Solution Space Smoothing Method and Its Application in VLSI Floorplanning

1. Solution Space Smoothing Method and Its Application in VLSI Floorplanning Sheqin Dong, Song Chen, Xianlong Hong EDA Lab., Tsinghua Univ. Beijing

2. Content • Principle of Solution Space Smoothing (SSS) • Applying SSS Strategy to VLSI Floorplanning • Problem • Smoothing the solution space of Floorplan • Experimental Results • Conclusion

3. Principle of Solution Space Smoothing • Local Minimum Points make a search problem hard • The less the number of local minimum points, the more effective a local search algorithm is • Search Space Smoothing technique limits the number of local minimum points in the search space

4. Principle of Solution Space Smoothing (Con’t)

5. Principle of Solution Space Smoothing (con’t) • To apply search space smoothing techniques to local search, one is often faced with a contradictory situation. • A weaker smoothing operation, however, results in less reduction in the number of local minimum points in the original search space. • In order to increase the chance of finding the global minimum points in the smoothed search space, we expect a strong smoothing operation that produces a flatter search space, but we may lose some heuristic guidance information.

6. Principle of Solution Space Smoothing (Con’t)

7. Applying the SSS strategy to VLSI floorplanning • Problem • Previous Work • Smoothing the search space of Floorplanning • Search Strategy • Experimental results

8. Problem • A set of rectangular blocks M={M1, M2, …, Mn} of • A set of nets specifying the interconnections between pins of blocks and a set of pads (external pins) are also given. • A placement P={Mi(xi, yi) , 1 < = i < = n} is an assignment of coordinates to the lower left corners of n rectangular blocks such that there is no two rectangular blocks overlapping.

9. Previous Work • Application of random optimization algorithm • Simple Rectangle-Packing problem is NP-hard • Simulated Annealing – Not Stable - , and etc. • Floorplan/Placement Representation • Sequence Pair, Bounded Slice-line Grid, O-tree, B*-tree, Corner Block List, and etc.

10. Smoothing the search space of Floorplanning • Intuitively, without consideration of connections among blocks, a placement of blocks with the same dimensions will have the most flat solution space. Therefore, we think that the search space will be more flatter if the blocks have more similar dimensions. • The smoothing of the solution space of Floorplan/Placement is achieved by change the dimensions of blocks. • A Serial of flattened solution space will be searched before the search of original solution space.

11. Smoothing Functions For calculation of blocks size

12. Variations of block dimensions a b Initial Dimensions Original Dimensions

13. Search Strategy applied on VLSI Floorplanning • SSS() • Begin • /* Initializtion*/ • P= get_a_placement_instance(); • α = α0； • /*Search*/ • While(α>=1) do • Begin • /*Generate a Simplified Placement Instance*/ • For i:=1 to n do • w(i) = compute_wi(α); h(i) = compute_hi(α); • /*Search*/ • P = Placement_local_search(w, P); • α = f(α ) • End; • End;

14. Comparison between the SSS and Simulated Annealing (1)

15. Comparison between the SSS and Simulated Annealing (2)

16. Comparison among different smoothing functions

17. Conclusion • We apply the optimization algorithm of SSS to the problem of VLSI Floorplan/placement by means of changing the dimensions of blocks size to smoothen the solution space of floorplanning/placement • Experimental shows that Solution Space Smoothing is a promising optimization strategy because of its stableness. • The SSS method is very heuristic. The further works should be contributed to the theory aspect.

18. Thanks for your attenstion!