Fig 1.
MDVRP model with 2 depots and 15 customers.
Fig 2.
Flow diagram of the proposed IWD.
Fig 3.
Solution representation scheme with indication of clustering.
Fig 4.
Example illustration of node cluster construction by IWD.
Fig 5.
Illustration of 2-opt operator as applied to SA.
Fig 6.
Flow diagram of the proposed SA based IWD.
Table 1.
The parameter values for IWD procedures.
Table 2.
The parameter values for SA procedures.
Table 3.
Computational results obtained for 33 Cordeau MDVRP benchmark instances for improved IWD, IWA-SA, and IWD-ASA.
Fig 7.
Average running times for IWD, IWD-SA and IWD-ASA on Pr01-Pr06 instances.
Fig 8.
Average running times for IWD, IWD-SA and IWD-ASA on Pr07-Pr10 instances.
Fig 9.
Average running times for IWD, IWD-SA and IWD-ASA on selected instances between P01-P21.
Fig 10.
Gaps between IWD and literature techniques.
Fig 11.
Gaps between IWD-SA and literature techniques.
Fig 12.
Gaps between IWD-ASA and literature techniques.
Table 4.
Comparison of IWD, Cordeau et al. [37], Pisinger and Ropke [39], Vidal et al. [30], and Juan et al.
[10].
Table 5.
Comparison of IWD-SA, Cordeau et al. [37], Pisinger and Ropke [39], Vidal et al. [30], and Juan et al.
[10].
Table 6.
Comparison of IWD -ASA, Cordeau et al. [37], Pisinger and Ropke [39], Vidal et al. [30], and Juan et al.
[10].
Table 7.
Average ranking returned by Friedman’s non-parametric test for the 33 MDVRP instances.
Table 8.
Application of post hoc analysis with Wilcoxon signed-rank tests using IWD, IWD-SA, and IWD-ASA as controlled algorithms.
Fig 13.
Mean rank of the IWD algorithm with other methods.
Fig 14.
Mean rank of the IWD-SA algorithm with other methods.
Fig 15.
Mean rank of the IWD-ASA algorithm with other methods.
Fig 16.
Convergence trends of IWD, IWD-SA, and IWD-ASA for the P01 instance.
Fig 17.
Convergence trends of IWD, IWD-SA, and IWD-ASA for the P04 instance.