Results given in Ref. [23]

Results given by hybrid genetic algorithm

Objective

Stage

Reliability

Component

Simulation result

Reliability

Component

Simulation result

Maximize

System

Reliability

1

2

3

4

0.866288

0.850029

0.918417

0.913049

6.0

6.0

4.0

4.0

Rs = 0.999881

Cs = 381.12183

Ws = 485.77850

Vs = 188.0

0.8971

0.8659

0.9358

0.8769

5

6

4

5

Rs = 0.9999

Cs = 381.5582

Ws = 475.1981

Vs = 195

Minimize

System

Cost

1

2

3

4

0.559777

0.599392

0.685273

0.703375

6.0

6.0

4.0

4.0

Rs = 0.971340

Cs = 54.472889

Ws = 485.778504

Vs = 188.0

0.7997

0.7896

0.7154

0.8393

4

4

5

4

Rs = 0.9939

Cs = 133.4582

Ws = 346.2031

Vs = 155

Minimize

System Weight

1

2

3

4

0.864883

0.944821

0.905934

0.880399

3.0

2.0

2.0

2.0

Rs = 0.971597

Cs = 295.029388

Ws = 107.352295

Vs = 370

0.9668

0.8715

0.9572

0.9382

2

2

2

2

Rs = 0.9769

Cs = 440.5520

Ws = 89.0309

Vs = 32

Multi-

Objective

Optimization

1

2

3

4

0.820009

0.806433

0.869349

0.865680

4.0

3.0

3.0

2.0

Rs = 0.971641

Cs = 119.04067

Ws = 177.234863

Vs = 69.0

0.8536

0.7977

0.9189

0.8133

3

3

2

3

Rs = 0.9757

Cs = 114.0175

Ws = 147.0485

Vs = 57