Table 9 Pareto front solutions for case study problem-2.

1.

5

344

8,371,562

[r₂, r₂, r₄, r₁, r₂]

[1,5,6,10,7,14] [2,17,3,12,18,4,19] [20,15,8,16,11,21,25] [22,9,23,26,30,31,24,27] [13,32,33,28,34,35,29]

2.

5

355

7,328,207

[r₄, r₃, r₁, r₄, r₂]

[1,5,6,8,7,2] [12,3,18,4,10,17,19] [20,14,15,16,21,22,30,31] [9,32,11,23,25,26,24] [13,27,28,34,33,29,35]

3.

5

362

7,313,967

[r₄, r₃, r₁, r₄, r₂]

[1,5,6,8,2,7] [10,12,9,18,19,3,17,20] [14,15,16,21,30,22,23] [31,25,26,24,27,4] [34,32,13,11,28,33,35,29]

4.

5

366

6,505,320

[r₄, r₃, r₁, r₄, r₅]

[1,5,6,8,7,2] [12,18,19,3,10,17,9,20] [14,15,16,21,22,30,31,32] [25,23,26,24,27,4,34] [13,11,33,28,29,35]

5.

5

380

6,493,542

[r₄, r₃, r₁, r₄, r₅]

[1,5,6,8,7,2] [12,18,19,3,10,17,4,20] [14,15,16,21,22,30,31,32] [25,26,23,24,27,11,34] [9,13,33,28,29,35]

6.

5

383

6,216,641

[r₄, r₃, r₁, r₄, r₃]

[1,5,2,6,3,4,7] [10,12,18,17,19,20,14] [15,16,8,9,13,21,30,31,32] [22,25,26,23,24,27,11] [34,33,28,35,29]

7.

5

392

6,193,656

[r₄, r₃, r₁, r₄, r₃]

[1,5,2,6,7,17,3] [12,4,18,10,19,20,8] [14,15,16,9,21,13,30,31,32] [22,25,11,23,24,26,27] [34,28,29,33,35]

8.

5

448

5,911,957

[r₄, r₃, r₁, r₃, r₃]

[1,5,2,6,7,8,3,17] [10,12,18,4,19] [14,15,20,16,21,22,30,9,13,31] [23,25,24,26,27,11] [32,34,33,28,35,29]

9.

5

456

5,870,152

[r₄, r₃, r₁, r₃, r₃]

[1,17,10,5,2,6,3,7] [12,18,19,20,8,4] [14,15,9,16,21,30,31,32,22,13] [11,23,24,25,26,27] [28,29,34,33,35]

10.

5

477

5,843,853

[r₄, r₃, r₁, r₃, r₃]

[17,1,2,5,3,6,4,7] [12,18,19,10,11,20] [14,8,15,16,21,22,9,13,30,31] [23,32,25,24,26,27] [34,33,35,28,29]

11.

5

485

5,787,026

[r₄, r₃, r₃, r₃, r₃]

[17,1,5,2,6,7,3,8,10] [4,11,14,15,16,12] [18,19,20,21,25,22,23] [26,30,9,24,31,13,27] [34,28,32,33,29,35]

12.

4

457

6,165,234

[r₂, r₁, r₄, r₁]

[1,5,12,6,7,18,19,17] [10,14,15,16,20,8,9,21,30,31] [2,22,23,3,25,4,26,24,11] [32,27,13,34,33,35,28,29]

13.

4

465

6,094,538

[r₂, r₁, r₄, r₁]

[1,5,12,6,7,18,19,10] [17,8,14,20,15,16,9,21,30,22] [2,25,23,3,26,4,24,11,27] [13,34,31,32,33,35,28,29]

14.

4

469

6,002,389

[r₂, r₃, r₁, r₁]

[1,5,10,6,7,2,14,15,16] [12,3,18,19,8,17,20,4,9] [21,25,30,31,32,22,23,13,24] [26,11,27,34,33,35,28,29]

15.

4

481

5,972,957

[r₂, r₃, r₁, r₁]

[1,5,2,6,3,7,10,14,15,16] [12,4,18,17,8,19,11,20] [21,22,30,31,23,9,24,25,32] [26,27,34,13,33,28,29,35]

16.

4

489

5,568,147

[r₄, r₃, r₁, r₅]

[1,10,2,5,6,7,14,15,16] [12,3,18,19,8,17,20,4,9] [21,22,25,30,23,31,24,13,32] [26,27,11,33,34,35,28,29]

17.

4

505

5,472,513

[r₄, r₃, r₁, r₃]

[1,5,6,7,8,2,3,10,14] [9,17,12,18,4,19,20,15,16] [21,22,23,30,31,24,13,32,25,26] [27,34,11,28,33,29,35]

18.

4

506

5,463,439

[r₄, r₃, r₁, r₃]

[1,2,10,5,3,6,4,7,14] [15,8,17,12,18,19,9,20,16] [21,30,31,13,22,25,32,23,24,26] [27,11,28,29,34,33,35]

19.

4

522

5,429,154

[r₄, r₃, r₁, r₃]

[1,2,10,5,6,8,17,7,14] [12,18,3,4,19,20,11,15] [16,9,21,13,30,22,25,23,24,31,26] [27,28,32,33,34,29,35]

20.

4

525

5,416,809

[r₄, r₃, r₁, r₃]

[1,5,6,2,3,8,7,10,17,4] [12,14,18,19,20,11,15] [16,21,25,26,30,9,22,31,23,13,24] [27,28,34,32,29,33,35]

21.

4

529

5,288,292

[r₄, r₃, r₁, r₃]

[1,5,2,12,6,3,10,4,7] [17,18,11,19,20,8,9] [14,13,15,16,21,30,31,22,23,24,32] [25,26,27,33,28,29,34,35]

22.

4

543

5,275,865

[r₄, r₃, r₁, r₃]

[1,2,10,17,5,3,6,4,7] [12,18,19,20,11,8,9] [14,15,16,21,22,23,30,24,31,32,13] [25,26,27,34,33,35,28,29]

23.

4

546

5,208,442

[r₄, r₃, r₅, r₃]

[1,5,6,10,7,8,14,15,16] [12,18,19,17,9,20,21,22,23] [2,3,4,25,26,30,24,27,13,11] [31,32,28,33,34,35,29]

24.

4

680

4,642,021

[r₃, r₃, r₃, r₃]

[1,5,10,17,6,7,14] [12,2,15,3,18,19,20,16,21] [22,4,25,23,8,26,24,11,30] [31,9,13,32,27,28,33,35,34,29]

25.

4

686

4,638,791

[r₅, r₃, r₃, r₃]

[1,5,2,6,8,17] [7,10,14,3,4,15,9,12,18,13] [19,16,20,21,25,22,23,24,26] [27,11,30,28,31,32,29,34,33,35]

26.

4

697

4,611,598

[r₅, r₃, r₃, r₃]

[1,2,17,5,6,8,9] [7,10,12,13,14,18,19,20,15] [16,21,3,22,30,25,26,23,24] [27,34,4,11,31,32,28,29,33,35]

27.

3

591

5,422,283

[r₂, r₁, r₂]

[1,5,6,17,7,2,10,12,18,14,19] [20,15,16,8,21,30,9,3,31,22,23,32,13] [24,25,4,26,27,11,33,35,28,29,34]

28.

3

613

5,102,616

[r₂, r₁, r₄]

[1,5,10,6,2,7,17,12,18,19,14] [15,16,8,20,9,21,30,22,23,24,13,3,31,32] [4,25,11,26,27,28,29,33,35,34]

29.

3

619

4,831,000

[r₂, r₁, r₅]

[1,5,6,17,7,2,10,12,18,14,19] [20,15,16,8,21,30,9,3,31,22,23,32,13,24] [25,4,26,27,11,33,35,28,29,34]

30.

3

635

4,782,549

[r₂, r₁, r₅]

[1,10,12,5,2,6,7,17,18,14,19] [20,15,3,16,8,9,13,21,22,30,31,32,23,4] [25,24,11,26,27,34,28,33,29,35]

31.

3

646

4,749,816

[r₂, r₁, r₃]

[1,17,12,5,6,7,10,18,19,2,14,20] [15,16,3,4,21,22,23,8,30,31,32,24,9,13] [25,26,27,11,33,35,34,28,29]

32.

3

729

4,528,671

[r₂, r₃, r₃]

[1,10,5,2,12,6,7,8,9,17,13,14,18,3] [4,19,15,20,16,21,25,11,22,26,30] [23,31,24,27,32,34,33,28,35,29]

33.

3

802

4,155,741

[r₃, r₁, r₃]

[1,17,12,5,6,7,18,10] [19,20,14,15,8,9,16,21,30,13,22,2,31,23,24] [32,25,3,26,4,27,11,28,33,29,35,34]

34.

3

837

4,079,992

[r₃, r₁, r₃]

[1,10,5,6,7,12,18,19] [17,14,8,15,20,9,2,16,21,22,23,30,31,24,13,3] [4,11,25,26,32,27,28,34,29,33,35]

35.

3

849

4,043,959

[r₃, r₁, r₃]

[1,10,5,6,7,12,18,19] [14,15,17,2,16,20,3,8,21,25,30,26,31,9,13,22] [23,4,24,11,32,27,33,28,35,29,34]

36.

3

885

3,903,632

[r₅, r₃, r₃]

[1,17,5,10,6,8,2,3,7,9] [14,12,18,15,19,16,20,21,25,4,22,11,26] [13,30,31,23,32,24,27,33,28,34,35,29]

37.

3

894

3,875,585

[r₅, r₃, r₃]

[17,1,5,6,8,7,9,2,13] [12,10,18,14,19,3,15,4,20,16,21,22,25,26] [30,31,23,24,11,27,28,34,29,32,33,35]

38.

3

931

3,853,004

[r₃, r₅, r₃]

[1,10,5,6,7,14,12,18,17,15] [8,9,2,19,16,3,20,13,21,22,25,26] [30,23,4,31,24,27,11,28,32,33,35,34,29]

39.

3

952

3,838,295

[r₃, r₅, r₃]

[1,5,6,12,7,10,18,14,15] [8,17,16,9,2,19,3,20,21,22,25,30,26] [13,23,24,31,4,11,32,27,33,35,34,28,29]

40.

3

967

3,822,559

[r₃, r₅, r₃]

[1,5,12,10,6,7,18,14,15] [8,2,3,19,9,13,17,16,20,21,25,22,26] [23,4,30,24,11,31,27,32,34,28,33,29,35]

41.

2

912

4,325,017

[r₂, r₁]

[1,12,5,10,6,8,2,7,18,3,9,19,14,15,4,11,17,16] [20,21,22,25,23,30,13,24,26,27,34,31,32,33,28,35,29]

42.

2

917

4,272,918

[r₂, r₁]

[1,12,10,17,5,6,8,7,18,14,2,19,3,9,4,13,11,20] [15,16,21,22,23,25,24,26,30,27,31,28,34,32,33,29,35]

43.

2

926

4,240,050

[r₂, r₁]

[1,5,6,10,17,7,12,14,18,19,15,20,16,21,30,31,25,2] [26,8,22,9,3,4,32,23,24,27,11,34,13,28,33,35,29]

44.

2

932

4,229,309

[r₂, r₁]

[1,5,6,2,7,12,10,14,17,18,19,15,8,20,16,21,25] [22,30,9,23,3,24,4,31,11,26,13,27,32,34,33,28,29,35]

45.

2

1060

3,776,281

[r₂, r₃]

[1,10,5,2,12,6,7,17,8,18,19,14,9,15,20,16,13,21,25,30] [3,31,22,23,24,4,26,27,32,11,28,33,34,29,35]

46.

2

1109

3,556,525

[r₃, r₁]

[1,5,12,6,7,18,17,19,2,3,4,20,11,10] [14,15,16,21,22,25,30,23,31,8,32,9,24,13,26,27,28,34,29,33,35]

47.

2

1325

3,191,937

[r₃, r₃]

[1,10,5,6,17,7,12,18,19,20,14,15,16,2,21,3] [8,9,4,22,23,25,30,13,24,26,31,27,32,34,11,28,33,35,29]

48.

1

1794

3,424,773

[r₂]

[1,5,6,10,12,2,7,14,15,16,18,17,8,19,20,9,21,3,22,4,30,23,31,25,24,11,26,13,32,27,33,34,35,28,29]

49.

1

2104

3,094,672

[r₄]

[1,12,5,2,6,3,7,10,4,14,17,18,19,15,8,20,16,21,11,9,30,22,25,23,26,31,24,32,27,13,28,33,34,29,35]

50.

1

2318

2,942,056

[r₁]

[1,5,6,17,8,7,10,12,9,2,14,15,16,18,19,20,21,30,22,3,23,13,24,25,31,26,4,27,32,11,33,28,35,34,29]

51.

1

2617

2,466,898

[r₃]

[1,17,2,12,3,10,5,6,7,14,15,18,8,9,19,13,4,20,16,21,25,30,22,23,31,26,24,32,27,34,11,33,28,35,29]