Information Technology Reference
In-Depth Information
Tabl e 1.
Numerical results Class 1 (50 - 250 products)
sLAHC
LAHC
5000
LAHC
10000
VKV
∗
%
gap
V
LA
V
LA
V
LA
%
gap
%
gap
33 50 9 0
9
1,021
9
1,986
8
33 50 8 0
8
1,019
8
3,226
9
33 50 8 0
8
14,108
8
14,174
8
33 50 8 0
8
12,726
7
1,593
8
33 50 9 0
9
8,660
8
9,695
9
33 100 11 0,237
11
1,039
10
0,289
9
33 100 10 0,703
10
4,104
11
8,940
10
33 100 11 0,971
10
3,434
10
3,800
10
33 100 11 0,94
11
5,886
10
2,736
10
33 100 9 1,232
11
1,613
10
3,429
10
33 150 12 0,95
11
3,316
12
2,506
12
33 150 14 1,928
12
2,079
13
3,000
12
33 150 13 0,771
11
2,785
12
0,268
12
33 150 13 1,659
12
4,632
13
2,575
12
33 150 14 1,864
13
3,845
12
3,706
12
33 200 12 2,795
13
3,783
13
1,863
13
33 200 14 2,227
12
4,410
14
4,093
12
33 200 14 0,778
15
3,689
14
4,943
14
33 200 15 2,792
11
4,352
14
3,603
14
33 200 14 1,177
12
7,648
13
3,199
13
33 250 15 1,915
14
3,238
15
1,954
15
33 250 15 0,958
16
2,300
15
3,874
16
33 250 15 4,846
15
5,872
16
4,669
16
33 250 16 2,963
15
3,171
15
2,818
17
33 250 15 2,647
15
0,641
15
2,462
16
significant impact due to the fact that the late acceptance strategy is only used
for calculating the TSP in the sLAHC as described in Section 3.3. It can be
seen that the calculation with a list length
L
fa
= 10000 compares favorably to
the case with a list length of
L
fa
= 5000. The LAHC achieves better objective
function values for most instances with a longer list length.
In Table 3 we compare our results to results from literature, i.e., with the
(truncated) branch-and-cut approach of Laporte et al. [12]. As they built an
average over five random instances of Class 1 we also calculated the average
results for our algorithms to allow a comparison. Table 3 shows that the sLAHC
algorithm performs significantly better on average than the average results of
[12]. The LAHC implementation performs also better than the approach of [12]
for the instances with more than 50 products.
Figure 3 shows an iterations-to-target chart for the LAHC and the sLAHC.
It can be seen that the LAHC has a higher average starting value than the
sLAHC. For the sLAHC a rapid drop in the average objective function value
can be observed in the first hundred iterations and afterwards the sLAHC curve
