Optimization Using Particle Swarm with Near Neighbor Interactions

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Optimization Using Particle Swarm with Near
Neighbor Interactions

• Kalyan Veeramachaneni
• Thanmaya Peram
• Chilukuri K Mohan
• Lisa Ann Osadciw

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Overview

• Introduction
• Motivation
• Fitness- Distance Ratio
• FDR-PSO Algorithm
• Particle Dynamics
• Experimental Settings
• Results and Analysis
• Related Work
• Summary

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Introduction Particle Swarm Optimization

• Inspired from social impact theory
• Each particle influenced by its own previous
  experience, pbest
• Also influenced by local best in neighborhood,
  lbest
• Simulation results show that complete graph
  topology yields better results than other
  topologies

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Motivation

• Problems with PSO execution
• Premature convergence
• Clustering of particles
• Goal To overcome these problems, exploiting
  social impact theory

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Fitness-Distance Ratio

• Evaluating influence of jth particle on the ith
  particle (along the dth dimension)
• where Pj is the previous best position
  visited by the jth particle
• Xi is the position of the particle under
  consideration

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FDR-PSO Algorithm

• Each particle influenced by
• Its own previous best (pbest)
• Global best particle (gbest)
• Particle that maximizes FDR (nbest)
• Velocity Update Equation
• Position Update Equation

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FDR-PSO Algorithm

• Algorithm FDR-PSO
• For t 1 to the max. bound on the number of
  generations,
• For i1 to the population size,
• Find gbest
• For d1 to the problem
  dimensionality,
• Find nbest which maximizes the
  FDR
• Apply the velocity update
  equation
• Update Position
• End- for-d
• Compute fitness of the particle
• If needed, update historical
  information regarding Pi and Pg
• End-for-i
• Terminate if Pg meets problem
  requirements
• End-for-t
• End algorithm.

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Particle Dynamics I

• Different nearest best neighbors for a particle
  along different dimensions
• Nearest best neighbor often poorer than global
  best
• Possible overlap between gbest or pbest and nbest
  for small populations
• Overlap of 40 found in a population size of 10

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Particle Dynamics -II

• Greater exploration avoiding premature
  convergence
• Increased Population Diversity

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Particle Dynamics -II
Average
Best
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Particle Dynamics II
Average
Best
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Experimental Settings - I

• Experimental Settings

Swarm Size Generations Dimensions Trials
10 1000 20 30
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Experimental Settings - II

• FDR-PSO parameters
• Notation
• ?1, ?2, ?3 represent the weights given to pbest,
  gbest and nbest terms respectively
• Variations of FDR-PSO are obtained by varying the
  three weights
• PSO parameter selection
• Equal social and Cognitive learning rates

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Results and Analysis -I
Axis Parallel Hyper Ellipsoid
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Results and Analysis -II
Griewangks Function
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Summary of Results
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Results and Analysis III

• FDR-PSO variations consistently outperformed PSO
• FDR-PSO(112) was the best performer
• nbest term is more important for multimodal
  functions

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Performance of FDR-PSO Variations

• FDR-PSO(112) and FDR-PSO(012) outperform PSO on 5
  out of 6 benchmark problems
• FDR-PSO(102) outperform FDR-PSO(111) in 4 out of
  6 benchmark problems
• FDR-PSO(002) outperforms FDR-PSO(111) and PSO in
  3 out of 6 benchmark problems

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Related Work

• ARPSO Diversity measurement makes the algorithm
  alternate between attraction and repulsion phases
• PSO with mass extinction (HPSO) Velocities are
  reinitialized after each extinction interval
• Hybrid PSO Population is split into
  subpopulations and PSO algorithm is hybridized
  with features from genetic algorithms

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FDR-PSO Vs Other Variations -I
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FDR-PSO Vs Other Variations -II

• Many PSO variations introduce additional control
  parameters which are not easy to determine
• FDR-PSO achieves better minima without any
  additional parameters
• Other variations are extrinsic to particle
  dynamics, and hence can be applied to FDR-PSO as
  well

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Summary

• Designed a new algorithm which partly follows
  social impact theory
• Modeled the Fitness-Distance Ratio metric
• Improved performance compared to PSO and its
  previous variations
• Significantly less affected than PSO by problems
  such as premature convergence, loss of diversity
  in population

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Development and Research in Evolutionary
Algorithms for Multisensor Smart Networks

• DreamsNet
• 277, Link Hall
• Syracuse University
• Syracuse, NY 13244