On Mismatches Between Incremental Optimizers and Instance Perturbation in Physical Design Tools

1. On Mismatches Between Incremental Optimizers and Instance Perturbation in Physical Design Tools Andrew B. Kahng and Stefanus Mantik UCSD CSE & ECE Depts., La Jolla, CA UCLA CS Dept., Los Angeles, CA abk@ucsd.edu, stefanus@cs.ucla.edu Supported by MARCO GSRC and Cadence Design Systems, Inc.

2. Emerging Need for Incremental Optimizers • Design size , complexity , time-to-market  • reuse of design IP • timing closure (layout-logic synthesis unifications) • Construct-by-correction flow • placement  timing analysis  timing optimization • netlist changes (repeaters, resizing, clock) = ECO’s • Incremental optimization is needed • use previous solution as the starting point • ideally, next solution remains similar while maintaining quality

3. Incremental Optimization • An original instance, I0, is solved by a full algorithm to yield solution S0 • Perturbed instances, I1, …, In,are generated one by one in sequence (Ii = Ii-1 + Ii , i = 1, …, n; |Ii | = perturbation size) • Each perturbed instance is solved by an incremental algorithm which uses Si-1 as the starting point for finding solution Si , i = 1, …, n

4. Related Works • Physical Design Roadmap [itrs99] • incremental optimization has been a stated need in the roadmap (NTRS, ITRS) since 1997 • incremental optimization is needed for future technology (www.itrs.net) • Incremental optimization • incremental optimization formulations in physical design [CongSarrafzadeh00] • Problem-space metaheuristic • idea: change objective function to escape local minima [Hajek88, StorerWuVaccari92, OsmanKelly96]

5. Outline • Potential mismatch: instance perturbation vs. optimizer strength • Experimental design • Experimental results • partitioning • placement • routing • Conclusions and future work

6. I1 I2 S0 S1 S1 S2 Does the Size of IMatter? Size of Imatters!

7. Potential Mismatch: Instance Perturbation vs. Optimizer Strength • Consider the sequence of instances I0, I1, …, In and solutions S0, S1, …, Sn : • Can the quality of solution Sn be worse than that of solution S0? • If so, can the decrease in solution quality be attributed to: • aspects of the sequence I0, I1, …, In (in particular, the “distance” between successive instances)? • aspects of the incremental algorithm (in particular, its “strength” or “weakness”)?

8. Experimental Hypotheses:Perturbation Size vs. Optimizer Strength • A strong incremental algorithm + smallchanges  maintain good solution quality but waste computational resources • A weak incremental algorithm + large changes  steadily worsening solution • Instance changes must be compatible with the strength of the incremental algorithm • must escape basins of attraction to find good solutions • but, should not waste extra computational resources

9. Experimental Design • Are current incremental algorithms capable of escaping from a basin of attraction? • Reversal-based experiment • construct a series of instances I0, …, Ik-1, Ik, Ik+1, …, I2k where I0 = I2k, I1 = I2k-1, etc. • S2k is better than S0? • Does the size of perturbation Ihave any effect on the quality of the solution? • Dicing-based experiment • break I into smaller perturbations (I = 1 + 2 + … + m, I = I0 + I, I1 = I0 + 1, I2 = I1 + 2, ..., Im = Im-1 + m) • Sm is better than S?

10. Experiments in Partitioning Domain • Instance: netlist hypergraphs • Perturbation: weight changes for hyperedge weights • Incremental optimizer: UCLA MLPartitioner • Near best-known quality • Problem-space metaheuristic approach is very effective

11. Experiments in Placement Domain • Instance: circuit netlists • Perturbation: random deletion of cells • Incremental optimizer: Cadence QPlace in incremental mode (optimization level = 3) • Incremental placement algorithm is too strong

12. Experiments in Routing Domain • Instance: placed circuit netlists • Perturbation: changes in cell orientations • Incremental optimizer: Cadence WarpRoute in incremental mode • Incremental routing seems difficult!

13. 3.54+e06 3.52+e06 3.50+e06 3.48+e06 3.46+e06 3.44+e06 3.42+e06 0 200 400 600 800 1000 1200 Dicing Experiment Results for Routing Multiple small perturbations Wirelength One big perturbation # Flipped Cells Perturbation size should be sufficiently large before applying incremental optimization

14. Conclusions and Ongoing Work • Current design tools may not be correctly architected to handle incremental optimizations • problem-space metaheuristic approach may be very effective for partitioning • incremental placement algorithms are too strong • perturbation size should be large before attempting incremental routing • Ongoing research: • finding incremental algorithms that are sensitive to perturbation size and that preserve solution structure • V-cycling based incremental partitioning and top-down placement • distinguish incrementality w.r.t. objective from incrementality w.r.t. instance structure