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Table 1.

Unimodal Benchmark Functions.

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Table 1 Expand

Table 2.

Multimodal Benchmark Functions.

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Table 2 Expand

Table 3.

Algorithm-dependent parameters of the comparison algorithms.

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Table 3 Expand

Table 4.

Results of unimodal benchmark functions.

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Table 4 Expand

Table 5.

The mean value of unimodal benchmark functions for HFA, FA, DE and PSO over 30 runs.

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Table 5 Expand

Table 6.

P-values at α = 0.05 by Friedman test.

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Table 6 Expand

Fig 1.

Comparison between PSO, DE, FA and HFA for the Sphere function.

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Fig 1 Expand

Fig 2.

Comparison between PSO, DE, FA and HFA for Schwefel’s 1.20 function.

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Fig 2 Expand

Fig 3.

Comparison between PSO, DE, FA and HFA for Rosenbrock’s function.

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Fig 3 Expand

Table 7.

Results of multimodal benchmark functions.

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Table 7 Expand

Table 8.

The mean value of multimodal benchmark functions for HFA, FA, DE and PSO over 30 runs.

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Table 8 Expand

Table 9.

P-values at α = 0.05 by Friedman test.

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Table 9 Expand

Fig 4.

Comparison between PSO, DE, FA and HFA for Rastrigin’s function.

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Fig 4 Expand

Fig 5.

Comparison between PSO, DE, FA and HFA for Ackley’s function.

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Fig 5 Expand