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}

9

1

2

3 4

5 67

8

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

26

Results …100-modules Problem

Genetic Algorithm (1000 Evaluations)

% Difference from Optimal in Parentheses

27

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???