Scheduling of Multi-AGV Systems in Automated Electricity Meter Verification Workshops Based on an Improved Snake Optimization Algorithm
Abstract
:1. Introduction
- (1)
- Based on the complex environment of the automated meter verification workshop, we consider the multi-dimensional factors such as AGV path planning, collaborative obstacle avoidance, and charging constraints, and construct an AGV scheduling model for the automated meter verification workshop, considering the charging constraints with the goal of minimizing the distribution cost and charging cost.
- (2)
- For large-scale order scheduling and multi-AGV scheduling problems, we designed an improved snake optimization algorithm (ISO). By adopting a random reverse learning strategy to generate a larger initial population solution space followed by individualized memory strategy and Gaussian mutation operations to enhance global and local search capabilities, significant improvements in solving efficiency and solution quality were achieved. Experimental results show that the proposed algorithm can greatly reduce the total cost required for AGVs to complete orders compared to traditional methods.
- (3)
- In the simulation experiments, we use algorithm benchmarking, case analysis, and parameter sensitivity analysis to comprehensively verify the effectiveness of the designed method in dealing with high-dimensional optimization problems, reducing the path length of AGVs, and reducing charging costs. In addition, the algorithm process is analyzed through a visual method and the effectiveness of the proposed strategy is visually demonstrated.
2. Materials and Methods
2.1. Background
2.2. Model Assumptions
- We assume that the automated verification line materials fully meet the order demand, and only consider the AGVs out of the warehouse task and charging task scenarios;
- We assume the AGV reaches the pickup location and materials are loaded onto it, without accounting for the time needed for loading.
- We assume that the AGVs travel at a constant speed during the whole process, the power loss of the AGV has a linear relationship with the transportation distance, i.e., ignoring the start–stop time of the AGVs;
- When AGVs work, the discharge current is continuous and stable, ignoring the impact of power loss caused by the load of metering materials;
- Neglecting the AGV charging process by increasing the charging time window penalty required to complete the charging task.
- In previous studies, the paths of individual AGVs were considered to be asymmetric due to the influence of various factors such as orders, complex scenarios, and algorithm differences [31]. To study the path planning and motion control of AGVs in complex factory environments, this paper abstracts and models an automated electric meter verification workshop as a grid map. In the map (Figure 2), white grids represent traversable areas, with each grid representing a certain distance unit; blue grids denote shelves for storing materials; black grids are obstacle pillars; red grids indicate emergency handling areas; yellow grids represent charging stations; pink grids denote verification workshop platforms; and green grids represent material transfer points. Among them, pillars, emergency handling areas, platform areas, and the interiors of shelves are defined as obstacle areas. When an AGV sends a charging request, the system will randomly assign an available charging station, which is then no longer considered an obstacle. The raster map consists of 56 × 23 grids, in which a Cartesian coordinate system is established from the lower left corner, and each grid is represented by coordinates (X,Y), where X is between 1 and 56 and Y is between 1 and 23.
2.3. Symbol Description
2.4. Multi-AGV Scheduling Model of Automated Meter Verification Workshop Considering Charging Constraints
3. Algorithm Description
3.1. Standard SO Algorithm
3.2. Improved SO Algorithm
- (1)
- Random opposition-based learning initialization
- (2)
- Individualized memory strategy
- (3)
- Gaussian variational strategy
3.3. Improved A* Algorithm
3.4. AGV Encoding and Decoding
3.5. Large Neighborhood Search
4. Simulation Experiment Results and Analysis
4.1. Experiment 1: Algorithm Improvement Strategy Validation and Multi-Algorithm Data Comparison Analysis
4.2. Experiment 2: Solving Multi-AGV Scheduling Model of Automated Meter Verification Workshop Taking into Account Charging Constraints
4.3. Algorithm Time Complexity Analysis
4.4. Parameter Sensitivity Analysis
5. Results
6. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Appendix A. Test Results for the Algorithms
PSO | WOA | DE | MVO | GA | SO | ISO | ||
---|---|---|---|---|---|---|---|---|
Mean | 7.68 × 101 | 3.51 × 10−26 | 2.11 × 101 | 3.88 × 104 | 1.04 × 10−33 | 1.30 × 10−39 | 2.58 × 10−50 | |
Std | 4.07 × 101 | 1.81 × 10−25 | 6.05 × 100 | 7.06 × 103 | 2.56 × 10−33 | 2.97 × 10−39 | 5.92 × 10−50 | |
Mean | 2.01 × 101 | 1.82 × 10−19 | 1.16 × 100 | 9.62 × 1015 | 1.98 × 10−12 | 1.22 × 10−19 | 2.50 × 10−27 | |
Std | 5.29 × 100 | 5.91 × 10−19 | 1.49 × 10−1 | 2.79 × 1016 | 1.48 × 10−12 | 3.02 × 10−19 | 4.57 × 10−27 | |
Mean | 2.27 × 103 | 2.75 × 104 | 3.44 × 104 | 4.47 × 105 | 1.77 × 10−20 | 1.41 × 10−21 | 1.59 × 10−37 | |
Std | 1.01 × 103 | 9.48 × 103 | 5.01 × 103 | 4.79 × 105 | 5.71 × 10−20 | 3.45 × 10−21 | 4.52 × 10−37 | |
Mean | 2.02 × 101 | 3.15 × 101 | 4.03 × 101 | 6.90 × 101 | 3.64 × 10−13 | 1.98 × 10−13 | 7.57 × 10−23 | |
Std | 5.88 × 100 | 1.72 × 101 | 3.47 × 100 | 5.07 × 100 | 6.19 × 10−13 | 2.47 × 10−13 | 1.07 × 10−22 | |
Mean | 8.22 × 104 | 2.87 × 101 | 2.24 × 103 | 4.01 × 107 | 2.47 × 101 | 2.47 × 101 | 2.71 × 101 | |
Std | 7.22 × 104 | 1.68 × 10−1 | 6.51 × 102 | 1.68 × 107 | 9.17 × 100 | 9.14 × 100 | 9.34 × 10−1 | |
Mean | 7.95 × 101 | 1.24 × 100 | 2.12 × 101 | 4.14 × 104 | 4.87 × 100 | 5.42 × 10−2 | 9.72 × 10−1 | |
Std | 3.53 × 101 | 3.98 × 10−1 | 5.89 × 100 | 8.83 × 103 | 2.67 × 100 | 3.42 × 10−2 | 4.07 × 10−1 | |
Mean | 4.48 × 10−1 | 7.68 × 10−3 | 1.77 × 10−1 | 1.95 × 10−1 | 6.34 × 10−4 | 4.82 × 10−4 | 9.93 × 10−4 | |
Std | 1.66 × 10−1 | 9.10 × 10−3 | 3.50 × 10−2 | 6.23 × 10−2 | 6.37 × 10−4 | 2.78 × 10−4 | 1.01 × 10−3 | |
Mean | −7.08 × 103 | −5.76 × 103 | −8.48 × 103 | −6.45 × 103 | −1.23 × 104 | −1.19 × 104 | −9.84 × 103 | |
Std | 6.78 × 102 | 5.86 × 102 | 3.73 × 102 | 7.89 × 102 | 5.48 × 102 | 8.64 × 102 | 1.46 × 103 | |
Mean | 1.06 × 102 | 1.93 × 10−1 | 9.98 × 101 | 1.36 × 102 | 1.82 × 101 | 1.99 × 101 | 0.00 × 100 | |
Std | 1.67 × 101 | 1.06 × 100 | 7.44 × 100 | 2.68 × 101 | 2.03 × 101 | 2.49 × 101 | 0.00 × 100 | |
Mean | 8.14 × 100 | 1.92 × 10−14 | 2.89 × 100 | 1.82 × 101 | 2.37 × 10−12 | 4.44 × 10−15 | 6.46 × 10−1 | |
Std | 9.78 × 10−1 | 1.10 × 10−14 | 2.27 × 10−1 | 5.40 × 10−1 | 1.61 × −12 | 0.00 × 100 | 3.54 × 100 | |
Mean | 1.02 × 100 | 1.33 × 10−2 | 1.21 × 100 | 4.06 × 102 | 0.00 × 100 | 0.00 × 100 | 0.00 × 100 | |
Std | 3.38 × 10−2 | 7.30 × 10−2 | 6.11 × 10−2 | 5.80 × 101 | 0.00 × 100 | 0.00 × 100 | 0.00 × 100 | |
Mean | 2.61 × 101 | 9.51 × 10−2 | 1.21 × 100 | 1.22 × 108 | 5.50 × 10−1 | 1.74 × 10−2 | 3.57 × 10−2 | |
Std | 1.80 × 101 | 1.19 × 10−1 | 4.33 × 10−1 | 5.14 × 107 | 6.09 × 10−1 | 1.46 × 10−2 | 1.91 × 10−2 | |
Mean | 2.40 × 103 | 9.56 × 10−1 | 3.44 × 100 | 3.02 × 108 | 1.05 × 100 | 5.03 × 10−2 | 1.50 × 100 | |
Std | 8.78 × 103 | 3.35 × 10−1 | 9.34 × 10−1 | 1.46 × 108 | 1.26 × 100 | 3.78 × 10−2 | 3.27 × 10−1 | |
Mean | 3.18 × 100 | 3.09 × 100 | 1.23 × 100 | 1.33 × 101 | 1.69 × 100 | 1.43 × 100 | 2.53 × 100 | |
Std | 4.17 × 100 | 3.20 × 100 | 1.09 × 100 | 7.01 × 100 | 1.47 × 100 | 9.26 × 10−1 | 3.36 × 100 | |
Mean | 5.22 × 10−4 | 1.20 × 10−3 | 1.51 × 10−3 | 2.55 × 10−2 | 1.91 × 10−3 | 1.06 × 10−3 | 1.13 × 10−3 | |
Std | 3.15 × 10−4 | 2.42 × 10−3 | 1.06 × 10−3 | 4.00 × 10−2 | 4.24 × 10−3 | 2.49 × 10−3 | 3.66 × 10−3 | |
Mean | −1.03 × 100 | −1.03 × 100 | −1.03 × 100 | −9.23 × 10−1 | −1.03 × 100 | −1.03 × 100 | −1.03 × 100 | |
Std | 3.84 × 10−13 | 7.88 × 10−8 | 5.76 × 10−16 | 2.82 × 10−1 | 4.52 × 10−16 | 4.68 × 10−16 | 5.38 × 10−16 | |
Mean | 1.60 × 10−1 | 1.62 × 10−1 | 1.61 × 10−1 | 1.75 × 10−1 | 1.61 × 10−1 | 1.61 × 10−1 | 1.61 × 10−1 | |
Std | 2.76 × 10−4 | 3.57 × 10−3 | 7.99 × 10−4 | 2.99 × 10−2 | 3.61 × 10−3 | 3.60 × 10−3 | 3.66 × 10−3 | |
Mean | 3.00 × 100 | 3.00 × 100 | 3.00 × 100 | 3.54 × 101 | 3.90 × 100 | 3.00 × 100 | 3.00 × 100 | |
Std | 7.94 × −12 | 7.37 × 10−4 | 1.71 × 10−15 | 1.52 × 102 | 4.93 × 100 | 4.59 × 10−15 | 3.56 × 10−15 | |
Mean | −3.86 × 100 | −3.86 × 100 | −3.86 × 100 | −3.86 × 100 | −3.86 × 100 | −3.86 × 100 | −3.86 × 100 | |
Std | 1.04 × 10−3 | 9.81 × 10−3 | 2.49 × −15 | 7.13 × 10−5 | 2.13 × 10−15 | 2.20 × 10−15 | 2.44 × 10−15 | |
Mean | −3.22 × 100 | −3.27 × 100 | −3.32 × 100 | −3.27 × 100 | −3.31 × 100 | −3.31 × 100 | −3.28 × 100 | |
Std | 7.30 × 10−2 | 7.29 × 10−2 | 2.46 × 10−3 | 6.22 × 10−2 | 4.11 × 10−2 | 3.02 × 10−2 | 5.70 × 10−2 | |
Mean | −6.49 × 100 | −7.76 × 100 | −9.27 × 100 | −5.99 × 100 | −9.69 × 100 | −9.65 × 100 | −9.15 × 100 | |
Std | 3.47 × 100 | 2.63 × 100 | 1.84 × 100 | 3.73 × 100 | 1.11 × 100 | 1.04 × 100 | 2.60 × 100 | |
Mean | −7.38 × 100 | −7.26 × 100 | −9.71 × 100 | −4.14 × 100 | −9.61 × 100 | −9.94 × 100 | −9.67 × 100 | |
Std | 3.49 × 100 | 2.96 × 100 | 1.16 × 100 | 2.63 × 100 | 1.67 × 100 | 9.81 × 10−1 | 2.24 × 100 | |
Mean | −7.44 × 100 | −6.37 × 100 | −1.01 × 101 | −4.13 × 100 | −9.91 × 100 | −1.00 × 101 | −9.02 × 100 | |
Std | 3.67 × 100 | 3.01 × 100 | 5.47 × 10−1 | 3.03 × 100 | 1.42 × 100 | 1.21 × 100 | 3.10 × 100 |
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M. Mousavi (2017) [7] | J. Li (2202) [31] | A. Ammar (2016) [2] | M. Gen (2014) [10] | X. Shao (2023) [11] | J. C. Tu (2017) [12] | E. Hu (2023) [13] | B. Xin (2023) [14] | H. Niu (2023) [15] | X. A. Martin (2023) [16] | Z. Wang (2023) [17] | L. Meng (2023) [18] | Y. Gao (2023) [19] | Q. Liu (2023) [20] | Q. Zeng (2022) [21] | T. Adamo (2023) [22] | B.-H. Zhou (2023) [23] | W.-Q. Zou (2020) [24] | Z. Jiang (2023) [25] | N. Wu (2005) [26] | N. Singh (2022) [27] | M. Boccia (2020) [28] | Q.-V. Dang (2021) [30] | Current work | |
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
VRP | ||||||||||||||||||||||||
multi-vehicle | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | ||||||
single vehicle | x | x | x | x | x | x | ||||||||||||||||||
Pickup and delivery | x | x | x | x | x | x | x | x | x | |||||||||||||||
Capacitated | x | x | x | x | x | x | x | x | x | x | x | |||||||||||||
Vehicle fleet | ||||||||||||||||||||||||
Homogeneous | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | ||||||||
Heterogeneous | x | x | x | |||||||||||||||||||||
Time windows | ||||||||||||||||||||||||
None | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | x | ||||||
Soft | x | x | x | |||||||||||||||||||||
Hard | x | x | x | |||||||||||||||||||||
Battery management | x | |||||||||||||||||||||||
None | x | x | x | x | x | x | x | x | x | x | x | x | x | |||||||||||
Battery swapping | ||||||||||||||||||||||||
Full charge | x | x | x | x | x | |||||||||||||||||||
Partial Charge | x | x | x | x | x | |||||||||||||||||||
Search method | ||||||||||||||||||||||||
LNS | x | x | ||||||||||||||||||||||
Exact method | x | x | x | x | x | |||||||||||||||||||
RL | x | x | x | x | ||||||||||||||||||||
Heuristic algorithm | x | x | x | x | x | x | x | x | x | x | x | x | x | |||||||||||
Route planning | ||||||||||||||||||||||||
None | x | x | x | x | x | x | x | x | x | x | ||||||||||||||
A-star algorithm | x | x | x | |||||||||||||||||||||
Crashworthiness | x | x | x | x | x | x | x | x | ||||||||||||||||
Collaboration | x | x | x | x | x | x |
Parameter | Symbol Description |
---|---|
All order collections | |
The set of AGV-feasible nodes | |
Collection of all material storage spaces | |
Collection of material types | |
All verification line entrances | |
Collection of all AGVs | |
Collection of all time points on the timeline | |
Orders, | |
material storage space, | |
Measuring supplies, | |
Entrance to the verification line | |
Handling robot AGV, | |
Time | |
Quantity of i dosing material in the storage space | |
Transportation distance from the storage space to the verification line entrance | |
Demand for metering materials i at the entrance to the verification line | |
Quantity of metered materials sent from storage to verification line entrance | |
Number of free AGV carts at any given time | |
Average number of orders assigned to each picking station | |
Number of picking stations | |
Distance from m node to node n | |
AGV traveling speed | |
AGV battery full charge | |
Total AGV running time | |
Minimum amount of power needed to charge the AGV | |
Charging time of the kth unit | |
Charging rate of the AGV | |
Actual power consumption of the kth AGV | |
Power consumed by the kth AGV |
Variables | Symbol Description |
---|---|
Name | Function | Range | Fmin |
---|---|---|---|
Sphere Function | [−100,100] | 0 | |
Schwefel’s Problem 2.22 | [−10,10] | 0 | |
Schwefel’s Problem 1.2 | [−100,100] | 0 | |
Schwefel’s Problem 2.21 | [−100,100] | 0 | |
Generalized Rosenbrock’s Function | [−30,30] | 0 | |
Step Function | [−100,100] | 0 | |
Quartic Function i.e., Noise | [−1.28,1.28] | 0 | |
Generalized Schwefel’s Problem 2.26 | [−500,500] | −12,569.5 | |
Generalized Rastrigin’s Function | [−5.12,5.12] | 0 | |
Ackley’s Function | [−32,32] | 0 | |
Generalized Griewank’s Function | [−600,600] | 0 | |
Generalized Penalized Function | [−50,50] | 0 | |
Generalized Penalized Function | [−50,50] | 0 | |
Shekel’s Foxholes Function | [−65,65] | 1 | |
Kowalik’s Function | [−5,5] | 0.1484 | |
Six-Hump Camel-Back Function | [−5,5] | −1 | |
Branin Function | [−5,5] | 0.3 | |
Goldstein-Price Function | [−2,2] | 3 | |
Hartman’s Family | [1,3] | −3 | |
[0,1] | −3 | ||
Shekel’s Family | [0,10] | −1 | |
[0,10] | −1 | ||
[0,10] | −1 |
Algorithms | |||||||||
---|---|---|---|---|---|---|---|---|---|
Best | PSO | 2.31 × 101 | 5.92 × 102 | 2.67 × 101 | 2.68 × 10−1 | −8.76 × 103 | 6.17 × 100 | 3.24 × 101 | 9.98 × 10−1 |
WOA | 2.63 × 10−34 | 6.72 × 103 | 4.79 × 10−1 | 2.40 × 10−4 | −8.38 × 103 | 8.88 × 10−16 | 3.16 × 10−1 | 9.98 × 10−1 | |
DE | 1.64 × 101 | 2.47 × 104 | 1.18 × 101 | 1.16 × 10−1 | −9.11 × 103 | 2.44 × 100 | 1.19 × 100 | 9.98 × 10−1 | |
GWO | 1.37 × 10−41 | 5.28 × 10−26 | 2.87 × 10−1 | 1.39 × 10−4 | −1.25 × 104 | 8.88 × 10−16 | 7.75 × 10−1 | 9.98 × 10−1 | |
MVO | 1.82 × 10−5 | 2.86 × 101 | 2.42 × 10−1 | 1.56 × 10−3 | −1.25 × 104 | 6.98 × 10−16 | 3.19 × 10−1 | 9.98 × 10−1 | |
GA | 2.51 × 101 | 2.57 × 103 | 1.63 × 101 | 1.78 × 10−1 | −1.25 × 104 | 2.44 × 10−13 | 1.36 × 100 | 9.98 × 10−1 | |
SO | 4.04 × 10−37 | 8.69 × 10−25 | 3.77 × 10−2 | 1.65 × 10−4 | −1.26 × 104 | 2.39 × 10−13 | 1.13 × 10−5 | 9.98 × 10−1 | |
ISO | 2.53 × 10−56 | 2.90 × 10−43 | 8.4 × 10−3 | 1.31 × 10−5 | −1.26 × 104 | 8.88 × 10−16 | 9.08 × 10−3 | 9.98 × 10−1 | |
Avg | PSO | 8.07 × 101 | 2.25 × 103 | 7.21 × 101 | 5.26 × 10−1 | −7.22 × 103 | 8.34 × 100 | 1.21 × 104 | 4.62 × 100 |
WOA | 3.44 × 10−28 | 2.49 × 104 | 1.12 × 100 | 7.78 × 10−3 | −5.94 × 103 | 2.30 × 10−14 | 1.02 × 100 | 3.49 × 100 | |
DE | 2.47 × 101 | 3.42 × 104 | 2.30 × 101 | 1.88 × 10−1 | −8.51 × 103 | 2.91 × 100 | 3.88 × 100 | 1.39 × 100 | |
GWO | 2.78 × 10−39 | 9.19 × 10−21 | 9.60 × 10−1 | 1.32 × 10−3 | −1.04 × 104 | 3.31 × 100 | 1.58 × 100 | 1.72 × 100 | |
MVO | 1.89 × 10−8 | 1.56 × 10−13 | 1.54 × 101 | 1.33 × 10−3 | −5.72 × 103 | 2.62 × 100 | 1.81 × 100 | 2.93 × 100 | |
GA | 2.65 × 101 | 3.98 × 101 | 2.12 × 100 | 2.09 × 10−1 | −6.59 × 104 | 1.39 × 100 | 3.74 × 101 | 1.66 × 100 | |
SO | 4.78 × 10−34 | 2.97 × 10−20 | 4.43 × 100 | 6.45 × 10−4 | −1.19 × 104 | 2.80 × 10−12 | 1.58 × 100 | 2.00 × 100 | |
ISO | 1.01 × 10−5 | 1.01 × 10−35 | 4.39 × 10−2 | 4.64 × 10−4 | −1.21 × 104 | 4.32 × 10−15 | 6.22 × 10−2 | 1.06 × 100 | |
Std | PSO | 3.75 × 101 | 1.06 × 103 | 3.24 × 101 | 1.74 × 10−1 | 7.99 × 102 | 9.82 × 10−1 | 5.80 × 104 | 4.27 × 100 |
WOA | 8.65 × 10−28 | 9.58 × 103 | 3.68 × 10−1 | 9.47 × 10−3 | 8.24 × 102 | 1.20 × 10−14 | 3.18 × 10−1 | 3.32 × 100 | |
DE | 5.57 × 100 | 4.76 × 103 | 6.57 × 100 | 3.56 × 10−2 | 3.40 × 102 | 2.18 × 10−1 | 1.27 × 100 | 9.56 × 10−1 | |
GWO | 5.85 × 10−39 | 3.21 × 10−20 | 3.52 × 10−1 | 1.06 × 10−3 | 1.56 × 103 | 7.52 × 100 | 3.58 × 10−1 | 1.96 × 100 | |
MVO | 5.81 × 10−12 | 4.16 × 101 | 3.49 × 100 | 2.51 × 10−2 | 2.73 × 103 | 2.85 × 101 | 1.06 × 100 | 8.05 × 10−1 | |
GA | 3.61 × 10−9 | 3.68 × 103 | 2.02 × 101 | 3.09 × 10−3 | 1.98 × 103 | 1.23 × 10−7 | 3.35 × 101 | 3.54 × 100 | |
SO | 1.11 × 10−33 | 9.63 × 10−20 | 2.92 × 100 | 5.01 × 10−4 | 8.15 × 102 | 2.02 × 10−12 | 1.31 × 100 | 1.89 × 100 | |
ISO | 1.44 × 10−50 | 4.03 × 10−35 | 4.34 × 10−2 | 2.77 × 10−4 | 7.92 × 102 | 6.49 × 10−16 | 3.58 × 10−2 | 2.52 × 10−1 |
Algorithms | |||||||||
---|---|---|---|---|---|---|---|---|---|
Best | PSO | 5.27 × 104 | 3.76 × 105 | 4.82 × 101 | 4.85 × 104 | 2.60 × 102 | −5.74 × 104 | 1.67 × 101 | 1.43 × 108 |
WOA | 1.17 × 10−30 | 1.81 × 106 | 7.13 × 10−1 | 1.52 × 101 | 2.87 × 10−4 | −6.34 × 104 | 4.44 × 10−15 | 9.94 × 100 | |
DE | 2.65 × 105 | 2.50 × 106 | 9.78 × 101 | 2.60 × 105 | 2.98 × 103 | −2.85 × 104 | 1.92 × 101 | 3.11 × 109 | |
GWO | 4.67 × 10−27 | 8.51 × 10−18 | 3.45 × 10−11 | 6.37 × 101 | 2.91 × 10−4 | −1.00 × 105 | 3.57 × 10−11 | 2.97 × 101 | |
MVO | 2.32 × 10−5 | 3.21 × 105 | 5.26 × 10−1 | 1.62 × 102 | 2.53 × 10−3 | −1.25 × 105 | 1.84 × 10−6 | 3.73 × 106 | |
GA | 1.96 × 10−3 | 2.16 × 103 | 6.94 × 101 | 2.75 × 103 | 1.75 × 103 | −2.56 × 104 | 1.59 × 101 | 2.52 × 101 | |
SO | 3.73 × 10−24 | 1.76 × 10−16 | 2.39 × 10−12 | 6.21 × 10−1 | 8.80 × 10−5 | −1.26 × 105 | 1.21 × 10−11 | 7.22 × 10−1 | |
ISO | 3.10 × 10−32 | 3.55 × 10−20 | 1.94 × 10−12 | 6.26 × 10−1 | 1.14 × 10−4 | −1.26 × 105 | 4.44 × 10−15 | 1.57 × 10−2 | |
Avg | PSO | 6.46 × 104 | 6.58 × 105 | 5.50 × 101 | 6.75 × 104 | 4.39 × 102 | −5.22 × 104 | 1.77 × 101 | 4.11 × 108 |
WOA | 1.54 × 10−26 | 3.09 × 106 | 4.79 × 101 | 2.75 × 101 | 1.28 × 10−2 | −4.16 × 104 | 4.41 × 10−14 | 1.70 × 101 | |
DE | 2.85 × 105 | 3.47 × 106 | 9.85 × 101 | 2.88 × 105 | 3.91 × 103 | −2.70 × 104 | 1.95 × 101 | 4.16 × 109 | |
GWO | 1.90 × 10−23 | 4.44 × 10−11 | 5.43 × 10−11 | 6.78 × 101 | 2.28 × 10−3 | −8.52 × 104 | 5.60 × 100 | 2.99 × 101 | |
MVO | 3.95 × 10−6 | 3.13 × 105 | 5.02 × 10−1 | 2.51 × 102 | 1.99 × 10−3 | −2.23 × 104 | 2.63 × 10−3 | 1.62 × 102 | |
GA | 2.05 × 101 | 3.49 × 106 | 2.81 × 101 | 1.95 × 101 | 1.67 × 102 | −2.89 × 104 | 1.84 × 10−2 | 2.35 × 105 | |
SO | 2.01 × 10−21 | 2.33 × 10−10 | 1.12 × 10−11 | 5.07 × 101 | 5.40 × 10−4 | −1.22 × 105 | 1.60 × 10−10 | 1.20 × 101 | |
ISO | 4.33 × 10−30 | 8.31 × 10−11 | 1.31 × 10−11 | 1.84 × 100 | 5.12 × 10−4 | −1.23 × 105 | 4.56 × 10−15 | 1.36 × 100 | |
Std | PSO | 7.17 × 103 | 1.95 × 105 | 4.56 × 100 | 8.96 × 103 | 1.05 × 102 | 3.31 × 103 | 4.39 × 10−1 | 1.44 × 108 |
WOA | 4.60 × 10−26 | 1.01 × 106 | 2.20 × 101 | 6.00 × 100 | 1.86 × 10−2 | 8.63 × 103 | 9.74 × 10−14 | 4.36 × 100 | |
DE | 1.12 × 104 | 3.95 × 105 | 2.91 × 10−1 | 1.20 × 104 | 3.15 × 102 | 7.53 × 102 | 1.54 × 10−1 | 4.67 × 108 | |
GWO | 6.48 × 10−23 | 1.95 × 10−10 | 1.25 × 10−10 | 1.35 × 100 | 1.40 × 10−3 | 7.05 × 103 | 8.35 × 100 | 6.66 × 10−2 | |
MVO | 1.76 × 10−2 | 1.75 × 10−4 | 2.11 × 10−5 | 1.85 × 102 | 1.19 × 10−2 | 5.86 × 103 | 1.43 × 10−4 | 2.52 × 106 | |
GA | 1.34 × 103 | 2.59 × 102 | 1.62 × 101 | 1.26 × 103 | 2.05 × 103 | 4.47 × 103 | 1.37 × 10−1 | 1.63 × 102 | |
SO | 3.13 × 10−21 | 1.14 × 10−9 | 6.63 × 10−12 | 2.95 × 101 | 5.12 × 10−4 | 5.85 × 103 | 7.93 × 10−11 | 1.27 × 101 | |
ISO | 7.30 × 10−30 | 4.54 × 10−10 | 8.88 × 10−12 | 7.85 × 10−1 | 3.39 × 10−4 | 4.46 × 103 | 6.49 × 10−16 | 7.65 × 10−1 |
Cargo Type | Name | Crate Specifications | Dimensions (L × W × H) | Maximum Load Per Box |
---|---|---|---|---|
A | single-phase energy meter | 12 pcs/box | 720 450 120 (mm) | 25 kg/box |
B | three-phase energy meter | 4 pcs/box | ||
C | Low Voltage Transformers | 12 pcs/box | 720 450 200 (mm) | 50 kg/box |
Order Number | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | … | 299 | 300 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
Storage coordinates(X,Y) | 48,3 | 34,3 | 41,3 | 47,13 | 54,4 | 54,17 | 41,10 | 33,4 | 33,5 | … | 54,21 | 33,10 |
Delivery point(X,Y) | 4,21 | 8,21 | 16,21 | 16,21 | 8,21 | 4,21 | 12,21 | 12,21 | 8,21 | … | 12,21 | 4,21 |
Meter type | C | C | A | C | B | A | B | B | B | … | C | B |
Weight of material | 48 | 42 | 45 | 12 | 24 | 45 | 27 | 15 | 54 | … | 15 | 27 |
Quantity of material | 24 | 21 | 15 | 6 | 12 | 21 | 15 | 9 | 27 | … | 9 | 15 |
AGV1 | AGV2 | AGV3 | AGV4 | AGV5 | AGV6 | AGV7 | AGV8 | AGV9 | AGV10 | |
---|---|---|---|---|---|---|---|---|---|---|
Initial charge | 96% | 97% | 82% | 75% | 95% | 100% | 99% | 90% | 98% | 93% |
Initial position(X,Y) | 10,7 | 15,5 | 11,19 | 40,8 | 41,9 | 55,13 | 14,12 | 33,15 | 47,22 | 30,1 |
Maximum load (kg) | 120 | 120 | 120 | 120 | 120 | 120 | 120 | 120 | 120 | 120 |
Algorithms | FIFO | PSO | GA | MVO | DE | WOA | SO | ISO | |||||||||
Number of AGVs | Times | Costs | Times | Costs | Times | Costs | Times | Costs | Times | Costs | Times | Costs | Times | Costs | Times | Costs | |
AGV1 | 9 | 1955 | 7 | 1538 | 6 | 1700 | 8 | 1728 | 8 | 1721 | 7 | 1734 | 7 | 1679 | 6 | 1566 | |
AGV2 | 9 | 1887 | 7 | 1764 | 7 | 1757 | 7 | 1692 | 7 | 1701 | 7 | 1592 | 7 | 1715 | 6 | 1508 | |
AGV3 | 9 | 1865 | 8 | 1719 | 8 | 1728 | 8 | 1567 | 8 | 1730 | 7 | 1710 | 6 | 1689 | 5 | 1585 | |
AGV4 | 8 | 1787 | 7 | 1646 | 6 | 1741 | 6 | 1676 | 6 | 1635 | 6 | 1681 | 6 | 1674 | 6 | 1602 | |
AGV5 | 8 | 1741 | 7 | 1689 | 8 | 1761 | 6 | 1708 | 6 | 1654 | 6 | 1735 | 6 | 1682 | 5 | 1523 | |
AGV6 | 9 | 1735 | 8 | 1659 | 7 | 1627 | 6 | 1764 | 6 | 1761 | 6 | 1710 | 6 | 1704 | 5 | 1482 | |
AGV7 | 8 | 1709 | 7 | 1594 | 8 | 1689 | 8 | 1675 | 7 | 1736 | 8 | 1750 | 7 | 1682 | 5 | 1518 | |
AGV8 | 9 | 1763 | 8 | 1654 | 7 | 1697 | 7 | 1668 | 7 | 1561 | 7 | 1667 | 7 | 1681 | 5 | 1493 | |
AGV9 | 8 | 1720 | 8 | 1713 | 7 | 1573 | 7 | 1752 | 7 | 1764 | 7 | 1749 | 7 | 1569 | 5 | 1583 | |
AGV10 | 8 | 1715 | 7 | 1712 | 8 | 1534 | 8 | 1748 | 7 | 1658 | 7 | 1753 | 7 | 1717 | 5 | 1490 | |
Totals | 85 | 17,877 | 74 | 16,688 | 72 | 16,807 | 71 | 16,978 | 69 | 16,921 | 68 | 17,081 | 66 | 16,792 | 53 | 15,350 |
AGV Number | Carrier Orders |
---|---|
AGV1 | [186,92]→[131,168,109,253,225]→[114,72,41]→[22,216,144]→[100,90,107]→[286,95,247,138] →[258,50,60,178]→[111,148,273]→[194,271,12] |
AGV2 | [5,197,284,85]→[165,48,30]→ [192,80,214,264]→[183,294]→[38,279]→[25,10]→[161,98,282] →[52,207]→[202,238,222,137]→[28,120,134,21] |
AGV3 | [55,64,267,201,20,54]→[295,23]→[37,62,276]→[3,119,176,260]→[24,36,146,280]→[93,46,118,254] →[8,126,205,160,223]→[58,163] |
AGV4 | [167,252,70,191]→[269,43]→[1,33,78,113,239]→[200,256,71]→[208,162,136]→[177,249]→[175,232,115] →[129,219]→[149,6,240]→[45,39,94] |
AGV5 | [66,166,204,49]→[227,159,300,103]→[19,56,106,59]→[112,91,82]→[110,128]→[147,265,241]→[242,281,121,188] →[261,196,278]→[140,170]→245 |
AGV6 | [174,13,226]→[198,203,274]→[105,248]→[180,32,75,234]→[209,150]→[132,51]→[157,206,74]→[97,285,145,236,154] →[139,185,77,123]→[11,73] |
AGV7 | [231,47,151]→[298,9]→[35,268,244,277]→[27,164,101]→[292,117,124]→[259,67,217,228,288]→[270,96,290,34] →[42,116,230]→[53,7,29] |
AGV8 | [69,141,142]→[89,44,86]→[135,133,173]→[297,211,88]→[218,283]→[16,187]→[108,246,262,63,190]→[84,153,130,143] →[61,266]→[224,210,272] |
AGV9 | [181,182]→[195,15]→[220,289]→[40,152,221]→[250,235]→[251,243,122]→[102,81,26]→[199,2,237]→[287,215,171] →[169,83,18]→[155,299,257]→76 |
AGV10 | [193,4,87,125]→[158,99]→[156,14,104,127]→[291,31]→[172,296,275]→[57,255]→[263,229,179]→[65,184]→[293,68,17] →[213,189,233,79]→212 |
AGV1 | AGV2 | ||||
---|---|---|---|---|---|
Path Coordinates (X,Y) | Timestamp | Path Coordinates (X,Y) | Timestamp | ||
Ending coordinates | Ending coordinates | ||||
… | … | … | … | ||
35 | 15 | (288) | 38 | 8 | (288) |
34 | 15 | (287) | 39 | 8 | (287) |
33 | 15 | (286) | 40 | 7 | (286) |
32 | 15 | (285) | 40 | 6 | (285) |
… | … | … | … | … | … |
54 | 13 | (138) | 8 | 21 | (138) |
54 | 14 | (137) | 7 | 21 | (137) |
53 | 15 | (136) | 6 | 21 | (136) |
52 | 16 | (135) | 5 | 21 | (135) |
51 | 16 | (134) | 4 | 21 | (134) |
… | … | … | … | … | … |
20 | 15 | (10) | 25 | 3 | (10) |
19 | 15 | (9) | 24 | 3 | (9) |
18 | 15 | (8) | 23 | 3 | (8) |
17 | 14 | (7) | 22 | 3 | (7) |
16 | 13 | (6) | 21 | 3 | (6) |
15 | 12 | (5) | 20 | 3 | (5) |
14 | 11 | (4) | 19 | 3 | (4) |
13 | 10 | (3) | 18 | 3 | (3) |
12 | 9 | (2) | 17 | 3 | (2) |
11 | 8 | (1) | 16 | 4 | (1) |
starting coordinates | (0) | starting coordinates | (0) |
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Shi, K.; Zhang, M.; He, Z.; Yin, S.; Ai, Z.; Pan, N. Scheduling of Multi-AGV Systems in Automated Electricity Meter Verification Workshops Based on an Improved Snake Optimization Algorithm. Symmetry 2023, 15, 2034. https://doi.org/10.3390/sym15112034
Shi K, Zhang M, He Z, Yin S, Ai Z, Pan N. Scheduling of Multi-AGV Systems in Automated Electricity Meter Verification Workshops Based on an Improved Snake Optimization Algorithm. Symmetry. 2023; 15(11):2034. https://doi.org/10.3390/sym15112034
Chicago/Turabian StyleShi, Kun, Miaohan Zhang, Zhaolei He, Shi Yin, Zhen Ai, and Nan Pan. 2023. "Scheduling of Multi-AGV Systems in Automated Electricity Meter Verification Workshops Based on an Improved Snake Optimization Algorithm" Symmetry 15, no. 11: 2034. https://doi.org/10.3390/sym15112034