Use the novel formal model in the fitness function of genetic algorithm guarantees find the optimal mapping solution.

1. Vinitha A Palaniveloo Jude Angelo Ambrose
Arcot Sowmya
School of Computer Science and Engineering
The University of New South Wales
Sydney, Australia
Improving GA-based NoC mapping
algorithms using a formal model
7/10/2014 The University of New South Wales 1

2. Outline
• Introduction
• Background and Related work
• Case study: Application of formal model to
evaluate NMAP algorithm
• NoC mapping using formal NoC model and
Genetic Algorithm (GA)
• Results
• Conclusion
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3. 7/10/2014 The University of New South Wales 3
Network on Chip
Application
Tasks
Application Mapping
SWITCH
ROUTING
I/P O/P
NETWORK INTERFACE
PROCESSING
ELEMENT MEMORY
Router
PE – Processing Element
MEM - Memory
Network on Chip (NoC)

4. NoC Mapping
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Mapping algorithms aim at mapping
applications onto the NoC platform, while
optimizing certain metrics of interest such as
energy, performance,…
𝑛𝑃𝑟 =
𝑛!
𝑛 − 𝑟 !
Size Number of
Permutations
6 720
9 362880
16 2.09227x1013
25 1.55112x1025
Application
NoC
Infrastructure
Communication
scheme

5. Open Problems in Application
mapping
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• Simulation too expensive to use in optimization
loop of mapping algorithms, so analytical
models used for performance evaluation
• Analytical models usually abstract architecture
specific details, not robust
• Instead, propose use of formal NoC model
mapping- contains details of Architecture,
Communication scheme and Application

6. Types of Mapping Algorithms
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Mapping
algorithms
Static
Exact
mapping
Greedy
placement
Iterative
placement
Search based
mapping
Mapping
heuristics
Genetic
algorithms
Dynamic

7. Genetic Algorithms
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• Genetic algorithms (GA) uses global
search heuristics
• Particular class of evolutionary
algorithms that use techniques
inspired by evolutionary biology-
inheritance, mutation, selection and
crossover (also called recombination)

8. Genetic Algorithms
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Initialize Population
Check constraints ?
Evaluate Fitness
Select Survivors
Output Results
Vary Individuals
Yes
No
Reproduction
Crossover
Mutation

9. Crossover Operator
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• Crossover
– Generating offspring from two selected parents
• Single point crossover
• Two point crossover (Multi point crossover)
• Uniform crossover
• Example:
– Parent 1: X X | X X X X X
– Parent 2: Y Y | Y Y Y Y Y
– Offspring 1: X X Y Y Y Y Y
– Offspring 2: Y Y X X X X X
Crossover is explorative, it makes a big jump to an area somewhere “in between” two
(parents)

10. Mutation Operator
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Mutation
• Generating new offspring from single parent
by setting probability of mutation.
• Maintaining the diversity of the individuals
• Can “generate” new genes
• Example:
– Parent 1: X Y Y Y Y X Y
– Parent 2: X X X Y Y Y X
– Offspring 1: X Y Y X Y Y X
– Offspring 2: Y X X Y X X Y
Mutation is exploitative, it creates random small diversions, thereby staying near the parent

11. Fitness function
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Fitness function
f(x)
Individuals Ranked
T1 T2 T3 T4 T5 T6
T6 T2 T3 T1 T5 T4
T1 T3 T6 T4 T5 T2
T5 T2 T3 T4 T1 T6
T4 T2 T5 T3 T1 T6
T6 T2 T3 T4 T5 T1
T1 T2 T3 T4 T5 T6
T6 T2 T3 T1 T5 T4
T1 T3 T6 T4 T5 T2
T5 T2 T3 T4 T1 T6
T4 T2 T5 T3 T1 T6
T6 T2 T3 T4 T5 T1
M1
M2
M3
M4
M5
M6
M5
M1
M2
M6
M3
M4
Fitness Function
• Analytical model
• Formal model

12. Analytical model for Latency Estimation
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Latency : Time for packet to traverse network
• Latency = Hop Count+ Contention latency
– Contention latency: impacted by traffic loads and
buffers in the router, computed using probabilistic
models or queuing theory
– Hop Count: number of links traversed between
source and destination, depends on routing
algorithm, which can be computed analytically for
deterministic routing algorithms

13. Formal NoC model
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P8
receive_R8?
inject_pkt_R8 ()
switch_R8 ()
arbitrate_R8 ()
sink_pkt_R8 ()
transmit_R8!
P0
receive_R0?
inject_pkt_R0 ()
switch_R0 ()
arbitrate_R0 ()
sink_pkt_R0 ()
transmit_R0!
receive_R8?
inject_pkt_R8 ()
switch_R8 ()
arbitrate_R8 ()
sink_pkt_R8 ()
transmit_R8!
P0
receive_R0?
inject_pkt_R0 ()
switch_R0 ()
arbitrate_R0 ()
sink_pkt_R0 ()
transmit_R0!
P1 P8
Pt0 = P0 || P1 || P2 || P3 || P4 || P5 || P6 || P7 || P8
Pt0 = P0 . P1 . P2 . P3 . P4 . P5 . P6 . P7 . P8
Estimating worst-case latency of NoC formally
(by model checking)
- posing latency as reachability problem

14. GA Algorithms Termination Criteria
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The generational process repeated until
termination condition reached
Common terminating conditions are:
• A solution is found that satisfies minimum criteria
• Fixed number of generations reached
• Manual inspection
• Any Combinations of the above

15. Case study: NMAP algorithm & DSP
Filter Application
ARM Filter
FFT IFFT
Display
Memory
200
600
200200 200
Source Destination Rate
Memory ARM 200
Filter ARM 600
Filter FFT 200
Filter IFFT 200
ARM Filter 600
ARM Display 200
FFT Filter 200
IFFT Filter 200
[1] Mapping and Physical Planning of Networks-on-Chip Architectures with Quality-of-Service Guarantees
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Peak link bandwidth as 1000MB/S
200MB/s – 20% packet injection rate
- translates to one packet every 5 clock cycles
600MB/s – 60% packet injection rate
- translates to one packet every 2 clock cycles

16. Solution by NMAP Algorithm [1]
0 1 2
3 4 5
Memory
FFT
Filter
ARM
IFFT
Display
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Estimated worst-case latency using the formal model : 3.375 cycles

17. Exploration of mapping space by brute force
Modules
MAP
93
MAP
95
MAP
271
MAP
276
MAP
391
MAP
396
MAP
699
MAP
701
Memory R0 R0 R3 R5 R3 R5 R2 R2
Filter R5 R4 R1 R1 R1 R1 R4 R4
IFFT R3 R5 R0 R0 R2 R2 R3 R5
FFT R4 R3 R2 R2 R0 R0 R5 R3
ARM R1 R1 R4 R4 R4 R4 R1 R1
Display R2 R2 R5 R3 R5 R3 R0 R0
Mapping proposed in [1] is MAPPING 391 in out model, highlighted
above, it has minimum average worst case latency
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Mapping with worst-case latency of 3.375 cycles
Total number of solutions = 8

18. • It is not possible to perform exhaustive search for
large NoCs
– 3x2 took 17min 42 sec
– 3x3 took 6.5 days (148.62 hours)
• Results of different mapping algorithms developed
for the same constraint may be different
• Mapping algorithms may find only a near optimal
solution
• Mapping algorithms may find more than one
mapping solution
Discussion
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19. Evaluate possibility of using formal model to
enable mapping algorithms to find better optimal
solution
Proposal
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Popular static
mapping
approaches
Mapping
heuristics
Genetic
Algorithms based
mapping
Using analytical
model
Using formal
model

20. Sample Applications
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Application NoC Size Total traces
APP1 3x2 8
APP2 3x3 13
APP3 4x4 25
APP4 5x5 38
APP5 10x10 150
APP6 20x20 600
APP7 30x30 1349

21. Population size and Generation size
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Algorithm termination condition:
• Population size = 100
• Generation size = 10
WHY?
• APP1 & APP2 => always finds at least one optimal solution
• APP3 & APP4 => output solution is not significantly improved
by increasing population and generation size
Offspring generated using two types of genetic operators:
• random mutation operator R
• single point crossover operator S

22. Simple mapping heuristics
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23. Result
Application WCL
(Heuristic)
WCL
(R_FM)
WCL
(S_FM)
WCL
(R_AM)
WCL
(S_AM)
APP1 3.375 3.375 3.375 3.375 3.375
APP2 4.0 3.84 3.84 4.384 4.3
APP3 7.91 5.32 5.44 5.56 5.56
APP4 27.1 6.6 7.4 7.89 8.31
APP5 35.54 20.2 20.7 25.14 29.55
APP6 210.72 86.45 80.4 121.515 112.47
APP7 295.65 203.8 222.1 395.47 271.38
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24. Discussion of Mapping Results
• GA based mapping algorithm generally finds better
optimal solutions than the mapping heuristic,
especially as the size of the application increases
• all the GA-based algorithms perform equally well for
smaller applications [APP1...APP4]
• GA + formal is better than GA + analytical for larger
applications [APP5...APP7]
• With random mutation R, GA + formal has WCL 20%
lower than GA + analytical
• With single point crossover S, GA + formal has WCL
13% lower than GA + analytical
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25. Result
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26. Execution Time
• GA + formal takes longer to compute,
compared with GA + analytical
• Random mutation R introduces more
diversity in the population, and the solution
converges to an optimal solution more quickly.
But single point crossover S is faster to
compute
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27. Conclusion
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• Formal models can be applied to solve NoC
design problem in addition to functional
verification
• Formal NoC models may be enhanced to
estimate other QoS parameters such as
energy, power and throughput, resulting in a
good generic performance model

28. Thank You!
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