An Efficient Placement Strategy for Metaheuristics based Layout Optimization

1. An Efficient Placement StrategyforMetaheuristics based Layout Optimization by Abdul-Rahim Ahmad Otman Basir Systems Design Engineering, University of Waterloo Khaled Hassanein MGD School of Business, McMaster University Date: July 28, 2004

2. Outline • Introduction • Problem Definition • Existing Placement Heuristics • Proposed Placement Heuristic • Results • Future Directions • Conclusion An Efficient Placement Strategy for Metaheuristics based Layout Optimization

3. Introduction • Layout Design • Spatial Arrangement of Modules in a Given Space • Tedious Problem • NP-Hard • Subjective / Unstructured • Ubiquitous Applications: • VLSI • Facilities • Cutting / Packing • Visual Interface An Efficient Placement Strategy for Metaheuristics based Layout Optimization

4. Problem Definition • 2D Oriented Orthogonal Bin-Packing • A set of ‘n’ Rectangular Modules • A RectangularPacking Space • Pack Modules • Edges Parallel x- and y-axes of Packing Space • Max. Utility ?!? An Efficient Placement Strategy for Metaheuristics based Layout Optimization

5. Optimization Strategy • Ordering of Modules S = {2, 4, 1, 6, 5, 8, 10, 7, 3, 9} • Placement Strategy • Tractable Subset of Solutions • Metaheuristic Search • Genetic Algorithms • Simulated Annealing • Naïve Evolution • Random Search An Efficient Placement Strategy for Metaheuristics based Layout Optimization

6. Placement Heuristics • Placement Heuristic • Efficient • Efficant • Existing Heuristics • Bottom-Left (BL) --- (Jakobs, 1996) • Improved BL (IBL) --- (Liu & Teng, 1999) • Bottom-Left Fill (BLF) --- (Hopper et al., 2001) • Inefficient and Ineffective An Efficient Placement Strategy for Metaheuristics based Layout Optimization

7. BL Heuristic 4 3 2 1 • Placement at: • Bottom-most • Left-most An Efficient Placement Strategy for Metaheuristics based Layout Optimization

8. BL Heuristic y 4 4 Dead Area 3 2 1 x S = {1, 2, 3, 4} An Efficient Placement Strategy for Metaheuristics based Layout Optimization

9. Deficiencies of BL 8 7 6 5 1 3 4 2 Optimal Packing that can’t be created by BL S = {1, 2 , 3, 4, 5, 6, 7, 8} An Efficient Placement Strategy for Metaheuristics based Layout Optimization

10. BL Heuristic • Placement at: • Bottom-most • Left-most • Easy to Understand • Easy to Implement • Fast • Popular An Efficient Placement Strategy for Metaheuristics based Layout Optimization

11. Improved BL • Rotation of Modules An Efficient Placement Strategy for Metaheuristics based Layout Optimization

12. Rotation of Modules y 3 2 1 x 4 An Efficient Placement Strategy for Metaheuristics based Layout Optimization

13. Improved BL • Rotation of Modules • Substantial Improvement • Not Permissible in Many Applications • Priority to Downward Moves • Substantial Improvement • Filling Gaps • Quite Expensive An Efficient Placement Strategy for Metaheuristics based Layout Optimization

14. Proposed Algorithm • Hierarchical Optimization • Explore Placements on Corners • Min. of Enclosing Rectangle Area (MERA) • O(n2) An Efficient Placement Strategy for Metaheuristics based Layout Optimization

15. Proposed Algorithm … 1) Place module 1 at the bottom-left corner of the page 2) FOR K = 2 to Blocks FOR L = 1 to NPlaced FOR A = 1 to 4 FOR B = 1 to 4 Place corner B of MK on corner A of ML Check Overlap conditions Check Boundary conditions IF both conditions satisfied THEN Calculate the newOBJ IF newOBJ is less than OBJ THEN OBJ = newOBJ Save placement of module MK ENDIF ENDIF END B END A END L END K 3) Stop if no room for more modules.

16. Proposed Algorithm … 3 3 3 3 3 3 2 2 2 2 2 2 1 3 An Efficient Placement Strategy for Metaheuristics based Layout Optimization

17. Fitness Metrics • Packing Height • Contiguous Remainder • Area of Largest Contiguous Section of Bin Available for Further Placements • Subjective Evaluation • Symmetry • Aesthetic Value An Efficient Placement Strategy for Metaheuristics based Layout Optimization

18. Fitness Metrics … An Efficient Placement Strategy for Metaheuristics based Layout Optimization

19. Fitness Metrics … IBL MERA An Efficient Placement Strategy for Metaheuristics based Layout Optimization

20. Results 50-modules (random search … 100 iterations) An Efficient Placement Strategy for Metaheuristics based Layout Optimization

21. Results … 100-modules (random search … 100 iterations) An Efficient Placement Strategy for Metaheuristics based Layout Optimization

22. Results … Sequence Sorted by Decreasing Area % Difference from Optimal in Parentheses

23. Results … 100-modules Problem Genetic Algorithm (1000 Evaluations) % Difference from Optimal in Parentheses

24. CPU Time An Efficient Placement Strategy for Metaheuristics based Layout Optimization

25. GA Convergence 100-modules Problem An Efficient Placement Strategy for Metaheuristics based Layout Optimization

26. 25-module Optimal

27. 25-module BL

28. 25-module IBL

29. 25-module MERA

30. Future Work • Variations of the Algorithm • Situational Suitability • Multiple ‘Bin’ Scenario An Efficient Placement Strategy for Metaheuristics based Layout Optimization

31. Conclusion • Layout Design is a Tedious Problem • Ubiquitous Applications • Proposed a New Heuristic • Easy to Understand / Implement • Efficient / Efficant / Robust • Suitable for Decision Support • Increase Productivity An Efficient Placement Strategy for Metaheuristics based Layout Optimization

32. Thank You Questions???