IEEE Robotics & Automation Magazine - June 2023 - 42

iterations, we stop the algorithm and record its time spent as
CPU time. When the time window size is (,
(, +2tW
tt tW+ and
)
tt
), the compared optimization approaches include
EDD, Seed, MS-VND, and HRA. The experimental results
are shown in Figure 2 where bar graphs represent tardiness. It
can be found that the RAILS outperforms other approaches
in scenario 2.
1,000
2,000
3,000
4,000
5,000
6,000
7,000
MTCR
C
q
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
MTCR
C
q
2,000
4,000
6,000
8,000
10,000
MTCR
C
q
0.6 0.7 0.8 0.6 0.7 0.8
80
45
(e)
EDD
,
tt
).
Seed
HRA
MS-VND
RAILS
FIGURE 2. The tardiness where q 60= 80, and 100; MTCR = 0.6,0.7, and 0.8; m 2 ;= and ~ 2 .= (a)-(c) The tardiness w.r.t. (, + ).
(d)-(f) The tardiness w.r.t. (, +2tW
tt tW
42 IEEE ROBOTICS & AUTOMATION MAGAZINE JUNE 2023
75
0.6 0.7 0.8 0.6 0.7 0.8
100
45
(c)
2,000
4,000
6,000
8,000
10,000
12,000
14,000
16,000
MTCR
C
q
0.6 0.7 0.8 0.6 0.7 0.8
100
45
(f)
75
75
0.6 0.7 0.8 0.6 0.7 0.8
60
45
(a)
1,000
2,000
3,000
4,000
5,000
6,000
MTCR
C
q
0.6 0.7 0.8 0.6 0.7 0.8
60
45
(d)
75
75
When the time window size is (, +3tW
tt
) and (, +4tW
tt
),
the single solution-based heuristic MS-VND and the population-based
heuristics GA1 and GA2 are used as a baseline to
evaluate our proposed approach. Figure 3 gives the experimental
results where the line graphs represent the CPU time and
the bar graphs represent the tardiness of each algorithm. It can
be found that RAILS has the least tardiness, and MS-VND
2,000
4,000
6,000
8,000
10,000
12,000
MTCR
C
q
0.6 0.7 0.8 0.6 0.7 0.8
80
45
(b)
75
Tardiness (min)
Tardiness (min)
Tardiness (min)
Tardiness (min)
Tardiness (min)
Tardiness (min)

IEEE Robotics & Automation Magazine - June 2023

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