Distributed Energy-Efficient Assembly Scheduling Problem with Transportation Capacity
Abstract
:1. Introduction
2. Problem Description
- All machines are available at time 0.
- Each machine can fabricate, transport or assemble at most one job at a time.
- Each job can be fabricated, transported or assembled at most one machine at a time.
- is used to move components of at most one job at a time.
3. Introduction to ICA
- (1)
- Initialization. Randomly produce an initial population P and calculate the cost of each solution in P.
- (2)
- Initial empires. Choose solutions with the smallest cost as imperialists, calculate the normalized cost and the number of colonies and randomly allocate colonies for each imperialist k.
- (3)
- Assimilation. In each empire, each colony moves toward its imperialist and is replaced with the newly generated solution if possible.
- (4)
- Revolution. Perform revolution according to revolution probability .
- (5)
- Exchange. In each empire, compare each colony with its imperialist and replace the imperialist with the colony with a smaller cost than its imperialist.
- (6)
- Imperialist competition. Calculate total cost , normalized total cost and power for each empire k, construct the following vector , decide an empire g with the biggest and allocate the weakest colony of the weakest empire into empire g.
- (7)
- If the termination condition is not met, go to (3); otherwise, stop the search.Where is a random number following uniform distribution in [0,1].
4. AICA for DEASP with Three Stages
4.1. Coding and Decoding
4.2. Initialization and Initial Empires
4.3. Adaptive Assimilation
- (1)
- Let , decide the weakest empire g with the smallest .
- (2)
- For each colony , if random number , then if and rank value of its imperialist is greater than 1, then randomly select an imperialist l with rank value of 1; otherwise, directly use imperialist k; if , then execute order crossover (OX) between and the chosen imperialist; otherwise, implement a two-point crossover between and the selected imperialist, a new solution z is obtained, if z is not dominated by , z substitutes for and update external archive .
- (3)
- , if , go to step (2); otherwise, stop the assimilation.Where is obtained by sorting all solutions in P in the ascending order of makespan and is computed by sorting all solutions in the ascending order of . Archive is used to store non-dominated solutions produced by AICA.
4.4. Adaptive Revolution
- (1)
- Decide factory with biggest completion time and factory with biggest energy consumption
- (2)
- Let , repeat the following steps until :
4.5. Algorithm Description
- (1)
- Initialization. Produce initial population P by using heuristics and random way.
- (2)
- Sort all solutions in the ascending order of makespan and , respectively, and obtain , , and for each .
- (3)
- Execute adaptive assimilation.
- (4)
- Perform adaptive revolution and exchange imperialist and colony if possible in each empire.
- (5)
- Implement imperialist competition.
- (6)
- If the termination condition is not met, go to (2); otherwise, stop the search.
5. Computational Experiments
5.1. Instances, Comparative Algorithms and Metrics
5.2. Parameters Settings
5.3. Results and Discussions
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
DEASP | distributed energy-efficient assembly scheduling problem |
ICA | imperialist competitive algorithm |
AICA | adaptive imperialist competitive algorithm |
ASP | Assembly scheduling problem |
DASP | distributed assembly scheduling problem |
TS | tabu search |
PSO | particle swarm optimization |
SDST | sequence-dependent setup time |
SA | simulated annealing |
GA | genetic algorithm |
DEASP | distributed energy-efficient assembly scheduling problem |
n | the total number of jobs |
F | the total number of factories |
m | the total number of machines at the first stage in each factory |
h | the total number of transportation machines in each factory |
d | the total number of speeds for each machine |
the i-th job in set | |
the k-th dedicated parallel machine in the f-th factory | |
the l-th transportation machine in the f-th factory | |
the assembly machine in the f-th factory | |
Q | the capacity of transportation machine |
V | the set of speeds for each machine |
the energy consumption of per unit time in working mode | |
the energy consumption of per unit time in working mode | |
the energy consumption of per unit idle time | |
the energy consumption of per unit idle time | |
the energy consumption for a back and forth trip of a transportation machine | |
the time for a back and forth trip of a transportation machine | |
the k-th component of job | |
the weight of | |
processing time on machine for | |
assembly time on machine for | |
setup time for fabrication of | |
setup time for assembly of | |
completion time of job | |
completion time of all jobs | |
total energy consumption at fabrication stage | |
total energy consumption at transportation stage | |
total energy consumption at assembly stage | |
the total number of back and forth trips of | |
is 1 if works at speed at time t and 0 otherwise | |
is 1 if is idle at time t and 0 otherwise | |
is 1 if works at speed at time t and 0 otherwise | |
is 1 if is idle at time t and 0 otherwise | |
P | population |
the number of imperialists | |
the number of colonies for imperialist k | |
the normalized cost for imperialist k | |
the total cost for empire k | |
the normalized total cost for empire k | |
the power for empire k | |
random number | |
the number of all allocated jobs in factory f | |
the g-th job in factory f | |
the chosen speed of used to fabricate the k-th component of | |
the speed of assembly machine for | |
the earliest available time of transportation machine for | |
the i-th solution in population P | |
the rank value of | |
the crowding distance of | |
the set of all imperialists | |
the number of colonies | |
power of imperialist k | |
the set of all colonies possessed by imperialist k | |
the assimilation probability of | |
OX | order crossover |
sort results in ascending order of makespan for | |
sort results in ascending order of TEC for | |
archive | |
the factory with biggest completion time | |
the factory with biggest energy consumption | |
MOWSA | multi-objective whale swarm algorithm |
INSGA-II | improved non-dominated sorting genetic algorithm-II |
CMA | competitive memetic algorithm |
the non-dominated solution set in the union of non-dominated sets of all algorithms | |
the Euclid distance in the objective space between and its nearest solution |
Appendix A
Instance | (A,C) | (C,A) | (A,M) | (M,A) | (A,N) | (N,A) | (A,I) | (I,A) |
---|---|---|---|---|---|---|---|---|
2 × 8 × 2 | 0.615 | 0.147 | 0.345 | 0.329 | 0.827 | 0.154 | 0.850 | 0.161 |
2 × 8 × 3 | 0.891 | 0.057 | 0.366 | 0.213 | 0.938 | 0.036 | 0.743 | 0.258 |
2 × 8 × 4 | 0.859 | 0.052 | 0.425 | 0.165 | 1.000 | 0.000 | 0.656 | 0.294 |
2 × 10 × 2 | 0.581 | 0.145 | 0.049 | 0.459 | 0.902 | 0.047 | 0.539 | 0.401 |
2 × 10 × 3 | 0.566 | 0.182 | 0.320 | 0.286 | 0.794 | 0.143 | 0.626 | 0.355 |
2 × 10 × 4 | 0.585 | 0.197 | 0.453 | 0.071 | 0.916 | 0.059 | 0.593 | 0.283 |
2 × 12 × 2 | 0.654 | 0.210 | 0.479 | 0.107 | 0.572 | 0.239 | 0.534 | 0.403 |
2 × 12 × 3 | 0.660 | 0.095 | 0.073 | 0.439 | 0.897 | 0.061 | 0.502 | 0.481 |
2 × 12 × 4 | 0.500 | 0.230 | 0.090 | 0.540 | 0.930 | 0.010 | 0.667 | 0.275 |
3 × 8 × 2 | 0.451 | 0.265 | 0.375 | 0.197 | 0.955 | 0.029 | 0.623 | 0.382 |
3 × 8 × 3 | 0.738 | 0.176 | 0.419 | 0.304 | 1.000 | 0.000 | 0.824 | 0.287 |
3 × 8 × 4 | 0.974 | 0.034 | 0.833 | 0.162 | 1.000 | 0.007 | 0.792 | 0.216 |
3 × 10 × 2 | 0.794 | 0.138 | 0.349 | 0.344 | 1.000 | 0.000 | 0.873 | 0.094 |
3 × 10 × 3 | 0.986 | 0.032 | 0.317 | 0.372 | 0.987 | 0.000 | 0.869 | 0.229 |
3 × 10 × 4 | 0.753 | 0.106 | 0.565 | 0.245 | 1.000 | 0.005 | 0.734 | 0.191 |
3 × 12 × 2 | 0.590 | 0.102 | 0.247 | 0.404 | 0.877 | 0.060 | 0.702 | 0.235 |
3 × 12 × 3 | 0.526 | 0.142 | 0.309 | 0.278 | 1.000 | 0.006 | 0.547 | 0.341 |
3 × 12 × 4 | 0.753 | 0.103 | 0.391 | 0.210 | 1.000 | 0.004 | 0.695 | 0.262 |
4 × 8 × 2 | 0.544 | 0.270 | 0.348 | 0.327 | 0.945 | 0.028 | 0.714 | 0.312 |
4 × 8 × 3 | 0.983 | 0.051 | 0.434 | 0.182 | 1.000 | 0.010 | 0.813 | 0.253 |
4 × 8 × 4 | 0.843 | 0.148 | 0.352 | 0.344 | 1.000 | 0.041 | 0.725 | 0.344 |
4 × 10 × 2 | 0.464 | 0.215 | 0.339 | 0.331 | 0.986 | 0.015 | 0.556 | 0.485 |
4 × 10 × 3 | 0.812 | 0.087 | 0.526 | 0.150 | 0.836 | 0.044 | 0.729 | 0.300 |
4 × 10 × 4 | 0.917 | 0.071 | 0.500 | 0.264 | 1.000 | 0.007 | 0.632 | 0.336 |
4 × 12 × 2 | 0.606 | 0.124 | 0.187 | 0.352 | 0.947 | 0.026 | 0.723 | 0.202 |
4 × 12 × 3 | 0.464 | 0.145 | 0.382 | 0.295 | 1.000 | 0.000 | 0.495 | 0.430 |
4 × 12 × 4 | 0.706 | 0.102 | 0.514 | 0.194 | 1.000 | 0.000 | 0.571 | 0.369 |
Instance | A | C | M | N | I | Instance | A | C | M | N | I |
---|---|---|---|---|---|---|---|---|---|---|---|
2 × 8 × 2 | 0.517 | 0.000 | 0.367 | 0.041 | 0.075 | 3 × 10 × 4 | 0.721 | 0.000 | 0.168 | 0.000 | 0.112 |
2 × 8 × 3 | 0.604 | 0.000 | 0.359 | 0.000 | 0.036 | 3 × 12 × 2 | 0.443 | 0.000 | 0.389 | 0.000 | 0.168 |
2 × 8 × 4 | 0.497 | 0.000 | 0.420 | 0.000 | 0.083 | 3 × 12 × 3 | 0.521 | 0.000 | 0.318 | 0.000 | 0.161 |
2 × 10 × 2 | 0.225 | 0.000 | 0.519 | 0.000 | 0.257 | 3 × 12 × 4 | 0.705 | 0.000 | 0.172 | 0.000 | 0.123 |
2 × 10 × 3 | 0.520 | 0.000 | 0.309 | 0.046 | 0.126 | 4 × 8 × 2 | 0.641 | 0.023 | 0.250 | 0.000 | 0.086 |
2 × 10 × 4 | 0.444 | 0.047 | 0.325 | 0.026 | 0.158 | 4 × 8 × 3 | 0.520 | 0.000 | 0.439 | 0.000 | 0.041 |
2 × 12 × 2 | 0.329 | 0.008 | 0.386 | 0.041 | 0.236 | 4 × 8 × 4 | 0.492 | 0.000 | 0.344 | 0.000 | 0.164 |
2 × 12 × 3 | 0.290 | 0.100 | 0.338 | 0.010 | 0.262 | 4 × 10 × 2 | 0.385 | 0.000 | 0.333 | 0.009 | 0.274 |
2 × 12 × 4 | 0.451 | 0.013 | 0.405 | 0.008 | 0.122 | 4 × 10 × 3 | 0.675 | 0.006 | 0.135 | 0.055 | 0.129 |
3 × 8 × 2 | 0.468 | 0.000 | 0.377 | 0.000 | 0.156 | 4 × 10 × 4 | 0.654 | 0.008 | 0.211 | 0.000 | 0.128 |
3 × 8 × 3 | 0.603 | 0.017 | 0.314 | 0.000 | 0.066 | 4 × 12 × 2 | 0.524 | 0.042 | 0.296 | 0.011 | 0.127 |
3 × 8 × 4 | 0.704 | 0.000 | 0.173 | 0.000 | 0.123 | 4 × 12 × 3 | 0.505 | 0.011 | 0.242 | 0.000 | 0.242 |
3 × 10 × 2 | 0.689 | 0.000 | 0.277 | 0.000 | 0.034 | 4 × 12 × 4 | 0.605 | 0.005 | 0.174 | 0.000 | 0.215 |
3 × 10 × 3 | 0.556 | 0.000 | 0.350 | 0.006 | 0.087 |
Instance | A | C | M | N | I | Instance | A | C | M | N | I |
---|---|---|---|---|---|---|---|---|---|---|---|
2 × 8 × 2 | 4.120 | 5.756 | 5.587 | 5.999 | 4.967 | 3 × 10 × 4 | 5.493 | 6.068 | 6.826 | 5.881 | 5.929 |
2 × 8 × 3 | 4.082 | 6.263 | 5.519 | 6.226 | 4.466 | 3 × 12 × 2 | 5.355 | 6.516 | 6.073 | 6.095 | 5.995 |
2 × 8 × 4 | 5.139 | 6.650 | 6.861 | 5.128 | 5.164 | 3 × 12 × 3 | 5.857 | 8.270 | 6.836 | 7.123 | 5.721 |
2 × 10 × 2 | 4.808 | 5.934 | 5.920 | 5.241 | 5.056 | 3 × 12 × 4 | 5.432 | 8.058 | 7.382 | 6.498 | 5.520 |
2 × 10 × 3 | 4.930 | 5.457 | 6.427 | 5.849 | 5.392 | 4 × 8 × 2 | 4.445 | 6.412 | 7.836 | 7.399 | 4.935 |
2 × 10 × 4 | 4.886 | 6.957 | 6.071 | 6.078 | 5.210 | 4 × 8 × 3 | 5.911 | 7.121 | 6.335 | 7.736 | 6.329 |
2 × 12 × 2 | 4.827 | 5.963 | 5.308 | 5.278 | 4.467 | 4 × 8 × 4 | 6.267 | 7.260 | 8.231 | 6.272 | 6.602 |
2 × 12 × 3 | 5.075 | 6.657 | 7.564 | 5.835 | 5.850 | 4 × 10 × 2 | 4.312 | 5.652 | 6.570 | 5.739 | 5.224 |
2 × 12 × 4 | 4.929 | 5.313 | 6.860 | 6.301 | 5.069 | 4 × 10 × 3 | 5.286 | 6.124 | 7.761 | 9.027 | 5.651 |
3 × 8 × 2 | 4.458 | 6.127 | 5.661 | 5.736 | 4.388 | 4 × 10 × 4 | 5.084 | 7.875 | 9.246 | 7.138 | 5.886 |
3 × 8 × 3 | 5.373 | 7.853 | 8.213 | 7.627 | 5.798 | 4 × 12 × 2 | 5.258 | 6.336 | 5.996 | 7.926 | 5.642 |
3 × 8 × 4 | 5.722 | 7.255 | 6.784 | 8.571 | 6.434 | 4 × 12 × 3 | 5.380 | 7.949 | 7.429 | 7.629 | 5.625 |
3 × 10 × 2 | 4.421 | 6.282 | 5.901 | 5.998 | 5.142 | 4 × 12 × 4 | 5.502 | 7.244 | 8.106 | 6.810 | 6.007 |
3 × 10 × 3 | 4.994 | 7.129 | 7.022 | 6.815 | 5.245 |
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i | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
---|---|---|---|---|---|---|---|---|
61.56 | 58.61 | 23.30 | 56.36 | 64.58 | 37.37 | 22.74 | 90.20 | |
58.90 | 49.61 | 50.06 | 84.99 | 77.50 | 69.30 | 56.73 | 75.53 | |
21.51 | 83.73 | 84.69 | 58.06 | 55.76 | 86.40 | 61.14 | 98.92 | |
47.17 | 41.24 | 70.47 | 99.91 | 90.04 | 62.05 | 40.12 | 50.00 | |
9.81 | 7.66 | 9.02 | 6.23 | 5.18 | 8.32 | 6.94 | 8.29 | |
7.75 | 7.80 | 8.92 | 6.35 | 6.41 | 6.57 | 8.71 | 5.16 | |
6.01 | 7.93 | 6.73 | 9.50 | 5.48 | 8.89 | 8.06 | 9.34 | |
6.45 | 8.21 | 6.95 | 9.30 | 6.66 | 5.19 | 7.01 | 5.63 | |
72.38 | 43.00 | 49.39 | 93.68 | 87.92 | 48.20 | 28.69 | 63.05 | |
6.57 | 7.39 | 9.61 | 6.88 | 7.35 | 5.12 | 7.07 | 9.29 | |
19.48 | 21.35 | 46.09 | 21.80 | 27.48 | 35.27 | 24.34 | 39.23 | |
35.86 | 45.30 | 10.27 | 27.66 | 11.57 | 32.76 | 38.75 | 49.96 | |
45.36 | 43.14 | 20.21 | 43.95 | 41.37 | 30.99 | 28.85 | 15.00 | |
32.00 | 37.84 | 43.11 | 27.07 | 16.10 | 34.63 | 18.45 | 23.44 |
Parameters | Factor Level | |||
---|---|---|---|---|
1 | 2 | 3 | 4 | |
N | 60 | 80 | 100 | 120 |
6 | 7 | 8 | 9 | |
8 | 9 | 10 | 11 | |
2 | 3 | 4 | 5 |
Experiment Number | Factors | ||||
---|---|---|---|---|---|
1 | 1 | 1 | 1 | 1 | 0.04092 |
2 | 1 | 2 | 2 | 2 | 0.06138 |
3 | 1 | 3 | 3 | 3 | 0.15857 |
4 | 1 | 4 | 4 | 4 | 0.01023 |
5 | 2 | 1 | 2 | 3 | 0.08696 |
6 | 2 | 2 | 1 | 4 | 0.02788 |
7 | 2 | 3 | 4 | 1 | 0.02558 |
8 | 2 | 4 | 3 | 2 | 0.03069 |
9 | 3 | 1 | 3 | 4 | 0.10627 |
10 | 3 | 2 | 4 | 3 | 0.06790 |
11 | 3 | 3 | 1 | 2 | 0.14974 |
12 | 3 | 4 | 2 | 1 | 0.06035 |
13 | 4 | 1 | 4 | 2 | 0.02035 |
14 | 4 | 2 | 3 | 1 | 0.07046 |
15 | 4 | 3 | 2 | 4 | 0.03069 |
16 | 4 | 4 | 1 | 3 | 0.05205 |
Level | N | |||
---|---|---|---|---|
1 | 0.06778 | 0.06362 | 0.06765 | 0.04933 |
2 | 0.04277 | 0.05691 | 0.05984 | 0.06554 |
3 | 0.09606 | 0.09114 | 0.0915 | 0.09137 |
4 | 0.04339 | 0.03833 | 0.03101 | 0.04377 |
Delta | 0.05329 | 0.05282 | 0.06048 | 0.0476 |
Rank | 2 | 3 | 1 | 4 |
Instance | (A,C) | (C,A) | (A,M) | (M,A) | (A,N) | (N,A) | (A,I) | (I,A) |
---|---|---|---|---|---|---|---|---|
2 × 20 × 2 | 0.553 | 0.171 | 0.484 | 0.034 | 0.391 | 0.270 | 0.505 | 0.398 |
2 × 20 × 4 | 0.466 | 0.236 | 0.431 | 0.227 | 0.741 | 0.064 | 0.699 | 0.283 |
2 × 20 × 6 | 0.689 | 0.114 | 0.398 | 0.093 | 0.791 | 0.040 | 0.495 | 0.414 |
2 × 20 × 8 | 0.792 | 0.044 | 0.422 | 0.343 | 0.825 | 0.000 | 0.599 | 0.291 |
2 × 50 × 2 | 0.282 | 0.663 | 0.408 | 0.029 | 0.981 | 0.000 | 0.764 | 0.153 |
2 × 50 × 4 | 0.874 | 0.025 | 0.310 | 0.060 | 1.000 | 0.000 | 0.739 | 0.209 |
2 × 50 × 6 | 0.895 | 0.041 | 0.311 | 0.140 | 0.898 | 0.000 | 0.720 | 0.198 |
2 × 50 × 8 | 0.804 | 0.052 | 0.323 | 0.081 | 0.694 | 0.000 | 0.828 | 0.110 |
2 × 100 × 2 | 0.844 | 0.073 | 0.305 | 0.003 | 0.970 | 0.000 | 0.774 | 0.145 |
2 × 100 × 4 | 0.635 | 0.113 | 0.317 | 0.020 | 0.886 | 0.000 | 0.822 | 0.082 |
2 × 100 × 6 | 0.788 | 0.057 | 0.211 | 0.034 | 0.878 | 0.000 | 0.757 | 0.183 |
2 × 100 × 8 | 0.675 | 0.069 | 0.464 | 0.107 | 0.760 | 0.000 | 0.743 | 0.198 |
2 × 200 × 2 | 0.540 | 0.095 | 0.198 | 0.086 | 1.000 | 0.000 | 0.795 | 0.155 |
2 × 200 × 4 | 0.700 | 0.066 | 0.210 | 0.036 | 0.933 | 0.000 | 0.783 | 0.137 |
2 × 200 × 6 | 0.578 | 0.074 | 0.192 | 0.123 | 0.861 | 0.000 | 0.851 | 0.136 |
2 × 200 × 8 | 0.570 | 0.054 | 0.308 | 0.050 | 0.882 | 0.000 | 0.824 | 0.119 |
2 × 500 × 2 | 0.523 | 0.061 | 0.125 | 0.000 | 0.970 | 0.000 | 0.846 | 0.089 |
2 × 500 × 4 | 0.364 | 0.069 | 0.150 | 0.053 | 0.889 | 0.000 | 0.787 | 0.134 |
2 × 500 × 6 | 0.339 | 0.054 | 0.684 | 0.035 | 0.854 | 0.000 | 0.672 | 0.219 |
2 × 500 × 8 | 0.286 | 0.036 | 0.913 | 0.020 | 0.760 | 0.000 | 0.753 | 0.175 |
3 × 20 × 2 | 0.645 | 0.156 | 0.587 | 0.067 | 0.842 | 0.090 | 0.480 | 0.538 |
3 × 20 × 4 | 0.789 | 0.033 | 0.470 | 0.262 | 0.931 | 0.006 | 0.608 | 0.241 |
3 × 20 × 6 | 0.868 | 0.052 | 0.375 | 0.374 | 0.974 | 0.000 | 0.474 | 0.407 |
3 × 20 × 8 | 0.894 | 0.028 | 0.957 | 0.039 | 0.720 | 0.039 | 0.533 | 0.391 |
3 × 50 × 2 | 0.434 | 0.446 | 0.433 | 0.021 | 0.948 | 0.000 | 0.508 | 0.416 |
3 × 50 × 4 | 0.882 | 0.027 | 0.387 | 0.077 | 0.859 | 0.000 | 0.651 | 0.265 |
3 × 50 × 6 | 0.773 | 0.078 | 0.352 | 0.074 | 0.718 | 0.000 | 0.829 | 0.156 |
3 × 50 × 8 | 0.648 | 0.080 | 0.508 | 0.178 | 0.622 | 0.002 | 0.689 | 0.238 |
3 × 100 × 2 | 0.827 | 0.064 | 0.024 | 0.414 | 1.000 | 0.000 | 0.735 | 0.203 |
3 × 100 × 4 | 0.833 | 0.047 | 0.304 | 0.252 | 0.780 | 0.000 | 0.674 | 0.231 |
3 × 100 × 6 | 0.838 | 0.053 | 0.093 | 0.155 | 0.686 | 0.000 | 0.616 | 0.220 |
3 × 100 × 8 | 0.799 | 0.040 | 0.172 | 0.147 | 0.780 | 0.000 | 0.740 | 0.138 |
3 × 200 × 2 | 0.398 | 0.266 | 0.016 | 0.254 | 0.917 | 0.000 | 0.717 | 0.163 |
3 × 200 × 4 | 0.622 | 0.048 | 0.134 | 0.155 | 0.939 | 0.000 | 0.869 | 0.074 |
3 × 200 × 6 | 0.500 | 0.081 | 0.212 | 0.142 | 0.529 | 0.000 | 0.790 | 0.146 |
3 × 200 × 8 | 0.543 | 0.048 | 0.366 | 0.075 | 0.559 | 0.000 | 0.803 | 0.200 |
3 × 500 × 2 | 0.573 | 0.058 | 0.026 | 0.171 | 0.830 | 0.003 | 0.874 | 0.071 |
3 × 500 × 4 | 0.360 | 0.061 | 0.097 | 0.102 | 0.863 | 0.000 | 0.746 | 0.130 |
3 × 500 × 6 | 0.460 | 0.042 | 0.452 | 0.049 | 0.640 | 0.000 | 0.866 | 0.086 |
3 × 500 × 8 | 0.449 | 0.025 | 0.983 | 0.000 | 0.667 | 0.000 | 0.812 | 0.083 |
4 × 20 × 2 | 0.495 | 0.201 | 0.536 | 0.095 | 0.914 | 0.067 | 0.621 | 0.273 |
4 × 20 × 4 | 0.989 | 0.006 | 0.500 | 0.208 | 1.000 | 0.000 | 0.603 | 0.247 |
4 × 20 × 6 | 0.742 | 0.054 | 0.723 | 0.092 | 0.920 | 0.017 | 0.871 | 0.061 |
4 × 20 × 8 | 0.769 | 0.113 | 0.677 | 0.258 | 0.918 | 0.008 | 0.481 | 0.477 |
4 × 50 × 2 | 0.750 | 0.157 | 0.448 | 0.030 | 0.614 | 0.039 | 0.583 | 0.341 |
4 × 50 × 4 | 0.852 | 0.047 | 0.388 | 0.290 | 0.899 | 0.000 | 0.769 | 0.120 |
4 × 50 × 6 | 0.798 | 0.059 | 0.445 | 0.052 | 0.809 | 0.000 | 0.583 | 0.290 |
4 × 50 × 8 | 0.785 | 0.045 | 0.504 | 0.196 | 0.618 | 0.000 | 0.450 | 0.441 |
4 × 100 × 2 | 0.839 | 0.127 | 0.331 | 0.027 | 0.859 | 0.011 | 0.745 | 0.192 |
4 × 100 × 4 | 0.824 | 0.065 | 0.362 | 0.061 | 0.804 | 0.000 | 0.717 | 0.203 |
Instance | (A,C) | (C,A) | (A,M) | (M,A) | (A,N) | (N,A) | (A,I) | (I,A) |
---|---|---|---|---|---|---|---|---|
4 × 100 × 6 | 0.872 | 0.064 | 0.362 | 0.178 | 0.733 | 0.000 | 0.765 | 0.135 |
4 × 100 × 8 | 0.732 | 0.072 | 0.433 | 0.133 | 0.514 | 0.000 | 0.688 | 0.231 |
4 × 200 × 2 | 0.674 | 0.130 | 0.039 | 0.300 | 0.520 | 0.035 | 0.732 | 0.171 |
4 × 200 × 4 | 0.734 | 0.040 | 0.188 | 0.184 | 0.859 | 0.000 | 0.738 | 0.152 |
4 × 200 × 6 | 0.567 | 0.089 | 0.348 | 0.149 | 0.833 | 0.000 | 0.678 | 0.232 |
4 × 200 × 8 | 0.327 | 0.112 | 0.567 | 0.075 | 0.471 | 0.011 | 0.805 | 0.146 |
4 × 500 × 2 | 0.691 | 0.018 | 0.020 | 0.136 | 0.874 | 0.000 | 0.761 | 0.141 |
4 × 500 × 4 | 0.553 | 0.030 | 0.217 | 0.144 | 0.717 | 0.000 | 0.872 | 0.066 |
4 × 500 × 6 | 0.360 | 0.057 | 0.351 | 0.044 | 0.774 | 0.000 | 0.841 | 0.102 |
4 × 500 × 8 | 0.543 | 0.034 | 0.945 | 0.000 | 0.655 | 0.000 | 0.834 | 0.099 |
5 × 20 × 2 | 0.506 | 0.265 | 0.452 | 0.146 | 0.896 | 0.030 | 0.619 | 0.413 |
5 × 20 × 4 | 0.927 | 0.032 | 0.466 | 0.209 | 1.000 | 0.000 | 0.605 | 0.342 |
5 × 20 × 6 | 0.939 | 0.016 | 0.652 | 0.123 | 0.944 | 0.006 | 0.754 | 0.205 |
5 × 20 × 8 | 0.716 | 0.062 | 0.754 | 0.084 | 0.766 | 0.007 | 0.730 | 0.193 |
5 × 50 × 2 | 0.952 | 0.015 | 0.553 | 0.045 | 0.898 | 0.020 | 0.424 | 0.454 |
5 × 50 × 4 | 0.806 | 0.048 | 0.352 | 0.238 | 0.942 | 0.000 | 0.568 | 0.335 |
5 × 50 × 6 | 0.745 | 0.071 | 0.514 | 0.238 | 0.618 | 0.000 | 0.444 | 0.498 |
5 × 50 × 8 | 0.680 | 0.113 | 0.730 | 0.108 | 0.791 | 0.000 | 0.556 | 0.298 |
5 × 100 × 2 | 0.800 | 0.117 | 0.412 | 0.097 | 0.880 | 0.025 | 0.619 | 0.262 |
5 × 100 × 4 | 0.840 | 0.049 | 0.289 | 0.288 | 0.828 | 0.000 | 0.750 | 0.189 |
5 × 100 × 6 | 0.835 | 0.067 | 0.384 | 0.133 | 0.863 | 0.000 | 0.696 | 0.242 |
5 × 100 × 8 | 0.690 | 0.102 | 0.339 | 0.151 | 0.656 | 0.000 | 0.770 | 0.246 |
5 × 200 × 2 | 0.770 | 0.074 | 0.113 | 0.308 | 0.786 | 0.018 | 0.674 | 0.226 |
5 × 200 × 4 | 0.701 | 0.057 | 0.146 | 0.241 | 0.529 | 0.000 | 0.632 | 0.211 |
5 × 200 × 6 | 0.791 | 0.034 | 0.516 | 0.064 | 0.787 | 0.000 | 0.772 | 0.141 |
5 × 200 × 8 | 0.436 | 0.052 | 0.809 | 0.040 | 0.688 | 0.000 | 0.699 | 0.173 |
5 × 500 × 2 | 0.589 | 0.027 | 0.059 | 0.163 | 0.961 | 0.000 | 0.751 | 0.185 |
5 × 500 × 4 | 0.575 | 0.027 | 0.456 | 0.117 | 0.773 | 0.000 | 0.834 | 0.092 |
5 × 500 × 6 | 0.376 | 0.059 | 0.741 | 0.033 | 0.739 | 0.000 | 0.715 | 0.174 |
5 × 500 × 8 | 0.402 | 0.022 | 0.951 | 0.010 | 0.536 | 0.000 | 0.683 | 0.213 |
6 × 20 × 2 | 0.610 | 0.132 | 0.247 | 0.410 | 1.000 | 0.005 | 0.604 | 0.327 |
6 × 20 × 4 | 1.000 | 0.000 | 0.500 | 0.240 | 0.962 | 0.000 | 0.667 | 0.265 |
6 × 20 × 6 | 0.841 | 0.098 | 0.672 | 0.215 | 0.846 | 0.014 | 0.658 | 0.285 |
6 × 20 × 8 | 1.000 | 0.000 | 0.929 | 0.052 | 0.787 | 0.000 | 0.489 | 0.477 |
6 × 50 × 2 | 0.738 | 0.101 | 0.039 | 0.600 | 0.773 | 0.046 | 0.519 | 0.330 |
6 × 50 × 4 | 0.714 | 0.063 | 0.472 | 0.294 | 0.854 | 0.000 | 0.656 | 0.256 |
6 × 50 × 6 | 0.913 | 0.018 | 0.486 | 0.178 | 0.651 | 0.000 | 0.654 | 0.284 |
6 × 50 × 8 | 0.775 | 0.036 | 0.589 | 0.202 | 0.675 | 0.000 | 0.400 | 0.465 |
6 × 100 × 2 | 0.870 | 0.053 | 0.403 | 0.036 | 0.871 | 0.003 | 0.719 | 0.198 |
6 × 100 × 4 | 0.895 | 0.031 | 0.405 | 0.104 | 0.942 | 0.000 | 0.726 | 0.149 |
6 × 100 × 6 | 0.742 | 0.092 | 0.674 | 0.093 | 0.848 | 0.000 | 0.658 | 0.249 |
6 × 100 × 8 | 0.752 | 0.060 | 0.457 | 0.147 | 0.679 | 0.000 | 0.752 | 0.126 |
6 × 200 × 2 | 0.824 | 0.078 | 0.080 | 0.287 | 0.967 | 0.000 | 0.703 | 0.209 |
6 × 200 × 4 | 0.778 | 0.065 | 0.294 | 0.194 | 0.851 | 0.000 | 0.807 | 0.119 |
6 × 200 × 6 | 0.720 | 0.033 | 0.454 | 0.137 | 0.689 | 0.000 | 0.762 | 0.140 |
6 × 200 × 8 | 0.686 | 0.061 | 0.748 | 0.086 | 0.603 | 0.000 | 0.591 | 0.316 |
6 × 500 × 2 | 0.646 | 0.032 | 0.133 | 0.175 | 0.833 | 0.007 | 0.800 | 0.085 |
6 × 500 × 4 | 0.568 | 0.034 | 0.174 | 0.124 | 0.556 | 0.001 | 0.790 | 0.130 |
6 × 500 × 6 | 0.459 | 0.034 | 0.774 | 0.018 | 0.696 | 0.000 | 0.845 | 0.113 |
6 × 500 × 8 | 0.243 | 0.052 | 0.987 | 0.000 | 0.667 | 0.004 | 0.814 | 0.143 |
Instance | A | C | M | N | I | Instance | A | C | M | N | I |
---|---|---|---|---|---|---|---|---|---|---|---|
2 × 20 × 2 | 0.227 | 0.157 | 0.450 | 0.060 | 0.107 | 4 × 100 × 6 | 0.680 | 0.036 | 0.131 | 0.010 | 0.143 |
2 × 20 × 4 | 0.445 | 0.120 | 0.315 | 0.060 | 0.060 | 4 × 100 × 8 | 0.638 | 0.043 | 0.096 | 0.020 | 0.202 |
2 × 20 × 6 | 0.334 | 0.050 | 0.322 | 0.035 | 0.259 | 4 × 200 × 2 | 0.515 | 0.037 | 0.240 | 0.024 | 0.185 |
2 × 20 × 8 | 0.417 | 0.046 | 0.268 | 0.007 | 0.262 | 4 × 200 × 4 | 0.707 | 0.024 | 0.127 | 0.002 | 0.140 |
2 × 50 × 2 | 0.176 | 0.320 | 0.445 | 0.000 | 0.059 | 4 × 200 × 6 | 0.649 | 0.044 | 0.074 | 0.007 | 0.226 |
2 × 50 × 4 | 0.490 | 0.014 | 0.283 | 0.000 | 0.213 | 4 × 200 × 8 | 0.754 | 0.056 | 0.059 | 0.024 | 0.107 |
2 × 50 × 6 | 0.552 | 0.031 | 0.266 | 0.009 | 0.142 | 4 × 500 × 2 | 0.714 | 0.019 | 0.127 | 0.000 | 0.139 |
2 × 50 × 8 | 0.575 | 0.044 | 0.239 | 0.031 | 0.111 | 4 × 500 × 4 | 0.831 | 0.023 | 0.062 | 0.004 | 0.079 |
2 × 100 × 2 | 0.518 | 0.062 | 0.293 | 0.002 | 0.124 | 4 × 500 × 6 | 0.818 | 0.033 | 0.035 | 0.004 | 0.109 |
2 × 100 × 4 | 0.632 | 0.064 | 0.222 | 0.003 | 0.080 | 4 × 500 × 8 | 0.852 | 0.028 | 0.000 | 0.009 | 0.111 |
2 × 100 × 6 | 0.648 | 0.029 | 0.164 | 0.005 | 0.154 | 5 × 20 × 2 | 0.469 | 0.000 | 0.379 | 0.009 | 0.142 |
2 × 100 × 8 | 0.646 | 0.058 | 0.106 | 0.013 | 0.176 | 5 × 20 × 4 | 0.715 | 0.000 | 0.138 | 0.000 | 0.148 |
2 × 200 × 2 | 0.618 | 0.092 | 0.144 | 0.000 | 0.146 | 5 × 20 × 6 | 0.801 | 0.000 | 0.074 | 0.000 | 0.125 |
2 × 200 × 4 | 0.703 | 0.028 | 0.136 | 0.001 | 0.133 | 5 × 20 × 8 | 0.683 | 0.046 | 0.053 | 0.039 | 0.180 |
2 × 200 × 6 | 0.803 | 0.028 | 0.100 | 0.005 | 0.064 | 5 × 50 × 2 | 0.295 | 0.003 | 0.303 | 0.016 | 0.383 |
2 × 200 × 8 | 0.774 | 0.035 | 0.063 | 0.001 | 0.127 | 5 × 50 × 4 | 0.414 | 0.048 | 0.202 | 0.002 | 0.333 |
2 × 500 × 2 | 0.808 | 0.040 | 0.082 | 0.000 | 0.069 | 5 × 50 × 6 | 0.380 | 0.063 | 0.105 | 0.035 | 0.417 |
2 × 500 × 4 | 0.785 | 0.020 | 0.061 | 0.000 | 0.134 | 5 × 50 × 8 | 0.557 | 0.074 | 0.060 | 0.014 | 0.294 |
2 × 500 × 6 | 0.764 | 0.040 | 0.004 | 0.003 | 0.189 | 5 × 100 × 2 | 0.443 | 0.060 | 0.292 | 0.002 | 0.203 |
2 × 500 × 8 | 0.800 | 0.053 | 0.002 | 0.010 | 0.135 | 5 × 100 × 4 | 0.608 | 0.047 | 0.155 | 0.008 | 0.183 |
3 × 20 × 2 | 0.253 | 0.004 | 0.498 | 0.031 | 0.214 | 5 × 100 × 6 | 0.615 | 0.045 | 0.126 | 0.007 | 0.207 |
3 × 20 × 4 | 0.511 | 0.037 | 0.256 | 0.019 | 0.178 | 5 × 100 × 8 | 0.667 | 0.056 | 0.093 | 0.023 | 0.161 |
3 × 20 × 6 | 0.435 | 0.003 | 0.189 | 0.000 | 0.372 | 5 × 200 × 2 | 0.552 | 0.057 | 0.246 | 0.002 | 0.142 |
3 × 20 × 8 | 0.556 | 0.000 | 0.007 | 0.066 | 0.372 | 5 × 200 × 4 | 0.641 | 0.019 | 0.150 | 0.025 | 0.165 |
3 × 50 × 2 | 0.243 | 0.158 | 0.403 | 0.005 | 0.191 | 5 × 200 × 6 | 0.762 | 0.032 | 0.059 | 0.015 | 0.132 |
3 × 50 × 4 | 0.422 | 0.008 | 0.283 | 0.018 | 0.269 | 5 × 200 × 8 | 0.735 | 0.062 | 0.014 | 0.018 | 0.170 |
3 × 50 × 6 | 0.496 | 0.033 | 0.282 | 0.047 | 0.141 | 5 × 500 × 2 | 0.692 | 0.029 | 0.116 | 0.003 | 0.161 |
3 × 50 × 8 | 0.584 | 0.088 | 0.107 | 0.027 | 0.193 | 5 × 500 × 4 | 0.789 | 0.033 | 0.048 | 0.001 | 0.130 |
3 × 100 × 2 | 0.459 | 0.054 | 0.336 | 0.000 | 0.151 | 5 × 500 × 6 | 0.751 | 0.029 | 0.009 | 0.005 | 0.206 |
3 × 100 × 4 | 0.611 | 0.045 | 0.165 | 0.007 | 0.171 | 5 × 500 × 8 | 0.704 | 0.041 | 0.002 | 0.013 | 0.240 |
3 × 100 × 6 | 0.538 | 0.021 | 0.136 | 0.020 | 0.284 | 6 × 20 × 2 | 0.503 | 0.000 | 0.340 | 0.000 | 0.157 |
3 × 100 × 8 | 0.644 | 0.028 | 0.164 | 0.017 | 0.147 | 6 × 20 × 4 | 0.691 | 0.000 | 0.138 | 0.004 | 0.167 |
3 × 200 × 2 | 0.532 | 0.088 | 0.264 | 0.001 | 0.115 | 6 × 20 × 6 | 0.730 | 0.000 | 0.098 | 0.039 | 0.132 |
3 × 200 × 4 | 0.752 | 0.045 | 0.158 | 0.000 | 0.045 | 6 × 20 × 8 | 0.500 | 0.000 | 0.015 | 0.064 | 0.421 |
3 × 200 × 6 | 0.697 | 0.044 | 0.125 | 0.013 | 0.121 | 6 × 50 × 2 | 0.284 | 0.069 | 0.446 | 0.059 | 0.142 |
3 × 200 × 8 | 0.752 | 0.034 | 0.077 | 0.018 | 0.119 | 6 × 50 × 4 | 0.538 | 0.064 | 0.130 | 0.011 | 0.257 |
3 × 500 × 2 | 0.791 | 0.035 | 0.112 | 0.003 | 0.059 | 6 × 50 × 6 | 0.585 | 0.002 | 0.090 | 0.032 | 0.291 |
3 × 500 × 4 | 0.767 | 0.031 | 0.067 | 0.001 | 0.135 | 6 × 50 × 8 | 0.312 | 0.030 | 0.091 | 0.030 | 0.538 |
3 × 500 × 6 | 0.880 | 0.026 | 0.025 | 0.011 | 0.057 | 6 × 100 × 2 | 0.468 | 0.040 | 0.294 | 0.002 | 0.196 |
3 × 500 × 8 | 0.812 | 0.043 | 0.001 | 0.015 | 0.130 | 6 × 100 × 4 | 0.577 | 0.028 | 0.235 | 0.002 | 0.158 |
4 × 20 × 2 | 0.347 | 0.020 | 0.446 | 0.020 | 0.168 | 6 × 100 × 6 | 0.604 | 0.060 | 0.079 | 0.013 | 0.245 |
4 × 20 × 4 | 0.683 | 0.000 | 0.121 | 0.000 | 0.196 | 6 × 100 × 8 | 0.591 | 0.070 | 0.115 | 0.020 | 0.203 |
4 × 20 × 6 | 0.855 | 0.000 | 0.067 | 0.010 | 0.067 | 6 × 200 × 2 | 0.597 | 0.041 | 0.208 | 0.002 | 0.152 |
4 × 20 × 8 | 0.496 | 0.017 | 0.068 | 0.017 | 0.403 | 6 × 200 × 4 | 0.686 | 0.040 | 0.161 | 0.006 | 0.107 |
4 × 50 × 2 | 0.358 | 0.037 | 0.337 | 0.051 | 0.217 | 6 × 200 × 6 | 0.669 | 0.044 | 0.093 | 0.021 | 0.172 |
4 × 50 × 4 | 0.566 | 0.061 | 0.224 | 0.005 | 0.145 | 6 × 200 × 8 | 0.630 | 0.046 | 0.029 | 0.040 | 0.256 |
4 × 50 × 6 | 0.412 | 0.046 | 0.225 | 0.029 | 0.288 | 6 × 500 × 2 | 0.736 | 0.032 | 0.126 | 0.001 | 0.105 |
4 × 50 × 8 | 0.435 | 0.048 | 0.135 | 0.027 | 0.355 | 6 × 500 × 4 | 0.779 | 0.026 | 0.081 | 0.009 | 0.105 |
4 × 100 × 2 | 0.533 | 0.043 | 0.322 | 0.005 | 0.097 | 6 × 500 × 6 | 0.828 | 0.036 | 0.015 | 0.007 | 0.114 |
4 × 100 × 4 | 0.595 | 0.018 | 0.211 | 0.008 | 0.168 | 6 × 500 × 8 | 0.657 | 0.040 | 0.076 | 0.016 | 0.211 |
Instance | A | C | M | N | I | Instance | A | C | M | N | I |
---|---|---|---|---|---|---|---|---|---|---|---|
2 × 20 × 2 | 5.190 | 6.529 | 5.398 | 5.333 | 5.274 | 4 × 100 × 6 | 8.645 | 12.994 | 12.764 | 12.161 | 9.947 |
2 × 20 × 4 | 6.091 | 6.864 | 7.352 | 6.128 | 6.311 | 4 × 100 × 8 | 9.227 | 11.257 | 16.931 | 9.900 | 9.456 |
2 × 20 × 6 | 6.161 | 9.739 | 7.905 | 7.040 | 6.565 | 4 × 200 × 2 | 6.285 | 9.833 | 9.779 | 8.319 | 8.161 |
2 × 20 × 8 | 7.260 | 10.781 | 8.631 | 11.311 | 7.308 | 4 × 200 × 4 | 7.717 | 11.919 | 13.675 | 9.499 | 9.617 |
2 × 50 × 2 | 6.402 | 6.259 | 5.793 | 5.987 | 6.164 | 4 × 200 × 6 | 9.321 | 10.644 | 17.441 | 10.409 | 9.921 |
2 × 50 × 4 | 6.991 | 8.121 | 8.110 | 7.756 | 6.734 | 4 × 200 × 8 | 11.072 | 15.809 | 18.024 | 10.201 | 10.115 |
2 × 50 × 6 | 6.990 | 8.519 | 9.122 | 7.888 | 7.716 | 4 × 500 × 2 | 6.205 | 10.246 | 11.921 | 9.283 | 8.257 |
2 × 50 × 8 | 8.400 | 9.822 | 11.702 | 8.815 | 8.696 | 4 × 500 × 4 | 6.922 | 11.079 | 18.621 | 10.508 | 10.140 |
2 × 100 × 2 | 5.421 | 7.754 | 6.253 | 6.952 | 7.036 | 4 × 500 × 6 | 11.524 | 13.682 | 20.208 | 13.914 | 11.887 |
2 × 100 × 4 | 7.437 | 7.947 | 9.317 | 8.082 | 7.760 | 4 × 500 × 8 | 13.062 | 14.823 | 21.708 | 13.629 | 14.612 |
2 × 100 × 6 | 8.972 | 10.416 | 11.342 | 9.411 | 9.377 | 5 × 20 × 2 | 5.679 | 7.519 | 6.684 | 8.064 | 5.810 |
2 × 100 × 8 | 9.852 | 9.120 | 11.921 | 5.890 | 8.952 | 5 × 20 × 4 | 5.729 | 8.031 | 8.688 | 7.014 | 6.677 |
2 × 200 × 2 | 7.525 | 7.888 | 9.567 | 5.975 | 8.045 | 5 × 20 × 6 | 7.028 | 8.666 | 10.247 | 9.753 | 7.691 |
2 × 200 × 4 | 8.562 | 8.275 | 12.213 | 8.298 | 8.886 | 5 × 20 × 8 | 6.624 | 8.558 | 13.580 | 9.552 | 7.204 |
2 × 200 × 6 | 9.472 | 10.325 | 12.736 | 10.844 | 9.825 | 5 × 50 × 2 | 6.475 | 7.838 | 8.121 | 6.051 | 6.831 |
2 × 200 × 8 | 6.959 | 9.956 | 17.132 | 10.748 | 10.517 | 5 × 50 × 4 | 7.307 | 9.023 | 10.403 | 9.507 | 7.450 |
2 × 500 × 2 | 8.660 | 7.972 | 11.546 | 8.436 | 8.316 | 5 × 50 × 6 | 7.768 | 10.812 | 12.576 | 9.786 | 8.133 |
2 × 500 × 4 | 6.531 | 11.824 | 17.538 | 10.043 | 10.147 | 5 × 50 × 8 | 8.434 | 10.265 | 12.659 | 11.626 | 8.870 |
2 × 500 × 6 | 11.716 | 12.801 | 20.216 | 10.169 | 12.410 | 5 × 100 × 2 | 7.058 | 9.603 | 8.584 | 7.425 | 7.450 |
2 × 500 × 8 | 10.569 | 13.476 | 32.782 | 11.702 | 14.662 | 5 × 100 × 4 | 8.711 | 9.342 | 10.961 | 8.011 | 7.932 |
3 × 20 × 2 | 5.270 | 7.700 | 6.007 | 5.351 | 5.416 | 5 × 100 × 6 | 7.966 | 11.393 | 13.672 | 8.857 | 10.190 |
3 × 20 × 4 | 6.022 | 10.318 | 8.461 | 7.459 | 6.078 | 5 × 100 × 8 | 9.556 | 18.366 | 15.123 | 11.665 | 9.748 |
3 × 20 × 6 | 6.728 | 8.654 | 9.429 | 6.642 | 6.752 | 5 × 200 × 2 | 8.291 | 10.055 | 10.269 | 9.211 | 8.713 |
3 × 20 × 8 | 7.210 | 9.901 | 11.099 | 12.096 | 7.669 | 5 × 200 × 4 | 9.544 | 9.385 | 13.267 | 9.783 | 9.192 |
3 × 50 × 2 | 6.219 | 7.658 | 7.092 | 6.844 | 6.501 | 5 × 200 × 6 | 8.804 | 12.043 | 17.984 | 10.896 | 11.078 |
3 × 50 × 4 | 7.157 | 9.833 | 8.118 | 9.340 | 7.315 | 5 × 200 × 8 | 9.490 | 12.364 | 19.295 | 17.865 | 10.756 |
3 × 50 × 6 | 8.013 | 10.058 | 10.915 | 8.997 | 7.673 | 5 × 500 × 2 | 8.718 | 10.723 | 12.915 | 5.528 | 9.097 |
3 × 50 × 8 | 8.002 | 8.957 | 11.808 | 9.966 | 8.595 | 5 × 500 × 4 | 11.356 | 11.789 | 19.571 | 12.896 | 12.002 |
3 × 100 × 2 | 6.874 | 8.823 | 7.576 | 7.919 | 7.410 | 5 × 500 × 6 | 12.790 | 17.475 | 19.994 | 24.109 | 12.852 |
3 × 100 × 4 | 7.724 | 9.805 | 10.541 | 8.451 | 8.225 | 5 × 500 × 8 | 9.851 | 14.998 | 26.560 | 12.615 | 13.596 |
3 × 100 × 6 | 6.934 | 9.864 | 11.485 | 9.320 | 8.797 | 6 × 20 × 2 | 5.565 | 5.647 | 7.007 | 6.628 | 5.845 |
3 × 100 × 8 | 7.119 | 10.797 | 13.822 | 10.240 | 9.335 | 6 × 20 × 4 | 6.030 | 7.914 | 9.284 | 6.837 | 6.435 |
3 × 200 × 2 | 6.660 | 9.256 | 7.967 | 8.392 | 8.464 | 6 × 20 × 6 | 6.906 | 11.461 | 11.915 | 9.479 | 7.356 |
3 × 200 × 4 | 5.913 | 10.618 | 11.887 | 9.619 | 8.420 | 6 × 20 × 8 | 7.339 | 12.652 | 16.704 | 10.010 | 7.355 |
3 × 200 × 6 | 12.220 | 10.995 | 16.795 | 11.043 | 10.558 | 6 × 50 × 2 | 7.485 | 8.302 | 8.411 | 7.746 | 7.615 |
3 × 200 × 8 | 7.424 | 13.954 | 19.622 | 11.832 | 10.991 | 6 × 50 × 4 | 7.253 | 10.133 | 10.263 | 10.181 | 7.216 |
3 × 500 × 2 | 6.953 | 10.813 | 12.029 | 8.930 | 8.401 | 6 × 50 × 6 | 8.337 | 8.323 | 14.594 | 13.754 | 8.678 |
3 × 500 × 4 | 9.448 | 9.511 | 15.153 | 11.278 | 11.715 | 6 × 50 × 8 | 7.832 | 13.426 | 14.591 | 10.282 | 9.270 |
3 × 500 × 6 | 12.223 | 14.136 | 20.142 | 12.934 | 13.166 | 6 × 100 × 2 | 7.458 | 9.699 | 9.485 | 8.878 | 7.661 |
3 × 500 × 8 | 12.534 | 13.044 | 20.069 | 15.700 | 13.712 | 6 × 100 × 4 | 7.823 | 10.354 | 11.630 | 9.834 | 8.462 |
4 × 20 × 2 | 6.381 | 6.805 | 7.633 | 6.675 | 6.615 | 6 × 100 × 6 | 9.696 | 13.975 | 12.420 | 9.028 | 9.365 |
4 × 20 × 4 | 7.111 | 9.360 | 9.864 | 8.749 | 6.079 | 6 × 100 × 8 | 8.763 | 12.577 | 15.983 | 14.355 | 10.177 |
4 × 20 × 6 | 6.291 | 8.036 | 10.851 | 7.820 | 6.625 | 6 × 200 × 2 | 8.420 | 11.299 | 10.042 | 6.452 | 8.430 |
4 × 20 × 8 | 6.947 | 12.988 | 12.931 | 10.303 | 7.789 | 6 × 200 × 4 | 8.730 | 11.134 | 13.646 | 14.548 | 10.579 |
4 × 50 × 2 | 5.240 | 8.167 | 7.653 | 6.240 | 6.597 | 6 × 200 × 6 | 9.387 | 11.179 | 17.115 | 9.660 | 11.147 |
4 × 50 × 4 | 6.437 | 9.392 | 11.135 | 7.988 | 7.557 | 6 × 200 × 8 | 9.627 | 12.172 | 19.227 | 10.885 | 10.445 |
4 × 50 × 6 | 9.930 | 14.371 | 13.708 | 8.276 | 8.495 | 6 × 500 × 2 | 9.614 | 10.488 | 13.042 | 7.376 | 9.857 |
4 × 50 × 8 | 7.483 | 9.414 | 12.838 | 8.325 | 8.586 | 6 × 500 × 4 | 9.507 | 11.117 | 18.098 | 12.345 | 11.374 |
4 × 100 × 2 | 7.107 | 10.206 | 7.898 | 7.332 | 7.843 | 6 × 500 × 6 | 10.642 | 15.477 | 24.991 | 30.280 | 12.663 |
4 × 100 × 4 | 8.821 | 9.825 | 11.710 | 9.505 | 8.354 | 6 × 500 × 8 | 12.383 | 14.276 | 24.702 | 14.560 | 12.506 |
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Lei, D.; Li, J. Distributed Energy-Efficient Assembly Scheduling Problem with Transportation Capacity. Symmetry 2022, 14, 2225. https://doi.org/10.3390/sym14112225
Lei D, Li J. Distributed Energy-Efficient Assembly Scheduling Problem with Transportation Capacity. Symmetry. 2022; 14(11):2225. https://doi.org/10.3390/sym14112225
Chicago/Turabian StyleLei, Deming, and Jinlin Li. 2022. "Distributed Energy-Efficient Assembly Scheduling Problem with Transportation Capacity" Symmetry 14, no. 11: 2225. https://doi.org/10.3390/sym14112225
APA StyleLei, D., & Li, J. (2022). Distributed Energy-Efficient Assembly Scheduling Problem with Transportation Capacity. Symmetry, 14(11), 2225. https://doi.org/10.3390/sym14112225