Table 11 Statistical results of different methods on speed reducer problem.

From: Efficient implicit constraint handling approaches for constrained optimization problems

Algorithm

BU step

Best

Mean

Median

Worst

St. Dev

GA

Nonea

2997.353

2998.827

2998.933

2999.647

0.645

BU

3119.764

3126.639

3127.78

3129.697

2.792

Hybrid-cvtol

2997.002

2997.964

2998.023

2998.779

0.539

Hybrid-ftol

2996.371

2996.422

2996.404

2996.542

0.055

DE

None

2847.208

2982.631

2996.641

2997.054

42.848

BU

2706.172

2900.272

2881.668

3131.199

157.048

Hybrid-cvtol

2706.141

2838.565

2828.955

2996.729

108.803

Hybrid-ftol

2718.692

2996.422

2996.404

2742.44

0.055

ES

None

3001.0

3023.363

3025.0

3039.00

12.694

BU

3120.0

3123.727

3123.0

3129.00

2.561

Hybrid-cvtol

3007.0

3018.000

3018.0

3030.00

6.281

Hybrid-ftol

3005

3015.428

3015

3028.00

6.694

SRES

None

3012.0

3031.272

3025.0

3063.00

17.669

BU

3108.0

3123.181

3125.0

3128.00

5.236

Hybrid-cvtol

3015.0

3039.000

3038.0

3076.00

17.832

Hybrid-ftol

3108

3122.57

3125

3128

6.298

BRKGA

None

2997.996

3001.692

3001.084

3006.936

2.761

BU

3117.466

3123.452

3123.855

3127.798

3.386

Hybrid-cvtol

2997.312

3000.977

3000.109

3006.877

3.254

Hybrid-ftol

2875.699

2946.35

2951.593

3036.718

56.361

  1. a“None” means no BU method or hybrid is used and only feasibility rules as an explicit constraint handling method is worked alone.
  2. Significant values are in bold.