ANN-based Classifiers Automatically Generated

by New Multi-objective Bionic Algorithm

Shakhnaz Akhmedova and Eugene Semenkin

Siberian State Aerospace University, Krasnoyarsk, Russian Federation

Keywords: Neural Network Design, Multi-objective Optimization, Nature-inspired Algorithms, Medical Diagnostics.

Abstract: An artificial neural network (ANN) based classifier design using the modification of a meta-heuristic called

Co-Operation of Biology Related Algorithms (COBRA) for solving multi-objective unconstrained problems

with binary variables is presented. This modification is used for the ANN structure selection. The weight

coefficients of the ANN are adjusted with the original version of COBRA. Two medical diagnostic

problems, namely Breast Cancer Wisconsin and Pima Indian Diabetes, were solved with this technique.

Experiments showed that both variants of COBRA demonstrate high performance and reliability in spite of

the complexity of the optimization problems solved. ANN-based classifiers developed in this way

outperform many alternative methods on the mentioned classification problems. The workability of the

proposed meta-heuristic optimization algorithms was confirmed.

1 INTRODUCTION

A classification problem is a problem of identifying

to which predefined group or class an object needs

to be assigned based on a number of observed

attributes related to that object. Many problems in

business, science and industry can be treated as

classification problems. Various intelligent

information processing techniques exist for solving

classification problems, with one of them being an

artificial neural network (ANN).

The ANN models have three primary

components: the input data layer, the hidden layer(s)

and the output measure(s) layer. Each of these layers

contains nodes which are connected to nodes at

adjacent layer(s). Also there is an activation function

on each node. Thus, the number of hidden layers, the

number of nodes on each layer, and the type of

activation function on each node determine the

“ANN structure”. Each connection between neurons

has a weight coefficient; the number of these

coefficients depends on the problem being solved

and the number of hidden layers and neurons. Thus,

the goal is to generate a neural network with a

relatively simple structure which would effectively

solve a given classification problem. Therefore, the

modification of the collective bionic meta-heuristic

called Co-operation of Biology Related Algorithms

(COBRA) (Akhmedova and Semenkin, 2013(1)) for

solving multi-objective optimization problems with

binary variables (COBRA-bm) was used for

selecting the ANN structure.

The weighted summation function for neurons is

typically used in a feed-forward/back propagation

network model. Yet it has been established that

using other optimization methods for tuning the

weight coefficients of a network can be more

efficient (Sasaki and Tokoro, 1999). In this study the

collective bionic meta-heuristic COBRA was used

for the adjustment of the ANN weight coefficients.

Further, in Section 2 the problem statement is

presented. Then in Section 3 the description of the

proposed optimization techniques (COBRA and its

modification for solving multi-objective problems

with binary variables) is given. In Section 4 the

workability of the meta-heuristics is demonstrated

with ANN-based classifier design for two medical

diagnostic classification problems: Breast Cancer

Wisconsin and Pima Indians Diabetes. In the

conclusion results are discussed and directions for

further research are considered.

2 PROBLEM STATEMENT

The tuning of neural network structure and weight

coefficients is considered as the solving of two

unconstrained optimization problems: the first one is

310

Akhmedova S. and Semenkin E..

ANN-based Classiﬁers Automatically Generated by New Multi-objective Bionic Algorithm.

DOI: 10.5220/0005571603100317

In Proceedings of the 12th International Conference on Informatics in Control, Automation and Robotics (ICINCO-2015), pages 310-317

ISBN: 978-989-758-122-9

 2015 SCITEPRESS (Science and Technology Publications, Lda.)

a multi-objective problem with binary variables and

the second one is a one-criterion problem with real-

valued variables. The type of variables depends on

the representation of the ANN structure and

coefficients.

First of all let us assume that the maximum

number of hidden layers is equal to m and that the

maximum number of neurons on a hidden layer is

equal to n. So, the maximum number of neurons in a

network is equal to m×n. Frequently, a more

complex neural network solves a given classification

problem at least as well as a less complex network.

However, the large number of weight coefficients,

which depend on the number of the hidden layers

and neurons, influence on the network adjustment

process and later on the decision-making time.

Therefore, the aim of this study was to develop an

algorithm with an automated ANN-based classifier

design with relatively simple structures which would

effectively solve classification problems. Thus, the

structure design of a network was considered as a

multi-objective optimization problem: the first

objective function was related to classification error

and the second objective was related to the

complexity of the structure, which was measured by

the total number of neurons. Both objectives were

minimized.

In this study m and n were equal to 5, so the

maximum number of neurons was equal to 25. We

could have chosen a larger number of layers and

nodes, but our aim was to show that even a network

with a relatively small structure can show good

results if it is tuned with effective optimization

techniques. Each node was represented by a binary

string of length 4. If the string consisted of zeros

(“0000”) then this node did not exist in the ANN.

So, the whole structure of the neural network was

represented by a binary string of length 100 (25×4),

and each 20 variables represented one hidden layer.

The number of input layers depended on the

problem in hand. The ANN has one output layer.

We used 15 differentactivation functionsfor

nodes: sigmoidal, hyperbolic tangent, threshold

function,linearfunction,etc.Alistofthe

activationfunctionsusedaregivenbelow:

  



 

;

;exp1/1

xthxf

xxf





(1)











 



 



 

;/1

;1exp1/2

;

5.0,1

5.05.0,5.0

5.0,0

;

1,1

11,

1,1

;

;exp

;sin

;

;2/exp1

;2/exp

xsignxf

xxf













































(2)

For determining which activation function will be

used on a given node the integer that corresponds to

its binary string was calculated; this integer was

assigned as the number of the activation function.

Thus, we used the modification of the

optimization method COBRA for multi-objective

unconstrained problems with binary variables

(COBRA-bm) for finding the best structure and the

original version of COBRA for the adjustment of

every structure weight coefficient. The approach

COBRA-bm was developed with the use of Pareto

optimality theory, so a set of different structures

(non-dominated solutions) were obtained for every

classification problem solved. The aforementioned

set was considered as an ensemble of neural

networks with a weighted averaging decision

making scheme for inferring the ensemble decision

(Jordan and Jacobs, 1994).

3 CO-OPERATION OF BIOLOGY

RELATED ALGORITHMS

3.1 Original COBRA

The method for solving one-criterion unconstrained

real-parameter optimization problems based on the

cooperation of five nature-inspired algorithms such

as Particle Swarm Optimization (PSO) (Kennedy

and Eberhart, 1995), the Wolf Pack Search (WPS)

(Yang, Tu and Chen, 2007), the Firefly Algorithm

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

(CSA) (Yang and Deb, 2009) and the Bat Algorithm

(BA) (Yang, 2010) and called Co-Operation of

ANN-basedClassifiersAutomaticallyGeneratedbyNewMulti-objectiveBionicAlgorithm

311

Biology Related Algorithms (COBRA) was

introduced in (Akhmedova and Semenkin, 2013(1)).

The basic idea of this approach consists in

generating five populations (one population for each

mentioned algorithm) which are then executed in

parallel cooperating with each other.

The algorithm proposed in (Akhmedova and

Semenkin, 2013 (1)) is a self-tuning meta-heuristic.

Therefore there is no need to choose the population

size for algorithms. The number of individuals in the

population of each algorithm can increase or

decrease depending on whether the fitness value is

improving or not. If the fitness value was not

improved during a given number of generations,

then the size of all populations increases. And vice

versa, if the fitness value was constantly improved,

then the size of all populations decreases.

Additionally, 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. Besides, all populations

communicate with each other: they 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.

The performance of the proposed algorithm was

evaluated on the set of benchmark problems from

the CEC’2013 competition in (Akhmedova and

Semenkin, 2013 (1)). This set of 28 unconstrained

real-parameter optimization problems was given in

(Liang et al., 2012); there are also explanations

about the conducted experiments. A validation of

COBRA was carried out for functions with 2, 3, 5,

10, and 30 real variables. Experiments showed that

COBRA works successfully and is reliable on this

benchmark. Results also showed that COBRA

outperforms its component algorithms when the

dimension grows and more complicated problems

are solved.

3.2 COBRA-bm

The binary modification of the algorithm COBRA,

namely COBRA-b (Akhmedova and Semenkin,

2013 (2)), was modified for solving multi-objective

optimization problems, so there was no necessity to

modify component algorithms to solve optimization

problems with binary variables. Development of the

approach COBRA-bm for solving binary-parameter

multi-objective optimization problems required the

use of multi-objective versions of the above-listed

component algorithms. So, all these techniques were

extended to produce a Pareto optimal front directly:

PSO and WPS by using the σ-method (Mostaghim

and Teich, 2003) and the FFA (Yang, 2013), CSA

(Yang and Deb, 2011) and BA (Yang, 2012) as

suggested in corresponding papers.

Consequently, first of all a brief description of

COBRA and its component-algorithms will be given

and then COBRA-bm will be introduced.

3.2.1 Component Algorithms

Initially we will assume that the multiobjective

optimization problem with K objective functions

should be solved, namely all objectives should be

minimized.

The original Particle Swarm Optimization

algorithm (PSO) was discovered through simplified

social model simulation (Kennedy and Eberhart,

1995). It is related to bird flocking, fish schooling

and swarm theory. In the PSO algorithm, each

individual uses information about the best position

found by the whole swarm-population and the best

position found by itself. However there is no single

best position for multiobjective problems. That is

why while solving multiobjective problems by PSO

the procedure of choosing the best position for the

particle has to be modified. For this purpose the σ-

method (Mostaghim and Teich, 2003) was used.

Firstly, the external archive S for nondominated

solutions was generated. For each particle the σ-

parameter was calculated. So for the i-th particle the

current best position was found as follows: the

particle in archive S whose σ-parameter is closest to

the σ-parameter of the i-th particle was chosen as the

best current position for the i-th particle, where

closeness was measured by Euclidean distance.

The WPS algorithm was inspired by research on

the social behaviour of a wolf pack; it simulates the

hunting process of a pack of wolves (Yang, Tu and

Chen, 2007). As in the PSO optimization tool, in the

WPS approach each individual uses information

about the best found position by the whole

population for its movement in the search space. For

modification of the Wolf Pack Search algorithm the

same procedure was used as for the Particle Swarm

Optimization method. Namely, an external archive

of nondominated solutions was generated. And then

the σ-method was applied to search for the current

best wolf.

The Firefly algorithm (FFA) was inspired by the

flashing behaviour of fireflies (Yang, 2009). In the

FFA algorithm all fireflies are unisex so that one

firefly will be attracted to other fireflies regardless

of their sex. For any two flashing fireflies, the less

bright one will move towards the brighter one but if

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there is no brighter firefly than a particular one, then

it will move randomly. The brightness of a firefly is

affected or determined by the landscape of the

objective function.

For multiobjective optimization the Firefly

Algorithm was extended to produce a Pareto optimal

front directly (Yang, 2013). After evaluation of the

brightness or objective values of all the fireflies the

comparison of each pair of fireflies was conducted.

Then a random weight vector is generated (with the

sum of components equal to 1), so that a combined

best solution g* can be obtained. This combined best

solution g* was used in order to fulfil random walks

more efficiently. Also the i-th firefly was attracted

by the j-th firefly (moved towards it) only if it was

dominated by the j-th firefly. And finally the

nondominated solutions are then passed onto the

next iteration.

The Cuckoo Search Algorithm (CSA) is an

optimization algorithm inspired by the obligate

brood parasitism of some cuckoo species by laying

their eggs in the nests of other host birds (of other

species) (Yang and Deb, 2009). CSA uses three

idealized rules. First of all, each cuckoo lays one egg

at a time, and dumps its egg in a randomly chosen

nest. Secondly, the best nests with a high quality of

eggs will carry over to the next generations. And

finally, the number of available host nests is fixed,

and the egg laid by a cuckoo is discovered by the

host bird with a probability p

For simplicity, this last assumption can be

approximated by the fraction p

of the n nests being

replaced by new nests (with new random solutions).

For multiobjective optimization problems with K

different objectives the theory of Pareto optimality

was used and the first and last rules were modified

to incorporate the multiobjective idea (Yang and

Deb, 2011). For multiobjective problems the first

rule can be described as follows: each cuckoo lays K

eggs at a time and dumps them in a randomly chosen

nest, egg k corresponds to the solution to the k-th

objective. And the last rule can be described in this

way: each nest will be abandoned with a probability

pa and a new nest with K eggs will be built

according to the similarities or differences between

the eggs; some random mixing can be used to

generate diversity.

The Bat Algorithm (BA), which is the last

component-method of COBRA, was inspired by

research on the social behaviour of bats (Yang,

2010). The BA is based on the echolocation of bats

that they use to detect prey, avoid obstacles, and

locate their roosting crevices in the dark. For

multiobjective optimization the Bat Algorithm was

also extended to produce a Pareto optimal front

(Yang, 2012). Firstly, an external archive of

nondominated solutions is generated. Then, on each

iteration, all objectives are combined into a single

objective so that the Bat Algorithm is used for single

objective optimization. After that the archive of non-

dominated solutions is updated.

All mentioned algorithms PSO, WPS, FFA, CSA

and BA were originally developed for continuous

valued spaces. Binary modifications of these

algorithms were employed by using the technique

described in the study (Kennedy and Eberhart,

1997). Namely, they were adapted to search in

binary spaces by applying a sigmoid transformation

to the velocity component (PSO, BA) or coordinates

(FFA, CSA, WPS) to squash them into a range [0, 1]

and force the component values of the positions of

the individuals to be 0’s or 1’s.

The basic idea of this adaptation was firstly used

for the PSO algorithm (Kennedy and Eberhart,

1997). In PSO each particle has a velocity (Kennedy

and Eberhart, 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 and Eberhart, 1997). After that a random

number from the range [0, 1] is generated and the

corresponding component value of the position of

the particle is 1 if it is smaller than the sigmoid

function value for that velocity and 0 otherwise.

In BA each bat also has a velocity (Yang, 2009),

which is why exactly the same procedure for the

binarization of this algorithm was applied. Yet in

WPS, FFA and CSA individuals have no velocities.

For this reason, the sigmoid transformation is

applied to the position components of individuals

and then a random number is compared with the

obtained value.

Thus, at first all the mentioned bionic algorithms

were adapted for solving unconstrained multi-

objective real-parameter problems and then modified

for solving optimization problems with binary

variables.

3.2.2 Proposed Technique

The multiobjective modifications of the above-

described bionic algorithms for solving

unconstrained optimization problems with binary

variables were used as component algorithms. For

each component algorithm an external archive S

(i =

1, …, 5) of non-dominated solutions was generated

and a general external archive S was created. The

solutions in all archives S

were compared and

solutions which were non-dominated among all of

ANN-basedClassifiersAutomaticallyGeneratedbyNewMulti-objectiveBionicAlgorithm

313

them were placed in the archive S.

The development of the multi-objective

modification of optimization tool COBRA

(COBRA-bm) required changes in the procedure of

selecting the winning algorithm and in the migration

operator. For the procedure of selecting the winning

algorithm and migration operator on each stage of

the COBRA-bm execution, K weight coefficients

whose sum is equal to 1 were initialized randomly.

Then all objectives were combined into a single

objective (weighted sum of K objectives). This

single objective was called “fitness” on the current

stage. Therefore, the winning algorithm was

determined by this fitness and for migration

individuals were sorted according to the mentioned

single objective.

To validate the proposed algorithm COBRA-bm,

a subset of test multi-objective problems with

convex, non-convex and discontinuous Pareto fronts

was selected: Schaffer’s Min–Min problem (SCH)

(Schaffer, 1985), Kursawe problem (KUR)

(Kursawe, 1990), Fonseca and Fleming problem

(FAF) (Fonseca and Fleming, 1993), ZDT4 and

ZDT6 problems (Zitzler, Deb and Thiele, 2000). The

mentioned problems are defined as problems with

real-parameter functions; the number of variables for

them varied from 3 to 25. Each real-valued variable

was represented by a binary string with a length of

10 bit. Thus, the number of binary variables varied

from 30 to 250. For the component algorithms the

number of individuals was equal to 50; and the

number of iterations was equal to 1000. So in order

to compare the performance of the proposed

COBRA-bm with its components, the maximum

number of function evaluations for COBRA-bm was

established to be equal to 50000 (50×1000). The

maximum number of Pareto optimal points in the

external set was equal to 200. These settings are

adopted from the papers (Yang, 2013), (Yang and

Deb, 2011) and (Yang, 2012).

After generating Pareto points by COBRA-bm,

the corresponding Pareto front was compared with

the true front. We define the distance between the

estimated Pareto front PF

and its corresponding true

front PF

as follows:

E = || PF

– PF

(3)

The results obtained by the components and

COBRA-bm are summarized in Table 1 and Table 2.

Thus, the simulations for this subset of test functions

show that the proposed approach COBRA-bm is an

efficient algorithm for solving multi- objective

binary optimization problems. It can deal with

highly non-linear problems with diverse Pareto

optimal sets and different problem dimensions. Also

COBRA-bm outperforms its components; so it could

be recommended for use instead of them.

Table 1: Summary of results for component algorithms.

Func PSO WPS FFA CSA BA

SCH

4.812

e-007

5.083

e-007

4.626

e-007

4.270

e-007

6.099

e-007

KUR

3.017

e-004

3.968

e-004

2.559

e-004

3.229

e-004

4.052

e-004

FAF

(3)

1.026

e-002

1.720

e-002

1.718

e-002

1.799

e-002

1.903

e-002

FAF

(10)

1.089

e-002

7.808

e-003

1.144

e-002

1.686

e-002

2.657

e-002

FAF

(20)

2.727

e-002

2.840

e-002

2.958

e-002

2.918

e-002

3.431

e-002

FAF

(25)

3.681

e-002

3.404

e-002

3.298

e-002

3.032

e-002

5.238

e-002

ZDT4

3.550

e-003

4.009

e-003

4.049

e-003

4.254

e-003

2.572

e-003

ZDT6

1.014

e-003

1.508

e-003

8.204

e-004

7.112

e-004

6.776

e-004

Table 2: Summary of results for COBRA-bm.

Func COBRA-bm

SCH 3.290e-007

KUR 2.071e-004

FAF (3) 2.042e-003

FAF (10) 6.869e-003

FAF (20) 1.193e-002

FAF (25) 2.370e-002

ZDT4 2.336e-003

ZDT6 6.614e-004

4 EXPERIMENTAL RESULTS

In order to load the developed optimization

techniques with a really hard task we chose two

benchmark classification problems: Breast Cancer

Wisconsin and Pima Indians Diabetes. Our choice

was conditioned by the circumstance that these

problems had been solved by other researchers many

times with different methods. Thus there are many

results obtained by alternative approaches that can

be used for comparison.

For Breast Cancer Wisconsin Diagnostic there

are 10 attributes (the patient’s ID that was not used

for calculations and 9 categorical attributes which

possess values from 1 to 10), 2 classes, 458 records

of patients with benign cancer and 241 records of

patients with malignant cancer. For Pima Indians

Diabetes there are 8 attributes (all numeric-valued),

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2 classes, 500 patients that tested negative for

diabetes and 268 patients that tested positive for

diabetes). Benchmark data for these problems was

taken from (Frank and Asuncion, 2010).

From the viewpoint of optimization, for these

problems there are from 145 to 150 real-valued

variables for weight coefficients and 100 binary

variables for selecting the structure. For the structure

selection of the neural network the maximum

number of function evaluations was equal to 900.

For the final weight coefficient adjustment (for the

set of the best obtained structures) the maximum

number of function evaluations was equal to 10000.

Table 3: Classifier performance comparison for Pima

Indians Diabetes problem.

Author (year) Method

Accuracy

(%)

H. Temurtas et al. (2009) MLNN with LM 82.37

K. Kayaer et al. (2003) GRNN 80.21

This study (2015) ANN+COBRA-bm 80.17

Akhmedova et al. (2014) ANN+COBRA-b 80.15

Akhmedova et al. (2013) ANN+COBRA 79.83

H. Temurtas et al. (2009)

MLNN with

LM(10xFC)

79.62

H. Temurtas et al. (2009) PNN 78.13

H. Temurtas et al. (2009) PNN (10xFC) 78.05

S. M. Kamruzzaman et al.

(2005)

FCNN with PA 77.34

M.R. Bozkurt et al. (2012) DTDN 76.00

M.R. Bozkurt et al. (2012) LVQ 73.60

M.R. Bozkurt et al. (2012) PNN 72.00

L. Meng et al. (2005) AIRS 67.40

Table 4: Classifier performance comparison for Breast

Cancer Wisconsin problem.

Author (year) Method

Accuracy

(%)

Peng et al. (2009) CFW 99.50

Akhmedova et al. (2014) ANN+COBRA-b 98.95

This study (2015) ANN+COBRA-bm 98.80

Albrecht et al. (2002) LSA machine 98.80

Polat, Günes (2007) LS-SVM 98.53

Akhmedova et al. (2014) ANN+COBRA 98.16

Setiono (2000) Neuro-rule 2a 98.10

Karabatak, Cevdet-Ince

(2009)

AR + NN 97.40

Pena-Reyes, Sipper (1999) Fuzzy-GA1 97.36

Ster, Dobnikar (1996) LDA 96.80

Guijarro-Berdias et al.

(2007)

LLS 96.00

Abonyi, Szeifert (2003) SFC 95.57

Nauck and Kruse (1999) NEFCLASS 95.06

Hamiton et al. (1996) RAIC 95.00

Quinlan (1996) C4.5 94.74

The obtained results are presented in Tables 3

and 4 where a portion of the correctly classified

instances from testing sets is presented. There are in

Tables 3 and 4 also results of other researchers and

their approaches found in scientific literature

(Marcano-Cedeno, Quintanilla-Domínguez and

Andina, 2011) and (Temurtas, Yumusak and

Temurtas, 2009).

The results of this study are averaged on 20

algorithm executions. Mostly only 2-4 networks

were obtained as non-dominated solutions in one

program run for each medical diagnostic problem.

Here is an example of the obtained structure for the

Breast Cancer Wisconsin problem (2 neural

networks where the first has 5 hidden layers 10

neurons altogether and the second also has 5 hidden

layers with the total number of neurons equal to 13).

 The first network structure: the first layer is

(0100 0010), i.e. neurons with the 4th and 2nd

activation functions; the second layer is (1100

0001), i.e. neurons with the 12th and 1st

activation functions; the third layer is (0101 0100

0000), i.e. neurons with the 5th and 4th

activation functions; the fourth layer is (0011

1100 0010), i.e. neurons with the 3rd, 12th and

2nd activation functions; the fifth layer is (0001),

i.e. neuron with the 1st activation function;

 The second network structure: the first layer is

(1000 0001), i.e. neurons with the 8th and 1st

activation functions; the second layer is (0001

0100), i.e. neurons with the 1st and 4th activation

functions; the third layer is (0100 0011 1101

0010), i.e. neurons with the 4th, 3rd, 13th and

2nd activation functions; the fourth layer is

(0100 0010 0100), i.e. neurons with the 4th and

2nd activation functions; the fifth layer is (1000

0001), i.e. neurons with the 8th and 1st activation

functions.

In (Akhmedova and Semenkin, 2014) the same

problems were solved with ANN-based classifiers

automatically generated by the one-criterion

algorithms of COBRA and its binary modification

COBRA-b which demonstrated good results but the

networks designed were too complex. Experiments

show non-significant statistical difference in the

level of performance between the results obtained in

this study and the results from (Akhmedova and

Semenkin, 2014), i.e. essentially bigger ANNs did

not produce a positive effect on the classifier

performance.

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315

5 CONCLUSIONS

In this paper a new meta-heuristic, called Co-

Operation of Biology Related Algorithms, was

described, and its modification COBRA-bm was

introduced for solving multi-objective optimization

problems with binary variables.

We illustrated the performance estimation of the

proposed algorithms on subsets of test functions.

Then we used the described optimization

methods for the automated design of ANN-based

classifiers in two medicine diagnosis problems. The

binary multi-objective modification of COBRA was

used for the optimization of classifier structure and

the original COBRA was used for the adjustment of

weight coefficients both within the structure

selection process and for the final tuning of the best

selected structure.

This approach was applied to two real-world

classification problems. Solving these problems are

equivalent to solving big and hard optimization

problems where objective functions have many (up

to 150) variables and are given in the form of a

computational program. The suggested algorithms

successfully solved both problems with competitive

performance that allows us to consider the study

results as the confirmation of the reliability,

workability and usefulness of the algorithms in

solving real world optimization problems.

ACKNOWLEDGEMENTS

Research is performed with the financial support of

the Ministry of Education and Science of the

Russian Federation within the federal R&D

programme (project RFMEFI57414X0126).

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