Improved Quantum-Inspired Evolutionary Algorithm for Engineering Design Optimization

Table 1

Test functions.

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𝑓₁(𝑋)=5𝑥₁+5𝑥₂+5𝑥₃+5𝑥₄−5∑⁴_𝑖=1𝑥²_𝑖−∑¹³_𝑖=5𝑥_𝑖,

subject to

 2𝑥₁+2𝑥₂+𝑥₁₀+𝑥₁₁≤10,  2𝑥₁+2𝑥₃+𝑥₁₀+𝑥₁₂≤10,  −8𝑥₁+𝑥₁₀≤0,

2𝑥₂+2𝑥₃+𝑥₁₁+𝑥₁₂≤10,−8𝑥₂+𝑥₁₁≤0,−8𝑥₃+𝑥₁₂≤0,

−2𝑥₄−𝑥₅+𝑥₁₀≤0,−2𝑥₆−𝑥₇+𝑥₁₁≤0,  −2𝑥₈−𝑥₉+𝑥₁₂≤0,

0≤𝑥_𝑖≤1,𝑖=1,…,9,0≤𝑥_𝑖≤100,𝑖=10,11,12,  0≤𝑥₁₃≤1.

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𝑓₂(𝑋)=𝑥₁+𝑥₂+𝑥₃,

subject to

1−0.0025(𝑥₄+𝑥₆)≥0,1−0.0025(𝑥₅+𝑥₇−𝑥₄)≥0,

 1−0.01(𝑥₈−𝑥₅)≥0,𝑥₁𝑥₆−833.33252𝑥₄−100𝑥₁+83333.333≥0,

 𝑥₂𝑥₇−1250𝑥₅−𝑥₂𝑥₄+1250𝑥₄≥0,𝑥₃𝑥₈−1250000−𝑥₃𝑥₅+2500𝑥₅≥0,

100≤𝑥₁≤10000,1000≤𝑥_𝑖≤10000,𝑖=2,3,10≤𝑥_𝑖≤1000,𝑖=4,…,8.

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𝑓₃(𝑋)=(𝑥₁−10)²+5(𝑥₂−12)²+𝑥⁴₃+3(𝑥₄−11)²+10𝑥⁶₅+7𝑥²₆+𝑥⁴₇−4𝑥₆𝑥₇−10𝑥₆−8𝑥₇,

subject to

127−2𝑥²₁−3𝑥⁴₂−𝑥₃−4𝑥²₄−5𝑥₅≥0,  282−7𝑥₁−3𝑥₂−10𝑥²₃−𝑥₄+𝑥₅≥0,

196−23𝑥₁−𝑥²₂−6𝑥²₆+8𝑥₇≥0,−4𝑥²₁−𝑥²₂+3𝑥₁𝑥₂−2𝑥²₃−5𝑥₆+11𝑥₇≥0,

 −10≤𝑥_𝑖≤10,𝑖=1,…,7.

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𝑓₄(𝑋)=𝑥²₁+𝑥²₂+𝑥₁𝑥₂−14𝑥₁−16𝑥₂+(𝑥₃−10)²+4(𝑥₄−5)²+(𝑥₅−3)²+2(𝑥₆−1)²+5𝑥²₇

+7(𝑥₈−11)²+2(𝑥₉−10)²+(𝑥₁₀−7)²+45,

subject to

105−4𝑥₁−5𝑥₂+3𝑥₇−9𝑥₈≥0,−10𝑥₁+8𝑥₂+17𝑥₇−2𝑥₈≥0,

8𝑥₁−2𝑥₂−5𝑥₉+2𝑥₁₀+12≥0,−5𝑥²₁−8𝑥₂−(𝑥₃−6)²+2𝑥₄+40≥0,

−3(𝑥₁−2)²−4(𝑥₂−3)²−2𝑥²₃+7𝑥₄+120≥0,

−𝑥²₁−2(𝑥₂−2)²+2𝑥₁𝑥₂−14𝑥₅+6𝑥₆≥0,

−0.5(𝑥₁−8)²−2(𝑥₂−4)²−3𝑥²₅+𝑥₆+30≥0,

3𝑥₁−6𝑥₂−12(𝑥₉−8)²+7𝑥₁₀≥0,−10≤𝑥_𝑖≤10,𝑖=1,…,10.

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