A Memetic Algorithm for VLSI Floorplanning Maolin Tang, Member, IEEE, and Xin Yao, Fellow, IEEE IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS—PART B: CYBERNETICS, VOL. 37, NO. 1, FEBRUARY 2007 Presented By Chinmaya Kumar Swain Mohamed Hanoosh RajKumar Gajavelly

TALK FLOWS INTRODUCTION FLOORPLAN BACKGROUND MEMETIC ALGORITHM EMPIRICAL STUDIES ON THE MA CONCLUSION

INTRODUCTION Floorplanning is an important problem in Very Largescale Integrated-Circuit (VLSI) design automation as it determines the performance, size, yield, and reliability of VLSI chips VLSI floorplanning is an NP-hard problem This paper addresses Memetic Algorithm for VLSI floorplanning problem, which quickly produces optimal solution for all the tested benchmark problems. MA is a hybrid genetic algorithm

Floorplan Background VLSI is a process used to build electronic components such as microprocessors and memory chips comprising millions of transistors The first stage of the VLSI design process typically produces a set of indivisible rectangular blocks called cells In a second stage, interconnection information is used to determine the relative placements of these cells The third stage, Floorplan optimization,

Floorplan optimization problem with three cells and six possible configurations

PROBLEM STATEMENT A module m i is a rectangular block with fixed height h i and width w i, M = {m 1,m 2,..., m n } is a set of modules, and N is a net list specifying interconnections between the modules in M A floorplan F is an assignment of M onto a plane such that no module overlaps with another.

PROBLEM STATEMENT Minimize cost(F) – Area(F) = area of the smallest rectangle enclosing all the modules – Wirelength(F)= total length of the wires fulfilling the interconnections specified by N – Area ∗ - Estimated minimal area – Wirelength ∗ - Estimated minimal interconnection cost – w1 and w2 are weights assigned to the area minimization objective and the interconnection minimization objective where 0 ≤ w1, w2 ≤ 1, and w1 + w2 = 1.

O-Tree Representation A floorplan with n rectangular modules can be represented in a horizontal(vertical) O-tree of (n+1) bocks, of which n nodes correspond to n modules m 1,m 2,…,m n and one node corresponds to left boundary of the problem. There exists a directed edge from module m to m j iff x j = x i + w i where x i, x j are left edge coordinate of m i, m j and w i is width of m i.

(T, π) = ( , adbcegf)

Local Search Method 1) For each node m i in (T, π): a) delete m i from (T, π); b) insert m i in the position where we can get the smallest cost value among all possible insertion positions in (T, π) as an external node of the tree; c) perform (a) and (b) on its orthogonal O-tree. 2) Output (T, π).

Memetic Algorithm  Initialize population  While (Stopping criteria) Evaluate fitness of each individual Select parents Produce children Apply local search (This is additional step compared to GA. Local search is used optimize selected individuals so that it can lead to convergence faster) Advance to next generation

Proposed MEMETIC ALGORITHM MA is a hybrid GA that uses genetic search method to explore the search space and uses a local search method to exploit information in the search region. The exploration and exploitation are balanced by a bias search strategy.

Proposed MEMETIC ALGORITHM Representation of individual Fitness Function Initial Population Genetic Operators Local Search Description of the MA

Representation of individual – an admissible floorplan represented by an O-tree and encoded in a tuple (T, π) – T is a 2n-bit string identifying the structure of the O-tree, and π is a permutation of the nodes. Fitness function – f((T, π)) = 1/ cost (F (T, π) )

Initial population – Randomly generate a sequence of modules π and insert into the O-tree in the same order such that the cost is optimum for its insertion – Repeat above to get each individual

Genetic Operators – Exploration of search regions Meme : Sub tree – Crossover – Mutations

Crossover One sub tree selected from one parent and remaining from other parent

Mutation One top level tree is identified and its children's order changed Remove a sub tree and insert it back

Local search A Local search method discussed earlier is used. Individuals satisfying a certain criteria is optimized – Different individuals may lead to same optimum point. – Those individuals which are more closer to optimum(ie higher fitness) is better choice for optimization

Strategy to bias the search If Fitness value >= threshold then exploit(optimize) it

Algorithm for MA 1) t := 0; 2) generate an initial population P(t) of size PopSize; 3) evaluate all individuals in P(t) and find the best individual best 4) while the preset runtime is not up: a) t := t + 1; b) for each individual in P(t): i) this individual becomes the first parent p1; ii) select a second parent using roulette wheel selection p2; iii) probabilistically apply crossover to produce a child c1; iv) if fitness(c1) ≥ v, then optimize c1 using the local search method; v) if fitness(c1) ≥ fitness(p1), then p1 := c1; vi) if fitness(c1) ≥ fitness(best), then best := c1; vii) probabilistically apply the two mutators (picked up randomly) on c1 to produce a new individual f; viii) if fitness(f) ≥ v, then optimize f using the local search method; ix) if fitness(f) ≥ fitness(p1), then p1 := f; x) if fitness(f) ≥ fitness(best), then best := f. 5) output best.

EMPIRICAL STUDIES ON THE MA Two popular benchmarks are used here to 1.Study the performance of the MA 2. Determination of the Value of the Threshold v 3. The Effectiveness of the Threshold Strategy The benchmarks used in the empirical studies are two popular MCNC benchmark problems for the VLSI floorplanning problem: ami33 and ami49  ami33 has 33 modules, 123 nets, 480 pins, and 42 input–output (IO) pads  ami49 has 49 modules, 408 nets, 931 pins, and 42 IO pads.

Performance of the MA Best SolutionAverage Solution Over mDA1.10% to 2.94%0.36% to 2.46% Over GA1.55% to 4.23 %1.85% to 5.56% Improvements of MA

Performance of the MA Best SolutionAverage Solution Over mDA1.10% to 2.94%0.36% to 2.46% Over GA1.55% to 4.23 %1.85% to 5.56% Improvements of MA

Dynamic Performance Comparison for benchmark – ami33 Dynamic Performance Comparison for benchmark – ami49

On the Determination of the Value of the Threshold v Observations: 1.For fitness-value<0.6 there is no significant improvement after optimization. 2.Best of the 100 optimized floorplans is generated from an initial floorplan whose fitness-value ≥ 0.6.

On the Effectiveness of the Threshold Strategy Two Approaches used to test the effectiveness of MA 1.Threshold strategy for picking up the individuals 2.Randomly picking up the individuals

On the Tradeoff Between the Two Optimization Objectives Observations 1.MA is Sensitive to configuration 2.Two Objectives are mutually Constrained with each other

CONCLUSION Presented an MA for a non-slicing and hard module VLSI floorplanning problem—a challenging optimization problem in VLSI design automation. The exploration and exploitation are balanced by a threshold bias search strategy. Experimental results have shown that the MA outperforms both the mDA and GA for the benchmark problems.

Future Scope Dynamic threshold bias search strategies – It is conjectured that if v can dynamically change in the light of the status of the population of the MA, the performance of the MA could be further improved. Improving the crossover operator such that it can effectively preserve good memes contributing to both area and interconnection minimizations.

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