Spacecraft Solar Arrays Degradation Forecasting with Evolutionary

Designed ANN-based Predictors

Maria Semenkina, Shakhnaz Akhmedova, Eugene Semenkin and Ivan Ryzhikov

Institute of Computer Sciences and Telecommunication, Siberian State Aerospace University,

Krasnoyarskiy Rabochiy ave., 31, Krasnoyarsk, 660014, Russia

Keywords: Spacecraft Solar Array, Degradation Forecasting, ANN-based Predictors, Automated Design,

Self-configuring Evolutionary Algorithms, Bio-Inspired Algorithms Co-operation.

Abstract: The problem of forecasting the degradation of spacecraft solar arrays is considered. The application of

ANN-based predictors is proposed and their automated design with self-adaptive evolutionary and bio-

inspired algorithms is suggested. The adaptation of evolutionary algorithms is implemented on the base of

the algorithms’ self-configuration. The island model for the bio-inspired algorithms cooperation is used. The

performance of four developed algorithms for automated design of ANN-based predictors is estimated on

real-world data and the most perspective approach is determined.

1 INTRODUCTION

The future lies in the development of alternative

energy sources such as solar arrays (SA). However,

the efficiency of their application in systems of outer

space assignment strongly depends on the

environmental influence that results in their

degradation. The testing of ground-based solar

panels is an expensive and time-consuming

procedure, therefore the use of forecast tools for the

degradation of solar panels can significantly

improve the process of SA implementation.

Artificial neural networks (ANN) are often used

for prediction problems solving because of their

generalization ability (Zhang, 1998). However, the

efficiency of ANN-based predictors essentially

depends on the choice of an effective ANN structure

and the successful tuning of weight coefficients.

Different types of evolutionary algorithms (EA) as

well as so called bio-inspired approaches are often

used for both tasks. In this paper we use proven Self-

Configuring Evolutionary Algorithms (SelfCEA)

(Semenkin, 2012) and Co-Operation of Biology

Related Algorithms (COBRA) (Akhmedova, 2013)

for the automated design of ANN-based predictors.

The rest of the paper is organized as follows: in

Section 2 the problem description is given, in

Section 3 we give some information on optimization

techniques, in Section 4 approaches for the

automated design of neural networks are described,

in Section 5 we consider the outcomes of numerical

experiments, and in the last section some

conclusions and directions of further investigations

are presented.

2 PROBLEM DESCRIPTION

It is necessary to develop a mathematical model for

predicting solar array degradation according to

available SA parameter changes measured together

with the corresponding parameters of solar activity

during the fulfilment of the real spacecraft’s

mission.

The model is adjusted to determine the electrical

characteristics of solar panels based on the following

environment factors:

• integral fluence of protons with energies less

than 1 МеV;

• integral fluence of protons with energies less

than 10 МеV;

• integral fluence of protons with energies less

than 100 МеV;

• integral fluence of electrons with energies less

than 0,6 МеV;

• integral fluence of electrons with energies less

than 2 МеV;

421

Semenkina M., Akhmedova S., Semenkin E. and Ryzhikov I..

Spacecraft Solar Arrays Degradation Forecasting with Evolutionary Designed ANN-based Predictors.

DOI: 10.5220/0005122004210428

In Proceedings of the 11th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2014), pages 421-428

ISBN: 978-989-758-039-0

 2014 SCITEPRESS (Science and Technology Publications, Lda.)

• the parameter defined as the number of days

since the spacecraft separation that characterizes

the SA damage by meteoritic bodies and UV

radiation;

• the parameter that characterizes the degree of

spacecraft solar illumination.

We pose the following output parameters:

• open circuit voltage of the solar battery Ucv

(open circuit voltage);

• current intensity of solar panel Isc (amperage

short circuit)

for both sections of the spacecraft’s SA, i.e. four

output parameters are considered.

So it is necessary to design the SA degradation

predictor based on the flight data. We will design it

automatically in the form of an artificial neural

network. For this aim, we will use the specific

optimization approach that allows an automated

choice of ANN structure and adjustment of weight

coefficients.

3 SELF-ADAPTING

OPTIMIZATION TECHNIQUES

Evolutionary and bio-inspired algorithms are well

known and often used techniques for complicated

optimization problem solving. However, their

performance essentially depends on the choice of the

algorithm settings and adjustment of parameters. It

prevents the wide use of algorithms by end users

who are not experts in stochastic optimization, e.g.

aerospace engineers. Below we consider two

approaches to the automated choice of the

appropriate algorithmic scheme: co-evolution and

self-configuration.

3.1 Co-Operation of Biology Related

Algorithms (COBRA)

Five well-known optimization methods such as the

Particle Swarm Optimization Algorithm (PSO)

(Kennedy, 1995), the Wolf Pack Search Algorithm

(WPS) (Yang, 2007), the Firefly Algorithm (FFA)

(Yang, 2009), the Cuckoo Search Algorithm (CSA)

(Yang, 2009) and the Bat Algorithm (BA) (Yang,

2010) are combined in one meta-heuristic called Co-

Operation of Biology Related Algorithms (COBRA)

(Akhmedova, 2013). These biology related

optimization approaches work with continuous

variables. It is impossible to say in advance which of

the above-listed algorithms is the best one or which

algorithm should be used for solving the given

optimization problem (Akhmedova, 2013). This was

the main reason for the development of a new meta-

heuristic. At the same time these algorithms are very

similar. The idea is the use of the cooperation of

these algorithms instead of any attempts to decide

which one is the best for the current problem in

hand.

The following proposed approach is that five

populations are generated (one population for each

algorithm) which are then executed in parallel

cooperating with each other. It is not required to

choose the population size for each algorithm

because the proposed algorithm is a self-tuning

meta-heuristic. The number of individuals in each

algorithm’s population can increase or decrease

depending on the increasing or decreasing of the

fitness value. If the fitness value has not improved

during a given number of generations, then the size

of all populations increases. And vice versa, if the

fitness value has constantly improved, then the size

of all populations decreases. Besides, each

population can “grow” by accepting individuals

removed from other populations. A population

“grows” only if its average fitness is better than the

average fitness of all other populations. The result of

this kind of competition allows us to provide the

biggest resource (population size) to the most

appropriate (in the current generation) algorithm.

This property can be very useful in the case of a hard

optimization problem when, as it is known, there is

no single best algorithm at all stages of the

optimization process execution (Eiben, 2003).

One of the most important driving forces of this

meta-heuristic is the migration operator that creates

a cooperation environment for component

algorithms. All populations exchange individuals in

such a way that a part of the worst individuals of

each population is replaced by the best individuals

of other populations. It brings up-to-date information

on the best achievements to all component

algorithms and prevents their preliminary

convergence to its own local optimum that improves

the group performance of all algorithms.

The performance of the proposed algorithm was

evaluated on the set of benchmark problems from

the CEC’2013 competition (Akhmedova, 2013).

This set of benchmark functions (namely there were

28 unconstrained real-parameter optimization

problems) was given in (Liang, 2012); there are also

explanations about the conducted experiments. The

validation of COBRA was carried out for functions

with 10, 30 and 50 variables.

Experiments showed that COBRA works

successfully and is reliable on this benchmark.

ICINCO2014-11thInternationalConferenceonInformaticsinControl,AutomationandRobotics

422

Results also showed that COBRA outperforms its

component algorithms when the dimension grows

and more complicated problems are solved

(Akhmedova, 2013).

3.2 Binary Modification of COBRA

As was mentioned, all the algorithms listed above

(PSO, WPS, FFA, CSA and BA) were originally

developed for continuous valued spaces. However

many applied problems are defined in discrete

valued spaces where the domain of variables is

finite. For this purpose the binary modification of

COBRA (COBRA-b) was developed.

COBRA was adapted to search in binary spaces

by applying a sigmoid transformation to the velocity

component (PSO, BA) and coordinates (FFA, CSA,

WPS) to squash them into a range [0, 1] and force

the component values of the positions of the

particles to be 0’s or 1’s.

The basic idea of this adaptation was taken from

(Kennedy, 1997

); firstly it was used for the PSO

algorithm. It is known that in PSO each particle has

a velocity (Kennedy, 1995), so the binarization of

individuals is conducted by the use of the calculation

value of the sigmoid function which is also given in

(Kennedy, 1997

s(v) = 1/(1+exp(–v)).

After that a random number from the range [0, 1] is

generated and the corresponding component value of

the particle’s position is 1 if this random number is

smaller than s(v) and 0 otherwise.

In BA each bat also has a velocity (Yang, 2010),

which is why we can apply exactly the same

procedure for the binarization of this algorithm. But

in WPS, FFA and CSA individuals have no

velocities. For this reason, the sigmoid

transformation is applied to position components of

individuals and then a random number is compared

with the obtained value.

Experiments with the same 28 test problems

from (Liang, 2012) showed that the COBRA-b

works successfully and reliably but slower than the

original version of COBRA with a smaller success

rate obtained (Akhmedova, 2013).

Such a result was expected as the binary

modification needs more computing efforts in

continuous variables space and should not be used

instead of the original COBRA. However, it can be

recommended for solving optimization problems

with the binary representation of solutions.

3.3 Self-configuring Evolutionary

Algorithm

If somebody decides to use evolutionary algorithms

for solving real world optimization problems, it will

be necessary to choose the effective variant of

algorithm parameters such as the kind of selection,

recombination and mutation operators. Choosing the

right EA setting for each problem is a difficult task

even for experts in the field of evolutionary

computation. It is the main problem of effectively

implementing evolutionary algorithms for end users.

We can conclude that it is necessary to find the

solution for the main problem of evolutionary

algorithms before suggesting for end users any EAs

application for the automated design of tools for

solving real world problems.

We propose using the self-configuring

evolutionary algorithms (SelfCEA) which do not

need any end user efforts as the algorithm itself

adjusts automatically to the given problem. In these

algorithms (Semenkin, 2012), (Semenkin, 2012), the

dynamic adaptation of operators’ probabilistic rates

on the level of population with centralized control

techniques is applied (see Fig.1).

Instead of the adjusting real parameters, setting

variants were used, namely types of selection

(fitness proportional, rank-based, and tournament-

based with three tournament sizes), crossover (one-

point, two-point, as well as equiprobable, fitness

proportional, rank-based, and tournament-based

uniform crossovers (Semenkin, 2012)), population

control and level of mutation (medium, low, high for

two mutation types). Each of these has its own initial

probability distribution (see Fig. 2) which is changed

as the algorithm executes (see Fig. 3).

This self-configuring technique can be used both

for the genetic algorithm (SelfCGA) and for the

genetic programming algorithm (SelfCGP). In

(Semenkin, 2012) SelfCGA performance was

estimated on 14 test problems from (Finck, 2009).

As a commonly accepted benchmark for GP

algorithms is still an "open issue" (O’Neill, 2010),

the symbolic regression problem with 17 test

functions borrowed from (Finck, 2009) was used in

(Semenkin, 2012) for testing the self-configuring

genetic programming algorithm. Statistical

significance was estimated with ANOVA.

SpacecraftSolarArraysDegradationForecastingwithEvolutionaryDesignedANN-basedPredictors

423

Figure 1: Main part of SelfCEA block diagram.

Figure 2: Flowchart illustrating step 1 in SelfCEA block

diagram.

Analysing the results, related to SelfCGA

(Semenkin, 2012) and SelfCGP (Semenkin, 2012), it

can be seen that self-configuring evolutionary

algorithms demonstrate higher reliability than the

average reliability of the corresponding single best

algorithm but sometimes worse than the best

reliability of this algorithm.

Figure 3: Flowchart illustrating step 7 in SelfCEA block

diagram.

Both SelfCGA and SelfCGP can be used for the

automated choice of effective structures and weights

tuning of ANN-based predictors.

4 ANN AUTOMATED DESIGN

The appropriate structure of ANN must be chosen

for the effective solving of the forecasting problem.

Below we consider COBRA-b and SelfCGA for the

choice of the number of layers, the number of

neurons in each layer and the type of the activation

function of each neuron for the multi-layered

perceptron as well as SelfCGP for the automated

design of the feed-forward ANN with an arbitrary

structure.

4.1 ANN in Binary String

First of all we choose the perceptron with 5 hidden

layers and 5 neurons in each hidden layer as a

maximum size of the structure for ANN. Each node

is represented by a binary string of length 4. If the

string consists of zeros (“0000”) then this node does

not exist in ANN. So, the whole structure of the

neural network is represented by a binary string of

length 100 (25x4); each 20 variables represent one

hidden layer. The number of input neurons depends

on the problem in hand. ANN has one output layer.

We use 15 of the most common activation

functions. For determining which activation function

will be used on a given node, the integer that

corresponds to its binary string is calculated.

ICINCO2014-11thInternationalConferenceonInformaticsinControl,AutomationandRobotics

424

Thus we use the optimization methods for

problems with binary variables (COBRA-b,

SelfCGA) for finding the best structure and the

optimization method for problems with real-valued

variables (COBRA, SelfCGA hybridized with local

search) for the weight coefficients adjustment of

each structure.

Although the ANNs structure automated design

by self-adapting optimization technics improves

their efficiency, it can work unsatisfactorily with big

real-world problems. Therefore, the automation of

the most important input selection can have a

significant impact on the efficiency of neural

networks. In this paper, we use additional bits in

every string for the choice of relevant variables to

put them in model. The number of these bits equals

the number of input variables. If this bit is equal to

‘0’ then the corresponding input variable is not used

in the model and is removed from the sample.

During initialization, the probability for a variable to

be significant will be equal to 1/3. This idea can help

end users to avoid the significant and complicated

procedure of choosing the appropriate set of input

variables with essential impact on the model

performance.

For the choice of more flexible models more

sophisticated tools must be used.

4.2 ANN Design with SelfCGP

We have to describe our way to model and optimize

an ANN structure with genetic programming (GP)

techniques before the employment of our SelfCGP

algorithm.

Usually, the GP algorithm works with tree

representation, defined by functional and terminal

sets, and exploits specific solution transformation

operators (selection, crossover, mutation, etc.) until

the termination condition will be met (Poli, 2008).

The terminal set of our GP includes input

neurons and 15 different activation functions. The

functional set includes specific operations for neuron

placement and connections. The first operation is the

placing of a neuron or a group of neurons in one

layer. There will be no appearance of additional

connections in this case. The second operation is the

placing of a neuron or a group of neurons in

sequential layers in such a way that the neuron

(group of neurons) from the left branch of the tree

precedes the neuron (group of neurons) from the

right branch of the tree. In this case, new

connections will be added which connect the

neurons from the left branch of the tree with the

neurons from the right branch of the tree. Input

neurons cannot receive any signal but have to send a

signal to at least one hidden neuron. It might be so

that our GP algorithm does not include some of the

input neurons in the resulting tree, i.e., a high

performance ANN structure that does not use all

problem inputs can be found. This feature of the

approach allows the use of GP for the selection of

the most informative combination of problem inputs.

The tree and corresponding neural network example

are presented in Figure 4.

The GP algorithm forms the tree from which the

ANN structure is derived. The ANN training is

executed to evaluate its fitness which depends on its

performance in solving the problem in hand, e.g.,

approximation precision or number of misclassified

instances. For training this ANN, connection

weights are optimized with the self-configuring

genetic algorithm (SelfCGA) which does not need

any end user efforts as the algorithm itself adjusts

automatically to the given problem". When GP

finishes giving the best found ANN structure as the

result, this ANN is additionally trained with again

the SelfCGA hybridized with a local search. The

same approach is used for the application of

SelfCGP.

Figure 4: Tree and corresponding neural network example.

The efficiency of the proposed approach was

tested on the representative set of test problems

(approximation, time series prediction) (Panfilov,

2012). The test results showed that the neural

networks created by SelfCGP have a small number

of neurons in comparison with neural networks

obtained by means of neuro-simulator and are not

fully connected (few connections between neurons).

Besides, the automatically designed ANNs did not

include all inputs in model, i.e. reduced the input

space.

5 EXPERIMENTAL RESULTS

We used evolutionary designed ANN-based

predictors for the forecasting of the solar array

SpacecraftSolarArraysDegradationForecastingwithEvolutionaryDesignedANN-basedPredictors

425

Table 1: Results for solar arrays degradation prediction.

Algorithm 1 2 3 4 Mean

SelfCGP+ANN 4,3196

(5,0442)

4,1441

(4,9392)

4,65

(5,53)

5,4863

(6,2066)

4,65

(5,43)

SelfCGP 4,6726

(5,7688)

4,4827

(5,5344)

5,03

(6,21)

5,9346

(7,3268)

5,03

(6,21)

SelfCGA+ANN 4,8584

(5,2672)

4,661

(5,0531)

5,232

(5,671)

6,17056

(6,6897)

5,23

(5,67)

COBRA+ANN+S 5,1127 2,8841 4,5755 8,6907 5,3158

COBRA+ANN 5,04907 4,77149 4,95868 6,62939 5,3522

degradation. The list of used tools is as follows:

1. Self-configuring genetic programming algorithm

for the automated ANN design (SelfCGP+ANN)

(Panfilov, 2012);

2. Self-configuring genetic algorithm for the

automated ANN design and the significant

variables choice (SelfCGA+ANN);

3. Co-Operation of Biology Related Algorithms for

automated ANN structure search

(COBRA+ANN+S) (Akhmedova, 2014);

4. Co-Operation of Biology Related Algorithms for

adjusting weight coefficients in the single layer

perceptron with 3 neurons in the hidden layer

(COBRA+ANN).

Additionally, we used for the comparison some

other approaches:

1. Symbolic regression based predictor designed

with SelfCGP (Semenkin, 2012);

2. Fuzzy logic (FL) and neural-fuzzy logic (NFL)

based predictors designed with GA (Shabalov,

2012);

3. ANN based predictor designed with Genetic

Programming based Ensembling (GPEN)

technique (Bukhtoyarov, 2012);

4. ANN based predictor designed with Neural

Network Ensemble (GASEN) technique

(Bukhtoyarov, 2012).

For all approaches, the prediction error was

estimated in the same way:







yyms

error

minmax

11100

where s is the test sample size, m is the outputs

number, y is the true output value, and o is the

model output.

The problem sample for the prediction of solar

array degradation contains information about 295

days and has 7 inputs and 4 outputs. We used first

169 examples for training and the last part of the

examples for testing our models. Results for all

techniques presented in this paper are given in Table

1. The first number in each cell is the best found

result among all algorithm runs. The mean error

averaged over all runs is presented in brackets.

It is easy to see that SelfCGP for the ANN

automated design exhibits the smallest among the

best results; its mean result is better than the best

results of other techniques that do not use the self-

configuration. In particular, the relative error, that is

equal to 4.319, is equivalent to the first output error

that is equal to 0.1597V from a possible 3.6971V.

Typically, SelfCGP and SelfCGA used only six

inputs from seven and ignored the integral fluence of

protons with the smallest energy.

The results of alternative approaches are

presented in Table 2. Comparing this Table with

Table 1 it can be seen that the approaches described

in this paper essentially outperform alternatives that

use fuzzy logic (NFL, FL) and are outperformed by

ensembling methods, although self-configuring

algorithms outperform one ensembling method as

well (GASEN). The current best method (GPEN) to

a large extent does not outperform self-configuring

algorithms although it uses the ensembling

technique. One can reasonably conclude that an

ensembling technique based on the EA self-

configuration could further improve the quality of

the prediction.

Table 2: Best results for alternative methods.

Algorithm GPEN GASEN NFL FL

Mean 4,29 5,23 5,87 7,66

An additional observation is the differences in

required computational efforts for different methods.

The ensembling methods mentioned above have to

configure more than 10 individual intellectual

information technologies and generate formulae for

their interaction. This is at least 10 times more time

consuming than using one neural network. Certainly,

the methods presented in this paper do not use any

ensembling techniques and need much less

computing time. At the same time, the best

ICINCO2014-11thInternationalConferenceonInformaticsinControl,AutomationandRobotics

426

algorithm among those presented in the paper

(SelfCGP+ANN) requires 1,5 times more

computational efforts although it uses the same

number of fitness function evaluations.

Nevertheless, SelfCGP+ANN should be used for the

real-world SA degradation prediction as it has a

much smaller error while the extra time spent is just

some hours for computing that cannot be considered

as a serious drawback in a process requiring many

months of expensive experimentations.

6 CONCLUSIONS

In the paper four approaches to the automated design

of ANN-based predictors for the degradation of

spacecraft solar arrays were described and their

performance estimation on real-world data was

fulfilled. All these approaches differ from

alternatives in the way they are adapted to the

problem in hand. Namely, all these approaches are

self-adapted and do not require from end users any

expertise in computational intelligence (evolutionary

computations, neural networks, etc.). The most

perspective approach was determined, i.e. SelfCGP,

although others also deserve further development.

The evident way of approach improvement is the use

of an ensembling technique although other

directions should also be used, e.g. better

implementation of self-adaptation techniques.

ACKNOWLEDGEMENTS

This research is supported by the Ministry of

Education and Science of Russian Federation within

State Assignment № 2.1889.2014/K.

REFERENCES

Akhmedova, Sh., Semenkin, E., 2013. New optimization

metaheuristic based on co-operation of biology related

algorithms. Vestnik. Bulletine of Siberian State

Aerospace University, Vol. 4 (50), 2013, pp. 92-99.

Akhmedova, Sh., Semenkin, E., 2013. Co-Operation of

Biology Related Algorithms. In: Proc. of the IEEE

Congress on Evolutionary Computation (CEC 2013),

Cancún, Mexico, 2013, pp. 2207-2214.

Akhmedova, Sh., Semenkin, E., 2014. Co-Operation of

Biology Related Algorithms Meta-Heuristic in ANN-

Based Classifiers Design. In: Proceedings of the IEEE

Congress on Evolutionary Computation (IEEE CEC),

2014. –accepted to publication.

Bukhtoyarov, V., Semenkin, E., Shabalov, A., 2012.

Neural Networks Ensembles Approach for Simulation

of Solar Arrays Degradation Process. In Proc. of

Hybrid artificial intelligent systems 7th International

Conference, HAIS 2012, Salamanca, Spain, 2012, pp.

186-195.

Eiben, A. E., Smith, J. E., 2003. Introduction to

Evolutionary Computing. Springer Verlag, 2003,

299p.

Finck, S. et al., 2009. Real-parameter black-box

optimization benchmarking 2009. In: Presentation of

the noiseless functions. Technical Report Researh

Center PPE.

Kennedy, J., Eberhart, R., 1995. Particle Swarm

Optimization. In Proc. of IEEE International

Conference on Neural networks, IV, 1995, pp. 1942–

1948.

Kennedy, J., Eberhart, R.,1997. A discrete binary version

of the particle swarm algorithm. In Proc. of the World

Multiconference on Systemics, Cybernetics and

Informatics, Piscataway, NJ, 1997, pp. 4104-4109.

Liang, J. J., Qu, B. Y., Suganthan, P. N., Hernandez-Diaz,

A. G, 2013. Problem Definitions and Evaluation

Criteria for the CEC 2013 Special Session on Real-

Parameter Optimization. In Technical Report 2012,

Computational Intelligence Laboratory, Zhengzhou

University, Zhengzhou China, and Technical Report,

Nanyang Technological University, Singapore.

O’Neill, M., Vanneschi, L., Gustafson, S., Banzhaf, W.,

2010. Open issues in genetic programming. In:

Genetic Programming and Evolvable Machines 11,

2010, pp. 339–363.

Panfilov, I. A., Semenkin, E. S., Semenkina, M. E., 2012.

Neural Network Ensembles Design with Self-

Configuring Genetic Programming Algorithm for

Solving Computer Security Problems. In:

Computational Intelligence in Security for Information

Systems, Advances in Intelligent Systems and

Computing 189, Springer-Verlag, Berlin Heidelberg,

2012, pp. 25-32.

Poli, R., Langdon, W. B., McPhee, N. F., 2008. A Field

Guide to Genetic Programming. Published via

http://lulu.com and freely available at http://www.gp-

field-guide.org.uk, 2008. (With contributions by J. R.

Koza).

Semenkin, E., Semenkina, M., 2012. Self-Configuring

Genetic Programming Algorithm with Modified

Uniform Crossover Operator. In: Proceedings of the

IEEE Congress on Evolutionary Computation (IEEE

CEC), 2012, pp. 1918-1923.

Semenkin, E. S., Semenkina, M. E., 2012. Self-

configuring Genetic Algorithm with Modified

Uniform Crossover Operator. Advances in Swarm

Intelligence, Lecture Notes in Computer Science 7331,

Springer-Verlag, Berlin Heidelberg, 2012, pp. 414-

421.

Shabalov, A., Semenkin, E., Galushin, P., 2012.

Integration of Intelligent Information Technologies

Ensembles for Modeling and Classification. In Proc.

of Hybrid artificial intelligent systems 7th

SpacecraftSolarArraysDegradationForecastingwithEvolutionaryDesignedANN-basedPredictors

427

International Conference, HAIS 2012, Salamanca,

Spain, 2012, pp. 365-374.

Yang, C., Tu, X., Chen, J., 2007. Algorithm of Marriage in

Honey Bees Optimization Based on the Wolf Pack

Search. In Proc. of the International Conference on

Intelligent Pervasive Computing, 2007, pp. 462-467.

Yang, X. S., 2009. Firefly algorithms for multimodal

optimization. In Proc. of the 5th Symposium on

Stochastic Algorithms, Foundations and Applications,

2009, pp. 169–178.

Yang, X. S., Deb, S., 2009. Cuckoo Search via Levy

flights. In Proc. of the World Congress on Nature &

Biologically Inspired Computing, IEEE Publications,

2009, pp. 210-214.

Yang, X. S., 2010. A new metaheuristic bat-inspired

algorithm. In Nature Inspired Cooperative Strategies

for Optimization, Studies in Computational

Intelligence, Vol. 284, 2010, pp. 65-74.

Zhang G., Patuwo B. E., Hu M. Y., 1998. Forecasting with

artificial neural networks: The state of the art.

International Journal of Forecasting 14, 1998, pp. 35–

62.

ICINCO2014-11thInternationalConferenceonInformaticsinControl,AutomationandRobotics

428