A Hybrid Particle Swarm Optimization Considering Accuracy and Diversity of Solutions
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Transcript of A Hybrid Particle Swarm Optimization Considering Accuracy and Diversity of Solutions
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
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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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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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
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
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
- Slide 12
- Slide 13
- Slide 14
- Slide 15
- Slide 16
- Slide 17
-
Thank you for your kind attention
- Slide 1
- Slide 2
- Slide 3
- Slide 4
- Slide 5
- Slide 6
- Slide 7
- Slide 8
- Slide 9
- Slide 10
- Slide 11
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