application completion time [8] and maximizing the reliability of the system [9], [10], [11].

TAP can be divided into two categories: homogeneous and heterogeneous systems. In a homogeneous system, processors have the same computing capacity, and each task requires the same cost on each processor [12]. Compared to a homogeneous system, the heterogeneous system is more complicated. Each processor in the system is capacitated with various units of memory and processing resources. Thus, the execution cost of a task varies depending on the processor used. Moreover, the communication links among processors have various communication costs which will be incurred if there is a communication need between two tasks and they are executed on different processors [4], [13], [14].

TAP is a well-known NP-hard problem with computational effort growing exponentially with the number of tasks, processors and communication needs in the system [15]. The existing approaches can be mainly divided into four categories: graph-theoretic representation [16], [17], [18], integer linear programming [19], state-space search [20] and the evolutionary computation method. Due to numerical difficulties and computational burdens, only small-size instances of the problem can be solved optimally using exact methods. For large scale instances, most researchers concentrate on developing evolutionary computation methods that provide near-optimal solutions within a reasonable computation time.

Numerous evolutionary computation methods for solving TAP have been reported in the literature, such as Genetic algorithm [21], [22], [23], the Simulated annealing approach [24], [25], Particle Swarm Optimization [7], [9], [26], Harmony search algorithm [6] and Differential Evolution Algorithm [5]. The results show that they have made important contributions to TAP. However, there is still room to improve the effectiveness and efficiency of the above works. In this paper, a novel algorithm, Entropic Simplified Swarm Optimization (ESSO), is proposed as an alternative method for solving TAP.

This paper is organized as follows: the problem formulation is given in Section 2. The overviews of Entropy and Simplified Swarm Optimization (SSO) are provided in Section 3. The proposed ESSO and its overall procedure are detailed in Section 4. The two experiments and statistical analysis implemented for validating ESSO are illustrated in Section 5. Finally, the conclusions are presented in Section 6.

Section snippets

Problem formulation

The main purpose of TAP is to find an optimal arrangement with numerous tasks and multiple processors for minimizing the total cost under resource constraints. A general formulation of the TAP for a heterogeneous system can be formulated as the following integer nonlinear programming problem: $min f (X) = E (X) + C (X)$ $subject to m_{i} (X) \leq M_{i}$ r_i(X) ≤ R_iThe objective function in Eq. (1) minimizes the total sum of execution cost E(X) and communication costs C(X). According to Eqs. (2) and (3), the total memory and

Shannon information entropy

Information theory, introduced by Shannon [27], can quantify information, disorder or uncertainty from the probability distribution of some events contained in a sample set of possible events. These measures, called entropy, have been widely used in numerous areas [28], [29], [30], [31], [32], [33], [34]. Suppose that X is a triple (x, A, P), where the outcome x is the value of a random variable that takes on a finite number of possible values, A = {a₁, a₂, …, a_n}, having probabilities P = {p₁, p₂,

Proposed ESSO for TAP

The UM_f promotes SSO as an algorithm with satisfactory global searches, but which may take a long time to converge to an optimal or near-optimal solution [37]. One way to improve the performance of SSO is to hybridize it with a local search [41]. This paper proposes a novel local search based on the concept of entropy, and embeds it in SSO to further ameliorate the solution quality and convergence speed of SSO for solving TAP.

Experiment results and discussion

Two experiments: Ex-1 and Ex-2, are implemented in this Section. Ex-1 aims to verify the effect and find the best setting for Nels and Nunc using 12 designed treatments. Then, in Ex-2, ESSO with the best setting is compared with existing algorithms, including HPSO [7], IDE [5], NGHS [6] and SSO with UM_o in order to validate the quality and performance of the proposed method. All compared algorithms are corded and implemented in MATLAB R2015a on an Intel Core i7 4-GHz PC with 32GB memory. The

Conclusions

This work proposed a novel local search, known as ELS, inspired by information theory to facilitate ESSO for solving TAP, which is an NP-hard problem. In ELS, the uncertainty of each task is measured, and then the uncertainty set and the corresponding list of potential processors are constructed for the local search. This encourages solutions to exploit more promising neighbors since the search is not only arbitrary.

An extensive experimental study on 24 TAPs was conducted herein. The results

Acknowledgement

This research was supported by the National Science Council of Taiwan, R.O.C. under grant MOST 106–2218-E-606-001.

Chyh-Ming Lai is an assistant professor of the Institute of Resources Management and Decision Science, Management College, National Defense University, Taipei, Taiwan. He received his Ph.D. degree from the Department of Industrial Engineering and Engineering Management at the National Tsing Hua University. His research interests are Evolutionary Computation, Data Mining and network reliability theory.

References (41)

H.S. Stone
Multiprocessor scheduling with the aid of network flow algorithms
IEEE Trans. Softw. Eng.
(1977)
M. Qiu et al.
Cost minimization while satisfying hard/soft timing constraints for heterogeneous embedded systems
ACM Trans. Des. Autom. Electron. Syst. (TODAES)
(2009)
Z. Shao et al.
Efficient assignment and scheduling for heterogeneous dsp systems
IEEE Trans. Parallel Distrib. Syst.
(2005)
B. Ucar et al.
Task assignment in heterogeneous computing systems
J. Parallel Distrib. Comput.
(2006)
D. Zou et al.
An improved differential evolution algorithm for the task assignment problem
Eng. Appl. Artif. Intell.
(2011)
D. Zou et al.
A novel global harmony search algorithm for task assignment problem
J. Syst. Softw.
(2010)
P.Y. Yin et al.
A hybrid particle swarm optimization algorithm for optimal task assignment in distributed systems
Comput. Stand. Interf.
(2006)
G. Attiya et al.
Task allocation for minimizing programs completion time in multicomputer systems
P.Y. Yin et al.
Task allocation for maximizing reliability of a distributed system using hybrid particle swarm optimization
J. Syst. Softw.
(2007)
A. Dogan et al.
Matching and scheduling algorithms for minimizing execution time and failure probability of applications in heterogeneous computing
IEEE Trans. Parallel Distrib. Syst.
(2002)

S.M. Shatz et al.

Task allocation for maximizing reliability of distributed computer systems

IEEE Trans. Comput.

(1992)

C.H. Lee et al.

Optimal task assignment in homogeneous networks

IEEE Trans. Parallel Distrib. Syst.

(1997)

Q. Kang et al.

Task assignment in heterogeneous computing systems using an effective iterated greedy algorithm

J. Syst. Softw.

(2011)

K. Efe

Heuristic models of task assignment scheduling in distributed systems

Computer

(1982)

M.-S. Chern et al.

An LC branch-and-bound algorithm for the module assignment problem

Inf. Process. Lett.

(1989)

S.H. Bokhari

Assignment Problems in Parallel and Distributed Computing

(2012)

V. Chaudhary et al.

A generalized scheme for mapping parallel algorithms

IEEE Trans. Parallel Distrib. Syst.

(1993)

C.M. Woodside et al.

Fast allocation of processes in distributed and parallel systems

IEEE Trans. Parallel Distrib. Syst.

(1993)

W.W. Chu et al.

Task allocation in distributed data processing

Computer

(1980)

M. Kafil et al.

Optimal task assignment in heterogeneous distributed computing systems

IEEE Concurrency

(1998)

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View full text

Entropic simplified swarm optimization for the task assignment problem

Highlights

Abstract

Introduction

Section snippets

Problem formulation

Shannon information entropy

Proposed ESSO for TAP

Experiment results and discussion

Conclusions

Acknowledgement

Multiprocessor scheduling with the aid of network flow algorithms

IEEE Trans. Softw. Eng.

Cost minimization while satisfying hard/soft timing constraints for heterogeneous embedded systems

ACM Trans. Des. Autom. Electron. Syst. (TODAES)

Efficient assignment and scheduling for heterogeneous dsp systems

IEEE Trans. Parallel Distrib. Syst.

Task assignment in heterogeneous computing systems

J. Parallel Distrib. Comput.

An improved differential evolution algorithm for the task assignment problem

Eng. Appl. Artif. Intell.

A novel global harmony search algorithm for task assignment problem

J. Syst. Softw.

A hybrid particle swarm optimization algorithm for optimal task assignment in distributed systems

Comput. Stand. Interf.

Task allocation for minimizing programs completion time in multicomputer systems

Task allocation for maximizing reliability of a distributed system using hybrid particle swarm optimization

J. Syst. Softw.

Matching and scheduling algorithms for minimizing execution time and failure probability of applications in heterogeneous computing

IEEE Trans. Parallel Distrib. Syst.

Task allocation for maximizing reliability of distributed computer systems

IEEE Trans. Comput.

Optimal task assignment in homogeneous networks

IEEE Trans. Parallel Distrib. Syst.

Task assignment in heterogeneous computing systems using an effective iterated greedy algorithm

J. Syst. Softw.

Heuristic models of task assignment scheduling in distributed systems

Computer

An LC branch-and-bound algorithm for the module assignment problem

Inf. Process. Lett.

Assignment Problems in Parallel and Distributed Computing

A generalized scheme for mapping parallel algorithms

IEEE Trans. Parallel Distrib. Syst.

Fast allocation of processes in distributed and parallel systems

IEEE Trans. Parallel Distrib. Syst.

Task allocation in distributed data processing

Computer

Optimal task assignment in heterogeneous distributed computing systems

IEEE Concurrency