Table 2 Friedman test average rankings (α = 0.05).

From: Green supply chain management and coordinated optimization by an improved sparrow search algorithm

Algorithm

Total cost (↓)

Total carbon emissions (↓)

Resource utilization (↑)

Spacing metric (↓)

HV (↑)

Overall average rank

ISSA-NSGA-III

1.15

1.1

1.08

1.2

1.12

1.13

TS-SSA

2.6

2.25

2.25

2.2

2.2

2.3

NSGA-III

3.2

3.5

3.1

3.9

4.2

3.58

NSGA-II

3.85

4.1

4.95

3.15

5.05

4.22

MOPSO

4.9

4.8

5.12

4.85

4.55

4.84

SSA

5.3

5.25

4.5

5.7

3.88

4.93

Friedman χ²

135.8

141.2

143.5

129.4

139.1

-

p-value

< 0.001

< 0.001

< 0.001

< 0.001

< 0.001

-

  1. Values represent average rankings from 30 independent runs (1 = best). Arrows indicate the optimization direction (↓ = lower is better, ↑ = higher is better). “Overall average rank” is the arithmetic mean across all five metrics.
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