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 DAC’2006, San Francisco, California, July 24-28, 2006

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

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

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  What’s the problem?  RCS and TCS are Dual to Each Other

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

Design Space Model

Key Observations  A feasible configuration C covers a beam starting from (t min, C)  t min is the RCS result for C

Design Space Model

Key Observations  A feasible configuration C covers a beam starting from (t min, C)  Optimal tradeoff curve L is monotonically non-increasing as deadline increases

Design Space Model

Theorem  If C is the optimal TCS result at time t 1, then the RCS result t 2 of C satisfies t 2 <= t 1.  More importantly, there is no configuration C′with a smaller cost can produce an execution time within [t 2, t 1 ].

Theorem (continued)

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)

DSE Using Time/Resource Duality

Solving TCS/RCS problems  Exact method: ILP  Heuristic Methods  Force-Directed Scheduling  K-L Heuristic  Genetic Algorithms  Simulated Annealing

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

Ant System Heuristic

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]

ExpressDFG  A comprehensive benchmark for TCS/RCS  Classic samples and more modern cases  Comprehensive coverage  Problem sizes  Complexities  Applications  Downloadable from

Auto Regressive Filter

Cosine Transform

Matrix Inversion

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

Effectiveness of MMAS for TCS MMAS-TCS

DSE: MMAS-D vs. FDS

Experimental Results

Timing Performance

Conclusion  Leverage duality between TCS/RCS for DSE  ACO based TCS/RCS  More stable/Better Performance  Similar Computing Cost vs. FDS  Thanks! Questions?