![](bg9.png)
4.3 Influence of the Base Vector for
Mutation
The influence of the base vector for mutation is
evaluated by comparing DE/rand/1/bin,
DE/best/1/bin and DE/rand-to-best/1/bin
algorithms. Table 6 already indicates that DE/rand-
to-best/1/bin performs best on average even though
the best models show almost the same prediction
accuracy for the testing data sets (Table 10). When
studying the entropies of the solutions (Tables 8), it
is noticed that the lowest entropy is obtained with
DE/rand-to-best/1/bin indicating that the highest
rate of convergence is achieved with this algorithm.
This leads to clearly better prediction accuracy for
the testing data sets as shown in Tables 10 and 11.
The results provided show that it is advantageous
to use rand-to-best -strategy for selecting the base
vector for mutation.
4.4 Influence of the Crossover
Operator
The influence of the crossover operator can be
evaluated by studying DE/rand/1/bin and
DE/rand/1/exp algorithms. The results obtained with
the algorithms are almost equal. A slight difference
can be noticed from Table 8 and 11, which shows that
DE/rand/1/exp achieves a bit lower entropy and also a
bit lower SSEP for the testing data sets. However, the
difference is quite small and thus no suggestion about
the preferred algorithm can be given.
4.5 Comparison of the DE Algorithms
The DE algorithms are compared based on the
results given in Table 11. From the table, it is seen
that all the algorithms are able to reach almost equal
value for the training data SSEP. When the SSEP of
the testing data sets is investigated, it is seen that
DE/rand-to-best/1/bin gives the best results. Also
the overall entropy shows that the solutions found by
DE/rand-to-best/1/bin are close to each other
throughout the 500 repetitions. Thus DE/rand-to-
best/1/bin is the most suitable algorithm for the
studied problem. DE/best/1/bin and DE/rand/2/bin
show almost equal results and perform quite well
also. DE/rand/1/bin and DE/rand/1/exp exhibit the
poorest prediction accuracy and performance.
5 CONCLUSIONS
In this study, evolutionary algorithms were studied
and used for identifying the parameters of a fuel cell
model. The fuel cell model was nonlinear having 7
parameters. Five different DE algorithms were tested
and compared. DE varied in the number of
difference vectors, the selection of the base vector
for mutation and the crossover operator. The studied
DE algorithms were DE/rand/1/bin, DE/rand/2/bin,
DE/best/1/bin, DE/rand-to-best/1/bin and
DE/rand/1/exp. An appropriate population size for
all the algorithms was defined based on the plot of
the entropy of the initial population as the function
of the population size.
DE/rand-to-best/1/bin showed to be the most
suitable algorithm for the studied problem. Selection
of the crossover operator has no considerable effect
on the results.
REFERENCES
Bergey P. K. Ragsdale C. Modified differential evolution:
a greedy random strategy for genetic recombination.
Omega 2005; 33: 255-65.
Chakraborty, U. K., Abbott, T. E., Das, S. K. PEM fuel
cell modeling using differential evolution. Energy
2012; 40: 1, 387 – 399.
Chipperdale A. Introduction to genetic algorithms. In:
Zalzala AMS, Fleming PJ, editors. Genetic algorithms
in engineering systems, Stevenage, Herts: The
Institution of Electrical Engineers; 1997, p. 1-45.
Cover TM, Thomas JA. Elements of Information Theory.
Hoboken, N.J.: Wiley; 2005.
Fan H. Y, Lampinen J. A Trigonometric Mutation
Operation to Differential Evolution. J Global Optimiz.
2003; 27: 105-29.
Feoktistov V., Janaqi S. Generalization of the strategies in
differential evolution. In: Proceedings of the 18th
International Parallel and Distributed Processing
Symposium (IPDPS’04), Santa Fe, New Mexico: IEEE
Press; 2004, 165a, 2004.
Ikonen E, Najim K. Advanced process identification and
control. New York: Marcel Dekker; 2002.
Katare S., Bhan A., Caruthers J. M., Delgass W. N.,
Venkatasubramanian V. A hybrid genetic algorithm
for efficient parameter estimation of large kinetic
models. Comput. Chem. Eng. 2004; 28: 2569-81.
Larminie J., Dicks A. Fuel cell systems explained, 2nd
edition. West Sussex, England: John Wiley & Sons
Ltd; 2003.
Mann R. F., Amphlett J. C., Hooper MAI, Jensen H, M,,
Peppley BA, Roberge PR. Development and
application of a generalised steady-state
electrochemical model for a PEM fuel cell. J Power
Sources 2000; 86: 173-80.
Mo Z. J., Zhu X. J., Wei L. Y., Cao G. Y.. Parameter
optimization for a PEMFC model with a hybrid
genetic algorithm. Int. Journal Energy Res. 2006; 30:
585-97.
ICINCO2012-9thInternationalConferenceonInformaticsinControl,AutomationandRobotics
48