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
Jan 06, 2016
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
2
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
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
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3
4
8
1
3
4
2
4
Dead Area
BL Heuristic
y
x
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
S = {1, 2, 3, 4}
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1
2
3 4
5 67
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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
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
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• 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
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Improved BL
• Rotation of Modules
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
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1
3 4
2
Rotation of Modules
y
x
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
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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
1
2
2
33
3
2 2 2
3
3
3
23
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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
2
4
6
8
10
12
14
10 20 30 40 50 60 70 80 90 100N
Tim
e
BL
MERA
CPU Time
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
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GA Convergence
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
0
2
4
6
8
10
12
14
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
30
25-module BL
31
25-module IBL
32
25-module MERA
37
Future Work
• Variations of the Algorithm
• Situational Suitability
• Multiple ‘Bin’ Scenario
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
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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
An Efficient Placement Strategy for Metaheuristics based Layout Optimization
Thank You
Questions???