In this study, we solve this problem by running Matlab2017b and set the number of particle swarm to 100, inertia weight 0.729, social part acceleration coefficient 2, cognitive part acceleration coefficient 2, and penalty coefficient 10000. The final value of fitness value 135102.3553 million is obtained by 1000 iterations in 81 seconds, and the optimum distribution positions are obtained as A32 (3,19), A36 (12,12), A34 (18,2), A06 (5,10), A16 (21,13), A09 (6,4), A03 (21,21). Figures 3 and Figs. 4 represent the convergence of the specific optimal location distribution algorithm, respectively.
The immunogenetic algorithm was chosen to perform a scenario comparison to show the superiority of the particle swarm algorithm. The immune algorithm has many advantages, such as adaptivity, stochasticity, parallelism, global convergence, population diversity, etc. The total population was selected as 50 in the immunogenetic algorithm, and the value of memory bank capacity was 10, the crossover factor was set to 0.5, and the diversity evaluation factor was 0.95. The same iterations were evaluated 1000 times, and the results of optimal site selection were calculated as A36(12,12), A39(3,19), A14(10,3), A06(5,10), A17(22,15), A08 (20,5), A07 (20,21). The optimal fitness value is 137,307.1613 million yuan, and the run time is 185 seconds. The optimal distribution location and convergence of the algorithm are shown in Figs. 5 and Figs. 6, respectively.
A detailed list of the warehouse freight distribution derived from the two algorithms is presented in Table 2., where each column represents one layout scheme. In the comparison of the optimal location distributions derived by the two algorithms, A06 (5, 10), A20 (3, 19), and A36 (12, 12) are chosen as logistics center points, and each point covers the same subset. Among them, A06 (5, 10) corresponds to five demand points A19, A21, A24, A28, and A31; A20 (3, 19) corresponds to eight demand points A01, A10, A11, A12, A18, A32, A35, and A38. and A36 (12, 12) corresponds to two demand points A25 and A27. Allocation of freight for these three points is 18, 151, and 57 tons respectively. That is to say, these points yield the same freight allocation in the two different algorithms.
However, there are some similar points selected by both algorithms with different demand points covered. In the immune genetic algorithm A07 (20, 21) covers five demand points A02, A03, A05, A23, A33, and A17 covers six demand points A15, A16, A22, A26, A30, A40, and the sum of their demands is 125 and 81 tons, respectively. The logistics center point A03 derived in the particle swarm algorithm covers six demand points A02, A05, A07, A15, A33, A40, and A16 (21, 13) covers four demand points A17, A22, A26, and A30, which correspond to the sum of their demand of 162 and 52 tons, respectively.
On the contrary, the logistics center points A07 (20, 21) and A17 (22, 15) selected in the immune genetic algorithm are not the same as A03 (21, 21) and A16 (21, 13) selected in the particle swarm algorithm. In detail, in the immune genetic algorithm A07 (20, 21) covers five demand points A02, A03, A05, A23, and A33, with the sum of corresponding demands of 125 tons, and A17 covers six demand points A15, A16, A22, A26, A30, A40, with the total of corresponding demands of 81 tons. The logistics center point A03, derived from the particle swarm algorithm, covers six demand points A02, A05, A07, A15, A33, A40, and the sum of corresponding demand is 162 tons, and A16 (21, 13) covers four demand points A17, A22, A26, A30, and the sum of corresponding demand is 52 tons.
Table 2
Distribution of Warehousing Freight Volume Unit: ton
Users
|
Optimum points by IGA
|
Users
|
Optimum points by PSO
|
A06
|
A07
|
A08
|
A14
|
A17
|
A20
|
A36
|
A06
|
A03
|
A20
|
A09
|
A36
|
A34
|
A16
|
A01
|
|
|
|
|
|
23
|
|
A01
|
|
|
23
|
|
|
|
|
A02
|
|
23
|
|
|
|
|
|
A02
|
|
23
|
|
|
|
|
|
A03
|
|
22
|
|
|
|
|
|
A04
|
|
|
|
|
|
23
|
|
A04
|
|
|
|
23
|
|
|
|
A05
|
|
19
|
|
|
|
|
|
A05
|
|
19
|
|
|
|
|
|
A07
|
|
15
|
|
|
|
|
|
A09
|
|
|
|
2
|
|
|
|
A08
|
|
|
|
|
|
16
|
|
A10
|
|
|
|
|
|
25
|
|
A10
|
|
|
25
|
|
|
|
|
A11
|
|
|
|
|
|
14
|
|
A11
|
|
|
14
|
|
|
|
|
A12
|
|
|
|
|
|
4
|
|
A12
|
|
|
4
|
|
|
|
|
A13
|
|
|
|
5
|
|
|
|
A13
|
|
|
|
5
|
|
|
|
A15
|
|
|
|
|
13
|
|
|
A14
|
|
|
|
15
|
|
|
|
A16
|
|
|
|
|
16
|
|
|
A15
|
|
13
|
|
|
|
|
|
A18
|
|
|
|
|
|
14
|
|
A17
|
|
|
|
|
|
|
3
|
A19
|
4
|
|
|
|
|
|
|
A18
|
|
|
14
|
|
|
|
|
A21
|
5
|
|
|
|
|
|
|
A19
|
4
|
|
|
|
|
|
|
A22
|
|
|
|
|
19
|
|
|
A21
|
5
|
|
|
|
|
|
|
A23
|
|
23
|
|
|
|
|
|
A22
|
|
|
|
|
|
|
19
|
A24
|
12
|
|
|
|
|
|
|
A23
|
|
23
|
|
|
|
|
|
A25
|
|
|
|
|
|
|
23
|
A24
|
12
|
|
|
|
|
|
|
A26
|
|
|
|
|
3
|
|
|
A25
|
|
|
|
|
23
|
|
|
A27
|
|
|
|
|
|
|
15
|
A26
|
|
|
|
|
|
|
3
|
A28
|
25
|
|
|
|
|
|
|
A27
|
|
|
|
|
15
|
|
|
A29
|
|
|
|
4
|
|
|
|
A28
|
25
|
|
|
|
|
|
|
A30
|
|
|
|
|
3
|
|
|
A29
|
|
|
|
4
|
|
|
|
A31
|
25
|
|
|
|
|
|
|
A30
|
|
|
|
|
|
|
3
|
A32
|
|
|
|
|
|
24
|
|
A31
|
25
|
|
|
|
|
|
|
A33
|
|
23
|
|
|
|
|
|
A32
|
|
|
24
|
|
|
|
|
A34
|
|
|
6
|
|
|
|
|
A33
|
|
23
|
|
|
|
|
|
A35
|
|
|
|
|
|
24
|
|
A35
|
|
|
24
|
|
|
|
|
A37
|
|
|
8
|
|
|
|
|
A37
|
|
|
|
|
|
|
8
|
A38
|
|
|
|
|
|
15
|
|
A38
|
|
|
15
|
|
|
|
|
A39
|
|
|
|
12
|
|
|
|
A39
|
|
|
|
12
|
|
|
|
A40
|
|
|
|
|
24
|
|
|
A40
|
|
24
|
|
|
|
|
|
Total
|
81
|
125
|
30
|
61
|
81
|
151
|
57
|
Total
|
81
|
162
|
151
|
38
|
57
|
45
|
52
|