Task Allocation of Multi-Machine Collaborative Operation for Agricultural Machinery Based on the Improved Fireworks Algorithm
<p>Operation mode diagram of a fertilizer applicator.</p> "> Figure 2
<p>Schematic diagram of the fertilizer applicators operating in the order of distribution.</p> "> Figure 3
<p>Schematic diagram of two vertices of a field on the roadside.</p> "> Figure 4
<p>Schematic diagram of four vertices of a field on the roadside.</p> "> Figure 5
<p>Coding method proposed to solve the fertilizer distribution problem.</p> "> Figure 6
<p>CCFWA flowchart.</p> "> Figure 7
<p>Schematic diagram of the experimental field.</p> "> Figure 8
<p>Comparison of fitness values of the four algorithms.</p> ">
Abstract
:1. Introduction
2. Materials and Methods
2.1. Problem Description
2.1.1. Task Allocation of Multi-Machine Cooperative Operation of Fertilizer Applicators
- (1)
- Characteristics of fertilizer applicator operation scenario
- (2)
- Description of task allocation problem of fertilizer applicators
- According to the amount of applied fertilizer, the fields are classified into several categories, including positive large, positive small, medium, negative small, and negative large, which correspond to different operating speeds of fertilizer applicators;
- All fields can be fertilized by any one fertilizer applicator, and the speed of the fertilizer applicator is inversely proportional to the amount of fertilizer applied to the field;
- Each field can only be fertilized by one fertilizer applicator;
- The daily working hours of a fertilizer applicator shall not exceed the specified time;
- All fertilizer applicators start from the garage every day and return to the garage after the operation is completed or after the specified number of working hours;
- The completion of the field work represents the end of the task.
2.1.2. Fertilizer Distribution of Fertilizer Truck
2.2. Model Construction
2.2.1. Task Allocation Model for Multi-Machine Collaborative Operation of Fertilizer Applicators
- (1)
- Daily operational fields and sequences
- ;
- and a fertilizer applicator leaving field is on the other side of the specified entrance or exit point;
- and a fertilizer applicator leaving field is on the side of a specified entrance or exit point;
- .
- (2)
- The continuous operating time of fertilizer spreader
- Travel time of fertilizer applicator on the road;
- Time of field linear operation of fertilizer applicator , which is labeled as time ;
- Field turnaround time of fertilizer applicator .
- (3)
- Distance from garage to the field and between the fields
- The two vertices of the field are on the roadside, and the other two vertices are not on the roadside. As shown in Figure 3, for the two fields, it is stipulated that the left point of the two points on the roadside, like point or , represents the entrance of a fertilizer applicator, and the point on the right, like point or , denotes the exit of the fertilizer applicator;
- The four vertices of the field are all on the roadside. As shown in Figure 4, it is stipulated that the left point of the upper two points, like point or , represents the entrance of a fertilizer applicator, and the point on the right, like point or , is the exit of the fertilizer applicator.
- As shown in Figure 3, fields and are connected to each other on the opposite side of the entrance or exit side of the two fields. The distance from field to field is the distance from the point on the right side of the connected side of field to the point on the left side of the connected side of field ; similarly, the distance from field to field is the distance from the point on the right side of the connected side of field to the point on the left side of the connected side of field ;
- As shown in Figure 4, the opposite side of the entrance or exit side of field is on the same road as the entrance or exit side of field . The distance from field to field represents the distance from the point on the right side of the opposite side of the entrance or exit side of field to the point on the left side of the entrance or exit side of field ;
- As shown in Figure 4, the opposite side of the entrance or exit side of field is on the same road as the entrance or exit side of field . The distance from field to field denotes the distance from the point on the right side of the entrance or exit side of field to the point on the left side of the opposite side of the entrance or exit side of field .
2.2.2. Fertilizer Distribution Model of Fertilizer Truck
2.3. Improved Fireworks Algorithm
2.3.1. Coding and Discretized Decoding
- (1)
- Multi-Machine Cooperative Operation Task Allocation of Fertilizer Applicators
- (2)
- Fertilizer Distribution of Fertilizer Truck
2.3.2. Chaos Initialization
2.3.3. Cauchy Mutation
2.3.4. CCFWA Process
3. Results and Discussion
3.1. Validation Experiment on Task Allocation Problem of Multi-Machine Cooperative Operation of Fertilizer Applicators
3.2. Verification Experiment on Fertilizer Distribution Problem of Fertilizer Truck
4. Conclusions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
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Coding | 0.35 | 1.32 | 1.27 | 0.65 | 1.51 |
---|---|---|---|---|---|
Element position (corresponding to each field) | 1 | 2 | 3 | 4 | 5 |
Fertilizer applicator | |||||
Order of operations |
Fertilizer Applicator Number | Working Width (m) | Working Speed (km/h) | Speed on the Road (km/h) | Turning Time (h) |
---|---|---|---|---|
1 | 2.4 | 4–8 | 10 | 0.005 |
2 | 2.1 | 4–8 | 10 | 0.004 |
3 | 1.8 | 4–8 | 10 | 0.003 |
Field Number | Width (m) | Length (m) | Area (m2) |
---|---|---|---|
1 | 260 | 180 | 46,800 |
2 | 200 | 180 | 36,000 |
3 | 210 | 180 | 37,800 |
4 | 112 | 180 | 20,160 |
5 | 160 | 180 | 28,800 |
6 | 290 | 150 | 43,500 |
7 | 210 | 150 | 31,500 |
8 | 270 | 150 | 40,500 |
9 | 80 | 180 | 14,400 |
10 | 124 | 180 | 22,320 |
11 | 68 | 180 | 12,240 |
12 | 220 | 180 | 39,600 |
13 | 172 | 180 | 30,960 |
14 | 150 | 180 | 27,000 |
15 | 170 | 180 | 30,600 |
16 | 170 | 180 | 30,600 |
17 | 320 | 150 | 48,000 |
18 | 240 | 150 | 36,000 |
19 | 240 | 150 | 36,000 |
20 | 210 | 150 | 31,500 |
21 | 200 | 150 | 30,000 |
22 | 250 | 150 | 37,500 |
23 | 210 | 150 | 31,500 |
24 | 190 | 170 | 32,300 |
25 | 200 | 170 | 34,000 |
Field Classification | Field | Working Speed of Fertilizer Applicator (km/h) | Unit Fertilization Amount (kg/hm2) |
---|---|---|---|
Positive large | 1, 2, 3, 4 | 4 | 230 |
Positive small | 5, 6, 7, 8, 9, 10, 11 | 5 | 215 |
Medium | 12, 13, 14, 15, 16, 17, 18 | 6 | 200 |
Negative small | 19, 20, 21, 22 | 7 | 185 |
Negative large | 23, 24, 25 | 8 | 170 |
Algorithm | Parameter Settings |
---|---|
FWA | Population size: 100; Maximum explosion radius: 1000; Maximum number of sparks: 2000; Number of variation sparks: 60 |
GA | Population size: 100; Crossover probability: 0.8; Mutation probability: 0.1 |
PSO | Population size: 100; Inertia weight: 0.8; Self-learning factor: 0.5; Group learning factor: 0.5 |
CCFWA | The same parameters as for the FWA |
Statistic | FWA | GA | PSO | CCFWA |
---|---|---|---|---|
Mean value | 85.522 | 87.789 | 86.919 | 85.004 |
Variance | 0.173 | 0.280 | 0.282 | 0.117 |
Minimum value | 84.741 | 86.580 | 85.544 | 84.440 |
Maximum value | 86.455 | 88.745 | 88.087 | 85.793 |
Fertilizer Applicator Number | Daily Working Situation | |||
---|---|---|---|---|
1 | 2 | 3 | 4 | |
1 | 9→17→10 | 15→14→13 | 2→3 | 3→12 |
124 m | 172 m | 168 m | 220 m | |
7.738 h | 7.697 h | 7.998 h | 4.714 h | |
2 | 19→16→7 | 7→6→4 | 4→1 | 20→11 |
105 m | 54.6 m | 260 m | 68 m | |
7.991 h | 7.960 h | 7.589 h | 4.425 h | |
3 | 5→8 | 8→21→25→22 | 22→24→23 | 18 |
230.4 m | 79.2 m | 210 m | 240 m | |
7.996 h | 7.996 h | 7.984 h | 4.170 h |
Field Number | Daily Fertilization Amount (kg) | |||
---|---|---|---|---|
Day 1 | Day 2 | Day 3 | Day 4 | |
1 | 0 | 0 | 1076 | 0 |
2 | 0 | 0 | 828 | 0 |
3 | 0 | 0 | 695.5 | 173.9 |
4 | 0 | 226 | 237.6 | 0 |
5 | 619.2 | 0 | 0 | 0 |
6 | 0 | 935.3 | 0 | 0 |
7 | 338.6 | 338.6 | 0 | 0 |
8 | 743 | 127.7 | 0 | 0 |
9 | 309.6 | 0 | 0 | 0 |
10 | 479.9 | 0 | 0 | 0 |
11 | 0 | 0 | 0 | 263.2 |
12 | 0 | 0 | 0 | 792 |
13 | 0 | 619.2 | 0 | 0 |
14 | 0 | 540 | 0 | 0 |
15 | 0 | 612 | 0 | 0 |
16 | 612 | 0 | 0 | 0 |
17 | 960 | 0 | 0 | 0 |
18 | 0 | 0 | 0 | 720 |
19 | 666 | 0 | 0 | 0 |
20 | 0 | 0 | 0 | 582.8 |
21 | 0 | 555 | 0 | 0 |
22 | 0 | 219.8 | 474 | 0 |
23 | 0 | 0 | 535.5 | 0 |
24 | 0 | 0 | 549.1 | 0 |
25 | 0 | 578 | 0 | 0 |
Statistic | 1 | 2 | 3 | 4 | |
---|---|---|---|---|---|
Transport order | 1 | 9→19→5 | 7→8→15→14 | 4→22→2 | 3→20→11→12 |
2 | 8→16 | 6→4→13 | 24→1 | —— | |
3 | 17→10→7 | 22→25→21 | 3→23 | —— | |
Transport distance (m) | 1 | 5734 | 7370 | 7070 | 9490 |
2 | 6020 | 3484 | 6070 | —— | |
3 | 4024 | 6620 | 7760 | —— | |
Total transport distance (m) | 15,778 | 17,474 | 20,900 |
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Zhu, S.; Wang, B.; Pan, S.; Ye, Y.; Wang, E.; Mao, H. Task Allocation of Multi-Machine Collaborative Operation for Agricultural Machinery Based on the Improved Fireworks Algorithm. Agronomy 2024, 14, 710. https://doi.org/10.3390/agronomy14040710
Zhu S, Wang B, Pan S, Ye Y, Wang E, Mao H. Task Allocation of Multi-Machine Collaborative Operation for Agricultural Machinery Based on the Improved Fireworks Algorithm. Agronomy. 2024; 14(4):710. https://doi.org/10.3390/agronomy14040710
Chicago/Turabian StyleZhu, Suji, Bo Wang, Shiqi Pan, Yuting Ye, Enguang Wang, and Hanping Mao. 2024. "Task Allocation of Multi-Machine Collaborative Operation for Agricultural Machinery Based on the Improved Fireworks Algorithm" Agronomy 14, no. 4: 710. https://doi.org/10.3390/agronomy14040710