A A HYBRID HYBRID CHC GENETIC ALGORITHM CHC GENETIC ALGORITHM - PowerPoint PPT Presentation

A A HYBRID HYBRID CHC GENETIC ALGORITHM CHC GENETIC ALGORITHM FOR FOR MACRO CELL MACRO CELL GLOBAL ROUTING GLOBAL ROUTING AUTHORS G.Andal Jayalakshmi S.Sowmyalakshmi R.Rajaram 1

CONTENTS CONTENTS 1. INTRODUCTION 2. PROBLEM DEFINITION 3. THE GLOBAL ROUTER ALGORITHM a. PHASE I b. PHASE II 4. THE HYBRID CHC GENETIC ALGORITHM 5. SOLUTION ENCODING 6. CHC GENETIC OPERATORS. 7. IMPLEMENTATION AND RESULTS 8. CONCLUSION 2

INTRODUCTION – – VLSI VLSI INTRODUCTION Global Routing Global Routing 1. Macro cells are large, irregularly sized parameterized circuit modules that are generated by a silicon compiler as per a designer’s selected parameters . 2. Global Routing is the process of determining the connection pattern for each net to minimize the overall routing area. 3

INTRODUCTION- - INTRODUCTION Genetic Algorithm Genetic Algorithm 1. A Genetic Algorithm is an intelligent optimization technique used to solve many complex optimization problems. 2. A simple GA evolves a solution from an initial population of random solutions using crossover and mutation. 4

INTRODUCTION- - INTRODUCTION Hybrid CHC GA Hybrid CHC GA 1. A hybrid GA combines techniques particular to a problem with a simple GA. 2. A CHC genetic algorithm uses intelligent reproduction techniques and techniques to come out of local optima. 5

PROBLEM DEFINITION PROBLEM DEFINITION 1. The Minimum Rectilinear Steiner Tree (MRST) problem arises in global routing and wiring estimation where we seek low-cost topologies to connect the pins of signal nets. 2. Given n points in the Euclidean plane, we seek a tree that connects them all. A shortest such tree on a set of given points is a Minimal Rectilinear Steiner Tree(MRST) 6

THE GLOBAL ROUTER ALGORITHM – – THE GLOBAL ROUTER ALGORITHM PHASE I PHASE I The algorithm for SPANNING_TREE() is given below: SPANNING_TREE( ) Begin Initialize parameters : generation count , crossover and mutation probabilities Initialize parent population randomly Apply repair heuristics to the parent population /* Repair heuristic are To test cycle and self loops*/ 7

THE GLOBAL ROUTER ALGORITHM – – THE GLOBAL ROUTER ALGORITHM PHASE I(contd.) PHASE I(contd.) While ( termination condition not reached) Begin Select parents based on the total length of the Spanning tree Apply crossover and mutation /* Single Point Crossover and Exchange Mutation*/ Evolve new population Replace previous population by new population End End 8

THE GLOBAL ROUTER THE GLOBAL ROUTER ALGORITHM – – PHASE II PHASE II ALGORITHM The algorithm for STEINER_TREE() is given below: Begin Build the routing graph G For (each Net) Begin Initialize weights for edges. Find the minimum cost spanning tree T. For each (vertex, edge) pair of the spanning tree 9

THE GLOBAL ROUTER ALGORITHM – – THE GLOBAL ROUTER ALGORITHM PHASE II(contd.) PHASE II(contd.) Begin Find the optimum Steiner point to connect this edge to the vertex (at a suitable point) Find the longest edge on the generated cycle Compute the cost of the modified tree, and store the pair in a list, if the cost is less than the MST End 10

THE GLOBAL ROUTER ALGORITHM – – THE GLOBAL ROUTER ALGORITHM PHASE II(contd.) PHASE II(contd.) While the list is not empty Begin Remove the pair from the list which results in lowest cost Re compute the longest edge on the cycle and the cost of the tree If the edges to be replaced are in the tree and the cost is less, modify the tree End End End 11

THE HYBRID CHC GENETIC THE HYBRID CHC GENETIC ALGORITHM ALGORITHM The pseudo-code for the Hybrid CHC genetic algorithm is shown below: Begin Set the generation count c = 1 Set threshold value Initialize and evaluate parent population P(t) While (Termination Condition is not reached) do c = c + 1 Apply selection 12

THE HYBRID CHC GENETIC THE HYBRID CHC GENETIC ALGORITHM(contd.) ALGORITHM(contd.) Perform crossover on selected individuals to get Offspring C(t) Evaluate Offspring C(t) Select new parent population from previous parent population P(t-1) and the new child population C(t) using Elitism If P(t) is equal to P(t-1) then decrease the threshold value If Convergence occurs Reinitialize population by external mutation. End End 13

SOLUTION ENCODING SOLUTION ENCODING Our Encoding consists of an array of integers that represent the edges of the graph in the case of a Minimum Spanning Tree and the edges of a Steiner graph in the case of a Steiner Minimal Tree. 14

CHC GENETIC OPERATORS CHC GENETIC OPERATORS REPRODUCTION OPERATOR 1. We use Uniform crossover. 2. The Uniform crossover is implemented along with the repair algorithm. 3. The repair algorithm acts on the infeasible chromosomes and convert them to feasible ones. 15

CHC GENETIC OPERATORS CHC GENETIC OPERATORS MUTATION 1. We use Random mutation, which randomly changes a gene in the chromosome 2. In CHC genetic algorithm when premature convergence occur we reinitialize the whole population by means of random mutation. 16

IMPLEMENTATION AND IMPLEMENTATION AND RESULTS RESULTS Test Problem : B1 Nodes : 50 Edges : 63 Optimum : 82 Population Size for SGA : 110 Population Size for HCHC: 90 17

RESULTS – – TEST PROBLEM B1 TEST PROBLEM B1 RESULTS 302 282 262 242 222 202 Cost 1 82 1 62 1 42 1 22 1 02 82 Generation SGA HCHC Graph 1: Comparison of cost reduction in SGA and HCHC 18 algorithms for B1

RESULTS – – TEST PROBLEM B3 TEST PROBLEM B3 RESULTS Test Problem : B3 Nodes:50 Edges:63 Optimum : 138 Population Size for SGA : 110 Population Size for HCHC: 90 19

RESULTS – – TEST PROBLEM B3 TEST PROBLEM B3 RESULTS 298 278 258 238 Cost 21 8 1 98 1 78 1 58 1 38 Generation SGA HCHC Graph 2: Comparison of cost reduction in SGA and HCHC 20 algorithms for B3

RESULTS – – TEST PROBLEM B9 TEST PROBLEM B9 RESULTS Test Problem : B9 Nodes:75 Edges:94 Optimum : 220 Population Size for SGA : 110 Population Size for HCHC: 90 21

RESULTS – – TEST PROBLEM B9 TEST PROBLEM B9 RESULTS 400 380 360 340 Cost 320 300 280 260 240 220 Generation SGA HCHC Graph 3: Comparison of cost reduction in SGA and HCHC 22 algorithms for B9

CONCLUSION CONCLUSION 1. The HCHC algorithm shows much better performance over SGA, and generates comparable results for the Beasley’s problem set. 2. We further propose to improve the implementation for higher number of nodes and compare the results with the other existing algorithms. 23