1. Combinatorial Optimization for Embedded System Design
Michela Milano
Michele Lombardi, Alessio Bonfietti, Luca Benini, Andrea Bartolini, Davide Bertozzi, Alessio Guerri, Martino Ruggiero, Giuseppe Tagliavini

2. Embedded Systems A rough definition
“Any computing system which is not a computer”
Large variety of devices
High performance (as they often real time applications)
High energy efficiency (e.g. in case of battery supplied power)
Issue: efficiency
Classical design approaches
→ dedicated G.P. systems
→ dedicated hardware
Issue:
high design cost + poor flexibility

3. MultiProcessor Systems on Chip
MPSoCs address all such problems:
Flexibilty through software (or mixed HW/SW) applications
Performance through parallelism
Low power consumption by using low(er) frequency cores and power saving techniques
HOWEVER:
Thermal issues
Requires proper use of the exposed resources
Squeezing out the full power of a modern MPSoC can be defintiely HARD

4. This thing has to perform some automatic optimization
Ideally
Given:
Input application (code)
Target Platform description
Yield: optimized application
What’s the black box?
A compiler?
A CAD tool (less blackish)?
A run time support? ?
FOR SURE:
This thing has to perform some automatic optimization
OPTIMIZED APPLICATION

5. On-line vs off-line approaches
How should the black-box look like?
→ most likely: two distinct components ? ? ?
ON-LINE
OFF-LINE
OS level scheduler
On-line application-to-core dispatcher (Current multi-core CPUs...)
Out of order execution
...
Off-line code optimization (e.g. VLIW compilers)
Memory allocation (even hand made)
Off-line resource allocation (e.g. mixed HW/SW design)

6. Requirements for automatic optimization
1. A formal description of the application must be available
Formal =
can be undertood by a computer
can be manipulated by mathematics
Usually: task based models
Task = atomic computation unit (e.g. an instruction, a process, a code block...)
Tasks may have dependencies
Task have measurable “features” (e.g. execution time) which must be computed in some way
Tasks use hardware resources T0 T1 T2 T3 T4 T5 T6

7. Requirements for automatic optimization
2. A formal description of the platform must be available
Usually: resource based models
Resource = an “energy” provider over time
Each resoruce has a finite capacity
Platform = collection of resources
PROC
cores
Additionally, for off-line approaches:
3. A formal description of the performance metrics must be available
completion time (makespan)
throughput
energy consuption
number of bus transactions
...
PROC
MEM
memory devices
MEM

8. Compiled code + directives + run time support = OPTIMIZED APPLICATION
An example on MPSoCs
Mapping & Scheduling Problem:
Application description
Platform description
Through:
Off-line optimization algorithm
Provide directives for the run-time support:
Resource-to-task allocation
Task scheduling decisions ?
Compiled code + directives + run time support =
OPTIMIZED APPLICATION
OPT. APP.

9. Communication-aware approach
Communication aware: the approach minimizes inter-core communication between tasks
Decisions: task allocation and scheduling
Approach: Logic-based Benders decomposition
Validation on a cycle accurate simulator and target platform
Martino Ruggiero, Alessio Guerri, Davide Bertozzi, Michela Milano, Luca Benini: A Fast and Accurate Technique for Mapping Parallel Applications on Stream-Oriented MPSoC Platforms with Communication Awareness. International Journal of Parallel Programming 36(1): 3-36 (2008)
Luca Benini, Michele Lombardi, Michela Milano, Martino Ruggiero: Optimal resource allocation and scheduling for the CELL BE platform. Annals OR 184(1): (2011)

10. MP-OPT Cell Programming Interface Solver Runtime System
A High-Performance Data-Flow Programming Environment for the Cell BE Processor
Programming Interface
Solver
Runtime System

11. Communication-aware approach
Robustness and Variability
Performance
Cell SuperScalar
MPOpt
All experiments were executed on a PlayStation 3 (3.2 GHz Cell) running Yellow Dog Linux 6.0

12. Dynamic voltage and frequency scaling
Energy aware: the approach minimizes energy dissipation
Decisions: task allocation, frequency and scheduling
Approach: Logic-based Benders decomposition
Validation a cycle-accurate simulator
Martino Ruggiero, Davide Bertozzi, Luca Benini, Michela Milano, A. Andrei: Reducing the Abstraction and Optimality Gaps in the Allocation and Scheduling for Variable Voltage/Frequency MPSoC Platforms. IEEE Trans. on CAD of Integrated Circuits and Systems 28(3): (2009)

13. Energy-aware approach

14. Robust optimization for conditional task graphs
Robust optimization: minimizes expected execution time guaranteeing resource feasibility in all scenarios
Conditional task graphs
Approach: Constraint Programming solver: transformation of a probabilistic problem in a deterministic counterpart
Michele Lombardi, Michela Milano, Martino Ruggiero, Luca Benini: Stochastic allocation and scheduling for conditional task graphs in multi-processor systems-on-chip. J. Scheduling 13(4): (2010)
Michele Lombardi, Michela Milano: Allocation and scheduling of Conditional Task Graphs. Artif. Intell. 174(7-8): (2010)
Against scenario-based scheduling
Same performance of solvers considering 50% scenarios
Much higher solution quality: 49% improvements
Against scenario based scheduling: same performance of 50% scenarios – much higher solution quality 49% on average

15. Robust Optimization under duration uncertainty
Robust optimization: minimizes expected execution time guaranteeing deadline feasibility in all scenarios
Task graphs with WCET and BCET known
Approach: Partial Order scheduler with min-flow algorithm for identifying critical sets
Michele Lombardi, Michela Milano, Luca Benini: Robust Scheduling of Task Graphs under Execution Time Uncertainty. IEEE Trans. Computers 62(1): (2013)
Fixed priority scheduler based on tabu search

16. Synchronous data flow graphs
Syncronous data-flow graphs: Maximizes throughput
Approach: Constraint Programming solver: throughput constraint
Alessio Bonfietti, Michele Lombardi, Michela Milano, Luca Benini: Maximum-throughput mapping of SDFGs on multi-core SoC platforms. J. Parallel Distrib. Comput. 73(10): (2013)
Against SDF3 and SMS
SDF3 fastest
SDF3 has 12.1% average optimality gap
SMS has 4,8% average optimality gap
Against simulation and Swing modulo Scheduling implemented in gcc
The ‘‘SDF3’’ tool is
the fastest approach, however its solutions present an average gap
of 12.1% (with a peak of 47.7% in the MPEG-2 benchmark) w.r.t. the
4.8% of the SMS.

17. Cyclic scheduling
Cyclic applications: possibly more than one with different period. Approach: CP solver with a modular arithmetic based approach
Alessio Bonfietti, Michele Lombardi, Luca Benini, Michela Milano: CROSS cyclic resource-constrained scheduling solver. Artif. Intell. 206: (2014)
Presentation tomorrow by Alessio Bonfietti on a project with ABB

18. Empirical Model Learning
Machine learning and data analytics for characterizing the app and the platform
Insert the learned model into the optimization model
Michele Lombardi, Michela Milano, Andrea Bartolini: Empirical decision model learning Artif. Intell.: online (2016)

19. Empirical Model Learning
Thermal behaviour is complex
Depends on:
Room temperature
Core workload
Neighbor workload
Heat and sink position

20. Empirical Model Learning
Building and training a Neural Network to model the thermal behavior of a (simulated) quad core chip
temp_(0)
pwr_3
pwr_2
pwr_1
pwr_0
sigmoid
linear
temp_3(Δ)
Power input
Encoding the network in CP, using a “Neuron Constraint” to encode each neuron and decisions for the input
Building a CP model to perform thermal aware workload dispatching with temperature constraints

21. Empirical Model Learning
WITHOUT EML
WITH EML

22. Open issues Accuracy vs. efficiency
How to consider accuracy/confidence levels IN the optimization process
Definition of the training set
More inference methods for ML models