Distributed parallel cooperative coevolutionary multi-objective large-scale immune algorithm for deployment of wireless sensor networks
Introduction
In the wireless sensor network (WSN) deployment optimization procedure [1], wireless sensor nodes can be optimized via self-organization [2] to maximize the Coverage, optimize the Connectivity Uniformity and minimize the Deployment Cost. With the rapid development of sensor and wireless communication technologies, WSNs have been applied to various fields. The work of [3] presented an air temperature monitoring application for WSNs. Shen et al. [4] described the wireless sensor nodes for a medical service. Zhang et al. [5] illustrated the WSN k-barrier coverage problem. Zhou et al. [6] researched the energy issue, regarding which clustering and data compression were studied. Zhang et al. [7] utilized mobile sinks to alleviate the communication burden.
In addition, the response of the human immune system to antigens can be viewed as a process of self-organization. Based on this concept, the clonal selection algorithm (CLONALG) [8], which can be used for global optimization problems (GOPs) and multi-objective optimization problems (MOPs) [9], was proposed. Other nature-inspired algorithms also follow the self-organizing procedure. For example, Xue et al. [10] described the self-adaptive artificial bee colony algorithm, which is different from the immune algorithm.
In the real world, many problems require several (usually conflicting) objectives to be considered simultaneously. Multi-objective evolutionary algorithms (MOEAs) [[11], [12], [13]] are capable of producing a plurality of solutions during one run, which is convenient for approximating the Pareto front (PF). For NP-hard problems, evolutionary algorithms (EAs) [[14], [15], [16], [17]] can usually converge to near-optimal solutions using limited computational resources [18] within a reasonable time compared to brute force and deterministic methods.
The first multi-objective immune algorithm (MOIA) was proposed in [19]. In this study, the immune algorithm (IA) was integrated into the genetic algorithm (GA) to improve the selection of individuals for evolution. Gong et al. [20] presented the nondominated neighbor immune algorithm (NNIA), selecting a small quantity of nondominated individuals in a sparse area for cloning, recombination and mutation. In [21], simulated binary crossover (SBX) and differential evolution (DE) were combined and applied to cloned individuals in a hybrid evolutionary framework for MOIAs (HEIA), which performed well for both unimodal and multimodal problems.
EAs are based on an iterative evolution of the population (the solutions), which is time-consuming—especially for expensive problems. Distributed evolutionary algorithms (dEAs) [[22], [23]] allocate the tedious computational burden across numerous computational nodes, greatly reducing the required time. Cloudde [24] used DEs with various parameters to optimize multiple populations in a distributed parallel manner, yielding a promising performance from both the effectiveness and efficiency aspects. [25] provided a comprehensive study concerning parallel/distributed MOEAs. Utilizing the multi-objective optimization algorithm based on decomposition (MOEA/D) [13], parallel MOEA/Ds (pMOEA/Ds) [[26], [27]] were proposed.
With the arrival of “big data”, many complex problems have emerged; solving such problems is both time-consuming and storage-consuming [[28], [29]]. Similarly, many MOPs now have numerous variables (e.g., more than variables [30]). Some examples include classification [31], clustering [32], and recommendation systems [33]. However, the goal of traditional MOEAs is to solve multi-objective small-scale optimization problems (MOSSOPs). Consequently, the traditional algorithms may be incapable of tackling multi-objective large-scale optimization problems (MOLSOPs) because of the “curse of dimensionality”. Tooptimize numerous variables, some promising approaches first separate the variables into groups and then optimize them in a cooperative coevolutionary (CC) [34] manner. For large-scale global optimization problems (LSGOPs), many grouping mechanisms have been applied, including fixed grouping [34], random grouping [35], the Delta method [36], dynamic grouping [37], differential grouping (DG) [38], global differential grouping (GDG) [39] and graph-based differential grouping (gDG) [40]. Antonio et al. proposed the cooperative coevolutionary generalized differential evolution 3 (CCGDE3) method [41], which used fixed grouping.
MOLSOPs differ from LSGOPs in that no single solution optimizes all the conflicting objectives; instead, a solution set should be generated to approximate the PF. In MOLSOPs, variables have different properties [42], which can be classified as follows:
- 1.
position variables, which affect only the diversity of the solution set;
- 2.
distance variables, which affect only the convergence of the solution set; and
- 3.
mixed variables, which affect both the diversity and the convergence of the solution set.
Therefore, position variables should be permuted to approximate the PF as comprehensively as possible. However, distance variables should be optimized so that they can closely approach the PF.
To identify these variable types, the multi-objective evolutionary algorithm based on decision variable analyses (MOEA/DVA) [30] utilizes a mechanism called decision variable analyses (DVA). The position as well as mixed variables are categorized as diversity-related variables, while distance variables, as convergence-related variables. The convergence-related variables are allocated to multiple groups that are then optimized under the CC framework.
The use of multiple populations can impact the optimization performance. In cooperative multi-objective differential evolution (CMODE) [43], each objective is optimized by a subpopulation, and an archive is used to maintain good solutions and optimize all objectives. This approach has yielded good experimental results.
Compared to MOSSOPs, designing parallel/distributed MOEAs for MOLSOPs will be more beneficial. In this paper, we propose the distributed parallel cooperative coevolutionary multi-objective large-scale immune algorithm (DPCCMOLSIA), which is aimed at solving MOLSOPs effectively and efficiently.
The contributions of this paper can be highlighted as follows:
- 1.
Each objective is optimized by a subpopulation. Thus, the exploration with respect to each objective is enhanced, and all objectives are comprehensively optimized by an archive. Variables are grouped according to their properties and interactions, contributing to effective optimization.
- 2.
The idea of the IA is introduced, more computational resources are used to explore sparse areas in the objective space, and SBX is utilized for evolution.
- 3.
We construct a three-layer parallel structure. The evaluations of individuals in different groups of multiple populations can then be performed in parallel, which greatly reduces the computation time.
The remainder of this paper is organized as follows: Section 2 provides some preliminary information required for this paper. The details of the DPCCMOLSIA are discussed in Section 3. Then, in Section 4, we describe the experimental study and present the corresponding analyses. Finally, Section 5 concludes this paper.
Section snippets
MOP and variable properties
An MOP involves several objectives that usually conflict with each other. Therefore, addressing an MOP comprises obtaining a solution set that approximates the PF. For the minimization problem, we have the following formula: where is a point in the solution space . Here, denotes the variable quantity, , , represents the objectives, and denotes the point in the objective space that corresponds to .
Due to the conflicts among objectives,
The proposed algorithm: DPCCMOLSIA
Algorithm 2 lists the main steps in the framework of the DPCCMOLSIA. The main procedure is detailed in the following subsections.
3D deployment problem and terrain data
We use the 3D deployment problem proposed in [1], which includes three objectives: Coverage, Connectivity Uniformity and Deployment Cost. We also utilize the same real-world 3D terrain data (Fig. 2), which are composed of plain (Fig. 2a), hilly (Fig. 2b) and mountainous (Fig. 2c) terrains. These three terrains have different characteristics that are used to verify the proposed algorithm with respect to various conditions.
Parameter setup
We compare the DPCCMOLSIA with the CCGDE3 [41], the CMODE [43], the
Conclusions and prospects
In the present paper, we present a distributed parallel cooperative coevolutionary multi-objective large-scale immune algorithm (DPCCMOLSIA), which uses a three-layer parallel structure to substantially reduce the computation time. By decomposing the objectives and variables, the original complex MOLSOP is transformed into simpler, small-scale problems that are easier to address. Via tests on real-world terrain data, compared with several other algorithms (CCGDE3, CMODE, MOEA/DVA and NSGA-III),
Acknowledgments
This work was supported in part by the National Natural Science Foundation of China (NSFC) under Grant No. 61303001, in part by the Foundation of Key Laboratory of Machine Intelligence and Advanced Computing of the Ministry of Education under Grant No. MSC-201602A, in part by the Opening Project of Guangdong High Performance Computing Society under Grant No. 2017060101, and in part by the Special Program for Applied Research on Super Computation of the NSFC-Guangdong Joint Fund (the second
Bin Cao received the Ph.D. degree in computer application technology from Jilin University in 2012.
He is currently in the School of Computer Science and Engineering, Hebei University of Technology, Tianjin, China. From 2012 to 2014, he was a Postdoc in the Department of Computer Science and Technology, Tsinghua University, Beijing, China. His research interests include intelligent computation with its applications to cyber–physical system, big data, graphics and visual media; high performance
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Bin Cao received the Ph.D. degree in computer application technology from Jilin University in 2012.
He is currently in the School of Computer Science and Engineering, Hebei University of Technology, Tianjin, China. From 2012 to 2014, he was a Postdoc in the Department of Computer Science and Technology, Tsinghua University, Beijing, China. His research interests include intelligent computation with its applications to cyber–physical system, big data, graphics and visual media; high performance computing and cloud computing.
Jianwei Zhao received the Bachelor’s degree from Tianjin University of Technology in 2014. He is currently in the School of Computer Science and Engineering, Hebei University of Technology, Tianjin, China.
His main research interests include intelligent computation with its applications to cyber–physical system, big data, graphics and visual media; high performance computing and cloud computing.
Po Yang received the B.Sc. degree in computer science from Wuhan University, Wuhan, China, in 2004; the M.Sc. degree in computer science from Bristol University, Bristol, U.K., in 2006; and the Ph.D. degree in electronic engineering from the University of Staffordshire, Stafford, U.K., in 2011.
He is currently a Senior Lecturer with the Department of Computer Science, Liverpool John Moores University, Liverpool, UK. He has been a Postdoctoral Research Fellow with the Department of Computing, Bedfordshire University, Luton, U.K. Before he joined Bedford-shire University, he was a Research Assistant with the University of Salford, Salford, U.K. His main research interests include radio-frequency identification and sensor networking, document image processing, computer vision, GPU, and parallel computing.
Zhihan Lv received the Ph.D. Degree in computer applied technology from Ocean University of China in 2012.
He is an Engineer and Researcher in virtual/augmented reality and multimedia, with a major in mathematics and computer science, having plenty of work experience in virtual reality and augmented reality projects, and is engaged in the application of computer visualization and computer vision. During the past few years, he has successfully completed several projects on PCs, websites, smartphones, and smart glasses. His research application fields range widely, from everyday life to traditional research fields (geography, biology, medicine).
Xin Liu received the Master degree in economics from Jilin University in 2012.
She is currently with Hebei University of Technology, Tianjin, China. Her main research interests include intelligent computation techniques with applications to cyber–physical system, big data, graphics and visual media; high performance computing and cloud computing.
Xinyuan Kang received the Bachelor’s degree in computer science and technology from Henan Normal University in 2015. She is currently in the School of Computer Science and Engineering, Hebei University of Technology, Tianjin, China.
Her main research interests include intelligent computation with its applications to cyber–physical system and big data; high performance computing and cloud computing.
Shan Yang received the Bachelor’s degree in computer science and technology from Shijiazhuang University in 2015. She is currently in the School of Computer Science and Engineering, Hebei University of Technology, Tianjin, China.
Her main research interests include intelligent computation with its applications to cyber–physical system and big data; high performance computing and cloud computing.
Kai Kang received the Ph.D. degree in management science and engineering from Hebei University of Technology in 2006.
He is currently a Professor in Hebei University of Technology, Tianjin, China. His research interests include intelligent computation techniques with applications to Big Data, Internet of things and Network Management.
Amjad Anvari-Moghaddam received the Ph.D. degree (Hon.) from University of Tehran, Tehran, Iran, in 2015 in Power System Engineering.
Currently, he is a Postdoctoral Fellow at the Department of Energy Technology, Aalborg University. His research interests include smart microgrids, optimal control and management, and integrated energy systems. He has authored and co-authored 6 book chapters and more than 70 technical papers in energy systems operation and control. Dr. Anvari-Moghaddam is the Guest Editor of the IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS special issue: Next Generation Intelligent Maritime Grids, the journal of APPLIED SCIENCES special issue: Advances in Integrated Energy Systems Design, Control and Optimization, and the Editorial Board Member for SCIREA Journal of Electrical Engineering. He is also a Technical Committee Member (TCM) of Renewable Energy Systems-IEEE IES, TCM of IES Resilience and Security for Industrial Applications-IEEE PES, TCM in IEEE Working Group P2004 (HIL Simulation and Testing), TCM of the 2nd International Conference on Intelligent Information Technologies (ICIIT 2017), the 2nd EAI International Conference on Smart Grid and Internet of Things (SGIoT 2018) and the 10th IEEE International Conference on Internet of Things (iThings-2017).