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Design Space Exploration using Time and Resource Duality with the Ant Colony Optimization

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Title: Design Space Exploration using Time and Resource Duality with the Ant Colony Optimization


1
Design Space Exploration using Time and Resource
Duality with the Ant Colony Optimization
  • Gang Wang, Wenrui Gong, Brian DeRenzi and Ryan
    Kastner
  • Dept. of Electrical and Computer Engineering
  • University of California, Santa Barbara
  • DAC2006, San Francisco, California, July 24-28,
    2006

2
Design Space Exploration
  • DSE challenges to the designer
  • Ever increasing design options
  • Closely related w/ NP-hard problems
  • Resource allocation
  • scheduling
  • Conflict objectives (speed, cost, power, …)
  • Increasing time-to-market pressure

3
Our Focus Timing/Cost
  • Timing/Cost Tradeoffs
  • Known application
  • Known resource types
  • Known operation/resource mapping
  • Question find the optimal timing/cost tradeoffs
  • Most commonly faced problem
  • Fundamental to other design considerations

4
Common Strategies
  • Usually done in a Ad-hoc way
  • experience dependent
  • Or Scanning the design space with Resource
    Constrained (RCS) or Time Constrained (TCS)
    scheduling
  • Whats the problem?
  • RCS and TCS are Dual to Each Other

5
Main Contributions
  • New DSE algorithm leveraging duality
  • New TCS/RCS algorithms using Ant Colony
    Optimization
  • ExpressDFG a comprehensive benchmark

6
Design Space Model
7
Key Observations
  • A feasible configuration C covers a beam starting
    from (tmin, C)
  • tmin is the RCS result for C

8
Design Space Model
9
Key Observations
  • A feasible configuration C covers a beam starting
    from (tmin, C)
  • Optimal tradeoff curve L is monotonically
    non-increasing as deadline increases

10
Design Space Model
11
Theorem
  • If C is the optimal TCS result at time t1, then
    the RCS result t2 of C satisfies t2 lt t1.
  • More importantly, there is no configuration
    C'with a smaller cost can produce an execution
    time within t2, t1.

12
Theorem (continued)
13
What does it give us?
  • It implies that we can construct L
  • Starting from the rightmost t
  • Find TCS solution C
  • Push it to leftwards using RCS solution of C
  • Do this iteratively (switch between TCS RCS)

14
DSE Using Time/Resource Duality
15
Solving TCS/RCS problems
  • Exact method ILP
  • Heuristic Methods
  • Force-Directed Scheduling
  • K-L Heuristic
  • Genetic Algorithms
  • Simulated Annealing

16
Our approach Ant System Heuristic
  • Inspired by ethological study on the behavior of
    ants Goss et. al. 1989
  • A meta heuristic
  • A multi-agent cooperative searching method
  • A new way for combining global/local heuristics
  • Extensible and flexible

17
Ant System Heuristic
18
Ant System Heuristic
19
Ant System Heuristic
20
Ant System Heuristic
21
Ant System Heuristic
22
Ant System Heuristic
23
Ant System Heuristic
24
Ant System Heuristic
25
Ant System Heuristic
26
ACO Based TCS/RCS
  • Optimization ? Search
  • Solution ? A chain of decisions
  • Sub-decision ? global and local heuristics
  • Iteratively construction and evaluation
  • Heuristics is updated based on history
  • Max-Min Ant System (MMAS)
  • References Wang et al. 2005

27
ExpressDFG
  • A comprehensive benchmark for TCS/RCS
  • Classic samples and more modern cases
  • Comprehensive coverage
  • Problem sizes
  • Complexities
  • Applications
  • Downloadable from http//express.ece.ucsb.edu/benc
    hmark/

28
Auto Regressive Filter
29
Cosine Transform
30
Matrix Inversion
31
Experiments
  • Three DSE approaches
  • FDS Exhaustively scanning for TCS
  • MMAS-TCS Exhaustively scanning for TCS
  • MMAS-D Proposed method leveraging duality
  • Scanning means that we perform TCS on each
    interested deadline

32
Effectiveness of MMAS for TCS
MMAS-TCS
33
DSE MMAS-D vs. FDS
34
Experimental Results
35
Timing Performance
36
Conclusion
  • Leverage duality between TCS/RCS for DSE
  • ACO based TCS/RCS
  • More stable/Better Performance
  • Similar Computing Cost vs. FDS
  • Thanks! Questions?

37
Autocatalytic Effect
38
Extra Slides
39
Formulating Problems Using Ant Search
  • Problem model define search space, create
    decision variables
  • Pheromone model used as a global heuristic,
    distribution of pheromones, evaporation and
    strengthening strategies
  • Ant search strategy local heuristics and
    solution space traversal
  • Solution construction method of creating an
    answer from decision variables
  • Feedback provide assessment of solution quality
    and adjust pheromones accordingly

40
Hybrid Ants with Lists
  • Combine Ant System Optimization and List
    Scheduling
  • Ants determine priority list
  • List scheduling framework evaluates the
    goodness of the list
  • Iterative approach

41
Pheromone Model For Instruction Scheduling
Each instruction opi ? I associated with n
pheromone trails?? where j 1, …, n each
indicates the favorableness of assign instruction
i to position j
Each instruction also has a dynamic local
heuristic
42
Ant Search Strategy(1)
  • Each run has multiple iterations
  • Each iteration, multiple ants independently
    create their own priority list
  • Fill one instruction at a time

op1
op1
op4
op2
op2
op1
op3
op3
op5
op4
op4
op6
op5
op5
op2
op6
op6
op3
Instructions
43
Ant Search Strategy(2)
  • Each ant has memory about instructions already
    selected
  • At step j ant has already selected j-1
    instructions
  • jth instruction selected probabilistically

op1
1
op1
op4
op2
2
op2
op1
op3
3
op3
op5
op4
4
op4
op5
5
op5
op6
6
op6
Instructions
Priority List
44
Ant Search Strategy(3)
  • ?ij(k) global heuristic (pheromone) for
    selecting instruction i at j position
  • ?j(k) local heuristic can use different
    properties
  • Instruction mobility (IM)
  • Instruction depth (ID)
  • Latency weighted instruction depth (LWID)
  • Successor number (SN)
  • ?, ? control influence of global and local
    heuristics

45
Pheromone Update(1)
  • Lists constructed are evaluated with List
    Scheduling
  • Latency Lh for the result from ant h
  • Evaporation prevent stigmergy and punish
    useless trails
  • Reinforcement award trails with better quality

46
Pheromone Update(2)
  • Evaporation happens on all trails to avoid
    stigmergy
  • Reward the used trails based on the solutions
    quality

op1
op1
op4
op2
op2
op1
op3
op3
op5
op4
op4
op6
op5
op5
op2
op6
op6
op3
Instructions
47
Max-Min Ant System (MMAS)(1)
  • Risks of Ant System optimization
  • Positive feedback
  • Dynamic range of pheromone trails can increase
    rapidly
  • Unused trails can be repetitively punished which
    reduce their likelihood even more
  • Premature convergence
  • MMAS is designed to address this problem
  • Built upon original AS
  • Idea is to limit the pheromone trails within an
    evolving bound so that more broader exploration
    is possible
  • Better balance the exploration and exploitation
  • Prevent premature convergence

48
Max-Min Ant System (MMAS)(2)
  • Limit ?(t) within ?min(t) and ?max(t)
  • Sgb is the best global solution found so far at
    t-1
  • f(.) is the quality evaluation function, i.e.
    latency in our case
  • avg is the average size of decision choices
  • Pbest ? (0,1 is the controlling parameter
  • Conditional prob. of Sgb being selected when all
    trails in Sgb have ?max and others having ?min
  • Smaller Pbest ? tighter range for ? ? more
    emphasis on exploration
  • When Pbest ? 0, we set ?min ? ?max

49
Other Algorithmic Refinements
  • Dynamically evolving local heuristics
  • Example dynamically adjust Instruction Mobility
  • Benefit reduce search space progressively
  • Taking advantage of topological sorting of DFG
    when constructing priority list
  • Each step ants select from the ready instructions
    instead from all unscheduled instructions
  • Benefit greatly reduce the search space

50
MMAS Instruction Scheduling Algorithm
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