Genie A Genetic Placement Algorithm James P Cohoon

Genie: A Genetic Placement Algorithm James P. Cohoon William D. Paris © 1987 IEEE

Genetic Algorithms n n State Space Search –similar to SA Based on principles of natural selection and evolution q q Population of solutions, of varying fitness levels Solutions ‘mate’ or crossover, to form offspring Solutions randomly mutate to introduce new genes into the current population Best solutions have a better chance of surviving to the next generation

Pseudo Code overview Create an initial population P While (best score hasn’t improved in 10, 000 generations) { Offspring = Crossover(s 1, s 2 in P)* P = Selection(P U O)* For( i=1 to k*) Mutate(s in P) } *Solutions are selected for crossover proportional to the fitness level of individual. If (fitness < average) solution is rejected for crossover. *k = random normal function of mean K*Pop_Size*Num_Nets

Population Constructor Net 1: A, B, C, D Net 2: A, D, E, F, H Net 3: A, B, E, G, I, J A B E G I J Step 1: Randomly select a net (Z) Step 2: Place free modules in net Z on grid from L to R

Population Constructor Net 1: A, B, C, D Net 2: A, D, E, F, H Net 3: A, B, E, G, I, J A B E G I J Step 1: Randomly select a net (Z) Step 2: Place free modules in net Z on grid from L to R Step 3: Update free modules and nets

Population Constructor Net 1: A, B, C, D Net 2: A, D, E, F, H Net 3: A, B, E, G, I, J A B E G I J Step 1: Randomly select a net (Z) Step 2: Place free modules in net Z on grid from L to R Step 3: Update free modules and nets Step 4: Select next net Do { module m = previous module placed } Until ( m is in a free net || no mods left on net) if (success) go to Step 2 else go to Step 1

Population Constructor Step 1: Randomly select a net (Z) Step 2: Place free modules in net Z on grid from L to R Step 3: Update free modules and nets Net 1: A, B, C, D Net 2: A, D, E, F, H Net 3: A, B, E, G, I, J A B E G F H I J D Step 4: Select next net Do { module m = previous module placed } Until ( m is in a free net ) if (success) go to Step 2 else go to Step 1

Population Constructor Step 1: Randomly select a net (Z) Step 2: Place free modules in net Z on grid from L to R Step 3: Update free modules and nets Net 1: A, B, C, D Net 2: A, D, E, F, H Net 3: A, B, E, G, I, J A B E G F H C I J D Step 4: Select next net Do { module m = previous module placed } Until ( m is in a free net ) if (success) go to Step 2 else go to Step 1

Fitness Calculation n n Semi-perimeter bounding rectangle for each net Measure of excess channel usage q Penalized if channel has above average # nets n ie non-uniform channel usage

Crossover Operator Passing Parent Target Parent A B C G I B D E F F J L G H I K D C

Crossover Operator Passing Parent A B C D E F G H I Copy of Target Parent H J L K E A

Crossover Operator Passing Parent Copy of Target Parent A B C D E F G H I J L K

Mutation Operator n n n Selects a random net (Z) in Solution (s). Selects a random Module on Z Locates farthest module on net Z, and moves it as close as possible. Net 1: A, B, C, D n 2 A 3 1 D 1 is preferred (d. Y < d. X) q q if B or C @ 1, preferred If B, C @ 1, 2, required 2 is 3 is

Mutation Operator Step 1: Select a random net Step 2: Select a random module Net 1: A, B, C, D Step 3: Locate farthest module on net Initial Solution D E A C B

Mutation Operator Step 1: Select a random net Step 2: Select a random module Net 1: A, B, C, D Step 3: Locate farthest module on net Step 4: Slide module to closest possible location Initial Solution D E A C B

Results Authors Results My Results Vs TW* chip Genie Score Genie Time TW Score TW Time 10_1 40 2. 27 us 59 . 26 us 10_2 42 2. 2 us 60 . 31 us 50_1 2755 23 us 3794 36. 5 us 50_2 3295 35. 6 us 4959 29. 2 us *simplified algorithm, Implemented by me TW cost function used for both algorithms

Merits of GA’s n Pros: q q q n Large Population provides information about past solution space provides a more guided search Can keep inferior solutions without destroying the good ones crossover allows for the best parts of multiple solutions to form into one Cons: q q High memory requirement Difficult parameterization (population size, rate of mutation, weighted fitness for selection, etc)

My Thoughts n Potential Areas of improvement q q Crossover -Poor for small circuits (Converge to local optima too quickly) Mutation -too deterministic (almost always improves solution)

References Genetic Placement James P. Cohoon, member, IEEE, and William D. Paris IEEE Transactions on Computer Aided Design, Vol. Cad-6, November 1987 VLSI Cell Placement Techniques K. SHAHOOKAR AND P. MAZUMDER Department of Electrical Engineering and Computer Sc~ence, University of Michigan, Ann Arbor, Michigan 48109 ACM Computing Surveys, Vol. 23, No. 2, June 1991