A mutualism quantum genetic algorithm (MQGA) is proposed for an integrated supply chain scheduling with the materials pickup, flow shop scheduling, and the finished products delivery. The objective is to minimize the makespan, that is, the arrival time of the last finished product to the customer. In MQGA, a new symbiosis strategy named mutualism is proposed to adjust the size of each population dynamically by regarding the mutual influence relation of the two subpopulations. A hybrid
The coordination of logistics activities in a supply chain has received a lot of attention recently. From the manufacturer’s point of view, the important problem in the supply chain scheduling is the coordination of the three stages including material supply, production scheduling, and product delivery. Traditionally, research on scheduling generally focuses on the models with various machine setting, job characteristics, and performance measures [
In the past decades, many researchers studied the machine scheduling problems with transportation under consideration. Some of the results consider the transportation of the jobs between machines in the flow shop model, which incorporates transport times when the jobs are transferred from one machine to another. Maggu et al. [
Another type of scheduling model with transportation focuses on the delivery of finished jobs to customers. Lee and Chen [
This paper considers the scheduling model that integrates the pickup of materials, flow shop scheduling, and the delivery of finished jobs. In this model, the material warehouse, the factory, and the customer are located at three different places. There are two vehicles (namely, conveyor and truck) each with a limited capacity. One vehicle (conveyor) travels between the factory and the warehouse for material transportation, and the other vehicle (truck) travels between the customer and the factory for finished products delivery. This model applies to many situations in supply chain business activities. For example, a shoes manufacturer purchases materials from India and arranges the production in China. Finally, the finished products are delivered to the USA.
To the best of our knowledge, research on this model includes Hall and Potts [
The model considered in this paper is different from that in [
Quantum genetic algorithms (QGA) are heuristic search techniques inspired from the principles of survival of the fittest in natural genetic evolution and quantum theory. They are known to be efficient in a large search space, without explicitly requiring additional information (such as convexity or derivative information) about the objective. In addition, the
In order to solve the integrated supply chain scheduling model with the materials pickup, flow shop scheduling, and the finished products delivery, a technique called mutualism quantum genetic algorithm (MQGA) is developed, which differs from traditional QGA method in two aspects.
The remainder of this paper is organized as follows. In Section
In this paper, it is assumed that the material warehouse, the factory, and the customer are located at different addresses, and there is a set of jobs,
Schematic of the cooperative problem of flow shop production with pickup and delivery transportations.
Before the introduction of the notations, a number of assumptions are given as follows: all the facilities including conveyor, machines, and truck are available from time zero; there is no idle time between any consecutive two pickup journeys; the time of loading and unloading jobs is included in the pickup time and delivery time; the time of transporting jobs between machines is negligible; the storage or buffer capacities between successive machines are unlimited; there is no priority among jobs; machine failure is not considered.
The following notations are used in the problem model: : physical space of job
Tang and Gong [
As the long evolutionary process of nature, the relationship between living beings is complicated. The phenomenon that two species live together is generally referred to as the symbiosis. This paper studies a kind of symbiosis called mutualism, which refers to two species living together and depending on each other over a long period of time. The nutrition of one species is the food source of the other one.
Mutualism brings two advantages to our algorithm. Firstly, there is no need to design the fitness function, and the fitness value of an individual is obtained by the cooperation between two populations, which could reduce the dependence on the domain knowledge. Secondly, different from the traditional framework in which the evolution of populations depends on the fitness values of individuals, mutualism incorporates the cooperative behavior between an individual and its surroundings, so as to postpone the premature convergence and improve the convergence speed.
A differential equation of mutualism population growth model is introduced in this subsection. Assume two species A and B live in the same environment and they do not take each other as food, but the existence of one species can promote the population growth of the other one. For example, algae and fungi are two species living in lichen. Algae provide nutrient to fungi through photosynthesis, and fungi offer algae water and inorganic substance. If algae and fungi are separated in lichen, both of them will die.
Let
In the standard genetic algorithm, the fitness function will be given as an input, and the fitness is easy to reach the peak value. However, in the real environment the adaptability of a species is dynamic and is affected by its surroundings. Therefore, in MQGA, the fitness value of an individual is replaced by its cooperation degree with individuals in other species, and the details on the computation of the cooperation degree are given below.
Given two individuals
Consider
Consider
Consider
Consider
The cooperation degree of individual
Condition | Score |
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4 |
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2 |
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0 |
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1 |
Given two populations A and B, denote by
The cooperative degree of a population stands for the cooperative level of the population, and it can be calculated as follows:
In our mutualism population growth model, assume
If the cooperative degree of a population is high, its population size will increase. Thus the growth of a population size mostly depends on its ability to coordinate. If the ability is strong, the size will become bigger and bigger till the maximum value. Otherwise, the size will become small and eventually extinct. In order to survive, each population will try its best to gain good genes and cooperate with others. In this way, the quality of solution is improved and the performance of algorithm is enhanced.
A description of the mutualism strategy for population growth is given in Figure
Description of the mutualism strategy for population growth.
The genetic algorithm (GA) proposed by Holland has achieved a great success for solving complex combinational problem. To improve GA, Han and Kim [
The encoding in [
For example, given a 3-job, 3-machine problem, let 15
For Part 1, suppose the binary representation is
For Part 2 and Part 3, suppose the binary representations are
The encoding and decoding mode of
The final code for another problem with 8 jobs and 2 machines is presented in (
The rule is that the jobs in the positions after each “1” to the next “1” belong to a new batch. Therefore, in the pickup transportation, job 5 is in the first batch, job 8 and job 2 belong to the second batch, job 1, job 3, job 6, and job 4 are in the third batch, and job 7 is in the last batch. The third line is the delivery batch of truck. Similarly, in the delivery transportation, job 5, job 8, and job 2 are in the same batch, job 1 and job 3 belong to the next batch, and job 6, job 4, and job 7 are in the last batch. Figure
Job sequence and the job-to-batch assignment.
Assume the processing times of the 8 jobs on the two machines are given in Table
The processing times of the 8 jobs on 2 machines.
Processing time |
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3 | 1 | 2 | 1 | 2 | 3 | 3 | 4 |
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4 | 1 | 2 | 3 | 4 | 3 | 1 | 2 |
The decoding process and the Gantt chart.
When applying local search techniques to search better solutions, the neighborhood structure is very important, since it will directly affect the results. For the flow shop problem, the results in [
Denote by
Take the two-machine flow shop problem as an example. Let
For the flow shop problem with more than two machines, the details of obtaining the local optimal solution are given in Procedure
Obtain the subpermutation Calculate Denote by
Output the local optimal individual.
Because the total physical space of all jobs in a batch may exceed the capacity of the vehicle, our encoding could not ensure a feasible solution, and a modified mechanism is needed to update the solution, which is an important step, not only in encoding process, but also in the steps of crossover and mutation, as an unfeasible solution may affect the search process in local neighborhood.
Let TVol be the capacity of the vehicle and
If Find the job Let
The operations introduced below are performed at each generation of the quantum genetic algorithm (QGA). The fitness of each individual can be calculated by the mutualism strategy in Section
Crossover operation of MQGA.
In the mutation operation, a NOT Gate is used as the mutation operator. Firstly, select individuals with mutation probability
In this subsection, the details of the MQGA are introduced in Algorithm
generation GN, two subpopulations sizes
Apply mutualism strategy, rescale the size of subpopulations according to population growth model. End.
Perform catastrophe operation. Else Apply quantum rotation operation. End
and update the best solution if possible.
Output the global best result.
In this paper, all algorithms are programmed with MATLAB language, and all the computations are conducted on a Pentium PC 1.66 GHZ with 512 MB memory. In order to evaluate the performance of MQGA, an extensive set of instances with different characteristics are generated based on the flow shop benchmark problems, including FT benchmark and ABZ benchmark. In order to test the relative large-scale problem, three test instances are designed, where there are 50 jobs and 5 machines, 50 jobs and 10 machines, and 100 jobs and 5 machines, seen in the Appendix. Table
Parameters of the conveyor and truck.
Problem | Parameter | |||||
---|---|---|---|---|---|---|
|
Tr1 |
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|
Tr2 |
|
|
N(FT06) | 6 | 10 | 3 | 10 | 20 | 10 |
N(FT10) | 6 | 40 | 20 | 10 | 100 | 30 |
N(FT20) | 6 | 20 | 10 | 10 | 60 | 30 |
N(ABZ3) | 6 | 100 | 100 | 10 | 300 | 100 |
N(ABZ6) | 6 | 100 | 100 | 10 | 300 | 100 |
N(ABZ7) | 6 | 30 | 30 | 10 | 100 | 100 |
N(ABZ8) | 6 | 30 | 30 | 10 | 100 | 100 |
N(ABZ9) | 6 | 30 | 30 | 10 | 100 | 100 |
N(TA1) | 6 | 30 | 30 | 10 | 100 | 100 |
N(TA2) | 6 | 100 | 30 | 10 | 300 | 200 |
N(TA3) | 6 | 100 | 30 | 10 | 300 | 200 |
Note:
Physical space of jobs.
Jobs 1–20 | |
2 6 1 0.3 3 1.3 2 3.3 1.2 4 2.8 3.2 0.7 0.1 0.9 2 6 1 0.3 3 | |
|
|
Jobs 21–40 | |
1.3 2 3.3 1.2 4 2.8 3.2 0.7 0.1 0.9 2 6 1 0.3 3 1.3 2 3.3 1.2 4 | |
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Jobs 41–60 | |
2.8 3.2 0.7 0.1 0.9 3 4 3 6 1 2 6 1 0.3 3 1.3 2 3.3 1.2 4 | |
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Jobs 61–80 | |
2.8 3.2 0.7 0.1 0.9 2 6 1 0.3 3 1.3 2 3.3 1.2 4 2.8 3.2 0.7 0.1 0.9 | |
|
|
Jobs 81–100 | |
2 6 1 0.3 3 1.3 2 3.3 1.2 4 2.8 3.2 0.7 0.1 0.9 3 4 3 6 1 |
Two parameters including crossover rate
In this way, there are a total of 25 combinations. For each combination, MGA [
AOV results for the experiment on tuning the parameters.
Source | Sum of squares | Df | Mean square |
|
---|---|---|---|---|
A: |
0.0083 | 4 | 0.0021 | 3.3334 |
B: |
0.0072 | 4 | 0.0018 | 4.3732 |
Interactions AB | 0.0438 | 16 | 0.0029 | 7.3679 |
According to the theory of statistical analysis, the greater the
In order to validate the performance of MQGA, MGA [
Detailed comparison results of MQGA, QGA, and MGA on N(TA1) problem.
RUN | 500 × 10 | 1000 × 10 | 2000 × 20 | ||||||
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MQGA | MGA | QGA | MQGA | MGA | QGA | MQGA | MGA | QGA | |
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|||||||||
1 | 3166 | 3329 | 3199 | 3139 | 3326 | 3194 | 3152 | 3308 | |
2 | 3182 | 3336 | 3204 | 3166 | 3328 | 3193 | 3147 | 3327 | |
3 | 3165 | 3382 | 3229 | 3154 | 3351 | 3209 | 3154 | 3345 | |
4 | 3172 | 3277 | 3218 | 3162 | 3266 | 3210 | 3147 | 3210 | |
5 | 3164 | 3307 | 3220 | 3151 | 3323 | 3208 | 3148 | 3285 | |
6 | 3179 | 3330 | 3215 | 3165 | 3319 | 3170 | 3155 | 3324 | |
7 | 3164 | 3267 | 3222 | 3144 | 3253 | 3222 | 3128 | 3253 | |
8 | 3145 | 3371 | 3221 | 3138 | 3218 | 3191 | 3167 | 3313 | |
9 | 3154 | 3297 | 3226 | 3163 | 3293 | 3221 | 3140 | 3305 | |
10 | 3163 | 3298 | 3206 | 3140 | 3285 | 3145 | 3135 | 3276 |
Comparison results of MQGA, QGA, and MGA on N(TA1) problem.
Size | MQGA | MGA | QGA | ||||||
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BV | WV | AV | BV | WV | AV | BV | WV | AV | |
500 × 10 | 3155 | 3192 | 3165.4 | 3267 | 3382 | 3325.7 | 3199 | 3229 | 3216 |
1000 × 10 | 3138 | 3166 | 3150.2 | 3218 | 3351 | 3296.2 | 3145 | 3222 | 3196.3 |
2000 × 20 | 3128 | 3167 | 3147.3 | 3210 | 3345 | 3294.6 | 3131 | 3226 | 3186.3 |
Known from the results in Table
The convergence curves of MQGA, MGA, and QGA obtained for each combination are depicted in Figure
The convergence curves of MQGA, QGA, and MGA.
The solutions distributions of MQGA, QGA, and MGA are given in Figure
Distributions of solutions of MQGA, QGA, and MGA.
The maximum number of iterations is 1000, and the size of population is 100 (in MQGA, there are two subpopulations, and the size of each subpopulation is 50). To be fair, each algorithm runs 10 times for each instance. The experiment results are shown in Table
Computational results of MQGA and QGA, MGA.
Problem | Approach |
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Improved% |
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N(FT06) |
MGA | 103.3 | — | 73.3 | 13 |
QGA | 103.3 | 0 | 33.6 | 30 | |
MQGA |
|
0.48% | 9.8 | 113 | |
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N(FT10) |
MGA | 1282.2 | — | 300.8 | 29 |
QGA | 1280.7 | 0.12% | 97.3 | 98 | |
MQGA |
|
0.31% | 76.2 | 163 | |
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N(FT20) |
MGA | 1330 | — | 26.7 | 23 |
QGA | 1328.6 | 0.09% | 18.3 | 36 | |
MQGA |
|
0.32% | 36.7 | 133 | |
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N(ABZ3) |
MGA | 2088.6 | — | 430.8 | 29 |
QGA | 2079.4 | 0.44% | 146.6 | 101 | |
MQGA |
|
0.83% | 83.4 | 164 | |
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|||||
N(ABZ6) |
MGA | 1883.2 | — | 363.6 | 29 |
QGA | 1874.4 | 0.47% | 111.3 | 101 | |
MQGA |
|
1.16% | 123.3 | 164 | |
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N(ABZ7) |
MGA | 1276.2 | — | 140.3 | 68 |
QGA | 1233.8 | 3.32% | 104.3 | 172 | |
MQGA |
|
3.76% | 86.8 | 310 | |
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N(ABZ8) |
MGA | 1290.3 | — | 114.4 | 68 |
QGA | 1277.2 | 1.03% | 17.7 | 172 | |
MQGA |
|
1.71% | 19.8 | 310 | |
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N(ABZ9) |
MGA | 1273.3 | — | 143.9 | 68 |
QGA | 1238.3 | 1.18% | 29.7 | 171 | |
MQGA |
|
2.3% | 11.3 | 310 | |
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N(TA1) |
MGA | 3286.2 | — | 71.7 | 84 |
QGA | 3173.3 | 3.37% | 17 | 426 | |
MQGA |
|
4.02% | 21.1 | 778 | |
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N(TA2) |
MGA | 3346.6 | — | 91.2 | 130 |
QGA | 4917 | 11.33% | 9.1 | 480 | |
MQGA |
|
13.4% | 19.3 | 814 | |
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N(TA3) |
MGA | 10706.3 | — | 63.3 | 171 |
QGA | 9289.33 | 13.23% | 16.2 | 632 | |
MQGA |
|
14.76% | 17.8 | 963 |
Note:
In the performance of solution, from Table
This paper studies an integrated scheduling with the materials pickup, flow shop scheduling, and the finished products delivery. The objective is to find a coordinated schedule to minimize the arrival time of the last completed product to the customer. In order to solve the problem, a biologically inspired quantum genetic algorithm is proposed with a new mutualism strategy. The experiment results demonstrate that MQGA can find a satisfactory solution with an acceptable amount of computation time.
Future research could address problems with multiple customers or multiple transport vehicles or different shop environments, including flexible scheduling and job-shop. Problems with other performance measures, including minimum mean tardiness, and multimeasures should also be studied.
See Table
(a) N(TA1): 50 jobs * 5 machines. (b) N(TA2): 50 jobs * 10 machines. (c) TA3: 100 jobs * 5 machines.
Machines | Processing times |
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73 87 13 11 41 43 93 69 80 13 24 72 38 81 83 88 26 6 89 67 70 30 89 30 68 21 78 46 99 10 17 23 83 47 86 18 67 46 4 14 4 20 88 30 84 38 93 76 30 30 |
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26 37 23 93 49 12 39 17 46 20 32 44 92 73 93 33 10 43 2 62 62 82 29 29 94 20 42 80 94 33 8 41 63 4 71 30 14 32 30 30 27 98 39 84 63 12 38 43 49 13 |
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48 4 92 92 72 43 3 98 93 17 79 11 16 89 81 92 43 61 39 28 94 87 23 1 33 91 67 91 4 60 38 23 90 93 13 63 23 34 47 98 91 11 46 30 77 3 14 47 80 43 |
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26 67 4 14 93 34 21 20 6 18 73 23 16 77 28 24 13 77 36 16 32 46 21 81 28 70 89 34 96 62 46 60 19 97 13 7 44 7 73 13 66 70 97 33 97 64 73 28 4 87 |
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77 94 9 37 29 79 33 73 63 86 23 39 76 24 38 3 91 29 22 27 39 31 46 18 93 38 83 38 97 10 79 93 2 87 17 18 10 30 8 26 14 21 13 10 83 46 42 18 36 2 |
Machines | Processing times |
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46 32 79 43 97 10 44 24 83 73 66 49 93 61 19 47 84 13 11 19 98 2 83 44 7 73 19 69 12 73 83 23 33 16 88 8 26 42 38 63 7 2 44 38 24 76 83 61 32 90 |
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61 87 31 23 73 93 28 90 94 39 64 2 16 33 33 40 81 26 83 4 4 10 63 96 33 71 66 94 7 13 11 99 37 30 36 69 22 36 67 63 96 74 4 42 40 30 93 36 23 87 |
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31 38 83 33 71 38 36 64 43 48 69 96 33 82 33 64 11 61 36 33 87 88 10 32 38 23 24 90 7 11 49 2 76 17 32 39 9 83 69 67 28 88 23 91 71 3 26 41 96 |
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31 24 21 37 69 31 30 31 21 19 63 91 11 6 31 63 36 39 37 47 36 63 39 4 10 12 62 43 49 34 87 29 2 18 73 39 77 69 13 78 68 37 22 41 92 67 24 87 91 31 |
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37 16 42 47 94 14 94 34 72 36 88 31 41 71 94 99 11 97 44 77 69 91 38 23 87 7 66 34 86 49 3 48 44 93 37 82 31 39 78 33 36 3 38 10 98 6 44 62 24 94 |
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79 93 68 73 37 44 34 39 76 62 74 28 78 43 98 83 91 27 6 82 60 44 43 76 99 66 11 33 32 8 40 62 23 24 30 1 73 27 16 91 33 11 99 2 60 90 36 62 13 3 |
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83 87 38 38 86 67 23 19 97 78 66 67 7 23 67 8 77 71 83 29 49 3 94 76 93 48 4 37 82 37 61 6 97 3 27 93 46 92 46 32 8 11 7 34 72 37 83 22 87 63 |
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22 29 99 23 98 33 80 82 33 68 47 74 26 61 93 33 11 42 72 14 8 98 90 36 73 69 26 24 33 98 86 30 92 94 66 47 3 41 41 47 89 28 39 80 47 37 74 38 39 3 |
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27 92 73 94 18 41 37 38 36 20 2 39 91 81 33 14 88 22 36 63 79 23 66 3 13 31 2 81 12 40 39 32 16 87 78 41 43 94 1 93 22 93 62 33 30 34 27 30 34 77 |
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24 47 39 66 41 46 24 23 68 30 93 22 64 81 94 97 34 82 11 91 23 32 26 22 12 23 34 87 39 2 38 84 62 10 11 93 37 81 10 40 62 49 90 34 11 81 31 21 39 27 |
Machines | Processing times | ||||||
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84.6317 | 68.0327 | 97.8144 | 20.8223 | 22.0642 | 31.3817 | 40.4331 |
32.3333 | 4.4926 | 9.2277 | 31.4611 | 18.0836 | 83.0344 | 63.7339 | |
83.9330 | 27.7676 | 37.3838 | 30.3118 | 33.6348 | 32.3347 | 22.3726 | |
17.1233 | 22.6226 | 6.0628 | 74.2341 | 33.4834 | 39.4332 | 46.8303 | |
83.6232 | 12.0133 | 9.4702 | 27.0917 | 37.0777 | 36.4394 | 61.8333 | |
70.0938 | 30.8900 | 30.2302 | 43.1238 | 41.1160 | 31.3372 | 39.7248 | |
64.9842 | 21.4270 | 93.8391 | 42.2748 | 27.2131 | 37.3729 | 39.4439 | |
18.3346 | 31.9796 | 79.8378 | 11.1263 | 39.2043 | 28.3831 | 82.1932 | |
93.3273 | 27.8467 | 63.8107 | 48.3132 | 67.9713 | 30.4670 | 47.9016 | |
41.2603 | 34.3209 | 42.7133 | 4.6217 | 63.8433 | 23.6188 | 76.6038 | |
77.1361 | 60.7312 | 7.4211 | 13.2976 | 66.3300 | 4.0213 | 31.2134 | |
30.9947 | 33.1613 | 77.0320 | 42.0403 | 7.9610 | 74.3028 | 99.9878 | |
93.4269 | 19.8363 | 30.6913 | 83.1429 | 10.3026 | 89.1798 | 93.6973 | |
96.6370 | 67.6072 | 1.3964 | 30.3368 | 62.9276 | 29.0398 | 60.9821 | |
66.8269 | 44.3931 | ||||||
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|
3.8077 | 68.7184 | 67.7863 | 31.3860 | 4.0038 | 92.7664 | 82.9002 |
33.9639 | 32.9803 | 63.0667 | 88.7886 | 72.8946 | 80.2037 | 60.6660 | |
43.8637 | 26.0218 | 93.0429 | 64.2378 | 93.1670 | 44.7731 | 47.8723 | |
29.7237 | 24.9201 | 19.3493 | 17.8681 | 33.8913 | 8.7417 | 28.9312 | |
63.8303 | 89.6336 | 11.3332 | 40.3292 | 74.7622 | 86.1109 | 90.3164 | |
64.3916 | 74.1080 | 8.2019 | 90.6283 | 94.3113 | 92.2433 | 42.3333 | |
32.9836 | 37.3679 | 87.3114 | 71.4010 | 93.0243 | 39.3819 | 42.0138 | |
36.9339 | 31.2930 | 46.0303 | 2.3923 | 43.4493 | 22.6322 | 18.8634 | |
3.2671 | 88.2232 | 17.1819 | 19.3328 | 31.4467 | 6.9719 | 33.8983 | |
79.9701 | 33.3020 | 79.0346 | 73.3813 | 21.1483 | 68.0938 | 22.2373 | |
31.0398 | 37.3793 | 31.1383 | 38.7069 | 36.4293 | 33.9889 | 2.4179 | |
37.6434 | 21.2294 | 23.1638 | 39.8660 | 88.1233 | 18.2311 | 34.4082 | |
39.3800 | 34.1221 | 42.7137 | 86.3060 | 97.8039 | 23.4139 | 40.0631 | |
34.7736 | 73.7374 | 38.2443 | 73.9441 | 79.1348 | 31.9843 | 93.7063 | |
11.4333 | 43.9139 | ||||||
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37.0079 | 47.6363 | 86.7381 | 36.0169 | 23.9910 | 9.3497 | 91.3933 |
19.0191 | 92.3208 | 78.0443 | 77.9396 | 74.4131 | 9.1036 | 3.1612 | |
69.8134 | 32.7903 | 10.2037 | 63.0130 | 43.4309 | 62.3464 | 49.9032 | |
76.9814 | 23.6630 | 68.1342 | 24.8938 | 74.0296 | 77.4290 | 73.3663 | |
94.1423 | 91.3789 | 22.3412 | 34.2217 | 18.2232 | 99.8933 | 63.0020 | |
33.6438 | 89.0716 | 22.0123 | 10.2334 | 97.3328 | 32.2667 | 88.2888 | |
94.8882 | 22.4733 | 61.8833 | 80.0331 | 30.4777 | 2.3938 | 86.1700 | |
3.4326 | 24.9428 | 33.2202 | 76.1338 | 43.0818 | 91.6040 | 66.1194 | |
79.3679 | 48.9789 | 12.8067 | 94.3034 | 86.6166 | 13.3706 | 93.9793 | |
6.0822 | 37.3802 | 18.7386 | 21.6410 | 11.0119 | 83.0266 | 49.0443 | |
83.1172 | 27.6230 | 33.3916 | 92.4096 | 33.0112 | 39.0013 | 30.3430 | |
3.9994 | 74.3970 | 32.0863 | 77.0834 | 33.4703 | 29.9367 | 87.0861 | |
36.1939 | 38.6870 | 2.3033 | 41.1629 | 31.4037 | 18.4714 | 60.3132 | |
61.0278 | 23.8668 | 31.3109 | 16.4060 | 93.9227 | 30.7267 | 98.7219 | |
31.2407 | 13.8634 | ||||||
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79.3039 | 32.9897 | 47.6910 | 43.9032 | 36.0006 | 82.3696 | 66.3923 |
13.4142 | 93.8438 | 30.0931 | 20.0777 | 14.9284 | 8.6927 | 43.8123 | |
37.7344 | 9.7682 | 18.3971 | 7.6113 | 76.3946 | 63.8904 | 94.7271 | |
47.9722 | 47.8333 | 93.3017 | 48.3228 | 83.3002 | 71.6867 | 39.6977 | |
37.0047 | 94.8397 | 44.0043 | 28.4989 | 73.2636 | 70.9429 | 31.1982 | |
31.7673 | 67.9373 | 43.9669 | 90.9212 | 27.1023 | 33.3360 | 76.3692 | |
37.1149 | 13.7774 | 99.9414 | 72.7029 | 69.0932 | 18.7311 | 32.1909 | |
99.8103 | 93.3610 | 84.7230 | 97.3806 | 10.7734 | 78.1100 | 44.3464 | |
10.0022 | 44.4773 | 16.0306 | 46.4031 | 20.4337 | 93.7849 | 1.8234 | |
81.3674 | 43.6923 | 38.7263 | 37.3334 | 96.4237 | 18.6704 | 11.2710 | |
81.2803 | 27.3601 | 39.3646 | 22.3763 | 92.6382 | 43.3897 | 38.6866 | |
36.8882 | 99.7779 | 12.2373 | 16.3636 | 30.3478 | 89.7477 | 33.2003 | |
4.2014 | 4.7337 | 74.4997 | 17.4811 | 60.4477 | 38.0942 | 63.8836 | |
93.1060 | 93.7823 | 68.7374 | 78.9328 | 16.2863 | 31.7426 | 7.9919 | |
9.7908 | 63.7969 | ||||||
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46.0182 | 70.8827 | 42.3334 | 23.9494 | 78.7140 | 11.2288 | 87.7309 |
1.1682 | 73.2947 | 74.3247 | 33.3868 | 80.9084 | 30.3979 | 29.9039 | |
10.0888 | 83.4943 | 8.1367 | 31.3683 | 93.0997 | 38.3136 | 64.6483 | |
70.0836 | 73.4314 | 86.4972 | 34.8031 | 18.2930 | 30.8623 | 20.3774 | |
23.2021 | 20.4869 | 93.3820 | 74.4314 | 82.4732 | 34.6946 | 94.8308 | |
13.8809 | 36.4386 | 43.4073 | 32.8384 | 68.6438 | 99.1667 | 6.2637 | |
33.4487 | 29.1977 | 42.6223 | 39.6733 | 19.3706 | 13.3877 | 64.6711 | |
63.4906 | 63.7133 | 41.8206 | 93.1286 | 73.4143 | 87.1880 | 31.7227 | |
43.9343 | 63.0724 | 39.6809 | 33.3300 | 99.3787 | 21.3336 | 92.2013 | |
76.3623 | 23.4309 | 24.2814 | 81.0009 | 34.4622 | 46.7340 | 8.9193 | |
23.3668 | 99.9983 | 11.6722 | 92.1918 | 37.6619 | 93.3813 | 36.9370 | |
43.4437 | 40.4863 | 90.1080 | 90.7238 | 33.8413 | 39.7471 | 47.7907 | |
18.2683 | 44.6693 | 10.9124 | 22.2803 | 23.8896 | 72.8488 | 74.6871 | |
63.8373 | 44.3997 | 79.0272 | 34.2089 | 18.3843 | 13.0348 | 14.6130 | |
47.6381 | 9.2464 |
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work is supported by the National Natural Science Foundation of China (Grant nos. 11201282 and 61304209), Humanity and Social Science Youth Foundation of Ministry of Education of China (Grant no. 10YJCZH032), Innovation Program of Shanghai Municipal Education Commission (14YZ127), and the Fund of Scheme for Training Young Teachers in Colleges and Universities in Shanghai (ZZCD12006).