An Adaptation Multi-Group Quasi-Affine Transformation Evolutionary Algorithm for Global Optimization and Its Application in Node Localization in Wireless Sensor Networks
Abstract
:1. Introduction
- A proposed novel AMG-QUATRE algorithm overcomes the deficiencies of the original QUATRE.
- Full use of different mutation strategies along with proper parameters makes a better trade-off between exploration and exploitation capability.
- Compared results with three QUATRE variants, two DE variants, and two PSO variants on testing CEC2013 benchmark is to evaluate confirming the performance of the proposed algorithm.
- An applied AMG-QUATRE to the node localization in WSN by modifying the average hop distance improving the DV-Hop algorithm and implementing the proposed algorithm to obtain the position of the nodes in WSN.
2. Related Works
2.1. Original QUATRE Algorithm
2.2. Statement of the Location Problem
3. Adaptation Multi-Group QUATRE Algorithm and Its Application to Node Localization in WSN
3.1. Adaptation Multi-Group QUATRE Algorithm (AMG-QUATRE)
3.1.1. Population Division and Mutation Schemes
3.1.2. Adaptation Scale Factor
Algorithm 1. Shows the Pseudo Code of AMG-QUATRE Algorithm. |
// Initialization phase |
Initialize the searching space V, dimension D, Set the generation counter Gen=1, randomly initialize the population with individuals, and evaluate fitness values of all individuals, set initial , . |
// Main loop |
1: while stopping criterion is not satisfied do |
2: Randomly partition the population into three groups, , and |
3: Generate matrices and , and , and , using Equation (3). |
4: Calculate mutation matrix using QUATRE/target-to-best/1, using QUATRE/rand/1, using QUATRE/best/1. |
5: Evolve individuals in each group using Equation (1). |
6: Evaluate fitness values of all individuals. |
7: for do |
8: if then |
9: |
10: end if |
11: end for |
12: , . |
13: Update scale factor F according to Equation (12). |
14: |
15: end while |
Output: The global optimum , global best fitness value . |
3.2. Our Proposed Algorithm for DV-Hop Localization Algorithm
3.2.1. Modification of Hop Size
3.2.2. Using AMG-QUATRE Algorithm to Locate the Unknown Nodes
- Step 1,
- initialize parameters of AMG-QUATRE and individuals.
- Step 2,
- generate donor matrices.
- Step 3,
- generate trial matrices.
- Step 4,
- select a better vector between the trial vector and its corresponding target vector to enter the next generation. Repeat the above steps 2 to 4 until the stop condition is satisfied.
4. Experimental Analysis
4.1. Simulation Results on Standard Bound-Constrained Benchmarks
4.2. Simulation Results of Applied AMG-QUATRE to Node Localization in WSN
4.2.1. Sensitivity of Varying Anchor Node Ratio
4.2.2. Sensitivity of Varying Communication Range
4.2.3. Sensitivity of Node Density
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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No. | QUATRE/x/y | Equation |
---|---|---|
1 | QUATRE/rand/1 | |
2 | QUATRE/best/1 | |
3 | QUATRE/target/1 | |
4 | QUATRE/target-to-best/1 | |
5 | QUATRE/rand/2 | |
6 | QUATRE/best/2 | |
7 | QUATRE/target/2 |
Algorithm | Parameters Settings |
---|---|
DE | |
ODE | |
CLPSO | |
SLPSO | |
QUATRE variants | |
AMG-QUATRE |
50D | DE/best/1/bin | ODE/best/1/bin | CLPSO | SLPSO | QUATRE/best | QUATRE/rand | QUATRE/target-to-best | AMP-QUATRE |
---|---|---|---|---|---|---|---|---|
1 | 2.273 × 10−13(=) | 2.273 × 10−13(=) | 2.2737 × 10−13(=) | 2.2737 × 10−13(=) | 0.0000 × 10+00(+) | 0.0000 × 10+00(+) | 2.2737 × 10−13(=) | 2.2737 × 10−13 |
2 | 4.5454 × 10+07(−) | 4.871 × 10+07(−) | 5.9535 × 10+05(−) | 3.1277 × 10+05(+) | 3.8146 × 10+05(+) | 8.0401 × 10+06(−) | 3.7393 × 10+05(+) | 5.8732 × 10+05 |
3 | 1.9098 × 10+09(−) | 1.775 × 10+09(−) | 8.0541 × 10+06(−) | 1.2111 × 10+05(+) | 1.0726 × 10+06(−) | 5.1302 × 10+06(−) | 1.7985 × 10+05(+) | 8.3722 × 10+05 |
4 | 4.0671 × 10+04(−) | 4.629 × 10+04(−) | 3.818 × 10+03(−) | 2.3913 × 10+04(−) | 4.5832 × 10+01(+) | 1.7578 × 10+04(−) | 1.7273 × 10+01(+) | 3.8289 × 10+03 |
5 | 1.1369 × 10+1 (=) | 1.136 × 10−13(=) | 1.1369 × 10−13(−) | 1.1369 × 10−13(=) | 1.1369 × 10−13(=) | 1.3642 × 10−12(−) | 1.1369 × 10−13(=) | 1.1369 × 10−13 |
6 | 4.3447 × 10+01(−) | 4.415 × 10+01(−) | 4.3447 × 10+01(−) | 4.3447 × 10+01(=) | 4.3447 × 10+01(=) | 4.3447 × 10+01(−) | 4.3447 × 10+01(=) | 4.3447 × 10+01 |
7 | 6.4767 × 10+01(−) | 6.1526 × 10+01(−) | 3.5117 × 10+01(−) | 7.1569 × 10−01(+) | 2.9215 × 10+01(+) | 3.1212 × 10+01(+) | 9.8822 × 10+00(+) | 3.3071 × 10+01 |
8 | 2.1041 × 10+01(−) | 2.1044 × 10+01(−) | 2.1060 × 10+01(−) | 2.1044 × 10+01(−) | 2.1060 × 10+01(−) | 2.1012 × 10+01(−) | 2.1062 × 10+01(−) | 2.1003 × 10+01 |
9 | 5.5049 × 10+01(−) | 3.7639 × 10+01(−) | 2.4972 × 10+01(−) | 1.2712 × 10+01(+) | 2.0720 × 10+01(+) | 5.9709 × 10+01(−) | 2.7689 × 10+01(−) | 2.6244 × 10+01 |
10 | 1.1534 × 10+00(−) | 1.7926 × 10+00(−) | 5.9149 × 10−02(−) | 1.0602 × 10−01(−) | 1.7241 × 10−02(+) | 9.4477 × 10−01(−) | 1.4780 × 10−02(+) | 6.6495 × 10−02 |
11 | 5.6843 × 10−14(+) | 5.6843 × 10−14(+) | 2.0090 × 10+01(+) | 1.4924 × 10+01(+) | 5.2875 × 10+01(−) | 1.0379 × 10+00(+) | 7.4948 × 10+01(−) | 2.2921 × 10+01 |
12 | 2.5041 × 10+02(−) | 1.5262 × 10+02(−) | 6.4672 × 10+01(−) | 3.0614 × 10+02(−) | 7.1792 × 10+01(−) | 2.5256 × 10+02(−) | 2.2941 × 10+02(−) | 6.6662 × 10+01 |
13 | 3.1407 × 10+02(−) | 2.5190 × 10+02(−) | 1.3242 × 10+02(−) | 3.1176 × 10+02(−) | 1.2214 × 10+02(+) | 2.4339 × 10+02(−) | 2.8762 × 10+02(−) | 1.2265 × 10+02 |
14 | 6.0810 × 10+00(+) | 6.3847 × 10+00(+) | 3.7529 × 10+02(+) | 6.9829 × 10+02(−) | 1.2919 × 10+03(−) | 7.9588 × 10+01(+) | 3.6695 × 10+03(−) | 6.0000 × 10+02 |
15 | 1.1449 × 10+04(−) | 6.7771 × 10+03(−) | 5.0860 × 10+03(−) | 3.6314 × 10+03(+) | 8.5293 × 10+03(−) | 1.0372 × 10+04(−) | 1.1384 × 10+04(−) | 5.1193 × 10+03 |
16 | 2.9382 × 10+00(−) | 2.5038 × 10+00(−) | 2.7308 × 10−01(−) | 2.8265 × 10+00(−) | 2.5942 × 10+00(−) | 2.3831 × 10+00(−) | 2.1997 × 10+00(−) | 7.0698 × 10−01 |
17 | 5.0786 × 10+01(+) | 5.0800 × 10+01(+) | 7.2026 × 10+01(+) | 3.1820 × 10+02(−) | 1.1320 × 10+02(−) | 5.9894 × 10+01(+) | 1.3404 × 10+02(−) | 6.8152 × 10+01 |
18 | 4.0051 × 10+02(−) | 3.6304 × 10+02(−) | 9.8335 × 10+01(−) | 3.7049 × 10+02(−) | 2.6744 × 10+02(−) | 3.5631 × 10+02(−) | 3.5551 × 10+02(−) | 1.0152 × 10+02 |
19 | 6.6847 × 10+00(−) | 8.9514 × 10+00(−) | 4.0347 × 10+00(+) | 4.5031 × 10+00(−) | 5.0660 × 10+00(−) | 9.5681 × 10+00(−) | 1.0231 × 10+01(−) | 3.4843 × 10+00 |
20 | 2.1634 × 10+01(−) | 2.1809 × 10+01(−) | 1.8929 × 10+01(−) | 2.1551 × 10+01(−) | 2.0609 × 10+01(−) | 2.1465 × 10+01(−) | 2.0438 × 10+01(−) | 1.7868 × 10+01 |
21 | 2.0000 × 10+02(=) | 2.0000 × 10+02(=) | 2.0000 × 10+02(−) | 2.0000 × 10+02(=) | 2.0000 × 10+02(=) | 2.0000 × 10+02(=) | 2.0000 × 10+02(=) | 2.0000 × 10+02 |
22 | 2.6406 × 10+01(+) | 3.0189 × 10+01(+) | 6.2665 × 10+02(+) | 7.3845 × 10+02(−) | 1.7683 × 10+03(−) | 1.0261 × 10+02(+) | 3.3192 × 10+03(−) | 4.8452 × 10+02 |
23 | 1.2346 × 10+04(−) | 9.3380 × 10+03(−) | 4.8609 × 10+03(−) | 3.1419 × 10+03(+) | 8.5494 × 10+03(−) | 1.1668 × 10+04(−) | 1.1481 × 10+04(−) | 4.9707 × 10+03 |
24 | 3.1693 × 10+02(−) | 3.2104 × 10+02(−) | 2.4601 × 10+02(−) | 2.3006 × 10+02(+) | 2.5158 × 10+02(−) | 2.2959 × 10+02(+) | 2.3078 × 10+02(+) | 2.4894 × 10+02 |
25 | 3.5881 × 10+02(−) | 3.6268 × 10+02(−) | 3.0172 × 10+02(−) | 2.8333 × 10+02(+) | 2.8807 × 10+02(+) | 3.3466 × 10+02(−) | 2.8322 × 10+02(+) | 2.9743 × 10+02 |
26 | 2.0453 × 10+02(−) | 2.0252 × 10+02(−) | 2.0021 × 10+02(−) | 2.0010 × 10+02(+) | 2.0008 × 10+02(+) | 2.0071 × 10+02(−) | 2.0004 × 10+02(+) | 2.0019 × 10+02 |
27 | 1.5258 × 10+03(−) | 1.6157 × 10+03(−) | 7.9749 × 10+02(+) | 6.9280 × 10+02(+) | 8.2461 × 10+02(+) | 1.5090 × 10+03(−) | 7.3735 × 10+02(+) | 9.2220 × 10+02 |
28 | 4.0000 × 10+02(=) | 4.0000 × 10+02(=) | 4.0000 × 10+02(=) | 4.0000 × 10+02(=) | 4.0000 × 10+02(=) | 4.0000 × 10+02(=) | 4.0000 × 10+02(=) | 4.0000 × 10+02 |
−/=/+ | 20/4/4 | 20/4/4 | 20/2/6 | 12/5/11 | 14/4/10 | 19/2/7 | 14/5/9 | −/−/− |
50D | DE/best/1/bin | ODE/best/1/bin | CLPSO | SLPSO |
1 | 2.2737 × 10−13/0.0000 × 10+00(=) | 2.2737 × 10−13/0.0000 × 10+00(=) | 2.2737 × 10−13/0.0000 × 10+00(=) | 2.2737 × 10−13/0.0000 × 10+00(=) |
2 | 6.7630 × 10+07/1.4092 × 10+07(−) | 8.1854 × 10+07/1.7030 × 10+07(−) | 3.9702 × 10+07/7.0886 × 10+06(−) | 8.9731 × 10+05/3.1582 × 10+05(=) |
3 | 3.2967 × 10+09/1.8024 × 10+09(−) | 4.4957 × 10+09/1.4925 × 10+09(−) | 1.8074 × 10+09/9.5165 × 10+08(−) | 1.1610 × 10+07/1.4090 × 10+07(+) |
4 | 4.9175 × 10+04/4.9989 × 10+03(−) | 5.7660 × 10+04/8.7742 × 10+03(−) | 3.3408 × 10+04/6.0160 × 10+03(−) | 3.3850 × 10+04/1.0284 × 10+04(−) |
5 | 2.2737 × 10−13/3.6885 × 10−14(=) | 1.9895 × 10−13/5.0507 × 10−14(=) | 2.8990 × 10−13/5.8028 × 10−14(−) | 1.9895 × 10−13/5.0507 × 10−14(=) |
6 | 4.4426 × 10+01/7.7214 × 10−01(−) | 4.5560 × 10+01/1.4691 × 10+00(−) | 4.6402 × 10+01/7.0628 × 10−01(−) | 4.3447 × 10+01/1.2356 × 10−11(+) |
7 | 8.3113 × 10+01/1.0175 × 10+01(−) | 8.8732 × 10+01/1.2892 × 10+01(−) | 1.0165 × 10+02/8.5250 × 10+00(−) | 5.9876 × 10+00/4.8864 × 10+00(+) |
8 | 2.1127 × 10+01/3.5876 × 10−02(=) | 2.1143 × 10+01/3.7340 × 10−02(=) | 2.1143 × 10+01/3.7719 × 10−02(=) | 2.1119 × 10+01/3.3008 × 10−02(=) |
9 | 5.8061 × 10+01/1.8481 × 10+00(−) | 5.0049 × 10+01/5.9272 × 10+00(−) | 5.3471 × 10+01/2.5860 × 10+00(−) | 1.8053 × 10+01/3.5882 × 10+00(+) |
10 | 3.9408 × 10+00/2.0661 × 10+00(−) | 6.3503 × 10+00/4.4398 × 10+00(−) | 6.0611 × 10+00/1.4295 × 10+00(−) | 2.6597 × 10−01/1.1229 × 10−01(−) |
11 | 1.9402 × 10+00/1.6920 × 10+00(+) | 1.9402 × 10+00/1.5970 × 10+00(+) | 8.8107 × 10−14/2.9014 × 10−14(+) | 3.4565 × 10+01/1.1287 × 10+01(=) |
12 | 3.1874 × 10+02/2.7910 × 10+01(−) | 2.5954 × 10+02/3.3785 × 10+01(−) | 2.7169 × 10+02/2.8911 × 10+01(−) | 3.4056 × 10+02/1.4672 × 10+01(−) |
13 | 3.4943 × 10+02/1.7881 × 10+01(−) | 3.1646 × 10+02/3.3786 × 10+01(−) | 3.5904 × 10+02/3.9979 × 10+01(−) | 3.3874 × 10+02/1.0522 × 10+01(−) |
14 | 9.2118 × 10+01/9.8833 × 10+01(+) | 5.4027 × 10+01/6.5389 × 10+01(+) | 4.3188 × 10+01/1.1086 × 10+01(+) | 1.1953 × 10+03/3.3024 × 10+02(−) |
15 | 1.2980 × 10+04/6.5858 × 10+02(−) | 1.1202 × 10+04/1.7749 × 10+03(−) | 9.2360 × 10+03/5.1031 × 10+02(−) | 1.2144 × 10+04/2.9152 × 10+03(−) |
16 | 3.3028 × 10+00/2.1856 × 10−01(−) | 3.2672 × 10+00/3.4818 × 10−01(−) | 2.6884 × 10+00/2.9832 × 10−01(−) | 3.3398 × 10+00/2.5719 × 10−01(−) |
17 | 5.0939 × 10+01/2.1260 × 10−01(+) | 5.1808 × 10+01/1.0106 × 10+00(+) | 5.3451 × 10+01/5.9901 × 10−01(+) | 3.5993 × 10+02/2.4006 × 10+01(−) |
18 | 4.2249 × 10+02/1.4402 × 10+01(−) | 3.9685 × 10+02/1.5608 × 10+01(−) | 4.0577 × 10+02/2.3800 × 10+01(−) | 3.9239 × 10+02/1.2010 × 10+01(−) |
19 | 8.7896 × 10+00/7.5759 × 10−01(−) | 1.0217 × 10+01/4.9098 × 10−01(−) | 3.0401 × 10+00/4.7453 × 10−01(+) | 6.3564 × 10+00/9.8914 × 10−01(−) |
20 | 2.2341 × 10+01/2.9931 × 10−01(−) | 2.2343 × 10+01/2.7942 × 10−01(−) | 2.3215 × 10+01/5.3751 × 10−01(−) | 2.2119 × 10+01/3.1389 × 10−01(−) |
21 | 6.3252 × 10+02/4.5144 × 10+02(=) | 7.4552 × 10+02/3.8638 × 10+02(=) | 3.5629 × 10+02/1.7059 × 10+02(+) | 8.3775 × 10+02/3.5207 × 10+02(=) |
22 | 2.1962 × 10+02/5.4330 × 10+02(+) | 8.2888 × 10+02/8.9069 × 10+02(=) | 1.1107 × 10+02/8.2297 × 10+01(+) | 1.3757 × 10+03/3.8553 × 10+02(−) |
23 | 1.3292 × 10+04/4.4167 × 10+02(−) | 1.1793 × 10+04/1.2168 × 10+03(−) | 1.0989 × 10+04/7.4371 × 10+02(−) | 1.2284 × 10+04/2.2400 × 10+03(−) |
24 | 3.2829 × 10+02/8.3062 × 10+00(−) | 3.3833 × 10+02/1.0558 × 10+01(−) | 3.4471 × 10+02/8.4855 × 10+00(−) | 2.5367 × 10+02/1.0552 × 10+01(+) |
25 | 3.7028 × 10+02/7.0668 × 10+00(−) | 3.7432 × 10+02/4.9628 × 10+00(−) | 3.8750 × 10+02/7.9298 × 10+00(−) | 2.9793 × 10+02/7.6039 × 10+00(+) |
26 | 2.0754 × 10+02/1.6936 × 10+00(+) | 2.1829 × 10+02/5.4942 × 10+01(+) | 2.0422 × 10+02/1.0483 × 10+00(+) | 3.2412 × 10+02/4.4937 × 10+01(+) |
27 | 1.7343 × 10+03/8.7052 × 10+01(−) | 1.7591 × 10+03/7.7658 × 10+01(−) | 1.5672 × 10+03/4.9764 × 10+02(−) | 7.9272 × 10+02/6.7907 × 10+01(+) |
28 | 8.7540 × 10+02/1.1611 × 10+03(=) | 7.1055 × 10+02/9.5585 × 10+02(=) | 4.0000 × 10+02/3.8809 × 10−05(=) | 4.0000 × 10+02/1.8070 × 10−13(+) |
−/=/+ | 18/5/5 | 18/6/4 | 18/3/7 | 13/6/9 |
50D | QUATRE/best | QUATRE/rand | QUATRE/target-to-best | AMP-QUATRE |
1 | 2.1600 × 10−13/5.0842 × 10−14(=) | 4.5475 × 10−14/9.3312 × 10−14(+) | 2.2737 × 10−13/0.0000 × 10+00(=) | 2.2737 × 10−13/0.0000 × 10+00 |
2 | 1.0164 × 10+06/3.7357 × 10+05(=) | 1.5023 × 10+07/4.6299 × 10+06(−) | 5.5836 × 10+05/1.8107 × 10+05(+) | 1.0360 × 10+06/3.4365 × 10+05 |
3 | 2.3504 × 10+07/2.4206 × 10+07(+) | 4.4566 × 10+07/3.8021 × 10+07(=) | 3.6782 × 10+06/4.3941 × 10+06(+) | 5.9671 × 10+07/7.3033 × 10+07 |
4 | 1.3953 × 10+02/1.1877 × 10+02(+) | 2.7389 × 10+04/4.9350 × 10+03(−) | 4.8391 × 10+01/3.2542 × 10+01(+) | 6.8604 × 10+03/1.8305 × 10+03 |
5 | 1.5348 × 10−13/5.5634 × 10−14(+) | 5.3547 × 10−12/2.1671 × 10−12(−) | 1.9895 × 10−13/5.0507 × 10−14(=) | 2.1600 × 10−13/5.0842 × 10−14 |
6 | 4.5714 × 10+01/1.0138 × 10+01(=) | 4.3448 × 10+01/2.3788 × 10−04(−) | 4.3447 × 10+01/1.5166 × 10−13(+) | 4.3741 × 10+01/1.2778 × 10+00 |
7 | 6.7584 × 10+01/2.9108 × 10+01(=) | 4.7842 × 10+01/8.1591 × 10+00(=) | 3.2089 × 10+01/1.3516 × 10+01(+) | 5.0112 × 10+01/1.1419 × 10+01 |
8 | 2.1186 × 10+01/4.1762 × 10−02(−) | 2.1130 × 10+01/4.0969 × 10−02(=) | 2.1132 × 10+01/3.3735 × 10−02(=) | 2.1129 × 10+01/4.3053 × 10−02 |
9 | 3.7688 × 10+01/9.3369 × 10+00(=) | 6.2639 × 10+01/1.3582 × 10+00(−) | 5.1629 × 10+01/1.2135 × 10+01(−) | 3.5635 × 10+01/5.3692 × 10+00 |
10 | 4.8407 × 10−02/2.7521 × 10−02(+) | 1.0614 × 10+00/4.4795 × 10−02(−) | 5.1479 × 10−02/2.2316 × 10−02(+) | 1.6877 × 10−01/9.1756 × 10−02 |
11 | 8.2337 × 10+01/1.8602 × 10+01(−) | 3.2253 × 10+00/1.5308 × 10+00(+) | 8.7687 × 10+01/6.7867 × 10+00(−) | 3.2670 × 10+01/7.8026 × 10+00 |
12 | 1.7239 × 10+02/5.2618 × 10+01(−) | 2.8889 × 10+02/1.8586 × 10+01(−) | 2.6828 × 10+02/2.2955 × 10+01(−) | 9.6453 × 10+01/1.9272 × 10+01 |
13 | 2.4279 × 10+02/6.2197 × 10+01(−) | 3.2962 × 10+02/2.8567 × 10+01(−) | 3.2354 × 10+02/1.9088 × 10+01(−) | 1.8994 × 10+02/3.9348 × 10+01 |
14 | 2.0942 × 10+03/4.5566 × 10+02(−) | 1.0795 × 10+02/2.0880 × 10+01(+) | 4.0460 × 10+03/2.6165 × 10+02(−) | 9.4145 × 10+02/2.6942 × 10+02 |
15 | 1.0621 × 10+04/1.3099 × 10+03(−) | 1.2616 × 10+04/7.7705 × 10+02(−) | 1.2556 × 10+04/4.3565 × 10+02(−) | 6.7499 × 10+03/9.2335 × 10+02 |
16 | 3.2825 × 10+00/3.6056 × 10−01(−) | 3.2270 × 10+00/3.4962 × 10−01(−) | 3.1910 × 10+00/3.5035 × 10−01(−) | 2.1841 × 10+00/6.6439 × 10−01 |
17 | 1.4570 × 10+02/2.2191 × 10+01(−) | 6.3096 × 10+01/2.0368 × 10+00(+) | 1.4326 × 10+02/6.5122 × 10+00(−) | 8.4913 × 10+01/1.1647 × 10+01 |
18 | 3.3174 × 10+02/4.0023 × 10+01(−) | 3.9469 × 10+02/1.6971 × 10+01(−) | 3.8234 × 10+02/1.6744 × 10+01(−) | 1.3042 × 10+02/1.7501 × 10+01 |
19 | 8.9865 × 10+00/2.3915 × 10+00(−) | 1.1791 × 10+01/1.0069 × 10+00(−) | 1.1623 × 10+01/6.9306 × 10−01(−) | 5.7073 × 10+00/1.2275 × 10+00 |
20 | 2.1561 × 10+01/6.1393 × 10−01(−) | 2.2261 × 10+01/2.7190 × 10−01(−) | 2.1631 × 10+01/4.1090 × 10−01(−) | 1.9466 × 10+01/9.0364 × 10−01 |
21 | 7.5331 × 10+02/4.6351 × 10+02(=) | 3.3833 × 10+02/3.3784 × 10+02(+) | 6.9616 × 10+02/4.2920 × 10+02(=) | 8.3451 × 10+02/3.9226 × 10+02 |
22 | 2.7567 × 10+03/5.0416 × 10+02(−) | 1.5228 × 10+02/3.7961 × 10+01(+) | 4.0302 × 10+03/3.6030 × 10+02(−) | 1.0156 × 10+03/3.1553 × 10+02 |
23 | 1.0749 × 10+04/1.2205 × 10+03(−) | 1.2862 × 10+04/5.9890 × 10+02(−) | 1.2310 × 10+04/4.3309 × 10+02(−) | 7.3067 × 10+03/1.1271 × 10+03 |
24 | 2.8054 × 10+02/1.6244 × 10+01(=) | 2.5232 × 10+02/2.0385 × 10+01(+) | 2.5944 × 10+02/1.5156 × 10+01(+) | 2.7678 × 10+02/1.4085 × 10+01 |
25 | 3.1143 × 10+02/1.3222 × 10+01(=) | 3.6970 × 10+02/1.5311 × 10+01(−) | 3.0858 × 10+02/1.7011 × 10+01(=) | 3.1547 × 10+02/1.2938 × 10+01 |
26 | 3.7335 × 10+02/4.4089 × 10+01(=) | 2.7737 × 10+02/1.1776 × 10+02(=) | 3.4616 × 10+02/6.6582 × 10+01(+) | 3.7563 × 10+02/4.3086 × 10+01 |
27 | 1.1743 × 10+03/2.1424 × 10+02(=) | 1.8024 × 10+03/1.0782 × 10+02(−) | 9.5415 × 10+02/1.3437 × 10+02(+) | 1.1754 × 10+03/1.3799 × 10+02 |
28 | 1.1486 × 10+03/1.3303 × 10+03(=) | 4.0000 × 10+02/3.5987 × 10−09(+) | 8.4294 × 10+02/1.0819 × 10+03(=) | 1.1617 × 10+03/1.3536 × 10+03 |
−/=/+ | 13/11/4 | 16/4/8 | 13/6/9 | −/−/− |
Simulation Parameters | Parameters Settings |
---|---|
Sensing region area | 100 m × 100 m |
Total number of sensor nodes | 100–400 |
Communication range | 15–40 m |
Percentage of anchor nodes | 5–40% |
Initial population size | 20 |
Maximum generations | 100 |
Anchor Nodes | 5 | 10 | 15 | 20 | 25 | 30 | 35 | 40 | Avg |
---|---|---|---|---|---|---|---|---|---|
DV-Hop | 0.495 | 0.4227 | 0.423 | 0.349 | 0.3513 | 0.346 | 0.322 | 0.3213 | 0.378788 |
Hyperbolic-DV-Hop | 0.4847 | 0.3716 | 0.3641 | 0.3382 | 0.3004 | 0.3185 | 0.3023 | 0.2834 | 0.3454 |
PSO-DV-Hop | 0.4855 | 0.2979 | 0.2554 | 0.2289 | 0.2004 | 0.2001 | 0.1931 | 0.188 | 0.256163 |
DE-DV-Hop | 0.4423 | 0.2634 | 0.2525 | 0.2207 | 0.1995 | 0.1997 | 0.1937 | 0.1849 | 0.244588 |
AMG-QUATRE-DV-Hop | 0.4255 | 0.2605 | 0.2525 | 0.2209 | 0.1993 | 0.1995 | 0.1934 | 0.1855 | 0.242138 |
Communication Range | 15 | 20 | 25 | 30 | 35 | 40 | Avg. |
---|---|---|---|---|---|---|---|
DV-Hop | 0.5286 | 0.349 | 0.3219 | 0.2968 | 0.3149 | 0.3002 | 0.3519 |
Hyperbolic-DV-Hop | 0.5603 | 0.3382 | 0.3 | 0.2546 | 0.2931 | 0.2634 | 0.334933 |
PSO-DV-Hop | 0.2919 | 0.2286 | 0.2081 | 0.203 | 0.2053 | 0.1945 | 0.2219 |
DE-DV-Hop | 0.281 | 0.2204 | 0.2042 | 0.1909 | 0.2038 | 0.194 | 0.215717 |
AMG-QUATRE-DV-Hop | 0.2806 | 0.2209 | 0.205 | 0.1911 | 0.2037 | 0.1939 | 0.215867 |
Sensor Nodes | 100 | 150 | 200 | 250 | 300 | 350 | 400 | Avg. |
---|---|---|---|---|---|---|---|---|
DV-Hop | 0.4645 | 0.3711 | 0.349 | 0.3771 | 0.3513 | 0.3022 | 0.2887 | 0.3577 |
Hyperbolic-DV-Hop | 0.3745 | 0.3368 | 0.3382 | 0.3067 | 0.3166 | 0.2998 | 0.2818 | 0.322057 |
PSO-DV-Hop | 0.3106 | 0.3178 | 0.2342 | 0.2303 | 0.1887 | 0.1784 | 0.1741 | 0.233443 |
DE-DV-Hop | 0.2967 | 0.2777 | 0.2205 | 0.2234 | 0.1828 | 0.1769 | 0.1741 | 0.221729 |
AMG-QUATRE-DV-Hop | 0.2979 | 0.284 | 0.2209 | 0.2225 | 0.1816 | 0.1773 | 0.1742 | 0.222629 |
© 2019 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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Liu, N.; Pan, J.-S.; Wang, J.; Nguyen, T.-T. An Adaptation Multi-Group Quasi-Affine Transformation Evolutionary Algorithm for Global Optimization and Its Application in Node Localization in Wireless Sensor Networks. Sensors 2019, 19, 4112. https://doi.org/10.3390/s19194112
Liu N, Pan J-S, Wang J, Nguyen T-T. An Adaptation Multi-Group Quasi-Affine Transformation Evolutionary Algorithm for Global Optimization and Its Application in Node Localization in Wireless Sensor Networks. Sensors. 2019; 19(19):4112. https://doi.org/10.3390/s19194112
Chicago/Turabian StyleLiu, Nengxian, Jeng-Shyang Pan, Jin Wang, and Trong-The Nguyen. 2019. "An Adaptation Multi-Group Quasi-Affine Transformation Evolutionary Algorithm for Global Optimization and Its Application in Node Localization in Wireless Sensor Networks" Sensors 19, no. 19: 4112. https://doi.org/10.3390/s19194112