Transcript PSO (Gbest model)

2010 IEEE International Conference on Systems, Man, and Cybernetics
(SMC2010)
A Hybrid Particle Swarm Optimization
Considering
Accuracy and Diversity of Solutions
Takeya Matsui1 Masato Noto1
Masanobu Numazawa2
1Kanagawa
University, Japan
2Otaru University of Commerce, Japan
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Outline
1. Introduction
2. Particle Swarm Optimization (PSO)
3. Proposed Method
4. Simulation Experiments
5. Conclusion and Future Work
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Introduction
Particle Swarm Optimization (PSO)
An optimization method that emulates the behavior of
creatures such as a flock of birds or a school of fish.
Each of a number of candidate points (particles) has
information about its own position and velocity.
 That information is shared within the swarm, and the search
proceeds while information on the best solution is shared.
A characteristic of PSO
 The PSO algorithms are extremely simple.
 PSO is applied to various different types of problem and its
validity has been confirmed.
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Particle Swarm Optimization (PSO)
 Gbest model
 The best solution discovered by the entire swarm is shared by
the entire swarm.
 The most basic model for PSO.
 This model can converge quickly on a solution and may
become trapped at a local solution.
 Lbest model
 Divides the swarm into a number of groups.
 Shares the best solution that is discovered by each group
within that group.
 This model converges slowly on the solution but its global
search capability is better.
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In this study
 We propose a hybrid PSO algorithm.
 In order to resolve the drawback of PSO in that it can easily
get trapped at a local solution.
 The initial stages of the search maintain the diversity of
the search by using the Lbest model.
 Then the method intensifies the search in the later
stages by switching to the Gbest model.
 The method searches the optimal solution candidates
vicinity carefully by limiting update of the shared
information.
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PSO (Gbest model) algorithm
 Each Particle in the
-dimension space
 Current position:
 Current velocity:
 Own best solutions:
 Evaluation value:
( is the Particle number, is the number of iterations)
 Shared by the entire swarm
 Best solutions discovered by the entire swarm:
 Evaluation value:
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Travel of Particle in Gbest model
 Updating velocities
 Updating positions
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Lbest model
 Each Particle forms a group consisting of itself and
neighboring Particles.
 Shares the best solution that is discovered by each group
as
within that group.
 Each group search regions that are mutually different.
 The global search capability is increased.
 Since the particles are formed into groups with
overlapping portions, this means that there is some
sharing of information within the entire swarm.
 The processing eventually converges on the best value
within the
values.
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Degree of activity of swarm
 The degree of activity of the swarm has been proposed
as an indicator for quantitively comprehending the
search situation in PSO.
 The degree of activity of the swarm is defined as the
root mean square of the velocities of the particles.
: Number of Particles
: Number of dimensions of the problem
: -dimensional element of the velocity of the th
particle in iterations
 Use of the degree of activity of the swarm makes it
possible to know the activity state of the entire swarm.
 When the degree of activity is large --> Expanding
 When the degree of activity is small --> Converging
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Proposed method
 By using the degree of activity of the swarm to monitor
the diversity of the search.
 The initial stages of the search maintain the diversity of the
search by using the Lbest model.
 The final stages of the search intensifies the search by
switching to the Gbest model.
 Furthermore, the method is adopting the lowest
number of iterations
of the shared information.
 Updating the shared information of the swarm, and then
searching carefully in the vicinity of the optimal solution
candidates without further updating the shared information
until
is reached.
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Simulation experiments
 2nminima function
 Rastrigin function
Subj. to
Subj. to
Globally optimal solution:
Globally optimal solution:
2nminima function (
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Rastrigin function (
)
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Simulation Parameters
Dimension of the problem
Number of Particles
Weighting parameters
Maximum number of iterations
Threshold degree of activity for
switching the search model
Lowest number of iterations for
sharing information
Number of trials
100
: The maximum value of the degree of activity of the swarm
during the
iterations.
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Simulation Results
2nminima function Rastrigin function
Gbest model
Lbest model
Proposed
method
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Average
-735.2585
8.9745
Best
-783.3233
1.9899
Worst
-641.9561
26.8639
Average
-749.9607
7.7748
Best
-783.3233
0.9950
Worst
-698.5030
39.5371
Average
-767.7719
5.8604
Best
-783.3233
3.7373E-9
Worst
-698.5030
12.9350
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Transitions in degree of activity
2nminima function
Rastrigin function
 The proposed method maintains the degree of activity of the swarm
right up to the end.
 This is thought to be because the diversity of the search is
maintained for a long while with the proposed method.

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By using the Lbest model to search in different ranges for each group, until
the degree of activity falls to a certain amount.
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Transitions in best values
2nminima function
Rastrigin function
 The proposed method took longer to converge on the solution than the
Gbest model.


Uses the Lbest model in the initial stages of the search.
The adoption of
delays the convergence on the solution.
 No great difference in convergence on the solution was seen in
comparison with the Lbest model.

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The search is intensified by switching to the Gbest model in the final
stages of the search.
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Conclusion and Future Work
 In this study, we proposed a hybrid method in order to
resolve the drawback of PSO in that it can easily get
trapped by a local solution.
 We have confirmed from the results of simulation
experiments that the proposed method has superior
search capabilities.
 Future work
 Optimization of
and
.
 Evaluations of various different benchmark problems.
 Verification of the validity of the method in real-life systems.
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Thank you for your
kind attention!