Environmental Engineering Reference
In-Depth Information
Table 3 Problem instances
Problem instance
Number of bays
Number of rows
Number of
tiers
1
40
8
5
40
10
5
2
40
10
6
3
4
40
12
5
40
12
6
5
50
10
6
6
7
50
10
7
50
12
6
8
60
12
6
9
Through a pilot experiment, the GA parameters are as follows. The population
size and maximum generation are 50 and 100, respectively. The crossover prob-
ability is 0.9 and uniform crossover is used. Mutation rate is 0.08 and bit-flip
mutation is used. The GA procedure stops when maximum generation (maximum
iteration for GA procedure) is reached or there is no change in the value of objec-
tive function in 20 consecutive iterations. Due to the stochastic results of simula-
tion, we take ten runs for each problem instances. The number of available periods
is 8. The average and standard deviation of each instance are presented in terms
of the value of the objective function (the total emissions over truck idling time).
Table 4 shows the result of these experiments. In each instance, the standard devia-
tion is very small (less than 1 %) compared with the average value, which demon-
strates the good and stable performance of the proposed algorithm.
In order to present the benefits of our study, some experiments, where differ-
ent numbers of periods (the parameter m in the model) are available for picking
up containers, are conducted. We consider two scenarios in which the number
of available periods is 8 and 12. The results of these experiments are shown
in Table 5 where a 48 h time period benchmark is also included. Note that the
8-available-period scenarios are presented in Table 4 . The emission reduc-
tion can be seen by comparing these scenarios with the current situation which
has 48 available periods. It can be seen that the proposed approach can reduce
Table 4 Experiment results of the problem instances
Problem
instance
Average of
objective
value
Standard
deviation
of objective
value
Problem
instance
Average of
objective
value
Standard
deviation of
objective value
140,927
876.79
6
356,993
2,096.50
1
2
182,461
1,219.72
7
356,140
1,816.31
3
243,862
1,585.11
8
436,081
2,136.80
222,552
1,468.84
9
599,750
4,078.30
4
5
293,058
1,729.04
 
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