A Cooperative Approach to Particle Swarm …...A Cooperative Approach to Particle Swarm Optimization...
Transcript of A Cooperative Approach to Particle Swarm …...A Cooperative Approach to Particle Swarm Optimization...
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A Cooperative Approach to Particle Swarm Optimization
Authors: Frans van den Bergh, Andries P. Engelbrecht
Journal: Transactions on Evolutionary Computation, vol 8, No. 3, June 2004
Presentation: Jose Manuel Lopez Guede
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Introduction
• “Curse of dimensionality”
• PSO
• CPSO
• CPSO-Sk
• CPSO-Hk
• GA comparation
• Results
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Particle Swarm Optimizers I
• PSO:– Stochastic optimization technique
– Swarm: a population
– During each iteration each particle accelerates influenced by:
• Its own personal best position
• Global best position
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Particle Swarm Optimizers II
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Particle Swarm Optimizers III
– During each iteration, each particle is updated:
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Particle Swarm Optimizers III
– During each iteration, each particle is updated:
– The global best position is updated:
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Cooperative Learning I
• PSO:
– Each particle represents an n-dim vector that can be used as a potential solution.
position
Best position of the particle
Best position of the swarm
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Cooperative Learning II
– Drawback:• Authors show a numerical example where PSO goes to a
worst value in an iteration.
• Cause: error function is computed only after all the components of the vector have been updated to their new values.
– Solution:• Evaluate the error function more frecuently.
• For every time a component in the vector has been updated.
– New problem:• The evaluation is only possible with a compete vector.
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Cooperative Learning III
• CPSO-S:– n-dim vectors are partitioned into n swarms of 1-D
– Each swarm represents 1 dimension of the problem
– “Context vector”:• f requires an n-dim vector
• To calculate the context vector for the particles of swarm j, the remainig components are the best values of the remaining swarms.
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Cooperative Learning IVcontext vector
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Cooperative Learning V
• Advantage:– The error function f is evaluated after each component
in the vector is updated.
• However:– Some components in the vector could be correlated.
– These components should be in the same swarm, since the independent changes made by the different swarms have a detrimental effect on correlated variables.
– Swarms of 1-D, and swarms of c-D, taken blindly.
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Cooperative Learning VI
• CPSO-Sk:– Swarms of 1-D, and swarms of c-D, taken blindly,
hoping that some correlated variables end up in the same swarm.
– Split factor: The vector is split in K parts (swarms)
– It is a particular CPSO-S case, where n=K.
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Cooperative Learning VII
CPSO-S
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Cooperative Learning VII
– Drawback:• It is possible that the algorithm become trapped in a state
where all the swarms are unable to discover better solutions: stagnation.
• Authors show an example.
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Hybrid CPSOs – CPSO-Hk I
• Motivation:– CPSO-Sk can become trapped.
– PSO has the hability to scape from pseudominimizers.
– CPSO-Sk has faster convergence.
• Solution:– Interleave the two algorithms.
• Execute CPSO-Sk for one iteration, followeb by one iteration of PSO.
• Information interchange is a form of cooperation.
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CPSO-Sk
CPSO-Sk
Overwite 1 particle k of the swarm Q
PSO
Swarms of theCPSO-Sk
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Experimental Setup I
• Compare the PSO, CSPO-Sk, CSPO-Hk algorithms.
• Measure: #function evaluations.
• Several popular functions in the PSO comunity were selected for testing.
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Experimental Setup II
“all the functions wheretested under coordinaterotation using Salomon’s
algorithm”
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Experimental Setup III
• PSO configuration:– All experiments were run 50 times
– 10, 15, 20 particles per swarm.
– Results reported are averages os the best value in the swarm.
Domain: “magnitude towhich the initial random
particles are scaled”
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Experimental Setup IV
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Experimental Setup V
• GA configuration:
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Experimental Setup VI
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Results I
• Fixed-Iteration Results I– 2.10^5 function evaluations.
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Results II
• Fixed-Iteration Results II– 2.10^5 function evaluations.
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Results III
• Fixed-Iteration Results III– PSO-based algs. performed better that GA algs. in
general.
– Cooperative algorithms collectivelly performed betterthan the standard PSO in 80% of the cases.
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Results IV
• Robustness and speed Results I– “Robustness”: the algorithm succeed in reducing the
the f below a specified threshold using fewer that thana number of evaluations.
– “A robust algorithm”: one that manages to reach thethreshold consistentle (during all runs).
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Results V
• Robustness and speed Results II
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Results VI
• Robustness and speed Results III– CPSO-H6 appears to be the winner because it achieved
a perfect score in 7 of 10 cases.
– There is a tradeoff between the convergence speedand the robustness of the algorithm.