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Differential Evolution Algorithm with Adaptive Control Parameters

Differential Evolution Algorithm with Adaptive Control Parameters. Junhong Liu Jouni Lampinen Department of Information Technology, Lappeenranta University of Technology P. O. Box 20, FIN-53851 Lappeenranta, Finland Phone: +358-5-6212813 Fax: +358-5-6212899

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Differential Evolution Algorithm with Adaptive Control Parameters

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  1. Differential Evolution Algorithm with Adaptive Control Parameters • Junhong Liu Jouni Lampinen • Department of Information Technology, Lappeenranta University of Technology • P. O. Box 20, FIN-53851 Lappeenranta, Finland • Phone: +358-5-6212813 • Fax: +358-5-6212899 • Email: junhong.liu@lut.fi, Jouni.Lampinen@lut.fi

  2. Agenda • Introduction of Setting the Searching Parameters • Introduction of the Differential Evolution algorithm (DE) • Principle of Fuzzy Adapting • Implementation and Experimental study • Conclusions

  3. Setting the Searching Parameters’ Values • Parameter tuning: to find good values for the parameters before the run of the algorithm, then run the algorithm using these values, which remain fixed during the run. • Parameter control: to start a run with initial parameter values, which are changed during the run. Methods for changing the value of a parameter can be classified into three categories:

  4. Parameter Control: Three Categories • Deterministic parameter control: Modifies the strategy parameter(s) deterministically without using feedback from the search. • Adaptive parameter control: Takes place when there is some form of feedback from the search that is used to determine the direction and/or magnitude of the changes to the strategy parameter(s). • Self-adaptive parameter control:The parameters to be adapted are coded into the chromosomes that undergo mutation and recombination. Better values for these encoded parameters result in better individuals that in turn are more likely to survive, produce offspring and propagate these values.

  5. Introduction of Differential Evolution: 1 The problem to be solved with DE can be stated as follows: Minimize: f(X): D (1) by finding a suitable parameter vector: X =(x1,x2,…, xD) (2)

  6. Three control parameters: Mutation control parameter, F –a real and constant factor that controls the mutation operation. Crossover control parameter, CR – controls the crossover operation. Population size, NP – the number of population members. The ranges for F, CR and NP have been pointed out suitably in former research. However, only a few attempts have been made to study on how the control parameter settings affect the performance of DE (effectiveness, efficiency and robustness). The target of setting control parameters find an acceptable solution within an acceptable number of function evaluations. Introduction of DE

  7. Principle of the Fuzzy System - 1 • System parameters and fuzzy sets membership functions: the linguistic values of PC, FC (inputs) and F and/or CR(outputs); membership functions in Table II. , • Fuzzy rules: “9*2” rules in Table I determine the parameter F and/or CR based on the values of PC and FC. • Control strategy: Mamdani’s fuzzy inference method. • Defuzzification strategy: Centroidal Defuzzification Technique (CDT).

  8. Principle of the Fuzzy System - 2 • (See Fig. 2) Gaussian membership functions for the linguistic variables PC, FC, F & CR. • Two parameters  (standard deviation) and c (center) determine the shape and position of gaussian curve. • Decide  &c according experimental results in [13] and values of PC, FC, F and CR: (1)    ForCRshould be large when PC is large, indicating that the actual solution is away from the expected. • (2)  ForCRshould be small when FC is small, showing that the actual solution is close to the expected.

  9. Implementation & Experiment • Control surface: The setting of FLC presents a subjective view of an expert with respect to the objective characteristics of DE. As DE’s control surface, it’s viewable (Fig. 3). • Parameter setting: Table III. • Example: Behavior of the ADE algorithm for the sphere function (Fig. 4). • Comparisons of the Differential Evolution algorithm with and without adaptation: Fig. 5 and Table IV.

  10. Conclusions • The experimental results suggest that the proposed ADE algorithm performs better than those using all fixed parameters do , i.e., the process converges faster, when the dimensionality of the problem is higher. • Based on human knowledge and expertise, ADE algorithms are designated to expedite the convergence velocity of DE by using adaptive parameter(s).

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