1. GENIE
Eric Jackowski

2. GENIE Genetic Algorithm for Placement
“Genetic Placement,” Cohoon and Paris
“VLSI Placement Techniques,” Shahookar and Mazumder
Uses Directed-Evolution Methodology
Obtains optimal solutions faster
Avoids Premature Homogeneity
Uses randomness in the functions
Evaluates Several Functions
Population, Choice, Crossover, Selector, Mutation

3. Genie Data Structures Net Cell Layout
Name, # of Connections, Array of Cells
Cell
Name, # of Ports, Array of Nets
Layout
# of Rows, # of Columns, Array of Cells

4. Scoring Function σ
hi = # of nets whose bounding rectangle crosses a horizontal channel
vi = # of nets whose bounding rectangle crosses a vertical channel
h = average h, v = average v
Sh and Sv= one standard deviation of vertical and horizontal usage
Score = − −

5. Population Constructor Ξ
Ξ1 place random cells at random locations
Ξ2 and Ξ3 choose the same order cells are assigned.
Randomly select a net
Place all unplaced cells on net
Select an unselected net from the
last cell placed
Randomly select a cell on that net
Ξ2 places in boustrophedon fashion
Ξ3 places in row major fashion Ξ2 Ξ3

6. Crossover Function ψ
Ψ1 randomly select cell from parent and place in child.
“Slide” neighboring cells to new locations
Ψ2 randomly select a k x k square from parent and copy it into the child.
For the cells in the child block that are not in the parent block, move them to the cell locations of the cells in the parent block that are not in the child block.

7. Crossover Choice Function Φ
Φ1 chooses random string and best scoring string for crossover
Φ2 randomly chooses both strings for crossover
Φ3 and Φ4 choose random string with probability based on the score
Φ3: Φ4:

8. Selector Function ρ
ρ1 chooses the best scoring string from the Population and the Offspring
ρ2 randomly choose P strings from the Population and Offspring
ρ3 randomly chooses string αj from the population and offspring with probability

9. Mutation Function μ
μ1 randomly chooses two cells and interchanges them
μ2 uses a directed evolution transformation to reduce the bounding rectangle for a random net
Randomly select a net
Randomly select a Cell, es, on that net
Find farthest Cell, et, from the selected cell
Place the et next to the es and slide surrounding cells
Find the next farthest cell from es
Place the second farthest cell next to es
μ2* swaps the position of two cells if they are already adjacent

10. GENIE Algorithm Ξ1 Ξ3 Iterations<10000 .25p .75p Population Φ4
Parentx
Parenty
i < p * KΨ Ψ2
Offspring σ2
Population
i < k μ2
Population

11. GENIE vs TW Total Wirelength Number of Iterations Overall Time
GENIE 1.2x better on large circuits
TW .8 better on smaller circuits
Number of Iterations
GENIE orders of magnitude less
Overall Time
TW 2x faster on large circuits
GENIE 2x faster on small circuits

12. Discussion Challenges Lessons Learned “Sliding”, μ2, Ξ3
Need mutation otherwise converge to quickly
The order in which you “slide” is very important

13. Questions

14. Appendix
GENIE ALGORITHM

15. Appendix GENIE1: 25% Ξ1 75% Ξ3 Φ4 ψ2 σ2 μ2

16. Appendix Initialize; Np  population size; No  Np * Pψ;
/* where Pψ is the desired ratio of the number of offspring to the population size */
Construct_population(Np);
FOR i  1 To Np
score(population[i]); ENDFOR;
FOR i + 1 TO Number_ of_ Generations
FOR j  To No
(x, y)  Choose _Parents;
offspring[ j]  generate _Offspring( x, y);
Score(offspring[ j]); ENDFOR;
population  Select(population, offspring, NP);
FORj  i To Np
With probability Pμ Mutate(population[j] ); ENDFOR;
ENDFOR
Return highest scoring configuration in population;