Discrete Set Handling - Differential Evolution: A Topic for Global Permutation-Based Combinatorial Optimization - page 197

Table 7.25. Flowshop scheduling results

GA PSO spv DE spv DE spv + exchange DE DSH DE DSH + EXH

Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ avg std avg std avg std avg std avg std avg std

20x5 3.13 1.86 1.71 1.25 2.25 1.37 0.69 0.64 1.2 0.42 1.07 0.55

20x10 5.42 1.72 3.28 1.19 3.71 1.24 2.01 0.93 2.5 0.41 2.35 0.6

20x20 4.22 1.31 2.84 1.15 3.03 0.98 1.85 0.87 2.52 0.32 1.92 0.53

50x5 1.69 0.79 1.15 0.7 0.88 0.52 0.41 0.37 0.84 0.56 0.5 0.56

50x10 5.61 1.41 4.83 1.16 4.12 1.1 2.41 0.9 5.09 1.02 3.21 1.11

50x20 6.95 1.09 6.68 1.35 5.56 1.22 3.59 0.78 7.05 1.08 4.21 0.85

100x5 0.81 0.39 0.59 0.34 0.44 0.29 0.21 0.21 0.73 0.32 0.32 0.24

100x10 3.12 0.95 3.26 1.04 2.28 0.75 1.41 0.57 3.11 1.2 1.5 1.08

100x20 6.32 0.89 7.19 0.99 6.78 1.12 3.11 0.55 5.98 0.57 4.19 0.82

200x10 2.08 0.45 2.47 0.71 1.88 0.69 1.06 0.35 3.77 1.31 1.781 1.1

200x20 9.82 0.7 4.32 0.68

500x10 6.28 0.39 4.13 0.41

Table 7.26. Comparison results of heuristics without local search

GA PSO spv DE spv DE DSH

Δ Δ Δ Δ Δ Δ Δ Δ avg std avg std avg std avg std

20x5 3.13 1.86 1.71 1.25 2.25 1.37 1.2 0.42

20x10 5.42 1.72 3.28 1.19 3.71 1.24 2.5 0.41

20x20 4.22 1.31 2.84 1.15 3.03 0.98 2.52 0.32

50x5 1.69 0.79 1.15 0.7 0.88 0.52 0.84 0.56

50x10 5.61 1.41 4.83 1.16 4.12 1.1 5.09 1.02

50x20 6.95 1.09 6.68 1.35 5.56 1.22 7.05 1.08

100x5 0.81 0.39 0.59 0.34 0.44 0.29 0.73 0.32

100x10 3.12 0.95 3.26 1.04 2.28 0.75 3.11 1.2

100x20 6.32 0.89 7.19 0.99 6.78 1.12 5.98 0.57

200x10 2.08 0.45 2.47 0.71 1.88 0.69 3.77 1.31

200x20 9.82 0.7

500x10 6.28 0.39

The experimentation of DE DSH + EXH was done on two parts, one with local search
and one without. The comparison result of DE DSH is given in Table 7.26.
DE DSH was able to find the better average values for the problem sets of 20x5, 20x10,
20x20, 50x5 and 100x20. The others sets was dominated by DE spv . A graphical output
for the different sets is given in Fig 7.46. The deviation output is given in Fig 7.47.
The second set is the comparison of the heuristics with local search, namely
DE spv + exchange and DE DSH + EXC as presented in Table 7.27.
As observed DE spv + exchange is the better performing heuristic. The last two columns
gives the analysis comparisons and on average DE DSH + EXH is only 0.42% away from
DE spv + exchange . The graphical displays are given in Figs 7.48 and 7.49.