1. Off-Line AGV Routing on the 2D Mesh Topology with Partial Permutation
Zeng Jianyang and Hsu Wen-Jing
Center for Advanced Information Systems
School of Computer Engineering
Nanyang Technological University, Singapore

2. Outline Introduction Literature Review Off-Line Mesh Routing
Conclusions and Future Work
The outline of my presentation is as following. Firstly, I will begin with the introduction, and literature review, next, I will talk about the linear path layout and its routing algorithm. Then, I will introduce the conflict-free routing algorithm for the mesh topology. After that, I will present an on-line and an off-line routing algorithm for the mesh path layout. Finally, I will give the conclusions and my future work.
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3. Outline Introduction Literature Review Off-Line Mesh Routing
Conclusions and Future Work
The outline of my presentation is as following. Firstly, I will begin with the introduction, and literature review, next, I will talk about the linear path layout and its routing algorithm. Then, I will introduce the conflict-free routing algorithm for the mesh topology. After that, I will present an on-line and an off-line routing algorithm for the mesh path layout. Finally, I will give the conclusions and my future work.
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4. Introduction AGV: Automated Guided Vehicles Problem of AGV Routing
Feasible or even optimal path
Simultaneously, without conflict, deadlock, and congestion
Compared with Shortest Path Problem (SPP)
SPP is simpler than AGV routing problem
Compared with Vehicle Routing Problem (VRP)
Length of vehicle is negligible in VRP
Collisions can be ignored in VRP
Topology is fixed and irregular in VRP
Firstly, we introduce what is AGV, AGV means automated guided vehicle.
The AGV routing problem is to find a feasible or even optimal path for each AGV, and route all AGVs from their sources to their destinations simultaneously without conflict, deadlock, and congestion.
Although it seems that the AGV routing problem is quite similar to the vehicle routing problem, there are still some differences between them, the length of vehicle can be neglected in Vehicle routing problem, but sometimes can not in AGV routing. And collisions or congestions usually are ignored in VRP, but can not ignore in AGV routing problem. Thirdly, topologies of VRP are usually fixed and irregular, but can be designed and regular in AGV routing problem.
Also, the AGV routing is a different problem from the shortest path in the graph theory. In fact, SPP is just a simpler subproblem of AGV routing.
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5. Outline Introduction Literature Review Off-Line Mesh Routing
Conclusions and Future Work
The outline of my presentation is as following. Firstly, I will begin with the introduction, and literature review, next, I will talk about the linear path layout and its routing algorithm. Then, I will introduce the conflict-free routing algorithm for the mesh topology. After that, I will present an on-line and an off-line routing algorithm for the mesh path layout. Finally, I will give the conclusions and my future work.
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6. Literature Review AGV routing for arbitrary topologies
Shortest path method
Time-window-based method
Dynamic method
Dijkstra’s alg,
0-1 integer programming:
[Gaskins et al. 87] [Kaspi et al. 90] [Goetz et al. 90]
Small scale, simple, does not consider congestion, deadlocks
[Huang et al. 89], [Fujii et al. 89], [Kim et al. 93]
Increased path utilization, expensive in computation, small system
[Taghaboni et al. 95], [Langevin et al. 96]
Local information required, quick in routes finding, small system
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7. Literature Review (cont’d)
AGV routing on large scalable systems
Linear path layout:
[Qiu et al 01]
Conflict-free, but low utilization of land space
Loop topology:
[Banerjee et al. 95] [Bozer et al. 91] [Barad et al. 95], [Sinriech et al. 92]
Easy to implement, require little computation, low throughput
Mesh path layout:
[Hsu et al. 94], [Qiu et al. 00]
Conflict-free, extra distance traveled, large time complexity
First, we take a look at the AGV routing on arbitrary topologies. There are two main method, 0-1integer programming and time-window-based method.
The AGV routing on large scalable systems mainly focus on the linear path layout, loop topology and mesh path layout.
We also do a survey on packet routing, the detail of which can be found in this good survey paper.
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8. Literature Review (cont’d)
Packet routing on mesh topology
On-line routing:
Central-control model [Gramatikakis et al. 98]
Distributed-control model [Leighton et al. 95] [Sibeyn et al. 97] [Valiant et al 82]
Off-line routing:
[Nassimi et al. 80] [Mou et al. 92] [Krizanc et al. 91] [Kaklamanis et al. 92]
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9. Literature Review (cont’d)
Comparisons between AGV and packet routing
Similarities:
Movement patterns: permutation, k-k routing,…
Static and dynamic routing
Randomized and deterministic methods
Other issues: deadlock, live-lock, fault tolerance,…
Differences
Different definitions of link bandwidth at each step
Different sizes of buffers
Packets can be discarded, copied, but not AGV’s loads
We also make some comparisons between AGV routing problem and packet routing problem.
Firstly, we know that in packet routing model, in each step, each link can only support one packet, but usually, in ARGV routing model, it is possible that each link can support more than one AGV.
Secondly, the sizes of buffers in these two models are different, the buffer for AGV is usually smaller than that of packet routing.
Thirdly, the packets can be discarded, copied, but the load of AGV can not be done in such a way.
The open issues for the existing result is as following,
Firstly, the previous results mainly focus on the systems with a small number of AGV, and mainly concern time complexity, not consider other resources, such as energy, and usually, only consider the static routing problem, namely, the given job set is known before routing. Therefore, the following issues are still open.
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10. Literature Review (cont’d)
New issues
Routing in large scale systems
Energy-efficient routing algorithms
Dynamic routing problems
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11. Outline Introduction Literature Review Off-Line Mesh Routing
Conclusions and Future Work
The outline of my presentation is as following. Firstly, I will begin with the introduction, and literature review, next, I will talk about the linear path layout and its routing algorithm. Then, I will introduce the conflict-free routing algorithm for the mesh topology. After that, I will present an on-line and an off-line routing algorithm for the mesh path layout. Finally, I will give the conclusions and my future work.
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12. Off-Line Mesh Routing # of AGVs= ,
Movement pattern: partial permutation
Partition of mesh path layout
We also divide the mesh into submesh, the size of each submesh is na, at the same time, we also partition the mesh into several groups. Each group include x submesh_row of the submeshes. X will be determined later.
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13. Approach Adopted from Valiant’s Algorithm
Valiant’s routing algorithm
From sources to random intermediate nodes
From intermediate nodes to destinations
Insight of Valiant’s algorithm
Packets are evenly distributed over global network
Packets are routed to their destinations
Use Valiant’s ideas for partial permutation
Distribute AGVs evenly in each group
Shorten the longest distance travelled
Before we give the off-line routing algorithm, we take a look at the Valiant’s algorithm. We know that Valiant’s routing algorithm consists of two step, at the first step, packets are routed from their sources to randomly choose intermediate nodes, at the second step, packets are routed from intermediate nodes to their destinations.
The insight of Valiant’s algorithm is that at the first step, packets …………, at the second step, ……
Because we consider the partial permutation, then can we randomly distribute AGVs in each local region, instead of over global network? In the next, we will show that actually we can do it in each group.
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14. Distribute AGVs Evenly in Each Group1 2 3 4 10 5 6 7 8 9 17 11 12 13 14 15 16 18 19 21 22 23 24 20 1 4 7 10 2 5 8 3 6 19 13 16 11 14 12 22 17 20 23 18 9 15 21 24 # =3 =2 =8
To have a better understanding of the renaming scheme, we use the diagram to show its basic ideas.
Suppose that the green circle represents the AGV destinated to submesh_column 1, the red one represents the AGV destinated to submesh_mesh column 2, and the yellow one represent the AGV destinated to submesh column 3, the size of group is 3. We rename each AGV according to our renaming scheme. Here is the results of the renaming scheme. After renaming, each AGV move the submesh_row according to relationship between di and Ni. After the movement, we can see that in each submesh, the number of AGV that destinated to the same submesh_column is almost balanced.
AGV destinated to submesh_column 2
AGV destinated to submesh_column 1
AGV destinated to submesh_column 3
Size of group: x=3 rows
of submeshes
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15. Off-Line Routing Algorithm
Phase 1: Distribute AGVs evenly in each group
Phase 2: Route AGVs to destinations
Along submesh row
Along submesh column
At the 3rd step, we route each AGV to submesh Di along column in each group, the running time of this step is ….
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16. Analysis of Off-Line Routing Algorithm
Theorem 6.1 : Our routing algorithm works successfully in 2n+o(n) steps, provided,
To analyze the time complexity of our routing algorithm, we just add up the running time of each step, we get the total running time of the routing algorithm.
where, n: size of mesh;
: size of submesh;
: number of AGVs;
x: size of group;
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17. Outline Introduction Literature Review Off-Line Mesh Routing
Conclusions and Future Work
The outline of my presentation is as following. Firstly, I will begin with the introduction, and literature review, next, I will talk about the linear path layout and its routing algorithm. Then, I will introduce the conflict-free routing algorithm for the mesh topology. After that, I will present an on-line and an off-line routing algorithm for the mesh path layout. Finally, I will give the conclusions and my future work.
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18. Future Work Fault tolerance Energy evaluation model Movement patterns
k-to-1
k-to-k
Routing on higher-dimensional mesh
3D AS/RS(Automated Storage and Retrieval System)
As the size of the AGV system and the number of AGVs increase, the probability of a component failure will also increase. In the past one year, we did not consider the case that some AGVs break down during the routing. However, the fault tolerance is very important for AGV routing.
The existing results of AGV routing mainly focus on the time complexity, but the energy requirement is also an important issue.
In the previous work, we only consider the 1-1 routing problem, but other movement patterns such as one-to-many, many-to-many are also common in real-world AGV system.
The routing on higher-dimensional mesh means the routing on the 3D AS/ RS system.
Past research mainly focus on the static routing problem, in which the input or initial job set is known before routing. Many realistic routing problems are dynamic processes, where the input is continuously injected into the system, and routing algorithms should be measured by its long term, steady state, and performance. In the next stage, we will try to analyze the dynamic routing problem.
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19. Thanks!
Q&A