An Analysis of the Effects of Neighborhood size and Shape on Local Selection Algorithms

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An Analysis of the Effects of Neighborhood size
and Shape on Local Selection Algorithms
- Jayashree Sarma and
Kenneth De Jong
Presented By Ashwini D Khadakbhavi
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• Flow
• Introduction
• About Neighborhood
• Growth Curve Analysis
• Effects Of Neighborhood Size, Shape, radius
• Quantitative Model
• Conclusion
• Future Work
• Strengths
• Weakness
• Questions

Ashwini D Khadakbhavi
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Introduction

• The Parallel Architecture is the main idea
  behind parallel
  Evolutionary Algorithms (EA).
• This paper extends the idea of improving the
  Parallel Evolutionary algorithm by focusing on
  size and shape of the neighborhoods.
• The Parallel EAs which have been tested before
  gave results that were similar to sequential EAs
  but with a slower growth rate.

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About Neighborhood ...its size ...its shape.
Neighborhood is defined in the terms of number of
steps taken (up, down, left, right) from
the particular grid point when the population is
taken in form of a toroidal grid made of n number
of grid points Jayashree sarma and Kenneth De
Jong,1996 Size is the number of grid points
which constitutes a neighborhood for a
particular grid point. There are two kinds of
shape defined here.
1. Linear All points reachable
in lt n steps taken in a fixed direction as
above. 2. Compact Contains closest n-1 point
from central grid point
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Neighborhood Patterns
L Linear Neighborhood C Compact
Neighborhood n size of the population
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Growth Curve Analysis
Best Proportion
No Of Generations
Selection algorithms used Proportional Selection
and Linear ranking selection Sequential
Population size 1024 Emergent Population size
32 x 32, neighborhood size 9.
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Growth Curve Analysis
The reason for the observed gap was considered to
be the combined effects of 1. Logistic
growth occurring in each of the local
neighborhoods. 2. Propagation time.
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Effects of Neighborhood Size
Propagation time inversely related to the
neighborhood size. So we can decrease the
propagation time by increasing the neighborhood
size. Experiments setup Used Different
kinds of neighborhoods such as L5, C9, L9, C13,
L13.
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Effects of Neighborhood Size Emergent Growth
Curve For
No Of Generations

• Fitness Proportional Selection (32x32)
• Linear Ranking Selection (32x32)

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Effects of Neighborhood Shape
Looking at the graph, they decided that not only
size but also the shape has something to do with
the growth rate of Parallel EAs. Decided that
radius was the main factor.
and
where
Radius C9 1.16 L9 1.49
C13 1.47
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Effects of Neighborhood Radius
Experiments were conducted by considering
different radius keeping the grid size
constant. Experimental setup Mainly
focused on radius sizes and not on
shapes. Results proved that expectation
regarding the effects of radius was considered to
be correct.
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Effects Of Neighborhood Radius
Best Proportion
No Of Generations

• Fitness Proportional Selection (32x32)
• Linear Ranking Selection (32x32)

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Effects of Neighborhood Radius Contd...
To prove their hypothesis, further experiments
were conducted by keeping the radius constant and
decreasing the grid size Experimental setup
Neighborhood L5, with grid size of 32x32, 16x16
and 8x8 But Oops!!!.It didn't work
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Effects of different Grid Radius Emergent Growth
Curve (L5, radius 0.89) For
Best Proportion

• No Of Generations

• Fitness Proportional Selection (32x32),
  (16x16),(8x8)
• Linear Ranking Selection (32x32), (16x16),(8x8)

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Effects of Neighborhood Radius Contd...
This made them believe that main factor is ratio
of the neighborhood radius to the grid radius.
Experimental setup Neighborhood L5, on
32x32 with ratio 0.06815 Neighborhood C21,
on 64x64 with ratio 0.06891 The results showed
that both gave the output same in quality and
quantity.
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Effects of Constant Radius Ratios Emergent Growth
Curve (L5 and C21) For
Best Proportion
No Of Generations

• Fitness Proportional Selection (32x32)
• Linear Ranking Selection (32x32)

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Qualitative model for Selection Intensity
A simple Quantitative model was developed for
these local neighborhood models. Approximated
logistic equation
Since 1(asymptotic value of N), We get
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Conclusion
The main conclusion made in this paper was that
the most important parameter for controlling the
selection intensity is the ratio of neighborhood
radius to the radius of the grid. Looking at the
graph, it was concluded that parallel EAs can be
made quantitatively equal to the sequential EAs
by just increasing the ratio to 0.5.
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Future Work
These Experiments can be tried on different kind
of topologies using different selection
algorithms. It is expected that the observation
would prove correct for these too.
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Strengths

• The paper had
• - Well Organized information
• - Intuitive graphs
• - Good Continuity
• - Simple use of language
• The fundamentals they provided give a very good
  base for
• future works.

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Weakness

• They were weak at explaining the equations
• More elaboration was needed on radius equation
• Lack of explanation for an important equation.
• Should have been more clear about the
  neighborhood configurations.

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Questions ?? Thank you
Ashwini D Khadakbhavi