An Efficient Placement Strategy for Metaheuristics based Layout Optimization
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An Efficient Placement Strategyfor
Metaheuristics based Layout Optimization
by
Abdul-Rahim AhmadOtman Basir
Systems Design Engineering, University of Waterloo
Khaled HassaneinMGD School of Business, McMaster University
Date: July 28, 2004
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Outline
• Introduction
• Problem Definition
• Existing Placement Heuristics
• Proposed Placement Heuristic
• Results
• Future Directions
• Conclusion
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
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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
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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
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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
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• 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
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• Placement at:– Bottom-most
– Left-most
BL Heuristic
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Dead Area
BL Heuristic
y
x
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
S = {1, 2, 3, 4}
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3 4
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Optimal Packing that can’t be created by BL
S = {1, 2 , 3, 4, 5, 6, 7, 8}
Deficiencies of BL
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• Placement at:– Bottom-most – Left-most
• Easy to Understand
• Easy to Implement
• Fast
• Popular
BL Heuristic
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Improved BL
• Rotation of Modules
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Rotation of Modules
y
x
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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
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Proposed Algorithm
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
• Hierarchical Optimization
• Explore Placements on Corners
• Min. of Enclosing Rectangle Area (MERA)
• O(n2)
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Proposed Algorithm … 1) Place module 1 at the bottom-left corner of the page2) FOR K = 2 to BlocksFOR L = 1 to NPlacedFOR 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 THENCalculate the newOBJIF 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.
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Proposed Algorithm …
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
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2 2 2
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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
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Fitness Metrics …
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
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Fitness Metrics …
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
IBL
MERA
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Results
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
50-modules (random search … 100 iterations)
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Results …
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
100-modules (random search … 100 iterations)
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Results …Sequence Sorted by Decreasing Area
% Difference from Optimal in Parentheses
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Results …100-modules Problem
Genetic Algorithm (1000 Evaluations)
% Difference from Optimal in Parentheses
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0
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10 20 30 40 50 60 70 80 90 100N
Tim
e
BL
MERA
CPU Time
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GA Convergence
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
0
2
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1 100 200 300 400 500 600 700 800 900 1000 1100
Iterations
% d
iffe
renc
e fr
om o
ptim
al
MERA
IBL
BL
100-modules Problem
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25-module Optimal
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25-module BL
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25-module IBL
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25-module MERA
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Future Work
• Variations of the Algorithm
• Situational Suitability
• Multiple ‘Bin’ Scenario
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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
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Thank You
Questions???