A Hybrid Particle Swarm Optimization Considering

Accuracy and Diversity of Solutions

Takeya Matsui1 Masato Noto1 Masanobu Numazawa2

1Kanagawa University Japan2Otaru University of Commerce Japan

2010 IEEE International Conference on Systems Man and Cybernetics (SMC2010)

11 Oct 2010

Outline

1 Introduction

2 Particle Swarm Optimization (PSO)

3 Proposed Method

4 Simulation Experiments

5 Conclusion and Future Work

11 Oct 2010 SMC2010 in IstanbulTURKEY 2

Introduction

Particle Swarm Optimization (PSO)Particle Swarm Optimization (PSO)An optimization method that emulates the behavior of creatures such as a flock of birds or a school of fishEach 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

11 Oct 2010 SMC2010 in IstanbulTURKEY 3

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 This model can converge quickly on a solution and may

become trapped at a local solutionbecome 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 better11 Oct 2010 SMC2010 in IstanbulTURKEY 4

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 5

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 6

Outline

1 Introduction

2 Particle Swarm Optimization (PSO)

3 Proposed Method

4 Simulation Experiments

5 Conclusion and Future Work

11 Oct 2010 SMC2010 in IstanbulTURKEY 2

Introduction

Particle Swarm Optimization (PSO)Particle Swarm Optimization (PSO)An optimization method that emulates the behavior of creatures such as a flock of birds or a school of fishEach 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

11 Oct 2010 SMC2010 in IstanbulTURKEY 3

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 This model can converge quickly on a solution and may

become trapped at a local solutionbecome 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 better11 Oct 2010 SMC2010 in IstanbulTURKEY 4

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 5

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 6

Introduction

Particle Swarm Optimization (PSO)Particle Swarm Optimization (PSO)An optimization method that emulates the behavior of creatures such as a flock of birds or a school of fishEach 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

11 Oct 2010 SMC2010 in IstanbulTURKEY 3

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 This model can converge quickly on a solution and may

become trapped at a local solutionbecome 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 better11 Oct 2010 SMC2010 in IstanbulTURKEY 4

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 5

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 6

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 This model can converge quickly on a solution and may

become trapped at a local solutionbecome 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 better11 Oct 2010 SMC2010 in IstanbulTURKEY 4

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 5

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 6

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 5

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 6

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 6

Travel of Particle in Gbest model

Updating velocities

Updating positions

11 Oct 2010 SMC2010 in IstanbulTURKEY 7

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 8

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

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 --gt Expanding When the degree of activity is small --gt Converging

11 Oct 2010 SMC2010 in IstanbulTURKEY 9

Number of Particles

Number of dimensions of the problem

-dimensional element of the velocity of the th particle in iterations

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 10

Simulation experiments

2nminima function

Subj to

Globally optimal solution

Rastrigin function

Subj to

Globally optimal solution

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4

-3-2

-10

12

34

5

0 10 20 30 40 50 60 70 80

-5 -4 -3 -2 -1 0 1 2 3 4 5-5-4

-3-2

-10

12

34

5

-200

-100

0

100

200

300

400

500

2nminima function ( ) Rastrigin function ( )

11 Oct 2010 SMC2010 in IstanbulTURKEY 11

The maximum value of the degree of activity of the swarm during the iterations

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 12

Simulation Results

2nminima function Rastrigin function

Gbest model

Average -7352585 89745

Best -7833233 19899

Worst -6419561 268639

Lbest model

Average -7499607 77748

Best -7833233 09950

Worst -6985030 395371

Proposed method

Average -7677719 58604

Best -7833233 37373E-9

Worst -6985030 129350

11 Oct 2010 SMC2010 in IstanbulTURKEY 13

Transitions in degree of activity

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 By using the Lbest model to search in different ranges for each group until

the degree of activity falls to a certain amount

0

05

1

15

2

25

3

35

4

0 1000 2000 3000 4000 5000

Iteration

GbestmodelLbestmodel

Proposedmethod

0

05

1

15

2

25

3

35

4

0 1000 2000 3000 4000 5000

Iteration

GbestmodelLbestmodel

Proposedmethod

2nminima function Rastrigin function

11 Oct 2010 SMC2010 in IstanbulTURKEY 14

Transitions in best values

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 The search is intensified by switching to the Gbest model in the final

stages of the search

-800

-750

-700

-650

-600

-550

-500

-450

-400

-350

0 1000 2000 3000 4000 5000

Iteration

GbestmodelLbestmodel

Proposedmethod

0

20

40

60

80

100

120

140

0 1000 2000 3000 4000 5000

Iteration

GbestmodelLbestmodel

Proposedmethod

11 Oct 2010 SMC2010 in IstanbulTURKEY 15

2nminima function Rastrigin function

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 16

Thank you for your kind attention

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Transitions in degree of activity

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 By using the Lbest model to search in different ranges for each group until

the degree of activity falls to a certain amount

0

05

1

15

2

25

3

35

4

0 1000 2000 3000 4000 5000

Iteration

GbestmodelLbestmodel

Proposedmethod

0

05

1

15

2

25

3

35

4

0 1000 2000 3000 4000 5000

Iteration

GbestmodelLbestmodel

Proposedmethod

2nminima function Rastrigin function

11 Oct 2010 SMC2010 in IstanbulTURKEY 14

Transitions in best values

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 The search is intensified by switching to the Gbest model in the final

stages of the search

-800

-750

-700

-650

-600

-550

-500

-450

-400

-350

0 1000 2000 3000 4000 5000

Iteration

GbestmodelLbestmodel

Proposedmethod

0

20

40

60

80

100

120

140

0 1000 2000 3000 4000 5000

Iteration

GbestmodelLbestmodel

Proposedmethod

11 Oct 2010 SMC2010 in IstanbulTURKEY 15

2nminima function Rastrigin function

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 16

Thank you for your kind attention

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Transitions in best values

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 The search is intensified by switching to the Gbest model in the final

stages of the search

-800

-750

-700

-650

-600

-550

-500

-450

-400

-350

0 1000 2000 3000 4000 5000

Iteration

GbestmodelLbestmodel

Proposedmethod

0

20

40

60

80

100

120

140

0 1000 2000 3000 4000 5000

Iteration

GbestmodelLbestmodel

Proposedmethod

11 Oct 2010 SMC2010 in IstanbulTURKEY 15

2nminima function Rastrigin function

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

11 Oct 2010 SMC2010 in IstanbulTURKEY 16

Thank you for your kind attention

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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

11 Oct 2010 SMC2010 in IstanbulTURKEY 16

Thank you for your kind attention

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Thank you for your kind attention

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