Fast Force-Directed/Simulated Evolution Hybrid for Multiobjective VLSI Cell Placement

1. Fast Force-Directed/Simulated Evolution Hybrid for Multiobjective VLSI Cell Placement Dr. Sadiq M. Sait Dept. of Comp. Engineering, King Fahd University of Petroleum & Minerals, Dhahran, Saudi Arabia. sadiq@ccse.kfupm.edu.sa Junaid Asim Khan Dept. of Elect. & Comp. Engineering, The University of British Columbia, Vancouver, BC, Canada. junaidk@ece.ubc.ca

2. Introduction • Standard Cell Placement • Assigning modules to locations on the silicon surface • An Intractable problem • Numerous Design Objectives, wire-length, power dissipation, delay etc. • One Solution • To use Iterative Heuristics e.g., Simulated Annealing, Genetic Algorithm, Tabu Search, Simulated Evolution etc.

3. Simulated Evolution • An excellent heuristic for placement • Both, solution quality, and run time, are better than other approaches • If used with fuzzy logic, can optimize multiple objectives • Problem: For large VLSI circuits, needs to be accelerated • Solution • Parallelization • Hybridize with Force Directed Algorithm

4. Simulated Evolution, Basic Steps • Comprises three step • Selection • Evaluation • Allocation

5. Algorithm Simulated_Evolution(B, Solinitial, Stopping Criteria) B = Bias Value Sol = Complete Solution mi = Module I gi = Godness of mi ALLOCATE( mi, Soli) = Function to allocate mi in partial solution Soli Begin Repeat S = {} EVALUATION: ForEachmi in Sol evaluate gi SELECTION: ForEachmi in Sol DO begin IF Random > min (gi,1) THEN begin S = SUmi Remove mi from Sol end end Sort the element of S ALLOCATION: ForEach mi in SDO begin ALLOCATE ( mi, Soli) end Until Sopping Condition is satisfied Return Best Solution End (Simulated Evolution) Simulated Evolution: Algorithm

6. Evaluation

7. Selection

8. Allocation • Previous Approaches (e.g. BLFSE) • Sort selected cells in descending order of their goodness • Pick the top of the list cell • Swap its location with other cells in the list • Accept the best swap • Remove the cell from sorted list • Go to 2 • Problem • O(n2) time complexity for Allocation • n is the number of selected cells • In VLSI n is too large and hence a O(n2) is not practical

9. Force-directed Allocation • Solution • Use Force-directed heuristic to find best x and y locations for a cell • y position indicates the best row, the row nearest to y position is selected, which satisfies the width constraint • x position indicates the exact location of the cell in the selected row • The selected x position may replace some already well placed cell and hence introduce hill climbing • Benefit • Needs only O(n) time • Because x and y locations can be found in O(1)

10. Force-directed ALLOCATION • Method • Problem • To find wij that satisfies multiple objectives • Solution • Use Fuzzy Logic

11. Fuzzy weights • Following fuzzy rule is used to find weights • IFa net is good in wire-length AND good in power AND good in delay THENit has a low weight • A goodness gijfor the net ij in the range [0,1] is found and then wijis calculated as wij= 1 – gij • Higher the goodness lower is the weight

12. aw ap Near optimal wirelength Near optimal power 1.0 1.0 amin_w amax_w amin_p amax_p Xijw Xijp anet Near optimal net-delay 1.0 apath Tmax(ij) is much smaller than Tmax 1.0 amin_net amax_net Xijnet 1.0 2.0 Xijpath Fuzzy weights (Membership functions)

13. Fuzzy weights • Using AND and OR like Fuzzy aggregation functions and the fuzzy rule we calculate gijas follows • And hence wij= 1 - gij

14. Experiments and Results • Fast Fuzzy Force Directed Simulated Evolution (FFSE) is compared with Biasless Fuzzy Simulated Evolution (BLFSE) • 12 ISCAS benchmark circuits are used • FFSE is same as BFSE except Allocation • For BLFSE execution is aborted when there is no improvement in last 500 iterations • FFSE is run for fixed 5000 iterations • 0.25 micron technology is used

15. Experiments and Results UH: Unreasonably high run time

16. 0.8 0.7 0.6 0.5 Overall membership of the solution 0.4 0.3 0.2 0.1 0 0 200 400 600 800 1000 1200 Execution time in seconds Experiments and Results

17. 6 x 10 7 m) m 6 5 Wire Length Cost ( 4 3 2 0 200 400 600 800 1000 1200 Execution time in seconds Experiments and Results

18. 8000 7000 6000 Delay Cost (ps) 5000 4000 3000 2000 0 200 400 600 800 1000 1200 Execution time in seconds Experiments and Results

19. 5 x 10 6.5 m) 6 m 5.5 5 4.5 4 Power Dissipation Cost ( 3.5 3 2.5 2 1.5 0 200 400 600 800 1000 1200 Execution time in seconds Experiments and Results

20. Conclusion • A Fast Fuzzy Force Directed Simulated Evolution Algorithm for VLSI standard cell placement was proposed • FFSE is capable of optimizing multiple objectives • Allocation was speedup from O(n2) to O(n) • FFSE performs much better than BLFSE in terms of execution time • There is not much performance degradation in terms of solution quality • In contrast to BLFSE, FFSE can be used for large circuits

21. Thank You Questions ?