Table 9 Results for solving small size issues.

From: Optimization of an appointment scheduling problem for healthcare systems based on the quality of fairness service using whale optimization algorithm and NSGA-II

Prob.

WOA (whale’s optimization algorithm)

NSGA-II

ε-constraint method

Quality

Spacing

Diversity

CPU time

Pareto Ans

Quality

Spacing

Diversity

CPU time

Pareto Ans

Quality

Spacing

Diversity

CPU time

Pareto Ans

3/4

85.2

0.92

985.2

155.2

380

14.8

0.78

740.7

73.4

301

27.2

0.88

832.4

81.2

301

5/4

83.5

0.51

1365.9

159.2

299

16.5

0.47

840.9

73.6

79

22.5

0.67

847.1

86.6

87

7/4

88.1

0.64

1439.9

160.1

534

11.9

0.56

850.2

80.1

47

16.2

0.60

870.2

90.1

64

10/4

100

1.06

1468.3

162.5

200

0

0.71

1130.6

89.2

301

0

0.91

1234.1

95.5

280

12/4

87.7

0.68

1582.2

163.1

198

12.3

0.44

1220.4

85.2

217

9.3

0.54

1256.2

97.8

225

16/4

87.6

0.91

1702.3

171.8

231

12.4

0.78

1261.3

105.7

211

6.3

0.88

1265.8

103.7

321

18/4

83.4

0.71

1708.9

181.8

187

16.6

0.47

1349.1

112.6

149

4.8

0.54

1367.7

109.4

102

18/5

85.8

0.73

1763.2

182.4

345

14.2

0.62

1360.6

124.5

348

12.1

0.65

1370.3

114.9

349

18/7

88.1

1.01

1930.2

184.7

488

11.9

0.49

1281.4

124.9

351

10.5

0.89

1381.6

123.6

380

20/7

88.7

1.32

2012.9

199.4

529

11.3

0.70

1495.4

136.7

400

7.2

0.98

1470.4

130.1

413

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