Bi-objective corridor allocation problem using a permutation-based genetic algorithm hybridized with a local search technique

Zahnupriya Kalita; Dilip Datta; Gintaras Palubeckis

doi:10.1007/s00500-017-2807-0

Soft Computing

February 2019, Volume 23, Issue 3, pp 961–986 | Cite as

Bi-objective corridor allocation problem using a permutation-based genetic algorithm hybridized with a local search technique

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Zahnupriya Kalita
Dilip Datta
Gintaras Palubeckis

Methodologies and Application

First Online: 04 September 2017

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Abstract

As a more practical form of the double-row layout problem, the bi-objective corridor allocation problem (bCAP) was introduced, in which a given number of facilities are to be placed on opposite sides of a central corridor so as to minimize both the overall flow cost among the facilities and the length of the corridor. Further, the bCAP seeks the placement of the facilities starting from the same level along the corridor without allowing any gap between two facilities of a row. In the initial proposal, the bCAP was solved as an unconstrained optimization problem using a permutation-based genetic algorithm (pGA). It is observed that the pGA alone is not sufficient to reach to the potential solutions of the complicated bCAP. In this work, incorporating a promising local search technique in the pGA, the hybridized pGA is found outperforming the simple pGA as well as a simulated annealing and tabu search-based approach in a number of instances of sizes 60 and above, in terms of both the best objective values and statistical analysis. Moreover, the hybridized pGA could explore multiple optimal solutions for some of such instances.

Keywords

Combinatorial optimization Corridor allocation Multi-objective optimization Genetic algorithm

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Notes

Compliance with ethical standards

Conflict of interest

All authors listed have agreed to be named as authors on this manuscript and they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Citation

Included all works (data, text, and theories) of other authors have been cited properly.

Originality

The work is original, and neither it was published previously nor it has been submitted somewhere simultaneously for publication in any form.

A obtained best permutations

A set of 20 instances of sizes in the range of [60, 80] is studied in Sect. 4.1, whose best objective values obtained by applying the proposed hybridized pGA are shown in Table 2. The corresponding orderings of the facilities are shown in Table 7.

Table 7

The best ordering of facilities for the 20 instances of sizes in the range of [60, 80], which are studied in Sect. 4.1 presenting the best objective values in Table 2

Instance	Case	Order of the facilities ([row 1] [row 2])
1. AKV_60-1	(a)	[11 48 28 15 3 40 6 46 57 9 44 16 13 4 26 2 42 14 22 41 29 38 31 53 10 52 19 60 55 39 1] [27 56 24 21 25 51 54 7 12 47 36 35 32 33 8 17 49 5 23 45 43 50 37 59 30 58 20 18 34]
1. AKV_60-1	(b)	[11 56 15 21 25 51 46 12 47 36 35 33 32 17 14 49 5 23 31 37 59 19 30 20 18 34] [27 48 28 24 3 40 6 54 7 57 9 44 13 16 4 8 26 2 42 22 41 38 29 45 43 50 53 10 52 58 60 55 39 1]
2. AKV_60-2	(a)	[20 44 57 19 2 48 12 3 7 38 16 55 43 27 36 45 54 17 24 5 37 28 33 40 34 14 42 9 50 13 53] [11 35 22 4 23 31 49 47 60 58 26 51 59 6 52 18 46 39 1 25 56 21 32 8 15 30 29 41 10]
2. AKV_60-2	(b)	[10 13 29 9 42 31 32 21 28 56 5 36 1 45 39 17 52 58 59 60 38 47 49 48 23 4 57 35 11 ] [ 53 41 50 30 15 14 40 34 33 37 25 24 46 18 54 43 6 51 26 55 16 27 7 3 12 8 2 19 22 44 20]
3. AKV_60-3	(a)	[5 42 16 48 22 13 41 52 7 34 26 9 25 45 50 43 17 8 30 40 35 58 18 55 31 44 21 20 53 59 4 ] [ 19 3 38 29 36 54 14 2 57 51 15 60 46 33 39 56 23 28 10 12 37 32 1 11 47 27 49 24 6]
3. AKV_60-3	(b)	[4 53 36 47 54 1 31 51 7 15 58 60 45 39 43 8 50 33 40 28 12 55 14 41 11 48 38 16 42 3 ] [ 5 6 49 27 22 13 32 34 52 10 23 56 25 30 26 17 46 35 18 9 37 57 2 21 44 20 29 24 59 19]
4. AKV_60-4	(a)	[20 19 10 39 44 36 22 33 21 23 17 46 53 3 14 27 58 18 8 60 42 54 30 52 9 38 1 4 25 ] [ 13 31 57 55 7 24 56 11 6 40 59 5 45 50 35 2 15 16 29 26 37 47 51 32 48 49 28 41 34 43 12]
4. AKV_60-4	(b)	[20 19 10 39 44 36 22 33 21 23 17 46 53 5 14 27 58 18 8 60 42 54 30 48 9 38 1 4 25 ] [ 13 31 57 55 7 24 56 11 6 40 59 3 45 50 35 2 15 16 29 26 37 47 51 32 52 49 28 41 34 43 12]
5. AKV_60-5	(a)	[12 44 34 38 11 1 43 29 23 57 22 51 5 58 31 45 56 27 28 36 30 35 17 2 54 19 59 7 37 ] [ 33 49 52 3 26 32 14 18 15 24 21 42 10 50 6 25 8 48 40 60 20 46 55 13 9 41 4 47 16 53 39]
5. AKV_60-5	(b)	[12 44 34 38 11 1 43 29 23 57 22 51 5 58 31 45 56 27 28 60 30 20 17 2 54 41 59 7 37 ] [ 33 49 52 3 26 32 14 18 15 24 21 42 10 50 6 25 8 48 40 36 35 46 55 13 9 4 19 47 16 53 39]
6. AKV_70-1	(a)	[53 40 22 28 15 8 63 51 68 16 61 41 38 67 44 26 33 49 13 30 23 36 54 11 6 52 66 3 45 25 48 57 35 50 ] [ 47 65 2 62 32 9 69 31 1 4 64 56 70 14 19 10 42 5 55 60 27 18 24 21 12 58 59 7 20 34 46 43 17 29 39 37]
6. AKV_70-1	(b)	[53 65 2 22 8 32 63 69 68 16 61 56 44 10 19 33 42 27 23 55 11 18 24 12 6 59 52 66 34 4 25 48 29 57 50 ] [ 47 40 39 28 62 15 9 31 51 1 64 41 38 67 70 26 14 49 5 36 30 60 21 13 54 58 7 20 3 45 46 43 17 35 37]
7. AKV_70-2	(a)	[56 64 51 48 70 38 17 12 32 34 15 5 54 20 4 40 8 24 44 6 14 63 62 29 45 33 9 69 7 26 21 10 53 39 28 ] [ 25 57 61 59 41 66 60 65 35 55 31 37 27 22 46 2 16 42 43 49 68 11 30 18 23 67 58 13 19 3 1 36 47 52 50]
7. AKV_70-2	(b)	[56 64 57 51 59 41 70 60 65 35 32 31 27 5 54 2 4 40 16 42 43 49 68 11 18 62 45 33 9 58 19 3 1 36 21 52 53 28 ] [ 25 61 48 66 38 17 12 55 34 37 15 22 20 46 8 24 44 6 14 63 30 29 23 67 69 13 7 26 47 10 50 39]
8. AKV_70-3	(a)	[8 63 54 27 29 32 20 41 67 47 26 4 61 70 19 2 37 14 5 25 18 28 66 36 39 60 45 12 59 46 15 69 34 31 57 16 ] [ 30 51 43 21 23 24 1 6 9 11 22 65 7 42 49 10 50 68 56 53 40 3 35 62 55 13 48 58 38 33 64 17 52 44]
8. AKV_70-3	(b)	[16 57 17 34 15 46 59 55 45 62 35 3 5 36 28 49 7 53 50 10 2 42 61 11 26 6 67 1 20 32 21 43 54 63 30 ] [ 44 52 31 69 64 33 38 12 48 13 60 40 39 18 66 56 25 14 68 19 37 70 65 22 4 9 47 41 24 23 58 29 27 51 8]
9. AKV_70-4	(a)	[25 15 30 47 9 64 22 11 42 12 14 58 60 26 24 53 46 2 18 1 37 27 56 69 57 19 21 55 40 48 3 13 32 65 39 4 35 66 ] [ 16 7 51 52 54 63 6 29 61 33 23 68 5 34 36 50 49 44 28 59 70 17 67 62 20 43 10 45 31 38 8 41]
9. AKV_70-4	(b)	[25 15 30 47 9 64 22 11 42 12 14 58 60 26 24 53 46 2 18 1 37 27 56 59 69 70 21 55 40 48 3 13 32 65 39 4 35 66 ] [ 16 7 51 52 54 63 6 29 61 33 23 68 5 34 36 50 49 44 28 19 57 17 67 62 20 43 10 45 31 38 8 41]
10. AKV_70-5	(a)	[19 1 23 31 40 50 10 6 16 65 49 41 43 21 56 24 35 30 12 53 29 60 46 15 42 55 25 57 47 18 33 64 44 28 ] [ 38 32 68 62 51 2 58 37 22 39 54 63 27 8 26 61 14 20 70 5 36 4 11 7 34 3 59 66 45 48 52 13 69 9 17 67]
10. AKV_70-5	(b)	[19 1 23 62 51 40 50 10 6 54 65 49 26 61 21 56 20 35 30 12 53 29 60 46 15 42 55 25 57 47 18 33 64 44 67 ] [ 38 32 68 31 2 58 37 22 39 16 63 27 8 41 43 24 14 70 5 36 4 11 7 34 3 59 66 45 48 52 13 69 9 17 28]
11. AKV_75-1	(a)	[47 46 9 63 54 51 5 21 8 22 11 75 53 70 68 4 1 31 34 12 24 37 40 71 6 7 23 49 15 18 59 27 57 67 69 60 58 ] [ 38 16 29 72 28 13 33 45 17 25 39 62 43 3 66 10 74 19 42 2 20 32 55 41 44 35 65 50 30 61 56 26 52 36 73 48 14 64]
11. AKV_75-1	(b)	[64 60 48 67 73 36 27 18 30 65 15 35 6 44 41 55 24 42 12 34 31 4 68 53 62 11 25 22 8 21 51 28 72 63 46 47 ] [ 58 14 69 57 52 59 26 56 61 49 50 23 7 71 40 37 32 2 20 19 74 10 1 66 70 3 43 75 39 17 45 33 13 5 54 9 29 16 38]
12. AKV_75-2	(a)	[49 64 61 21 2 6 63 60 42 18 1 58 5 4 65 75 20 34 11 22 8 38 68 55 17 74 9 57 41 10 54 35 50 30 70 37 43 25 ] [ 51 32 47 28 44 14 40 7 59 29 73 52 53 71 3 67 23 12 15 27 16 62 13 36 48 46 31 19 69 24 33 45 39 66 72 56 26]
12. AKV_75-2	(b)	[51 64 37 2 70 63 39 45 59 29 24 52 31 48 17 68 38 16 8 23 62 34 71 75 46 58 19 1 33 7 60 42 44 6 72 61 32 49 ] [ 26 43 21 66 30 40 35 69 41 73 53 9 74 55 36 20 27 15 11 3 67 22 12 13 65 5 4 54 10 57 18 50 14 28 47 56 25]
13. AKV_75-3	(a)	[47 50 33 43 51 46 72 39 70 66 48 71 13 16 59 57 32 40 24 21 67 28 12 11 30 61 68 38 60 26 55 41 1 22 ] [ 69 42 14 15 63 53 17 29 8 4 37 56 20 27 6 3 49 73 34 7 75 35 9 36 58 45 5 52 31 44 65 62 2 64 74 18 25 23 19 10 54]
13. AKV_75-3	(b)	[47 50 33 63 51 46 72 39 70 66 48 71 13 3 59 57 40 35 32 21 67 5 12 11 30 61 68 38 60 26 25 41 1 22 ] [ 69 42 14 15 43 53 17 29 8 4 37 56 20 27 6 16 49 73 34 7 75 24 9 36 58 45 28 52 31 44 65 62 2 64 74 18 55 23 19 10 54]
14. AKV_75-4	(a)	[60 14 15 7 42 37 70 30 20 40 33 39 64 3 65 28 52 53 34 45 32 1 2 19 55 66 56 26 23 59 43 31 74 61 6 27 68 69 49 21 ] [ 36 5 50 75 10 62 8 47 22 57 41 29 46 12 35 16 44 73 18 24 13 67 48 63 58 54 71 4 11 51 25 38 72 9 17]
14. AKV_75-4	(b)	[60 14 15 7 42 37 70 30 20 40 33 39 64 3 65 28 53 73 34 45 32 1 2 19 55 66 56 26 23 59 43 31 74 61 6 27 68 69 72 21 ] [ 36 5 50 75 10 62 8 47 22 57 41 29 46 12 35 16 44 52 18 24 13 67 48 63 58 54 71 4 11 51 25 38 49 9 17]
15. AKV_75-5	(a)	[33 9 19 6 62 14 16 18 39 21 56 48 54 57 36 34 45 25 55 12 17 30 3 10 8 49 22 31 66 65 7 32 71 44 1 43 50 51 37 24 ] [ 27 26 63 13 2 64 40 53 41 75 69 61 4 67 15 11 59 46 29 70 5 28 42 38 23 73 74 47 68 58 35 60 52 72 20]
15. AKV_75-5	(b)	[33 9 19 6 62 14 16 18 39 69 56 67 48 57 36 34 45 25 12 17 30 3 10 8 49 22 31 66 65 7 32 44 71 1 43 60 51 72 20 ] [ 27 26 63 13 2 64 40 53 41 61 75 21 4 15 54 11 59 46 29 55 70 5 28 42 38 23 73 74 47 68 58 35 50 52 37 24]
16. AKV_80-1	(a)	[25 57 71 1 28 64 3 59 30 72 5 24 7 13 74 6 23 31 36 42 50 10 41 54 66 34 49 51 47 52 12 61 43 46 29 40 27 80 60 55 ] [ 78 11 79 4 8 77 38 35 73 26 69 37 18 17 33 22 76 9 15 58 32 20 48 56 62 75 45 68 53 39 63 19 14 21 16 65 44 67 2 70]
16. AKV_80-1	(b)	[25 57 71 1 28 64 3 59 30 72 5 24 7 13 74 6 23 31 36 15 42 10 41 54 66 34 49 51 47 52 12 61 43 46 29 40 27 80 60 55 ] [ 78 11 79 4 8 77 38 35 73 26 69 37 18 17 33 22 76 9 58 50 32 20 48 56 62 75 45 68 53 39 63 19 14 21 16 65 44 67 2 70]
17. AKV_80-2	(a)	[11 66 48 43 69 51 64 37 71 52 30 73 76 68 19 42 44 65 8 9 38 39 4 3 21 25 28 27 1 77 29 41 32 56 46 14 5 10 18 57 ] [ 61 45 49 63 80 60 78 31 79 70 7 59 26 13 75 62 50 2 34 40 36 20 53 6 67 35 23 72 16 33 54 12 47 74 15 58 55 17 24 22]
17. AKV_80-2	(b)	[66 45 48 49 69 60 64 37 79 52 7 30 76 75 13 26 42 44 50 8 34 39 38 53 6 21 28 27 1 77 33 29 41 12 47 74 46 14 5 10 24 22 ] [ 11 61 43 63 51 80 78 71 31 70 73 59 68 19 20 62 2 65 9 40 36 4 3 67 35 23 25 72 16 54 32 56 15 58 55 17 18 57]
18. AKV_80-3	(a)	[63 54 53 26 29 32 35 72 25 76 10 50 3 8 78 17 44 11 23 41 19 15 75 71 55 38 6 28 79 4 42 45 46 43 69 34 36 20 58 40 ] [ 57 37 62 61 64 48 30 22 67 77 52 51 39 27 80 21 14 59 7 73 2 18 1 60 66 9 31 12 65 56 24 5 47 13 70 49 68 33 16 74]
18. AKV_80-3	(b)	[63 54 53 62 29 32 35 30 25 67 77 50 51 39 17 44 14 23 7 59 73 75 2 55 9 12 79 56 42 45 24 46 13 70 49 68 33 58 40 ] [ 57 37 61 26 64 48 72 22 76 10 52 8 3 78 27 80 21 11 19 41 15 1 18 71 60 66 38 31 6 28 65 4 5 47 43 69 34 36 20 16 74]
19. AKV_80-4	(a)	[69 64 71 78 30 28 42 80 74 76 14 29 62 6 18 15 7 16 72 79 52 1 37 77 49 51 65 11 59 45 23 73 34 55 36 58 57 61 50 41 ] [ 60 75 38 35 54 46 32 66 12 43 9 27 17 4 67 3 2 20 31 19 26 33 48 53 13 8 70 5 39 68 25 63 24 10 44 21 22 56 40 47]
19. AKV_80-4	(b)	[69 64 71 78 30 28 42 80 74 76 14 29 62 6 18 3 7 16 72 26 52 1 37 77 49 51 65 11 59 45 25 73 34 55 36 58 57 61 50 41 ] [ 60 75 38 35 54 46 32 66 12 43 9 27 17 4 67 15 2 20 31 19 79 33 48 53 13 8 70 5 39 68 23 63 24 10 44 21 22 56 40 47]
20. AKV_80-5	(a) and (b)	[17 48 60 78 13 42 16 51 64 28 15 50 63 40 45 43 39 32 35 6 44 30 36 76 9 8 70 1 37 10 21 61 38 52 2 ] [ 25 41 58 69 49 72 12 29 14 26 24 56 5 46 57 23 20 80 4 18 77 3 65 59 55 53 66 71 54 75 34 79 33 62 19 31 22 11 74 68 67 73 27 47 7]

Table 8

The best ordering of facilities for the first 18 instances of size 60, which are studied in Sect. 4.2 presenting the best objective values in Table 3

Instance	Case	Order of the facilities ([row 1] [row 2])
1. n60p30s30_1	(a)	[50 43 51 54 38 40 36 12 3 6 28 10 19 15 18 17 8 4 14 26 32 21 13 30 27 5 42 60 55 46 48] [57 53 35 56 39 58 11 31 9 49 23 20 16 2 1 7 25 37 22 44 24 29 47 33 34 52 45 59 41]
1. n60p30s30_1	(b)	[41 46 60 52 42 5 27 29 13 21 32 26 37 8 7 2 16 15 19 10 28 6 3 12 36 40 38 54 51 43 50] [48 59 55 45 34 33 47 30 24 44 22 4 14 25 17 1 18 20 23 49 9 31 11 58 39 56 35 53 57]
2. n60p30s30_2	(a)	[45 36 34 32 44 37 49 28 16 51 5 2 50 3 4 25 8 7 20 6 58 26 56 33 31 47 41 52 42] [48 35 39 19 57 38 55 11 12 30 14 23 9 15 29 10 17 22 53 21 27 24 13 59 18 54 43 40 1 46 60]
2. n60p30s30_2	(b)	[42 46 41 47 56 33 18 58 24 27 21 53 22 9 4 23 50 3 15 30 12 11 16 28 49 37 44 32 34 36 45] [60 52 1 40 43 31 54 59 26 13 6 20 7 8 17 29 14 25 10 2 5 51 55 38 57 19 39 35 48]
3. n60p30s30_3	(a)	[38 53 57 50 51 10 39 11 30 9 13 22 3 7 46 34 1 20 27 21 5 18 12 56 52 31 42 40 33 37] [35 49 59 55 58 41 45 24 26 44 4 6 19 43 15 25 29 8 23 16 17 14 36 2 60 28 48 54 47 32]
3. n60p30s30_3	(b)	[38 53 57 50 51 10 39 11 30 9 13 44 4 6 19 43 15 25 29 8 23 17 14 36 2 60 42 28 54 33 32] [35 49 59 55 58 41 45 24 26 22 3 7 46 34 1 20 27 21 16 5 18 12 56 52 31 48 40 47 37]
4. n60p30s40_1	(a) and (b)	[59 38 55 47 28 51 34 9 31 35 14 24 5 11 23 15 26 7 32 2 27 13 43 56 12 57 46 10 37 45] [58 44 50 25 48 29 39 22 8 30 36 20 1 4 17 21 33 3 18 19 40 16 41 6 53 52 54 60 42 49]
5. n60p30s40_2	(a)	[53 48 28 31 13 5 19 58 34 33 38 17 9 32 10 21 30 6 23 26 8 18 43 25 29 24 47 41 3 45 55 56] [57 46 44 4 54 15 50 39 20 60 14 40 36 27 49 12 37 1 11 7 2 22 16 51 42 35 52 59]
5. n60p30s40_2	(b)	[53 48 28 31 13 5 19 58 34 33 38 17 9 32 10 30 49 23 26 43 11 25 29 24 47 41 3 35 52 59] [57 46 44 4 54 15 50 39 20 60 14 40 36 27 21 6 12 37 8 18 1 7 2 22 16 51 42 45 55 56]
6. n60p30s40_3	(a) and (b)	[55 50 49 42 20 8 22 6 2 39 31 11 13 17 36 38 28 10 7 12 9 30 35 48 26 18 41 43 44 45 52] [54 59 29 57 19 25 37 4 47 40 27 34 3 21 5 51 14 16 1 32 56 33 53 15 23 46 24 58 60]
7. n60p30s50_1	(a)	[55 48 52 38 5 28 14 49 50 34 26 30 32 47 16 45 7 36 27 54 20 17 10 19 42 37 22 8 56 25 18 51] [59 60 9 24 31 11 2 53 40 6 13 21 39 44 15 41 35 33 46 4 12 29 3 23 43 1 57 58]
7. n60p30s50_1	(b)	[55 48 52 38 5 28 14 49 50 34 26 30 32 47 44 16 45 36 27 54 20 17 10 19 42 37 22 8 43 25 18 58] [59 60 9 24 31 11 2 53 40 6 13 21 39 41 15 7 35 33 46 4 12 29 3 23 56 1 57 51]
8. n60p30s50_2	(a)	[59 53 41 36 33 46 23 40 14 49 2 30 50 21 9 5 48 13 11 47 51 37 29 45 20 24 18 10 56 39 26 35 60] [54 55 52 31 43 27 28 8 6 32 12 7 38 22 1 19 4 42 3 34 15 25 17 44 58 16 57]
8. n60p30s50_2	(b)	[59 53 41 36 33 46 23 40 14 49 2 30 50 21 9 5 48 13 11 47 51 37 29 45 20 24 18 10 56 58 16 60] [54 55 52 31 43 27 28 8 6 32 12 7 38 22 1 19 4 42 3 34 15 25 17 44 39 26 35 57]
9. n60p30s50_3	(a)	[11 47 39 49 9 29 37 22 46 40 28 45 44 55 21 34 10 43 18 31 13 3 19 27 59 5 51 57 33 53 4] [56 42 54 2 1 23 35 36 14 32 50 20 15 6 30 12 48 17 41 7 8 16 38 25 26 24 60 58 52]
9. n60p30s50_3	(b)	[52 58 57 51 5 25 59 27 8 7 13 31 43 17 48 12 30 6 15 45 14 40 35 1 22 29 9 49 42 47 11] [4 53 33 60 24 26 38 16 19 3 18 41 10 34 21 55 44 20 50 32 28 36 37 23 46 2 54 39 56]
10. n60p30s60_1	(a) and (b)	[56 26 47 50 32 2 43 22 7 25 16 19 33 54 39 53 35 49 51 27 34 52 30 17 23 37 41 40 58 6 31] [11 48 46 13 18 5 21 38 3 59 42 1 20 57 29 36 28 60 10 24 14 9 44 55 8 12 45 4 15]
11. n60p30s60_2	(a)	[49 20 23 24 27 39 28 37 25 17 33 55 1 45 58 7 19 54 9 32 50 40 8 34 42 10 16 2 12] [22 3 60 31 15 4 36 21 51 48 38 35 18 41 52 44 11 46 5 43 59 6 57 53 56 47 29 14 13 26 30]
11. n60p30s60_2	(b)	[49 20 23 24 27 39 28 37 25 17 33 55 1 45 58 7 19 54 9 32 50 40 8 34 42 10 16 12 30] [22 3 60 31 15 4 36 21 51 48 38 35 18 41 52 44 11 46 5 43 59 6 57 53 56 47 29 14 13 26 2]
12. n60p30s60_3	(a)	[9 23 15 33 44 34 55 39 16 32 58 53 38 52 41 1 56 17 12 3 4 14 45 57 42 19 22 26 18] [24 47 21 7 60 36 50 40 20 46 54 5 59 11 25 27 28 37 8 35 6 43 13 2 30 51 48 31 29 49 10]
12. n60p30s60_3	(b)	[9 23 33 7 44 34 50 39 16 32 58 53 38 52 41 1 56 8 12 3 4 14 45 57 42 19 22 10 26] [24 47 21 15 60 36 55 40 20 46 54 5 59 11 25 27 28 37 17 35 6 43 13 2 30 51 48 31 29 49 18]
13. n60p60s30_1	(a)	[33 43 60 53 44 41 19 56 46 7 5 6 4 13 14 26 23 20 10 18 17 29 1 52 55 37 39 32 35] [59 42 51 54 50 45 31 12 9 8 30 16 21 3 22 28 25 15 40 2 11 24 48 58 27 36 57 47 34 49 38]
13. n60p60s30_1	(b)	[33 43 60 53 44 41 19 56 46 7 5 6 4 13 14 23 15 10 18 48 1 52 27 55 37 39 32 35] [59 42 51 54 50 45 31 12 9 8 30 16 21 3 22 28 26 25 20 40 2 11 24 17 29 58 36 57 47 34 49 38]
14. n60p60s30_2	(a)	[56 32 49 21 57 47 59 40 16 22 28 27 17 26 19 5 23 15 12 18 25 58 51 42 33 37 55 52 43] [45 35 34 48 53 14 11 60 44 13 10 7 29 1 3 2 8 6 9 4 20 39 24 30 41 36 31 38 46 54 50]
14. n60p60s30_2	(b)	[43 46 52 37 31 42 51 58 25 18 4 9 6 8 3 15 29 7 17 10 16 22 60 14 59 47 48 34 32 56] [50 54 55 38 33 36 41 30 24 39 20 12 2 1 23 5 19 26 27 28 13 44 40 11 53 57 21 49 35 45]
15. n60p60s30_3	(a)	[56 37 10 42 38 39 34 13 28 44 18 25 5 26 3 17 19 12 9 29 2 22 50 54 11 57 52 51 36 60 31] [47 55 43 53 46 33 16 4 32 24 8 20 23 7 1 27 15 6 30 21 14 58 48 35 40 59 45 41 49]
15. n60p60s30_3	(b)	[56 37 10 42 38 39 34 13 28 44 18 25 5 26 3 17 27 12 9 29 2 22 50 54 11 57 52 59 45 41 31] [47 55 43 53 46 33 16 4 32 24 8 20 23 7 1 19 15 6 30 21 14 58 48 35 40 51 36 60 49]
16. n60p60s40_1	(a)	[56 47 45 51 10 30 2 3 18 14 36 26 7 31 19 5 33 35 17 23 12 39 32 6 13 52 16 1 55 49 54 57] [48 50 41 9 38 11 34 37 20 22 21 40 24 4 27 29 15 25 28 44 8 59 43 58 53 42 46 60]
16. n60p60s40_1	(b)	[56 47 45 51 10 30 2 3 18 14 36 26 7 31 19 5 33 35 17 23 12 39 8 59 52 16 1 55 49 54 57] [48 50 41 9 38 11 34 37 20 22 21 40 24 4 27 29 15 25 28 44 32 6 13 43 58 53 42 46 60]
17. n60p60s40_2	(a)	[45 56 51 59 36 57 41 38 20 15 24 23 16 19 10 29 3 1 6 12 21 8 32 4 28 53 44 52 46 42] [48 60 43 58 17 37 39 18 14 11 9 34 5 2 26 22 31 33 7 25 27 40 30 35 13 47 49 54 55 50]
17. n60p60s40_2	(b)	[42 55 54 49 53 28 4 32 8 21 33 1 7 31 10 3 25 2 24 5 23 9 11 14 18 39 37 17 59 51 56 48] [50 46 52 44 47 13 35 30 40 27 6 12 29 22 19 26 16 34 15 20 38 41 57 36 58 43 60 45]
18. n60p60s40_3	(a)	[58 45 41 54 40 8 16 23 6 10 39 2 53 28 7 15 27 12 26 17 9 22 3 19 34 14 30 31 48 50 55 49] [56 43 47 46 60 20 21 36 33 29 38 37 13 32 1 18 25 11 35 24 4 5 51 59 57 44 42 52]
18. n60p60s40_3	(b)	[58 45 41 54 40 8 16 23 6 29 39 53 28 7 32 27 12 26 17 35 24 4 34 14 30 31 48 50 55 49] [56 43 47 46 60 20 21 36 33 10 38 2 37 13 15 1 18 25 11 9 22 3 19 5 51 59 57 44 42 52]

Table 9

The best ordering of facilities for the last 18 instances of size 60, which are studied in Sect. 4.2 presenting the best objective values in Table 3

Instance	Case	Order of the facilities ([row 1][row 2])
19. n60p60s50_1	(a)	[52 55 54 40 2 22 10 46 42 31 39 20 24 18 1 28 30 14 19 27 36 38 34 26 21 29 3 17 50 44 56 51] [58 59 47 41 13 35 25 37 16 11 12 7 49 45 23 43 9 8 4 33 5 48 6 32 15 53 57 60]
19. n60p60s50_1	(b)	[52 55 54 40 2 22 10 46 42 11 39 20 24 18 45 30 1 14 19 43 9 38 34 26 21 29 3 32 50 44 56 51] [58 59 47 41 13 35 25 37 16 31 12 7 49 28 23 27 36 8 4 33 5 48 6 17 15 53 57 60]
20. n60p60s50_2	(a)	[58 56 55 59 43 10 23 11 3 22 41 45 35 49 16 29 26 42 15 46 34 40 48 32 54 25 53] [51 57 30 19 12 14 47 13 28 31 36 50 24 2 5 38 44 39 37 27 6 21 7 1 17 18 8 20 4 60 33 9 52]
20. n60p60s50_2	(b)	[58 56 55 59 43 10 23 11 3 22 41 45 35 49 16 38 39 37 27 6 42 15 17 34 20 48 32 54 25 52] [51 57 30 19 12 14 47 13 28 31 36 50 24 2 5 44 29 26 21 7 1 46 8 18 40 4 60 33 9 53]
21. n60p60s50_3	(a)	[52 60 57 45 54 25 50 11 49 43 6 18 10 15 20 5 3 2 13 29 28 8 39 40 16 59 9 58 19 53] [56 51 32 26 35 44 1 47 46 38 22 36 34 41 33 21 12 27 31 14 42 48 37 30 23 4 7 55 17 24]
21. n60p60s50_3	(b)	[52 60 57 45 54 25 50 11 49 43 6 18 10 21 27 5 2 13 29 28 42 39 37 30 59 9 58 19 53] [56 51 32 26 35 44 1 47 46 38 22 36 34 41 33 15 12 20 3 31 14 8 48 40 16 23 4 7 55 17 24]
22. n60p60s60_1	(a) and (b)	[27 13 25 32 42 26 20 12 37 48 50 36 57 11 59 21 4 22 18 16 55 38 53 30 45 60 51 49 14] [44 33 23 39 15 6 28 40 52 17 5 24 19 34 7 8 29 3 58 9 1 56 43 41 46 47 35 54 31 2 10]
23. n60p60s60_2	(a)	[13 17 59 51 47 25 29 4 28 3 18 14 2 46 35 40 48 23 50 54 49 30 5 20 11 57 1 31 32] [9 44 26 16 7 60 27 42 39 33 12 53 21 55 6 56 38 19 10 52 36 41 58 22 8 34 37 45 24 15 43]
23. n60p60s60_2	(b)	[13 17 59 51 47 25 29 4 28 33 21 53 12 14 38 46 35 40 48 23 50 54 49 30 5 34 11 57 1 31 43] [9 44 26 16 7 60 27 42 39 3 18 55 6 56 2 19 10 52 36 41 58 22 8 20 37 45 24 15 32]
24. n60p60s60_3	(a)	[15 1 8 47 14 31 53 40 55 18 6 30 28 12 24 34 50 37 23 21 26 13 54 45 29 2 9 33 22 10 38 4] [27 36 48 51 19 20 59 46 17 11 41 39 44 25 52 60 43 5 35 16 56 3 42 57 32 7 58 49]
24. n60p60s60_3	(b)	[15 1 8 47 14 31 53 40 55 18 6 30 28 12 24 34 50 37 23 21 26 13 54 45 29 2 9 33 22 7 38 4] [27 36 48 51 19 20 59 46 17 11 41 39 44 25 52 60 43 5 35 16 56 3 42 57 32 10 58 49]
25. n60p90s30_1	(a)	[37 52 55 31 41 1 54 36 17 23 29 25 5 22 6 30 28 16 3 4 2 15 35 27 59 48 58 44 49 51] [39 56 50 33 43 38 60 57 24 9 14 11 19 12 26 20 13 10 8 18 53 21 32 7 47 45 42 34 46 40]
25. n60p90s30_1	(b)	[51 46 34 58 45 59 27 32 21 2 4 3 16 10 13 20 26 6 19 22 5 14 9 23 17 36 54 1 41 31 55 52 37] [40 49 44 42 48 47 7 15 35 53 18 8 28 30 12 11 25 29 24 57 60 38 43 33 50 56 39]
26. n60p90s30_2	(a)	[55 49 14 59 50 33 51 26 25 5 23 2 18 19 8 24 27 22 28 11 6 45 42 39 58 38 57 47 48] [56 60 41 43 52 35 34 12 40 15 16 9 13 17 30 3 1 29 20 10 21 7 36 46 4 32 37 54 31 53 44]
26. n60p90s30_2	(b)	[48 47 57 38 58 39 42 46 36 7 21 27 24 3 30 17 18 13 23 5 25 26 51 33 50 59 14 49 56] [44 53 31 54 37 32 4 45 6 11 28 22 10 20 29 1 8 19 2 9 16 15 40 12 34 35 52 43 41 60 55]
27. n60p90s30_3	(a)	[54 53 46 50 39 59 40 47 5 6 23 11 21 4 30 16 8 2 19 14 10 52 58 48 15 36 42 34 32] [37 38 43 41 57 51 45 27 1 3 29 18 9 17 24 13 25 12 28 7 26 20 22 31 35 33 44 56 60 55 49]
27. n60p90s30_3	(b)	[37 53 46 50 39 59 40 47 5 6 23 11 21 4 30 16 2 19 20 10 31 58 48 15 36 42 34 32] [54 38 43 41 57 51 45 27 1 3 29 18 9 17 24 13 25 8 12 28 7 26 14 22 52 35 33 44 56 60 55 49]
28. n60p90s40_1	(a)	[55 51 41 57 22 5 3 4 20 15 11 8 25 27 14 13 6 36 16 23 38 1 40 21 10 43 54 53 50 44 52] [46 42 45 48 49 2 29 33 9 39 37 32 31 7 30 12 28 34 17 35 26 18 19 24 59 60 47 58 56]
28. n60p90s40_1	(b)	[46 42 45 48 22 5 3 4 20 15 11 37 8 7 30 12 16 23 17 35 26 18 19 24 59 53 50 58 56] [55 51 41 57 49 2 29 33 9 39 32 31 25 27 14 13 6 36 28 34 38 1 40 21 10 43 54 60 47 44 52]
29. n60p90s40_2	(a)	[55 47 57 60 58 13 20 12 31 30 27 35 1 24 7 32 22 16 14 5 23 8 25 6 41 54 56 52 48] [42 44 43 50 28 49 15 4 29 21 19 10 18 26 36 33 3 38 37 39 17 2 11 9 40 53 45 34 46 51 59]
29. n60p90s40_2	(b)	[59 52 46 54 41 6 25 9 11 2 17 39 37 3 32 33 26 22 18 27 30 29 12 20 13 28 50 43 44 42] [48 51 56 34 45 53 40 8 23 5 14 16 38 7 36 24 1 35 10 19 21 31 4 15 49 58 60 57 47 55]
30. n60p90s40_3	(a) and (b)	[44 60 55 41 49 32 27 25 35 40 24 3 8 5 6 19 17 28 10 4 15 22 13 56 57 54 42 43] [51 52 46 53 59 29 9 36 1 21 37 39 12 20 33 30 11 7 31 23 2 26 18 38 34 16 14 47 58 45 50 48]
31. n60p90s50_1	(a)	[53 56 18 21 43 48 8 35 2 27 42 32 19 11 29 49 39 46 4 3 10 26 31 12 5 30 7 22 1 36 59 58] [51 54 13 60 47 45 28 38 23 50 14 20 37 44 40 16 41 34 6 17 9 25 33 15 24 52 57 55]
31. n60p90s50_1	(b)	[53 56 18 21 43 48 8 35 2 27 42 32 19 11 29 49 39 46 4 3 10 26 31 12 5 30 7 22 1 36 59 55] [51 54 13 60 47 45 28 38 23 50 14 20 37 44 40 16 41 34 6 17 9 25 33 15 24 52 57 58]
32. n60p90s50_2	(a)	[55 58 41 4 53 45 7 19 11 9 20 24 37 27 12 23 42 3 6 48 10 5 35 1 47 22 21 54 56] [57 51 52 32 13 28 34 8 30 50 49 26 46 38 31 36 17 25 15 43 39 2 16 29 33 40 44 14 18 60 59]
32. n60p90s50_2	(b)	[57 58 52 4 53 7 34 19 11 50 49 26 46 38 31 23 42 43 48 5 16 33 44 47 21 18 60 59] [55 51 41 32 13 45 28 8 30 9 20 24 37 27 12 36 17 25 15 3 6 39 10 2 29 35 40 1 22 14 54 56]
33. n60p90s50_3	(a)	[51 59 53 52 39 46 18 44 49 11 13 45 15 32 28 1 25 17 40 34 29 14 47 48 43 3 5 21 26 54 58] [56 55 57 2 24 23 30 33 42 27 37 50 7 19 31 20 35 36 41 16 6 8 4 9 22 12 38 10 60]
33. n60p90s50_3	(b)	[51 59 53 52 39 46 33 44 49 11 13 7 15 19 25 1 35 17 32 41 16 6 48 43 4 22 21 38 54 58] [56 55 57 2 24 23 30 18 42 27 37 50 45 36 20 28 40 34 31 29 14 47 8 3 9 5 12 26 10 60]
34. n60p90s60_1	(a)	[41 48 51 24 5 56 39 13 54 59 58 29 19 2 14 31 34 42 35 57 38 37 10 52 40 16 1 30 4] [28 25 9 43 32 33 6 27 8 55 21 60 53 7 26 20 18 12 36 49 3 47 15 11 23 46 44 22 50 45 17]
34. n60p90s60_1	(b)	[4 45 50 16 40 52 10 37 38 57 3 49 36 12 18 20 26 7 53 60 21 58 8 27 39 56 32 24 51 48 28] [17 30 1 22 44 46 23 11 15 47 35 42 34 31 14 2 19 29 59 55 54 13 6 33 5 43 9 25 41]
35. n60p90s60_2	(a)	[7 26 1 16 15 30 51 36 20 12 23 17 53 6 14 58 29 57 13 25 11 10 3 43 59 45 24 48 42] [33 40 32 35 56 4 22 60 37 5 2 19 39 28 55 46 47 34 54 27 8 38 21 52 44 18 9 31 41 50 49]
35. n60p90s60_2	(b)	[49 41 45 50 59 44 3 10 11 25 8 27 54 34 47 46 55 53 17 2 12 37 36 51 30 15 1 32 40 7] [42 24 48 31 9 18 43 52 21 38 13 57 29 58 14 6 28 39 19 23 5 20 60 22 4 56 35 16 26 33]
36. n60p90s60_3	(a) and (b)	[6 44 33 28 43 35 42 36 8 9 25 19 22 52 32 56 10 20 53 29 21 13 46 45 11 18 31 50 27 3] [15 39 41 17 55 1 7 59 54 30 16 40 4 5 48 37 51 26 14 23 49 38 47 34 58 24 57 60 12 2]

Table 10

The best ordering of facilities for the first 10 instances of sizes in the range of [110, 200], which are studied in Sect. 4.3 presenting the best objective values in Table 5

Instance	CAP	Order of the facilities ([row 1][row 2])
1. p110	(a) and (b)	[20 30 63 94 50 7 59 70 85 11 19 86 1 98 69 28 44 76 53 107 14 79 101 61 12 102 92 48 99 62 84 15 42 13 46 52 91 93 39 55 82 110 33 77 17 67 9 78 75 40 31 54 23 49 18] [97 4 38 103 109 96 2 83 47 34 100 3 89 27 45 74 81 22 71 21 73 36 56 65 37 87 106 32 25 26 66 80 51 90 6 35 104 58 10 41 43 72 16 29 88 105 60 57 64 108 5 68 24 95 8]
2. p120	(a) and (b)	[41 77 103 27 78 49 106 58 76 89 43 88 97 98 70 111 55 32 28 68 107 21 72 54 33 102 80 73 94 118 82 29 90 64 14 105 116 60 114 44 87 18 56 96 12 10 9 8 51 84 40 23 11 74 35 79 99 20] [120 112 7 24 31 1 47 25 75 30 65 50 48 6 85 119 57 63 66 93 83 71 19 95 59 101 16 52 69 36 38 67 17 2 53 13 42 113 39 62 100 86 15 117 45 26 5 3 104 91 37 34 110 46 22 61 108 81 92 115 4 109]
3. p130	(a) and (b)	[122 117 97 59 47 114 56 9 67 12 19 79 41 26 92 85 40 90 83 30 46 74 121 93 8 106 55 35 112 24 28 64 105 102 128 25 63 60 81 52 61 130 109 18 23 115 103 15 120 89 32 4 5 21 75 42 22 69 43 27 51 71 3 10 50] [113 39 77 123 1 101 129 6 124 44 2 29 99 11 116 66 80 126 57 82 96 20 14 17 86 95 45 125 65 72 127 13 31 107 38 68 70 84 49 7 108 87 34 119 58 16 33 91 110 111 100 54 48 76 94 104 37 53 73 98 62 88 36 118 78]
4. p140	(a) and (b)	[116 18 66 136 133 93 79 57 89 35 77 140 62 31 22 24 30 138 84 14 123 90 99 55 106 16 45 9 118 8 121 78 97 125 100 10 42 1 46 75 128 120 82 28 65 103 13 36 40 7 127 129 91 49 38 41 110 71 80 135 119 96 67 19 112 113 83 47 109 122] [68 48 69 34 2 86 6 56 94 114 11 132 53 107 4 25 20 111 130 59 12 74 105 37 117 60 98 64 15 92 27 52 50 131 21 104 23 33 51 81 124 5 95 73 70 139 102 26 85 54 58 63 17 101 108 76 29 39 115 43 126 72 87 61 3 137 44 88 32 134]
5. p150	(a)	[55 78 83 85 60 110 103 15 42 127 149 147 79 67 73 24 137 59 56 97 28 141 48 32 65 91 29 81 26 16 43 92 44 113 40 9 66 7 61 131 99 100 122 130 3 104 118 38 98 62 89 21 76 136 133 88 117 4 121 94 19 106 34 124 36 101 142 143 90 145 31 57] [54 45 64 5 84 146 20 2 126 58 49 134 6 150 74 96 144 33 120 47 1 75 148 52 139 132 112 23 82 72 11 129 140 70 37 111 108 138 86 17 68 30 39 128 135 35 119 87 107 125 71 102 95 10 27 93 53 50 114 63 77 115 116 46 8 18 41 12 13 25 51 22 69 109 123 105 80 14]
5. p150	(b)	[55 78 83 85 60 110 103 15 42 127 149 147 79 67 73 24 137 59 56 97 28 141 48 32 65 91 29 81 26 16 43 92 44 113 40 61 66 7 9 30 99 39 122 130 3 104 118 38 98 62 89 21 76 136 133 88 117 4 121 94 19 106 34 124 36 101 142 143 90 145 31 57] [54 45 64 5 84 146 20 2 126 58 49 134 6 150 74 96 144 33 120 47 1 75 148 52 139 132 112 23 82 72 11 129 140 70 37 111 108 138 86 17 68 131 100 128 135 35 119 87 107 125 71 102 95 10 27 93 53 50 114 63 77 115 116 46 8 18 41 12 13 25 51 22 69 109 123 105 80 14]
6. p160	(a)	[78 109 72 151 160 73 106 43 134 11 144 33 25 111 85 119 153 40 35 37 137 91 18 103 129 102 63 157 50 110 115 130 65 98 99 5 127 59 116 118 141 48 51 133 70 128 92 138 32 83 6 76 66 94 69 58 39 30 67 93 64 84 117 125 47 3 34 100 75 88 36 17 149 52 145 45 26 74 77] [142 68 120 108 107 79 21 8 19 155 95 62 136 150 10 124 122 1 27 9 158 44 143 61 135 60 46 101 147 4 23 112 140 105 41 154 121 7 82 54 114 104 20 28 71 96 148 29 80 56 89 152 16 139 132 13 126 90 113 49 42 24 22 15 57 97 131 38 87 12 86 31 53 81 55 156 146 14 123 2 159]
6. p160	(b)	[78 109 72 151 160 73 106 43 134 11 144 33 25 111 85 119 153 40 35 37 137 91 18 103 129 102 63 157 50 110 4 130 65 98 99 5 114 59 116 118 141 48 51 133 70 128 92 138 32 83 6 76 66 94 69 58 39 30 67 93 64 84 117 125 47 3 34 100 75 88 36 17 149 52 145 45 26 74 77] [142 68 120 108 107 79 21 8 19 155 95 62 136 150 10 124 122 1 27 9 158 44 143 61 135 60 46 101 147 115 23 105 82 112 41 154 121 7 140 104 127 54 20 28 71 96 148 29 80 56 89 152 16 139 132 13 126 90 113 49 42 24 22 15 57 97 131 38 87 12 86 31 53 81 55 156 146 14 123 2 159]
7. p170	(a) and (b)	[149 57 142 45 67 84 89 115 121 105 135 81 33 35 95 155 22 38 159 76 65 51 123 150 34 153 147 25 73 132 86 140 126 97 101 9 102 109 31 69 49 143 128 46 80 82 30 27 107 2 62 36 47 120 116 161 13 106 55 145 60 93 170 70 92 23 5 157 136 117 148 20 99 156 59 7 87 8 129 54 146 88 3 114 68 61 110] [125 40 15 85 4 138 53 28 165 26 44 56 118 168 39 166 139 66 100 104 10 43 41 144 119 16 83 63 52 112 21 17 50 14 152 141 75 71 127 96 164 124 162 130 163 79 133 19 64 122 103 32 78 74 58 42 12 11 113 18 160 158 111 169 137 24 72 108 167 134 98 90 48 37 77 1 94 91 29 6 154 131 151]
8. p180	(a)	[11 128 150 92 142 163 165 99 63 31 178 113 21 151 22 49 162 160 138 16 59 149 36 60 112 47 127 124 108 106 19 64 74 102 125 58 65 103 50 156 68 13 5 155 28 93 78 41 17 104 89 81 71 6 148 46 87 159 15 172 4 7 117 12 147 118 171 55 90 85 153 116 135 94 133 43 130 154 62 168 144 180 52 39 10 111 96 76 3] [140 132 137 136 109 54 51 166 66 82 29 69 175 91 88 177 37 70 26 24 107 95 84 48 18 14 9 75 120 32 25 139 152 44 61 98 83 23 119 123 170 86 30 131 129 56 174 179 122 34 80 115 79 2 126 1 100 169 77 141 145 53 110 97 143 114 105 176 38 27 73 157 8 164 45 40 67 121 72 57 167 134 33 146 42 161 20 35 158 173 101]
8. p180	(b)	[11 128 150 92 142 163 165 99 63 31 178 113 21 151 22 49 162 160 138 16 59 149 36 60 112 47 127 124 108 106 19 64 74 102 125 58 65 103 50 156 68 13 5 155 28 93 78 41 17 104 89 100 71 6 148 46 87 159 15 172 4 7 117 12 105 118 171 55 90 85 153 116 135 94 133 43 130 154 62 168 144 180 52 39 10 111 96 76 3] [140 132 137 136 109 54 51 166 66 82 29 69 175 91 88 177 37 70 26 24 107 95 84 48 18 14 9 75 120 32 25 139 152 44 61 98 83 23 119 123 170 86 30 131 129 56 174 179 122 34 80 115 79 2 126 1 81 169 77 141 145 53 110 97 143 114 147 176 38 27 73 157 8 164 45 40 67 121 72 57 167 134 33 146 42 161 20 35 158 173 101]
9. p190	(a) and (b)	[138 143 27 50 129 161 164 56 114 170 2 54 100 29 142 118 11 162 95 82 6 147 119 69 178 154 80 43 103 123 181 152 76 189 36 60 70 31 42 64 107 65 5 144 38 108 182 105 73 88 139 55 15 28 4 167 68 134 91 23 25 66 179 125 188 145 33 87 44 35 166 74 115 3 102 22 45 104 131 9 148 41 180 156 159 168 21 183 39 14 187 18 96] [49 84 59 177 140 61 160 155 97 112 94 128 130 111 106 126 124 121 132 174 20 72 185 158 40 116 51 26 173 7 8 175 113 171 77 79 98 63 184 190 85 71 149 117 151 141 17 120 78 93 46 1 137 172 32 135 13 136 19 58 186 75 81 169 133 89 153 157 67 101 92 48 163 10 83 12 57 127 110 150 122 52 34 165 16 176 146 37 30 90 109 62 86 24 99 53 47]
10. p200	(a) and (b)	[94 75 193 143 101 21 55 117 99 69 30 98 97 56 132 40 142 47 37 73 29 4 175 190 123 64 170 84 198 183 110 27 174 167 118 12 19 135 88 82 113 31 20 10 147 200 9 133 157 36 186 38 34 164 7 140 18 180 104 80 146 178 106 13 91 2 54 6 85 107 61 185 23 160 33 195 25 58 72 188 122 53 151 70 189 165 96 51 114 181 158 149 35 152 125 197 60 17 89 52 15 173 48 63] [67 176 154 11 153 1 172 169 3 199 78 191 116 39 59 95 156 127 166 139 100 81 93 32 131 168 192 24 162 28 182 66 42 187 77 105 108 112 79 22 134 43 171 163 76 5 115 92 126 144 141 86 150 179 128 74 26 90 137 129 44 194 124 62 130 57 41 138 8 45 49 148 159 119 83 87 184 111 196 68 145 50 161 71 103 46 14 177 120 16 109 155 121 102 65 136]

Table 11

The best ordering of facilities for the intermediate 6 instances of sizes in the range of [210, 260], which are studied in Sect. 4.3 presenting the best objective values in Table 5

Instance	CAP	Order of the facilities ([row 1] [row 2])
11. p210	(a) and (b)	[190 65 126 5 130 127 107 100 122 62 79 47 148 96 197 41 28 154 163 8 167 189 38 200 176 203 25 128 60 117 186 44 88 146 201 183 112 177 4 132 9 174 134 17 144 74 114 141 118 198 87 184 195 160 139 115 105 157 193 138 11 49 181 202 16 92 2 23 13 93 40 22 171 81 31 147 59 63 56 136 106 102 152 172 6 73 27 71 3 205 124 26 170 207 52 95 10 20 19 33 12 187 39 98 140] [42 151 58 7 99 192 21 129 46 150 161 36 14 80 76 29 85 68 159 199 137 210 32 149 69 133 50 135 113 156 121 209 75 18 168 120 178 15 72 1 182 175 155 70 145 173 37 179 64 158 125 86 116 78 111 180 153 77 43 24 82 108 142 48 30 165 34 188 191 53 67 55 97 194 66 110 54 103 89 84 119 131 185 208 91 109 143 164 196 204 166 57 206 169 61 104 123 90 35 162 51 83 45 101 94]
12. p220	(a) and (b)	[145 217 212 128 166 205 192 144 51 198 180 2 106 10 46 140 48 183 13 15 131 101 36 161 7 135 8 178 92 109 32 39 114 80 210 203 79 23 199 163 102 209 3 25 137 43 188 211 139 100 30 216 67 44 55 66 202 50 168 186 63 28 40 206 177 150 117 91 5 174 59 107 22 167 33 197 158 47 95 27 148 62 195 138 70 118 110 201 136 68 112 169 151 173 120 54 97 6 24 73 99 94 219 190 179 204 127 122 20 89] [182 29 9 196 156 111 130 141 38 159 60 194 87 129 126 45 189 214 71 218 93 207 185 132 181 157 65 26 108 121 31 85 103 98 64 21 41 74 42 49 152 133 155 184 16 104 58 116 142 172 52 18 86 81 78 61 124 17 76 215 213 11 53 4 134 82 154 220 69 37 170 164 187 162 125 149 75 160 56 105 57 72 176 1 34 113 19 175 14 191 77 171 165 200 84 119 123 12 143 153 115 35 147 193 88 83 208 96 90 146]
13. p230	(a)	[56 156 111 167 158 112 175 53 51 24 196 207 76 165 18 47 115 116 92 41 110 126 71 2 72 144 120 85 155 188 204 57 17 15 131 217 7 208 119 91 138 122 211 166 79 101 187 136 106 9 178 180 222 173 27 52 186 66 179 14 228 96 65 43 1 36 130 20 83 215 154 161 202 221 5 39 146 37 223 147 54 140 203 133 212 137 4 38 80 86 193 123 191 28 77 64 129 81 174 162 68 19 99 209 148 84 159 194 49 78 8 199 197 33 151 44 189 224 182] [70 100 69 61 206 108 135 42 107 164 60 139 218 29 89 40 88 3 62 26 12 93 103 87 142 30 16 63 10 171 134 50 35 160 109 45 67 198 117 48 184 225 190 170 169 55 152 214 105 195 216 11 226 34 46 82 145 97 230 75 13 102 153 90 25 98 227 74 219 177 149 163 132 118 113 176 185 124 141 205 32 172 95 31 213 143 104 114 157 94 121 73 210 128 58 183 21 23 127 168 6 150 192 201 22 125 229 220 59 181 200]
13. p230	(b)	[70 156 111 69 61 206 112 135 218 51 139 60 89 18 29 87 40 88 115 2 92 107 93 30 103 155 72 144 134 63 198 131 50 15 119 17 67 7 109 190 184 37 211 187 105 166 101 98 136 9 180 96 46 106 14 228 186 97 13 75 20 222 52 215 102 179 43 153 36 11 5 25 55 138 39 161 133 203 163 147 137 113 160 141 80 176 38 193 28 123 172 114 77 162 64 81 94 157 68 73 19 128 6 23 194 8 21 201 192 150 182 33 189 59 220 151 181] [56 108 53 100 167 24 175 158 76 196 42 165 207 41 164 47 62 142 26 116 3 188 12 126 110 71 16 85 120 10 171 35 57 204 217 140 208 212 117 91 45 219 132 48 146 122 154 170 169 79 216 195 178 1 27 65 230 226 173 130 145 34 66 83 225 82 90 74 221 214 202 152 227 177 223 54 149 4 118 124 191 95 185 213 86 32 129 104 205 121 174 31 99 143 210 58 209 148 159 168 49 127 183 84 229 78 199 125 197 200 22 224 44]
14. p240	(a) and (b)	[145 240 147 3 144 112 222 142 65 195 139 56 109 106 59 22 49 124 140 158 108 73 1 6 224 68 177 52 83 63 191 184 137 220 165 202 27 4 166 127 138 92 133 221 88 141 238 167 129 78 111 200 237 28 186 218 25 114 231 94 39 182 8 40 214 70 104 11 163 216 149 205 46 26 36 87 154 230 185 15 197 212 207 61 97 82 181 179 162 84 143 54 123 223 66 236 77 159 58 90 206 19 151 16 119 171 93 134 217 5 178 96 234 53 43 64 153 18 213] [99 225 110 215 155 203 189 131 130 9 161 115 229 86 42 116 235 170 35 121 232 41 201 79 47 132 17 190 233 172 227 60 208 209 2 13 176 152 101 20 7 80 228 210 204 219 136 120 76 211 74 122 194 71 126 23 156 239 193 14 168 125 32 173 180 85 187 98 188 57 192 34 199 95 100 160 198 146 29 75 135 38 157 48 117 31 89 226 55 62 102 148 12 175 183 105 51 24 113 21 103 174 150 118 169 81 50 30 10 196 164 37 107 72 69 45 91 67 44 33 128]
15. p250	(a)	[204 141 163 135 9 78 227 242 112 218 162 82 144 102 7 142 172 37 238 230 220 91 17 188 63 59 196 241 201 4 111 170 214 176 110 45 248 38 150 160 103 58 190 231 25 194 167 169 101 189 85 239 177 235 94 12 217 67 179 99 237 14 105 32 191 139 137 93 216 165 202 30 66 183 84 181 10 148 208 64 156 83 33 244 186 92 117 31 57 219 87 89 39 11 198 34 62 115 224 210 44 70 75 221 90 240 146 80 15 185 73 129 96 72 153 20 155 23 187 222 116 249] [41 203 225 192 234 61 60 46 149 109 47 209 151 193 95 26 229 69 182 81 29 88 138 13 126 161 68 131 195 53 232 24 145 212 5 107 86 133 51 1 174 200 121 132 36 128 243 166 48 79 157 199 178 77 18 152 100 56 164 205 122 27 2 65 74 21 54 247 71 52 40 108 125 147 114 35 3 120 213 113 158 215 55 42 127 245 197 124 173 104 168 180 118 6 143 106 223 207 154 43 134 233 19 140 97 22 228 50 206 98 136 171 159 76 250 119 236 175 16 226 184 8 123 130 246 211 28 49]
15. p250	(b)	[204 141 163 135 9 78 227 242 112 218 162 82 144 102 7 142 172 37 238 230 220 91 17 188 63 59 196 241 201 4 111 170 214 176 110 45 248 38 150 160 103 58 190 231 25 194 167 169 101 189 85 48 177 235 94 12 217 67 179 99 237 14 77 32 191 139 137 93 216 165 202 213 66 183 84 181 10 148 208 64 156 83 33 244 186 92 117 31 57 219 87 89 39 11 198 34 62 115 224 210 44 70 75 221 90 240 146 80 15 185 73 129 96 72 153 20 155 23 187 222 116 249] [41 203 225 192 234 61 60 46 149 109 47 209 151 193 95 26 229 69 182 81 29 88 138 13 126 161 68 131 195 53 232 24 145 212 5 107 86 133 51 1 174 200 121 132 36 128 243 166 239 79 157 199 178 105 18 152 100 56 164 205 122 27 2 65 74 21 54 247 71 52 40 108 125 147 114 35 3 120 30 113 158 215 55 42 127 245 197 124 173 104 168 180 118 6 143 106 223 207 154 43 134 233 19 140 97 22 228 50 206 98 136 171 159 76 250 119 236 175 16 226 184 8 123 130 246 211 28 49]
16. p260	(a)	[3 176 64 181 39 258 222 53 57 28 100 121 151 103 35 87 252 113 244 243 239 155 138 210 161 231 119 15 219 179 172 240 9 217 159 74 75 123 13 193 137 125 37 102 16 198 23 204 73 52 107 66 65 227 192 19 30 133 251 47 49 212 72 116 110 173 237 235 224 10 248 230 32 218 114 226 61 108 99 17 187 25 140 8 256 5 205 38 4 115 225 128 255 6 203 124 216 158 177 81 14 7 80 174 232 131 142 41 147 150 183 71 182 90 188 220 149 11 27 241 253 153 29 221 44 48 63 141 26] [191 117 157 260 58 85 233 185 96 250 95 144 143 208 257 168 184 259 12 67 242 194 62 146 163 134 112 130 148 92 126 77 76 162 247 78 213 98 199 207 93 122 89 36 60 214 1 20 97 135 236 40 145 129 50 196 118 190 167 2 234 200 166 206 152 70 170 127 139 195 24 202 106 171 186 175 83 156 59 109 69 215 22 8 18 82 164 154 201 79 51 120 189 211 246 105 254 132 160 86 101 223 68 197 56 136 45 55 34 43 169 88 238 104 249 21 46 209 54 94 84 111 33 42 229 245 22 31 165 178 91 180]
16. p260	(b)	[3 176 64 181 39 258 222 53 57 28 100 121 151 103 35 87 252 113 244 243 239 155 138 210 161 231 119 15 219 179 172 240 9 217 159 74 75 123 13 193 137 125 37 102 16 198 23 204 73 52 107 66 65 227 192 19 30 133 251 47 49 212 72 116 110 173 237 235 224 10 248 230 32 218 114 226 61 108 99 17 187 25 140 8 256 5 205 38 4 115 225 128 255 6 203 124 216 158 177 81 14 7 80 174 232 131 142 41 147 150 183 71 182 90 188 220 149 11 27 241 31 153 29 221 44 48 63 141 26] [191 117 157 260 58 85 233 185 96 250 95 144 143 208 257 168 184 259 12 67 242 194 62 146 163 134 112 130 148 92 126 77 76 162 247 78 213 98 199 207 93 122 89 36 60 214 1 20 97 135 236 40 145 129 50 196 118 190 167 2 234 200 166 206 152 70 170 127 139 195 24 202 106 171 186 83 175 156 59 109 69 215 228 18 82 164 154 201 79 51 120 189 211 246 105 254 132 160 86 101 223 68 197 56 136 45 55 34 43 169 88 238 104 249 21 46 209 54 94 84 111 33 42 229 245 22 253 165 178 91 180]

Table 12

The best ordering of facilities for the last 4 instances of sizes in the range of [270, 300], which are studied in Sect. 4.3 presenting the best objective values in Table 5

Instance	CAP	Order of the facilities ([row 1] [row 2])
17. p270	(a)	[128 83 18 188 233 124 122 120 102 229 175 96 267 110 107 37 22 176 131 205 85 104 227 13 223 173 88 134 170 256 268 39 12 231 220 207 114 264 154 243 167 140 178 182 251 218 237 193 161 55 259 150 187 4 224 148 35 190 133 214 6 197 179 202 34 212 192 90 177 160 208 66 253 63 80 158 20 245 265 149 217 95 240 64 60 93 174 78 56 111 143 163 165 246 221 209 247 32 141 9 191 117 166 136 40 62 48 172 24 130 28 99 17 65 82 54 138 145 92 127 73 76 262 91 210 255 219 270 234 248 260 269] [27 139 194 49 46 162 186 53 156 84 238 41 157 169 30 250 2 198 152 75 266 31 109 103 159 69 258 58 142 36 164 244 228 230 21 125 226 11 254 14 203 196 33 206 185 115 74 25 225 232 61 72 100 47 263 81 97 236 189 241 94 132 113 171 57 16 235 146 50 168 239 252 135 71 70 87 261 242 42 118 147 79 180 155 199 19 89 23 106 195 38 77 201 216 112 86 144 101 8 129 29 5 59 43 200 10 68 123 151 3 153 7 121 15 257 116 1 52 249 26 44 137 184 51 215 119 211 181 222 105 67 98 213 108 126 204 183 45]
17. p270	(b)	[128 83 18 188 233 124 122 120 102 229 175 96 267 110 107 37 22 176 131 205 85 104 227 13 223 173 88 134 170 256 268 39 12 231 220 207 114 264 154 243 167 140 178 182 251 218 237 193 161 55 259 150 187 4 224 148 35 61 133 214 6 197 179 202 34 212 192 90 177 160 208 66 253 63 80 158 20 245 265 149 217 95 240 64 60 93 174 78 56 111 143 163 165 246 221 209 247 32 141 9 191 117 166 136 40 62 48 172 24 130 28 99 17 65 82 54 138 145 92 127 73 76 262 91 210 255 219 270 234 248 260 269] [27 139 194 49 46 162 186 53 156 84 238 41 157 169 30 250 2 198 152 75 266 31 109 103 159 69 258 58 142 36 164 244 228 230 21 125 226 11 254 14 203 196 33 206 185 115 74 25 225 232 190 72 100 47 263 81 97 236 189 241 94 132 113 71 57 16 235 146 50 168 239 252 135 171 70 87 261 242 42 118 147 79 180 155 199 19 89 23 106 195 38 77 201 216 112 86 144 101 8 129 29 5 59 43 200 10 68 123 151 3 153 7 121 15 116 257 1 52 249 26 44 137 184 51 215 119 181 211 222 105 67 98 213 108 126 204 183 45]
18. p280	(a) and (b)	[243 41 185 19 171 190 245 43 153 57 272 123 69 108 279 112 234 114 11 227 82 203 6 156 136 77 154 253 235 26 267 62 55 218 152 105 155 146 5 29 263 147 233 266 3 144 24 71 162 260 271 100 74 7 193 240 58 16 167 139 214 111 194 222 78 34 201 276 157 10 242 220 17 277 165 66 117 90 129 33 187 134 125 13 160 135 265 131 61 188 138 244 65 103 180 116 192 226 149 200 184 70 80 64 48 39 72 216 83 247 122 53 225 202 44 113 256 110 161 4 176 91 150 205 183 140 164 23 275 229 37 198 182 38 35 2 25 238 104 237 42 274 248 85 195] [63 95 239 254 181 223 133 52 143 246 79 12 204 217 119 166 163 31 94 236 109 173 51 251 259 98 76 210 124 36 60 199 1 87 15 172 250 54 258 231 99 102 18 215 32 255 141 128 230 257 46 107 50 191 86 264 148 68 232 186 22 168 151 84 127 206 49 262 196 219 14 21 137 280 8 175 211 47 213 174 249 145 228 101 96 88 89 269 170 59 121 189 9 118 208 92 177 45 179 209 81 268 224 120 93 97 270 158 159 67 130 278 56 20 106 28 142 252 207 30 273 40 221 126 212 261 75 132 169 73 115 241 178 27 197]
19. p290	(a)	[181 2 253 3 185 59 198 86 194 143 207 85 84 208 280 144 163 168 111 115 206 21 16 101 99 136 31 10 83 127 88 149 44 26 239 142 202 164 27 75 62 105 148 29 225 94 199 70 135 130 254 49 251 159 215 235 71 106 76 104 50 35 237 259 273 90 1 23 108 110 66 41 77 152 81 46 123 240 39 189 56 213 126 249 250 15 212 205 132 277 186 65 288 190 63 154 61 171 24 193 264 231 25 60 30 257 232 227 276 4 114 93 162 255 112 8 266 147 122 242 139 5 33 289 87 275 252 214 12 222 244 67 121 125 187 118 224 196 141 172 238 267 184 37 58 278 54 51 36] [52 151 175 236 72 22 178 245 131 233 180 17 243 47 80 89 40 43 102 117 209 234 219 119 150 165 129 167 9 32 188 140 260 183 241 120 221 286 96 160 73 218 246 195 166 103 107 247 113 173 82 272 262 68 138 98 11 274 146 92 179 270 116 145 20 263 177 228 229 182 48 261 97 133 6 124 45 216 169 155 217 19 284 269 134 268 79 210 230 42 53 191 256 153 91 109 38 204 258 279 220 137 158 95 174 13 128 57 226 157 203 197 69 78 18 200 223 281 283 156 64 161 211 55 28 248 201 176 14 271 285 7 287 282 192 170 290 34 100 74 265]
19. p290	(b)	[37 265 278 253 74 287 54 207 7 238 47 28 84 211 172 248 163 222 111 55 283 18 69 244 197 119 223 242 44 157 83 10 165 8 221 93 128 114 25 4 120 183 91 153 30 193 231 264 154 262 146 24 268 130 79 230 42 35 1 126 186 277 228 110 45 15 169 155 108 19 182 205 213 189 56 123 66 116 124 77 152 273 263 81 41 90 50 240 132 261 76 11 173 103 135 92 70 272 210 82 199 166 95 256 29 195 266 38 164 202 227 286 26 158 112 142 260 140 167 31 218 5 16 252 214 21 43 156 147 99 233 280 180 85 285 17 14 59 131 161 178 271 58 72 175 185 151 52] [181 267 3 184 290 34 282 22 196 194 80 176 144 64 118 187 224 201 115 234 281 125 219 121 203 289 87 101 239 129 136 88 127 57 122 60 73 174 276 13 258 225 109 162 27 62 220 137 94 204 171 68 190 250 216 235 269 159 274 63 177 65 249 2 37 134 23 138 6 46 217 39 179 259 133 270 229 288 104 97 71 20 284 48 212 106 215 98 145 254 49 191 61 107 53 247 251 113 105 257 148 149 232 96 160 75 246 279 188 241 226 255 150 33 139 9 206 209 78 32 102 275 12 40 117 89 168 200 208 67 245 141 243 170 198 192 86 143 100 236 2 51 36]
20. p300	(a)	[236 33 17 214 53 134 131 168 213 120 39 97 238 281 90 263 122 43 79 164 123 186 278 75 280 73 269 180 250 227 125 287 100 36 188 105 50 218 127 41 176 133 212 93 30 129 138 45 26 209 201 222 225 83 191 28 258 27 275 139 19 143 234 251 111 62 152 177 247 92 77 124 223 1 284 285 57 68 65 118 98 167 184 172 86 80 94 130 56 290 154 24 46 51 10 268 153 233 166 135 156 198 173 261 144 21 200 245 260 70 270 34 87 197 262 20 25 11 37 283 148 282 23 108 232 44 55 274 259 103 253 142 267 193 252 102 291 215 35 6 226 219 40 63 22 110 210 171 279 242 228] [220 288 107 16 175 14 296 146 196 206 203 29 95 300 195 273 243 297 239 230 113 106 91 170 187 58 163 159 96 276 101 160 119 81 179 189 47 141 264 211 59 190 185 289 31 145 9 32 240 3 165 147 88 207 182 241 114 257 71 192 169 256 237 161 224 229 13 48 298 128 82 85 221 149 67 116 150 140 162 15 202 231 89 54 64 292 132 49 60 84 66 18 121 157 204 2 255 244 8 38 5 205 109 126 117 42 294 199 248 246 174 7 151 286 69 178 216 235 155 265 61 254 266 4 277 183 217 74 181 271 78 136 112 158 76 208 249 194 72 115 272 137 293 295 299 12 104 99 52]
20. p300	(b)	[236 33 17 214 53 134 131 168 213 120 39 97 238 281 90 263 122 43 79 164 123 186 278 75 280 73 269 180 250 227 125 287 100 36 188 105 50 218 127 41 176 133 212 93 30 9 138 45 26 209 201 222 225 83 191 28 258 27 275 139 19 143 234 251 111 62 152 177 247 92 77 124 223 1 284 285 57 68 65 118 98 167 184 172 86 80 94 130 56 290 154 24 46 51 10 268 153 233 166 135 156 198 173 261 144 21 200 245 260 70 270 34 87 197 262 20 25 11 37 283 148 282 23 108 232 44 55 274 259 103 253 142 267 193 252 102 291 215 35 6 226 219 40 63 22 110 210 171 279 242 228] [220 288 107 16 175 14 296 146 196 206 203 29 95 300 195 273 243 297 239 230 113 106 91 170 187 58 163 159 96 276 101 160 119 81 179 189 47 141 264 211 59 190 185 289 145 31 129 32 240 3 165 147 88 207 182 241 114 257 71 192 169 256 237 161 224 229 13 48 298 128 82 85 221 149 67 116 150 140 162 15 202 231 89 54 64 292 132 49 60 84 66 18 121 157 204 2 255 244 8 38 5 205 109 126 117 42 294 199 248 246 174 7 151 286 69 178 216 235 155 265 61 254 266 4 277 183 217 74 181 271 78 136 112 158 76 208 249 194 72 115 272 137 293 295 299 12 104 99 52]

Similarly, the obtained best orderings of facilities for the 20 instances each of size 60, which are studied in Sect. 4.2 along with their best objective values in Table 3, are shown in Tables 8 and 9.

Finally, the obtained best orderings of facilities for the 20 large-size instances of sizes in the range of [110, 300], which are studied in Sect. 4.3 along with their best objective values in Table 5, are shown in Tables 10, 11 and 12.

As in Tables 2, 3 and 5, the scenarios (a) and (b) in Tables 7, 8, 9, 10, 11, 12 indicate the bCAP scenarios with the best material handling cost and best corridor length, respectively.

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Zahnupriya Kalita
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Dilip Datta
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Gintaras Palubeckis
- 2

1.Department of Mechanical EngineeringTezpur UniversityNapaam, TezpurIndia
2.Faculty of InformaticsKaunas University of TechnologyKaunasLithuania

Bi-objective corridor allocation problem using a permutation-based genetic algorithm hybridized with a local search technique

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