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Table 4 Comparison of IWOA-ROMs with some familiar ROMs

From: An improved whale optimization algorithm for the model order reduction of large-scale systems

#Method#

Reduced second-order system

ISE

IWOA

\(R_{2} (s) = \frac{0.6318s + 7.112}{{0.6419s^{2} + 16.58s + 45.35}}\)

2.7330e−10

WOA

\(R_{2} (s) = \frac{1.972s + 28.25}{{0.3372s^{2} + 60s + 180}}\)

3.1355e−9

DE[29]

\(R_{2} (s) = \frac{1.977s + 31.02}{{0.291s^{2} + 65s + 197.7}}\)

5.7048e−09

PSO [28]

\(R_{2} (s) = \frac{1.506s + 31.39}{{0.477s^{2} + 65.24s + 200}}\)

6.2590e−09

EDE [36]

\(R_{2} (s) = \frac{0s + 1568.5185}{{s^{2} + 6090.422363s + 200}}\)

3.92e−04

EDE & Improved MMPA method [37]

\(R_{2} (s) = \frac{0.400757s + 200.396591}{{s^{2} + 780.5269s + 1276.7544}}\)

4.016e−04

PSO-DV[38]

\(R_{2} (s) = \frac{5.00995s + 129.01962}{{s^{2} + 523.004761s + 822.001831}}\)

4.1e−04

Sambapriya et.al [40]

\(R_{2} (s) = \frac{0.8664s + 7.328}{{s^{2} + 18.32s + 46.83}}\)

3.32e−04

Pole cluster & Pade Approximation[ 22]

\(R_{2} (s) = \frac{ - 18.77s + 119.7}{{s^{2} + 90s + 762.6}}\)

5.7586e−7

Srinivasan & Krishnan [42]

\(R_{2} (s) = \frac{1.603s + 27.57}{{s^{2} + 58.412s + 175.96}}\)

3.7411e−6

C.B. Vishwakarma [41]

\(R_{2} (s) = \frac{1.648s + 29.92}{{s^{2} + 62.59s + 190.64}}\)

9.7279e−9

Girish Parmar [43]

\(R_{2} (s) = \frac{3.326s + 48.3}{{s^{2} + 105.95s + 308.159}}\)

2.4507e−6

Y Shamash [44]

\(R_{2} (s) = \frac{0.5178s + 1.633}{{s^{2} + 6.159s + 10.41}}\)

2.2015e−07

Jayantha pal [6]

\(R_{2} (s) = \frac{9.751e13s + 5.211e14}{{2.28e14s^{2} + 1.53e15s + 3.32e15}}\)

2.3303e−07

VV Seshadri [4]

\(R_{2} (s) = \frac{0.5178s + 1.633}{{s^{2} + 6.159s + 10.41}}\)

2.2015e−07