A Multimodal Smart Quantum Particle Swarm Optimization for Electromagnetic Design Optimization Problems
Abstract
:1. Introduction
2. The Proposed Work
2.1. Process Analysis of Smart Particle of the Swarm
Pseudocode of updating rule ofin the archive |
If do |
Clear the previous of |
Store the new as in the archive |
elseif |
Ignore the new and upheld the previous one |
end if |
declare the global best from the updated archive. |
2.2. Optimal Strategy for Parameter Setting
3. Numerical Result Analysis
4. Result and Discussion
5. Numerical Validation for Engineering Problems
Objective Function of the TEAM Problem 22
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
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Modal | Name | Benchmark Functions | Search Space | |
---|---|---|---|---|
Unimodal | Sphere | 0 | ||
Schwefel’s 2.22 | 0 | |||
Multimodal | Rosenbrock | 0 | ||
Griewank | 0 | |||
Complex | Schwefel’s Problem 1.2 | and = −450 | 0 | |
Griewank | and = −180 | 0 |
Sphere f1 | |||||
QPSO | GQPSO | LIQPSO | MQPSO | SQPSO | |
Max | 3.00 | 2.00 | 0.00 | −4.00 | −26.66 |
Min | −32.60 | −14.40 | −41.50 | −160.00 | −282.40 |
Std | 13.95 | 4.43 | 12.69 | 60.38 | 72.92 |
Mn | −13.43 | −2.88 | −27.17 | −78.82 | −230.27 |
Schwefel’s 2.22 f2 | |||||
QPSO | GQPSO | LIQPSO | MQPSO | SQPSO | |
Max | 1.00 | 0.00 | 5.00 | −39.80 | −8.58 |
Min | 1.00 | −96.30 | −111.67 | −138.01 | −352.19 |
Std | 0.00 | 29.18 | 34.63 | 25.14 | 99.77 |
Mn | 1.00 | −43.47 | −75.96 | −125.62 | −175.87 |
Rosenbrock f3 | |||||
QPSO | GQPSO | LIQPSO | MQPSO | SQPSO | |
Max | 0.75 | 0.40 | 1.40 | −0.60 | 1.59 |
Min | 0.75 | −2.42 | −2.60 | −3.70 | −10.33 |
Std | 0.00 | 0.36 | 0.48 | 0.78 | 2.92 |
Mn | 0.75 | −0.19 | −1.06 | −3.46 | −7.30 |
Griewank f4 | |||||
QPSO | GQPSO | LIQPSO | MQPSO | SQPSO | |
Max | 1.20 | 1.60 | 1.80 | 1.20 | −7.83 |
Min | −4.20 | −7.20 | −5.30 | −12.01 | −36.04 |
Std | 2.17 | 1.74 | 1.19 | 2.79 | 6.47 |
Mn | −1.91 | −6.71 | −4.21 | −11.22 | −33.61 |
Schwefel’s Problem 1.2 f5 | |||||
QPSO | GQPSO | LIQPSO | MQPSO | SQPSO | |
Max | 0.10 | 0.05 | 0.12 | −1.70 | 6.04 |
Min | −7.48 | −3.20 | −5.90 | −7.10 | −8.38 |
Std | 2.89 | 0.95 | 1.80 | 1.32 | 4.31 |
Mn | −3.09 | −0.89 | −1.48 | −6.59 | −5.14 |
Complex Griewank f6 | |||||
QPSO | GQPSO | LIQPSO | MQPSO | SQPSO | |
Max | 0.25 | 0.15 | 0.25 | −4.80 | 1.38 |
Min | −6.30 | −1.50 | −3.10 | −6.20 | −6.31 |
Std | 2.61 | 0.58 | 1.30 | 0.21 | 1.68 |
Mn | −2.84 | −0.41 | −1.35 | −6.17 | −3.42 |
Algorithm | R2 | h2/2 | d2 | OF |
---|---|---|---|---|
QPSO | 3.0786 | 0.2414 | 0.3795 | 0.1077 |
GQPSO | 3.1723 | 0.2319 | 0.3892 | 0.1222 |
LI-QPSO | 3.0214 | 0.2732 | 0.3419 | 0.0959 |
MQPSO | 3.1396 | 0.3160 | 0.2871 | 0.0716 |
SQPSO | 3.0245 | 0.2561 | 0.2871 | 0.0278 |
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Fahad, S.; Yang, S.; Khan, R.A.; Khan, S.; Khan, S.A. A Multimodal Smart Quantum Particle Swarm Optimization for Electromagnetic Design Optimization Problems. Energies 2021, 14, 4613. https://doi.org/10.3390/en14154613
Fahad S, Yang S, Khan RA, Khan S, Khan SA. A Multimodal Smart Quantum Particle Swarm Optimization for Electromagnetic Design Optimization Problems. Energies. 2021; 14(15):4613. https://doi.org/10.3390/en14154613
Chicago/Turabian StyleFahad, Shah, Shiyou Yang, Rehan Ali Khan, Shafiullah Khan, and Shoaib Ahmed Khan. 2021. "A Multimodal Smart Quantum Particle Swarm Optimization for Electromagnetic Design Optimization Problems" Energies 14, no. 15: 4613. https://doi.org/10.3390/en14154613