An Efficient Placement Strategy for Metaheuristics 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 Rectangular Packing 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 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 Placement Heuristics An Efficient Placement Strategy for Metaheuristics based Layout Optimization

7 Placement at: –Bottom-most –Left-most BL Heuristic An Efficient Placement Strategy for Metaheuristics based Layout Optimization

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

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

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

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

Rotation of Modules y x An Efficient Placement Strategy for Metaheuristics based Layout Optimization

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

14 Proposed Algorithm An Efficient Placement Strategy for Metaheuristics based Layout Optimization Hierarchical Optimization Explore Placements on Corners Min. of Enclosing Rectangle Area (MERA) O(n 2 )

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 M K on corner A of M L 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 M K ENDIF END B END A END L END K 3) Stop if no room for more modules.

16 Proposed Algorithm … An Efficient Placement Strategy for Metaheuristics based Layout Optimization

17 50-module An Efficient Placement Strategy for Metaheuristics based Layout Optimization

module An Efficient Placement Strategy for Metaheuristics based Layout Optimization

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

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

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

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

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

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

25 Results … % Difference from Optimal in Parentheses 50-modules Problem Genetic Algorithm (1000 Evaluations)

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

27 CPU Time An Efficient Placement Strategy for Metaheuristics based Layout Optimization

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

29 25-module Optimal

30 25-module BL

31 25-module IBL

32 25-module MERA

module Optimal

module BL

module IBL

module MERA

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

38 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

Thank You Questions???

40 Genetic Algorithms very briefly tell what are genetic algorithms … and why we have chosen those Population based Search Robustness Global Perspective Set of Superior and Diverse Solutions An Efficient Placement Strategy for Metaheuristics based Layout Optimization

41 Encoding Scheme Data Structure –Sequence S of the module Indices Example S = {12, 4, 9, 25, 11, 47, 2, 0, 16, 13, 31, 45, 29, 19, 33, 5, 19, 7, 34, 50} Sequence of 20 Modules An Efficient Placement Strategy for Metaheuristics based Layout Optimization

42 Genetic Operators Selection --- Proportionate Mutation –Reverse a Subsequence –Exchange Elements of Two Subsequences Crossover –Tate & Smith (1995) a.Fill Each Position in Offspring by Randomly Selecting a Gene at the Same Position in a Parent (resolve conflicts) b.Insert Leftover Genes in Order (unresolved conflicts) –Jakobs (1996) a.Copy ‘q’ elements from One Parent to position ‘p’ in Offspring b.Fill Up Remaining Elements from Other Parent in the Same Order –Append a subsequence from One Parent to Another An Efficient Placement Strategy for Metaheuristics based Layout Optimization

43 ILG --- GA Crossover Parent 1:D C A H F E B G Parent 2:F A E H B D C G Common: H G Random:D A E H F -- B G Leftover:C Child:D A E H F C B G An Efficient Placement Strategy for Metaheuristics based Layout Optimization

44 Subjectivity … Preferences –Uncertain (tell what is uncertain and all other terms?) –Vague –Conflicting Performance Metrics –Space Utilization –Blank/White Space –Symmetry (Aesthetic Value) –Total Inter-module Distance An Efficient Placement Strategy for Metaheuristics based Layout Optimization

45 Computational Complexity … Infinite Search Space Superior (‘satisficing’) Outcome Placement Heuristics –Tractable Subset of Solutions An Efficient Placement Strategy for Metaheuristics based Layout Optimization