Diversity Teams in Soccer League Competition Algorithm for Wireless Sensor Network Deployment Problem
Abstract
:1. Introduction
2. Related Work
2.1. Soccer League Competition Algorithm
2.2. Deployment Problem for Wireless Sensor Networks
3. Diversity Team Soccer League Competition Algorithm
Algorithm 1: Pseudocode of the DSLC algorithm 

4. Experimental Results of Testing Problems
5. Applied DSLC for Deployment Optimization in WSN
5.1. Objective Function
5.2. Parameter Setting
5.3. Experimental Results
6. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
 Hussain, K.; Mohd Salleh, M.N.; Cheng, S.; Shi, Y. Metaheuristic research: A comprehensive survey. Artif. Intell. Rev. 2019, 52, 219102233. [Google Scholar] [CrossRef] [Green Version]
 Sedigheh, M.; Shiri, M.E. Metaheuristics in largescale global continues optimization: A survey. Inf. Sci. 2015, 295, 407–428. [Google Scholar]
 Nguyen, T.T.; Pan, J.S.; Dao, T.K. A Compact Bat Algorithm for Unequal Clustering in Wireless Sensor Networks. Appl. Sci. 2019, 9, 1973. [Google Scholar] [CrossRef] [Green Version]
 Du, Z.G.; Pan, J.S.; Chu, S.C.; Luo, H.J.; Hu, P. QUasiAffine TRansformation Evolutionary Algorithm with Communication Schemes for Application of RSSI in Wireless Sensor Networks. IEEE Access 2020, 8, 8583–8594. [Google Scholar] [CrossRef]
 Shaheen, A.M.; Spea, S.R.; Farrag, S.M.; Abido, M.A. A review of metaheuristic algorithms for reactive power planning problem. Ain Shams Eng. J. 2018, 9, 215–231. [Google Scholar] [CrossRef] [Green Version]
 Shanmugasundaram, G.; Thilagavathi, N.; Ramya, S.; Kanimozhi, K. An Investigation of Meta Heuristic Algorithms Applied on Capacitated Vehicle Routing Problem. In Proceedings of the 2019 IEEE International Conference on System, Computation, Automation and Networking (ICSCAN), Pondicherry, India, 29–30 March 2019; pp. 1–6. [Google Scholar]
 Souier, M.; Sari, Z.; Hassam, A. Realtime rescheduling metaheuristic algorithms applied to FMS with routing flexibility. Int. J. Adv. Manuf. Technol. 2013, 64, 145–164. [Google Scholar] [CrossRef]
 Chu, S.C.; Du, Z.G.; Pan, J.S. Symbiotic Organism Search Algorithm with MultiGroup QuantumBehavior Communication Scheme Applied in Wireless Sensor Networks. Appl. Sci. 2020, 10, 930. [Google Scholar] [CrossRef] [Green Version]
 Tian, A.Q.; Chu, S.C.; Pan, J.S.; Cui, H.; Zheng, W.M. A Compact PigeonInspired Optimization for Maximum ShortTerm Generation Mode in Cascade Hydroelectric Power Station. Sustainability 2020, 12, 767. [Google Scholar] [CrossRef] [Green Version]
 Sörensen, K.; Sevaux, M.; Glover, F. A history of metaheuristics. In Handbook of Heuristics; Springer: Berlin, Germany, 2018; ISBN 9783319071244. [Google Scholar]
 Holland, J.H. Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence; MIT Press: Cambridge, MA, USA, 1975; ISBN 9780262082136. [Google Scholar]
 Yang, X.S. Firefly Algorithms for Multimodal Optimization BT—Stochastic Algorithms: Foundations and Applications; Watanabe, O., Zeugmann, T., Eds.; Springer: Berlin, Heidelberg, 2009; pp. 169–178. [Google Scholar]
 Zhang, J.; Sanderson, A.C. JADE: Adaptive differential evolution with optional external archive. IEEE Trans. Evol. Comput. 2009, 13, 945–958. [Google Scholar] [CrossRef]
 Chu, S.A.; Tsai, P.W.; Pan, J.S. Cat swarm optimization. In Proceedings of the Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics, Guilin, China, 7–11 August 2006. [Google Scholar]
 Elbeltagi, E.; Hegazy, T.; Grierson, D. Comparison among five evolutionarybased optimization algorithms. Adv. Eng. Informatics 2005, 19, 43–53. [Google Scholar] [CrossRef]
 Nguyen, T.T.; Dao, T.K.; Kao, H.Y.; Horng, M.F.; Shieh, C.S. Hybrid Particle Swarm Optimization with Artificial Bee Colony Optimization for Topology Control Scheme in Wireless Sensor Networks. J. Internet Technol. 2017, 18, 743–752. [Google Scholar]
 Dao, T.K.; Pan, T.S.; Nguyen, T.T.; Pan, J.S. Parallel bat algorithm for optimizing makespan in job shop scheduling problems. J. Intell. Manuf. 2018, 29, 451–462. [Google Scholar] [CrossRef]
 Naser Moosavian, B.K.R. Soccer League Competition Algorithm, a New Method for Solving Systems of Nonlinear Equations. Int. J. Intell. Sci. 2014, 4, 7–16. [Google Scholar] [CrossRef]
 Moosavian, N.; Roodsari, B.K. Soccer League Competition Algorithm: A Novel Metaheuristic Algorithm For Optimal Design of Water Distribution Networks. Swarm Evol. Comput. 2014, 17, 14–24. [Google Scholar] [CrossRef]
 Chagwiza, G.; Jaison, A.; Masamha, T. Parameter Improvement of the Soccer League Competition Algorithm by Introducing Stubborn Players: Application to Water Distribution Network. Math. Probl. Eng. 2016, 2016, 3425374. [Google Scholar] [CrossRef] [Green Version]
 Hedieh Sajedi, S.K. Cognitive Soccer League Competition algorithm for solving knapsack problems. In Proceedings of the 1ST International Conference on Advances Research on Electrical and Computer Engineering, Tehran, Iran, 13 May 2016; p. 10240. [Google Scholar]
 Jaramillo, A.; Gómez, A.; Mansilla, S.; Salas, J.; Crawford, B.; Soto, R.; Olguín, E. Using the Soccer League Competition algorithm to solve the set covering problem. In Proceedings of the 2016 11th Iberian Conference on Information Systems and Technologies (CISTI), Gran Canaria, Spain, 15–18 June 2016; pp. 1–4. [Google Scholar]
 O’Donovan, T.; O’Donoghue, J.; Sreenan, C.; Sammon, D.; O’Reilly, P.; O’Connor, K.A. A context aware wireless Body Area Network (BAN). In Proceedings of the 2009 3rd International Conference on Pervasive Computing Technologies for Healthcare—Pervasive Health 2009, London, UK, 1–3 April 2009. [Google Scholar]
 Anastasi, G.; Farruggia, O.; Re, G.L.; Ortolani, M. Monitoring HighQuality Wine Production using Wireless Sensor Networks. In Proceedings of the 2009 42nd Hawaii International Conference on System Sciences, Waikoloa, HI, USA, 5–8 January 2009; pp. 1–7. [Google Scholar]
 Akyildiz, I.; Su, W.; Sankarasubramaniam, Y.; Cayirci, E. Wireless sensor networks: A survey. Comput. Networks 2002, 38, 393–422. [Google Scholar] [CrossRef] [Green Version]
 Chakrabarty, K.; Iyengar, S.S.; Qi, H.; Cho, E. Grid coverage for surveillance and target location in distributed sensor networks. IEEE Trans. Comput. 2002, 51, 1448–1453. [Google Scholar] [CrossRef] [Green Version]
 Pan, J.S.; Nguyen, T.T.; Dao, T.K.; Pan, T.S.; Chu, S.C. Clustering Formation in Wireless Sensor Networks: A Survey. J. Netw. Intell. 2017, 02, 287–309. [Google Scholar]
 Nguyen, T.T.; Pan, J.S.; Wu, T.Y.; Dao, T.K.; Nguyen, T.D. Node Coverage Optimization Strategy Based on Ions Motion Optimization. J. Netw. Intell. 2019, 4, 1–9. [Google Scholar]
 Garcíahernández, C.F.; Ibargüengoytiagonzález, P.H.; Garcíahernández, J.; Pérezdíaz, J. A Wireless Sensor Networks and Applications: A Survey. J. Comput. Sci. 2007, 7, 264–273. [Google Scholar]
 Nguyen, T.T.; Pan, J.S.; Lin, J.C.W.; Dao, T.K.; Nguyen, T.X.H. An Optimal Node Coverage in Wireless Sensor Network Based on Whale Optimization Algorithm. Data Sci. Pattern Recognit. 2018, 2, 11–21. [Google Scholar]
 Fei, Z.; Li, B.; Yang, S.; Xing, C.; Chen, H.; Hanzo, L. A Survey of MultiObjective Optimization in Wireless Sensor Networks: Metrics, Algorithms, and Open Problems. IEEE Commun. Surv. Tutor. 2017, 19, 550–586. [Google Scholar] [CrossRef] [Green Version]
 Jourdan, D.B.; Roy, N. Optimal sensor placement for agent localization. ACM Trans. Sens. Networks 2008, 4, 1–40. [Google Scholar] [CrossRef]
 Chen, Y.; Chuah, C.N.; Zhao, Q. Sensor placement for maximizing lifetime per unit cost in wireless sensor networks. In Proceedings of the MILCOM 2005—2005 IEEE Military Communications Conference, Atlantic City, NJ, USA, 17–20 October 2005; pp. 1097–1102. [Google Scholar]
 Nguyen, T.T.; Pan, J.S.; Dao, T.K. A Novel Improved Bat Algorithm Based on Hybrid Parallel and Compact for Balancing an Energy Consumption Problem. Information 2019, 10, 194. [Google Scholar] [CrossRef] [Green Version]
 Nguyen, T.T.; Pan, J.S.; Dao, T.K. An Improved Flower Pollination Algorithm for Optimizing Layouts of Nodes in Wireless Sensor Network. IEEE Access 2019, 7, 75985–75998. [Google Scholar] [CrossRef]
 Nguyen, T.T.; Dao, T.K.; Horng, M.F.; Shieh, C.S. An Energybased Cluster Head Selection Algorithm to Support Longlifetime in Wireless Sensor Networks. J. Netw. Intell. 2016, 1, 23–37. [Google Scholar]
 Dao, T.K.; Pan, T.S.; Nguyen, T.T.; Chu, S.C. A compact Articial bee colony optimization for topology control scheme in wireless sensor networks. J. Inf. Hiding Multimed. Signal Process. 2015, 6, 297–310. [Google Scholar]
 Liang, J.J.; Qu, B.Y.; Suganthan, P.N. Problem definitions and evaluation criteria for the CEC 2014 special session and competition on single objective realparameter numerical optimization. In Computational Intelligence Laboratory, Zhengzhou University, Zhengzhou China and Technical Report, Nanyang Technological University, Singapore; Technical Report: Zhengzhou, China, 2013; p. 635. [Google Scholar]
 Wu, G.; Mallipeddi, R.; Suganthan, P.N. Problem definitions and evaluation criteria for the CEC 2017 competition on constrained realparameter optimization. In National University of Defense Technology, Changsha, Hunan, PR China and Kyungpook National University, Daegu, South Korea and Nanyang Technological University, Singapore, Technical Report; Technical Report: Zhengzhou, China, 2017. [Google Scholar]
 Kalayci, T.E.; Uğur, A. Genetic algorithm–based sensor deployment with area priority. Cybern. Syst. 2011, 42, 605–620. [Google Scholar] [CrossRef]
 Tuba, E.; Tuba, M.; Beko, M. Mobile wireless sensor networks coverage maximization by firefly algorithm. In Proceedings of the 2017 27th International Conference Radioelektronika (RADIOELEKTRONIKA), Brno, Czech Republic, 19–20 April 2017; pp. 1–5. [Google Scholar]
Number  Function Name  Function Expression  Range  Dimension  Iteration 

1  Spherical  ${f}_{1}\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{N}}x{\text{}}_{i}^{2}$  $\pm 100$  30  100 
2  High Conditioned Elliptic  ${f}_{2}\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{D}}{({10}^{6})}^{\frac{i1}{D1}\text{}}{x}_{i}^{2}$  $\pm 100$  30  100 
3  Sum Square  ${f}_{3}\left(x\right)=\text{}{\displaystyle {\displaystyle \sum}_{i=1}^{D}}i{x}_{i}^{2}$  $\pm 100$  30  100 
4  Schwefel  ${f}_{4}\left(x\right)=418.983n{\displaystyle {\displaystyle \sum}_{i=1}^{N}}{x}_{i}\times sin\left(\sqrt{\left{x}_{i}\right}\right)$  $\pm 100$  30  100 
5  Rotated Schwefel2  ${f}_{5}\left(x\right)=418.983n{\displaystyle {\displaystyle \sum}_{i=1}^{N}}{x}_{i}\times \mathrm{sin}\left(\sqrt{\left{x}_{i}\right}\right)+{f}_{5}^{\ast}$  $\pm 100$  30  100 
6  Quadric  ${f}_{6}\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{n}}{\displaystyle {\displaystyle \sum}_{k=1}^{i}}{x}_{i}$  $\pm 10$  30  100 
7  Quartic Noisy  ${f}_{7}\left(x\right)=random\left[0,1\right)+{\displaystyle {\displaystyle \sum}_{i=1}^{N}}i\times {x}_{i}^{4}$  $\pm 10$  30  100 
8  Rosenbrock  $\text{}{f}_{8}\left(x\right)=\text{}{\displaystyle {\displaystyle \sum}_{i=1}^{n1}}(100\times {\left({x}_{i1}{x}_{i}^{2}\right)}^{2}+{\left(1{x}_{i}\right)}^{2}$  $\pm 600$  30  100 
9  Rastrigin  ${f}_{9}\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{D}}[10+{x}_{i}^{2}10cos2\pi {x}_{i}$  $\pm 100$  30  1000 
10  Noncontinuous Rotated Rastrigin’s  ${f}_{10}\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{D}}\left({x}_{i}^{2}10\mathrm{cos}\left(2\pi {x}_{i}\right)+10\right)+{f}_{10}^{\ast}$  $\pm 10$  30  1000 
11  Girewank  ${f}_{11}\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{D}}\frac{{x}_{i}^{2}}{4000}{\displaystyle {\displaystyle \prod}_{i=1}^{D}}cos\left(\frac{{x}_{i}}{\sqrt{i}}\right)+1$  $\pm 32$  30  100 
12  Ackley  $\begin{array}{l}{f}_{12}\left(x\right)\\ =20+\mathrm{e}20\mathrm{exp}\left(\frac{1}{5}\sqrt{(\frac{1}{D}}{\displaystyle {\displaystyle \sum}_{i=1}^{D}}\mathrm{cos}\left(i,j\right)\right)\\ \mathrm{exp}\left(\frac{1}{\mathrm{D}}{\displaystyle {\displaystyle \sum}_{i=1}^{D}}{x}_{i}^{2}\right)\end{array}$  $\pm 10$  2  100 
13  Levy  ${f}_{13}\left(x\right)={\left(1{\mathrm{w}}_{\mathrm{d}}\right)}^{2}\left[{\mathrm{sin}}^{2}\left(2\pi {w}_{D}\right)+1\right]+{\displaystyle {\displaystyle \sum}_{i=1}^{D1}}{\left(1{w}_{i}\right)}^{2}\left[1+10{\mathrm{sin}}^{2}\left(1+\pi {w}_{i}\right)\right]+{\mathrm{sin}}^{2}\left(\pi {w}_{1}\right)$  $\pm 512$  2  100 
14  Weierstrass  ${f}_{14}\left(x\right)=\text{}{\displaystyle {\displaystyle \sum}_{i=1}^{D}}\left({\displaystyle {\displaystyle \sum}_{k=0}^{kmax\text{}}}\left[{a}^{k}\mathrm{cos}\left(2\pi {b}^{k}\left({x}_{i}+0.5\right)\right)\right]\right)D{\displaystyle {\displaystyle \sum}_{k=0}^{kmax}}\left[{a}^{k}\mathrm{cos}\left(2\pi {b}^{k}\xb70.5\right)\right]$  $\pm 10$  30  100 
15  Schaffer  ${f}_{15}=\frac{1}{2}+\frac{si{n}^{2}\left({x}_{1}^{2}{x}_{2}^{2}\right)0.5}{{\left[1+0.001\times \left({x}_{1}^{2}{x}_{2}^{2}\right)\right]}^{2}}$  $\pm 100$  2  100 
16  Penalized1  ${f}_{16}\left(x\right)=\frac{\mathsf{\pi}}{\mathrm{D}}{\displaystyle {\displaystyle \sum}_{i=1}^{D}}{\left(10\mathrm{sin}\left(\pi {x}_{i}\right)\right)}^{2}+{\displaystyle {\displaystyle \sum}_{i=1}^{D}}{\left(0.25\left({x}_{i}+1\right)\right)}^{2}$  $\pm 10$  30  100 
17  Penalized2  ${f}_{17}\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{D}}{\left(0.1(\mathrm{sin}\left(\pi {x}_{i}\right)\right)}^{2}$  $\pm 10$  30  100 
18  Alpine  ${f}_{18}\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{D}}\left{x}_{i}\ast \mathrm{sin}\left({x}_{i}\right)+0.1{x}_{i}\right$  $\pm 10$  30  100 
19  Himmelblau  ${f}_{19}\left(x\right)=\frac{1}{D}{\displaystyle {\displaystyle \sum}_{i=1}^{D}}({x}_{i}^{4}16\ast {x}_{i}^{2}+5{x}_{i})$  $\pm 10$  30  100 
20  Shifted rastrigin  ${f}_{20}\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{D}}({x}_{i}^{2}10\mathrm{cos}\left(2\pi {x}_{i}\right))+10+\mathrm{f}22$  $\pm 10$  30  100 
21  Shifted griewank  ${f}_{21}\left(x\right)={\displaystyle {\displaystyle \sum}_{i=1}^{D}}\frac{{x}_{i}^{2}}{4000}{\displaystyle {\displaystyle \prod}_{i=1}^{D}}cos\left(\frac{{x}_{i}}{\sqrt{i}}\right)+1$  $\pm 10$  30  100 
Test Functions  DSLC1  SLC  r  FA  r  GA  r 

1  1.50 × 10^{−323}  6.10 × 10^{−321}  +  2.54 × 10^{−06}  +  7.63 × 10^{−10}  + 
2  2.00 × 10^{−323}  8.15 × 10^{−322}  +  1.48 × 10^{−11}  +  4.68 × 10^{−10}  + 
3  6.90 × 10^{−323}  5.67 × 10^{−320}  +  4.92 × 10^{−08}  +  3.66 × 10^{−09}  + 
4  4.90 × 10^{−324}  2.50 × 10^{−323}  +  3.10 × 10^{−03}  +  8.27 × 10^{−05}  + 
5  4.90 × 10^{−324}  4.90 × 10^{−324}  ~  2.80 × 10^{−04}  +  1.63 × 10^{−05}  + 
6  9.80 × 10^{−322}  2.50 × 10^{−323}  –  2.35 × 10^{−13}  +  9.40 × 10^{−22}  + 
7  7.01 × 10^{−05}  7.99 × 10^{−05}  +  6.11 × 10^{−04}  +  2.03 × 10^{−02}  + 
8  1.96 × 10^{+01}  2.15 × 10^{+01}  +  2.32 × 10^{+01}  +  1.01 × 10^{−00}  – 
9  3.20 × 10^{−14}  1.60 × 10^{−14}  +  2.89 × 10^{+01}  +  1.54 × 10^{−08}  + 
10  1.70 × 10^{−15}  1.78 × 10^{−15}  –  5.30 × 10^{+01}  +  1.24 × 10^{−07}  + 
11  5.50 × 10^{−15}  4.44 × 10^{−15}  +  9.90 × 10^{−03}  +  8.73 × 10^{−11}  + 
12  8.88 × 10^{−16}  8.88 × 10^{−16}  ~  5.23 × 10^{−04}  +  8.23 × 10^{−05}  + 
13  5.67 × 10^{−30}  3.01 × 10^{−28}  +  9.81 × 10^{−06}  +  2.07 × 10^{−05}  + 
14  −1.50 × 10^{+01}  −1.50 × 10^{+01}  ~  −1.59 × 10^{+01}  –  −4.90 × 10^{−01}  – 
15  6.14 × 10^{−14}  2.78 × 10^{−16}  –  1.27 × 10^{−01}  +  9.72 × 10^{−03}  + 
16  3.68 × 10^{−16}  4.99 × 10^{−13}  +  6.25 × 10^{−09}  +  4.01 × 10^{−06}  + 
17  2.02 × 10^{−31}  2.27 × 10^{−13}  +  7.43 × 10^{−08}  +  9.45 × 10^{−12}  + 
18  4.90 × 10^{−324}  1.50 × 10^{−323}  +  3.10 × 10^{−04}  +  4.58 × 10^{−06}  + 
19  −7.41 × 10^{+01}  −7.54 × 10^{+01}  –  −7.46 × 10^{+01}  +  −7.83 × 10^{+01}  – 
20  3.55 × 10^{−15}  −7.54 × 10^{−15}  +  3.08 × 10^{+01}  +  2.03 × 10^{−08}  + 
21  7.55 × 10^{−15}  5.55 × 10^{−16}  –  2.30 × 10^{−08}  +  4.22 × 10^{−10}  + 
Summary  13+ 3~ 5–  20+ 0~ 1–  18+ 0~ 3– 
Test Functions  DSLC2  SLC  r  FA  r  GA  r 

1  4.90 × 10^{−324}  6.10 × 10^{−321}  +  2.54 × 10^{−06}  +  7.63 × 10^{−10}  + 
2  1.50 × 10^{−323}  8.15 × 10^{−322}  +  1.48 × 10^{−11}  +  4.68 × 10^{−10}  + 
3  4.90 × 10^{−324}  5.67 × 10^{−320}  +  4.92 × 10^{−08}  +  3.66 × 10^{−09}  + 
4  1.50 × 10^{−323}  2.50 × 10^{−323}  +  3.10 × 10^{−03}  +  8.27 × 10^{−05}  + 
5  4.90 × 10^{−324}  4.90 × 10^{−324}  ~  2.80 × 10^{−04}  +  1.63 × 10^{−05}  + 
6  2.96 × 10^{−322}  2.50 × 10^{−323}  –  2.35 × 10^{−13}  +  9.40 × 10^{−22}  + 
7  7.14 × 10^{−05}  7.99 × 10^{−05}  +  6.11 × 10^{−04}  +  2.03 × 10^{−02}  + 
8  2.13 × 10^{+01}  2.15 × 10^{+01}  +  2.32 × 10^{+01}  +  1.01 × 10^{−00}  – 
9  1.78 × 10^{−15}  1.60 × 10^{−14}  +  2.89 × 10^{+01}  +  1.54 × 10^{−08}  + 
10  3.55 × 10^{−15}  1.78 × 10^{−15}  –  5.30 × 10^{+01}  +  1.24 × 10^{−07}  + 
11  8.99 × 10^{−15}  4.44 × 10^{−15}  +  9.90 × 10^{−03}  +  8.73 × 10^{−11}  + 
12  8.88 × 10^{−16}  8.88 × 10^{−16}  ~  5.23 × 10^{−04}  +  8.23 × 10^{−05}  + 
13  3.90 × 10^{−12}  3.01 × 10^{−28}  –  9.81 × 10^{−06}    2.07 × 10^{−05}  – 
14  −1.50 × 10^{+01}  −1.50 × 10^{+01}  ~  −1.59 × 10^{+01}  +  −4.90 ×10^{−01}  + 
15  5.55 × 10^{−17}  2.78 × 10^{−16}  +  1.27 × 10^{−01}  +  9.72 × 10^{−03}  + 
16  5.32 × 10^{−14}  4.99 × 10^{−13}  +  6.25 × 10^{−09}  +  4.01 × 10^{−06}  + 
17  4.03 × 10^{−19}  2.27 × 10^{−13}  +  7.43 × 10^{−08}  +  9.45 × 10^{−12}  + 
18  3.50 × 10^{−323}  1.50 × 10^{−323}  –  3.10 × 10^{−04}    4.58 × 10^{−06}  – 
19  −7.17 × 10^{+01}  −7.54 × 10^{+01}  –  −7.46 × 10^{+01}    −7.83 ×10^{+01}  – 
20  2.13 × 10^{−14}  −7.54 × 10^{−15}  –  3.08 × 10^{+01}  +  2.03 × 10^{−08}  + 
21  3.33 × 10^{−16}  5.55 × 10^{−16}  +  2.30 × 10^{−08}    4.22 × 10^{−10}  + 
Summary  12+ 3~ 6–  20+ 0~ 1–  18+ 0~ 3– 
Test Functions  DSLC3  SLC  r  FA  r  GA  r 

1  1.00 × 10^{−323}  6.10 × 10^{−321}  +  2.54 × 10^{−06}  +  7.63 × 10^{−10}  + 
2  5.90 × 10^{−323}  8.15 × 10^{−322}  +  1.48 × 10^{−11}  +  4.68 × 10^{−10}  + 
3  2.19 × 10^{−321}  5.67 × 10^{−320}  +  4.92 × 10^{−08}  +  3.66 × 10^{−09}  + 
4  4.90 × 10^{−324}  2.50 × 10^{−323}  +  3.10 × 10^{−03}  +  8.27 × 10^{−05}  + 
5  4.90 × 10^{−324}  4.90 × 10^{−324}  ~  2.80 × 10^{−04}  +  1.63 × 10^{−05}  + 
6  3.10 × 10^{−322}  2.50 × 10^{−323}  –  2.35 × 10^{−13}  +  9.40 × 10^{−22}  + 
7  1.22 × 10^{−04}  7.99 × 10^{−05}  –  6.11 × 10^{−04}  +  2.03 × 10^{−02}  + 
8  1.35 × 10^{+01}  2.15 × 10^{+01}  +  2.32 × 10^{+01}  –  1.01 × 10^{−00}  + 
9  1.15 × 10^{−13}  1.60 × 10^{−14}  –  2.89 × 10^{+01}  +  1.54 × 10^{−08}  + 
10  2.29 × 10^{−13}  1.78 × 10^{−15}  –  5.30 × 10^{+01}  +  1.24 × 10^{−07}  + 
11  3.33 × 10^{−16}  4.44 × 10^{−15}  –  9.90 × 10^{−03}  +  8.73 × 10^{−11}  + 
12  8.88 × 10^{−16}  8.88 × 10^{−16}  ~  5.23 × 10^{−04}  +  8.23 × 10^{−05}  + 
13  1.23 × 10^{−29}  3.01 × 10^{−28}  +  9.81 × 10^{−06}  +  2.07 × 10^{−05}  + 
14  −1.50 × 10^{+01}  −1.50 × 10^{+01}  ~  −1.59 × 10^{+01}  +  −4.90 ×10^{−01}  – 
15  1.67 × 10^{−16}  2.78 × 10^{−16}  +  1.27 × 10^{−01}  +  9.72 × 10^{−03}  + 
16  1.56 × 10^{−31}  4.99 × 10^{−13}  +  6.25 × 10^{−09}  +  4.01 × 10^{−06}  + 
17  8.27 × 10^{−30}  2.27 × 10^{−13}  +  7.43 × 10^{−08}  +  9.45 × 10^{−12}  + 
18  1.00 × 10^{−323}  1.50 × 10^{−323}  +  3.10 × 10^{−04}  +  4.58 × 10^{−06}  + 
19  −7.44 × 10^{+01}  −7.54 × 10^{+01}  +  −7.46 × 10^{+01}  –  −7.83 ×10^{+01}  – 
20  4.09 × 10^{−14}  −7.54 × 10^{−15}  –  3.08 × 10^{+01}  +  2.03 × 10^{−08}  + 
21  2.66 × 10^{−15}  5.55 × 10^{−16}  –  2.30 × 10^{−08}  +  4.22 × 10^{−10}  + 
Summary  11+ 3~ 7–  19+ 0~ 2–  19+ 0~ 2– 
Test Functions  JADE  DSLC1  r  DSLC2  r  DSLC3  r 

1  6.10 × 10^{−323}  1.50 × 10^{−323}  –  4.90 × 10^{−324}    1.00 × 10^{−}^{323}   
2  8.15 × 10^{−322}  2.00 × 10^{−323}  –  1.50 × 10^{−323}    5.90 × 10^{−}^{323}   
3  5.67 × 10^{−320}  6.90 × 10^{−323}  –  4.90 × 10^{−324}    2.19 × 10^{−}^{321}   
4  2.50 × 10^{−323}  4.90 × 10^{−324}  –  1.50 × 10^{−323}    4.90 × 10^{−}^{324}   
5  4.90 × 10^{−324}  4.90 × 10^{−324}  –  4.90 × 10^{−324}  ~  4.90 × 10^{−}^{324}  ~ 
6  2.50 × 10^{−323}  9.80 × 10^{−322}  +  2.96 × 10^{−322}  +  3.10 × 10^{−}^{322}  + 
7  7.99 × 10^{−05}  7.01 × 10^{−05}  +  7.14 × 10^{−05}    1.22 × 10^{−}^{04}  + 
8  2.15 × 10^{+01}  1.96 × 10^{+01}  –  2.13 × 10^{+01}    1.35 × 10^{+01}  
9  1.60 × 10^{−14}  3.20 × 10^{−14}  +  1.78 × 10^{−15}    1.15 × 10^{−}^{13}  + 
10  1.78 × 10^{−15}  1.70 × 10^{−15}  +  3.55 × 10^{−15}  +  2.29 × 10^{−}^{13}  + 
11  4.44 × 10^{−15}  5.50 × 10^{−15}  –  8.99 × 10^{−15}  +  3.33 × 10^{−}^{16}  + 
12  8.88 × 10^{−16}  8.88 × 10^{−16}  ~  8.88 × 10^{−16}  ~  8.88 × 10^{−}^{16}  ~ 
13  3.01 × 10^{−28}  5.67 × 10^{−30}  –  3.90 × 10^{−12}  +  1.23 × 10^{−}^{29}  
14  −1.50 × 10^{+01}  −1.50 × 10^{+01}  ~  −1.50 × 10^{+01}  ~  −1.50 × 10^{+01}  ~ 
15  2.78 × 10^{−16}  6.14 × 10^{−14}  +  5.55 × 10^{−17}    1.67 × 10^{−}^{16}   
18  4.99 × 10^{−13}  3.68 × 10^{−16}  –  5.32 × 10^{−14}    1.56 × 10^{−}^{31}   
19  2.27 × 10^{−13}  2.02 × 10^{−31}  –  4.03 × 10^{−19}    8.27 × 10^{−}^{30}   
20  1.50 × 10^{−323}  4.90 × 10^{−324}  +  3.50 × 10^{−323}  +  1.00 × 10^{−}^{323}   
21  −7.24 × 10^{+01}  −7.41 × 10^{+01}  –  −7.17 × 10^{+01}  +  −7.44 × 10^{+01}   
22  7.11 × 10^{−15}  3.55 × 10^{−15}  +  2.13 × 10^{−14}  +  4.09 × 10^{−}^{14}  + 
23  5.55 × 10^{−16}  7.55 × 10^{−15}  –  3.33 × 10^{−16}    2.66 × 10^{−}^{15}  + 
Summary  8+ 2~ 11–  5+ 3~ 13–  7+ 3~ 11– 
Parameters Noticed  Denoted Symbols  Initial Values 

$\mathrm{Initial}\text{}\mathrm{node}\text{}\mathrm{energy}$  ${E}_{j}$  $0.5$ J 
Receiving and transmitting energy  E_{fs}  10 pJ/bit/m^{2} 
Number of nodes in WSN  N  100/200/300/nodes 
$\mathrm{Data}\text{}\mathrm{aggregation}\text{}\mathrm{energy}$  E_{DA}  5 pJ/bit/signal 
Number bit of a data message  l  1024 bit 
$\mathrm{Radio}\text{}\mathrm{electronics}\text{}\mathrm{energy}$  E_{elec}  $50$ nJ/bit 
$\mathrm{Amplifier}\text{}\mathrm{energy}$  E_{mp}  0.013 pJ/bit/m^{4} 
Space distribution  M  $30/50/90/300$ m 
Generations  MaxIter  $200$ 
Parameters of physical characteristics  ${\tau}_{1},{\tau}_{2}$ and ${\omega}_{1},{\omega}_{2}$  1, 0.95 and 0.9, 0.01 
Number of runs  $runs$  $20$ 
Radius of the sensor reaching  r;${r}_{e}$  3; 1.5 m 
GA, FA  Initialize parameters  ${N}_{P}=80$, ${F}_{c}=0.8,{P}_{m}=0.1$ 
DSCL, SCL  Initialize parameters  ${N}_{P}=80$, ${R}_{1,}=10,$ 
$\mathbf{Deployed}\text{}\mathbf{Area}\text{}\left({\mathbf{m}}^{2}\right)$  Moving Nodes  DSLC1  DSLC2  DSLC3  SLC  FA  GA 

40 × 40  20  83.49%  84.78%  86.12%  79.34%  69.11%  74.01% 
70 × 70  30  82.21%  84.06%  85.10%  78.33%  71.33%  73.01% 
90 × 90  50  84.19%  85.18%  87.13%  81.94%  72.93%  78.01% 
© 2020 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).
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Qiao, Y.; Dao, T.K.; Pan, J.S.; Chu, S.C.; Nguyen, T.T. Diversity Teams in Soccer League Competition Algorithm for Wireless Sensor Network Deployment Problem. Symmetry 2020, 12, 445. https://doi.org/10.3390/sym12030445
Qiao Y, Dao TK, Pan JS, Chu SC, Nguyen TT. Diversity Teams in Soccer League Competition Algorithm for Wireless Sensor Network Deployment Problem. Symmetry. 2020; 12(3):445. https://doi.org/10.3390/sym12030445
Chicago/Turabian StyleQiao, Yu, ThiKien Dao, JengShyang Pan, ShuChuan Chu, and TrongThe Nguyen. 2020. "Diversity Teams in Soccer League Competition Algorithm for Wireless Sensor Network Deployment Problem" Symmetry 12, no. 3: 445. https://doi.org/10.3390/sym12030445