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Table 1: Average results of our MA per group of instances.
Group Cost Time Group Cost Time
1 327,85 1,61 9 677,97 4,32
2 370,89 2,80 10 725,66 5,12
3 427,45 1,84 11 683,89 3,84
4 403,49 4,12 12 2232,56 5,66
5 483,41 3,94 13 1593,85 5,78
6 643,60 3,50 14 1308,52 7,14
7 687,91 3,92 15 851,64 4,96
8 848,06 4,10 16 708,10 3,50
Table 2: Average results for set 1 (CVRP) of Iori instances
(groups from 1 to 16).
Groups Best MA
Cost Time Cost Time
1 278,73 0,11 278,73 3,1
2 334,96 0,02 334,96 0,04
3 358,85 0,69 358,85 2,8
4 430,88 0,83 430,88 2,1
5 375,28 0,13 375,28 3,4
6 485,85 0,66 495,85 1.3
7 568,56 0,25 568,56 4
8 568,56 0,19 568,56 3,5
9 607,65 3,97 607,65 4,7
10 535,8 0,59 558,27 4,1
11 505,01 0,8 531,30 4,2
12 610.00 12,6 646,46 3,6
13 2006,3 0,83 2248,21 4,4
14 837,67 0,74 913,18 4,1
15 837,67 1,36 1136,70 2,3
16 698,61 22,8 708,42 4,3
Table 3: Average results for sets from 2 to 5 (2L-CVRP) of
Iori instances (groups from 1 to 16).
Groups Best MA
Cost Time Cost Time
1 284,42 0,90 286,89 1,3
2 339,26 0,10 339,26 1,40
3 376,32 0,50 381,34 2,5
4 435,01 0,20 443,25 1,1
5 379,04 0,10 401,01 5,00
6 497,04 0,40 506,13 4,00
7 691,11 1,40 720,79 3,8
8 678,84 0,80 747,32 3,9
9 612,01 0,60 625,50 1,9
10 675,79 15,10 744,65 5,6
11 705,95 11,30 771,83 5,6
12 611,26 16,90 663,18 4,3
13 2490,62 78,00 2859,10 5,9
14 984,42 79,90 1199,27 7,1
15 1144,69 257,70 1275,25 7,7
16 699,79 6,00 709,75 5,1
tained by Duhamel et al. (Duhamel et al., 2011). For
this purpose, a restriction on the number of vehicles
is added. We consider non-sequential packing with-
out items rotation. In average, our MA has a distance
of 6% from the best known solutions.
In Table 2, the results on the first group of in-
stances are reported. this group corresponds to a pure
transportation problem. Our algorithm finds the best
known solutions for 8 out of 16 instances. The com-
putation time of our MA does not exceed 5 seconds,
while it may be much higher for some results obtained
by Duhamel et al. (Duhamel et al., 2011).
Table 3 gives the average results for sets from 2 to
5. Our algorithm finds the best known average only
for set 2. For the other sets, our results are very close
to the best known results in the literature, particularly
for instances of the first groups (groups 1 to 6). For
8 groups out of 16, the gap is less than 4%. For 7
other groups the gap ranges from 6% to 14%. Only
the gap of the group 14 is over 20%. The average gap
obtained for all studied instances to the best known
solutions is about 6.6%.
5 CONCLUSIONS
This paper presents a first study for the two-
dimensional loading with partial conflicts capacitated
vehicle routing problem. A memetic algorithm with
population management is designed to solve routing
part, while a heuristics is used to solve packing prob-
lem. The first results are promising. Further results
would be given in the conference.
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