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Fig 1.

Populations generated by the initialization of the good nodes set.

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Fig 2.

Comparison of Common and the Proposed .

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Table 1.

Standard benchmark functions.

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Table 2.

Running environment.

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Table 3.

Parameter settings for metaheuristic algorithm.

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Fig 3.

Iteration curves in ablation study.

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Fig 4.

GWOA vs WOA flowchart.

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Fig 5.

Results of the GWOA qualitative analysis (F1-F8).

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Fig 6.

Results of the GWOA qualitative analysis (F9-F18).

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Fig 7.

Results of the GWOA qualitative analysis (F17-f23).

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Fig 8.

Iteration curves for comparison of different algorithms.

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Table 4.

Ave and Std of different algorithms.

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Table 5.

Results of Wilcoxon rank-sum test and Friedman test for different algorithms.

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Table 6.

Wilcoxon Rank-sum Test and Friedman Test Results for Different Algorithms in 50 and 100 Dimensions.

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Table 7.

Overall effectiveness of GWOA and other algorithms.

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Fig 9.

The structure of a pressure vessel.

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Fig 10.

Iteration curves in pressure vessel design.

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Fig 11.

The structure of a tension/compression spring.

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Fig 12.

Iteration curves in tension/compression spring design.

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Fig 13.

The structure of a piston lever.

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Fig 14.

Iteration curves in piston lever design.

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Fig 15.

The structure of a speed reducer.

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Fig 16.

Iteration curves in speed reducer design.

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Table 8.

Results of the algorithms in solving engineering design optimization problems.

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Table A1.

Details of the metaheuristic algorithms.

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Table A2.

Details of parameter settings.

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