Evolving Analog Electronic Circuits for Fuzzy Membership

Functions Generation

P. H. G. Coelho, J. F. M. do Amaral, Y. C. Bacelar, E. N. Da Rocha and M. C. Bentes

State Univ. of Rio de Janeiro, FEN/DETEL, R. S. Francisco Xavier,524/Sala 5001E, Maracanã, RJ,20550-900, Brazil

Keywords: Fuzzy Systems, Genetic Algorithms, Artificial Intelligence Applications, Evolutionary Electronics.

Abstract: Recent research advances in fuzzy systems applications as controllers of increasingly complex systems

motivate the consideration of analog circuits capable of implementing fuzzy logic. The purpose of this paper

is to evolve the component values of known topologies of analog circuits to generate membership functions.

In order to accomplish that, a hybrid model is used for the evolution of electronic circuits, based on genetic

algorithms, using a fuzzy system to evaluate multiple objectives. The traditional fitness assessment of genetic

algorithms is modified, so that a fuzzy system is effectively responsible for the assessment, thus being able to

aggregate the different objectives of the electronic design and generating a fitness value for each circuit in the

population. The proposed model presents a simpler and more interpretable way of inserting preferences and

specifications, as it uses fuzzy logic. Such specifications are inserted before the evolution of the circuit,

ensuring that it is guided in the desired direction, preventing the designer from having to choose the most

appropriate solution at the end of the process. An implementation based purely on simulation of circuit models

was chosen, providing a flexible environment.

1 INTRODUCTION

Evolutionary Electronics was conceived in 1997 and

applies Evolutionary Algorithms in the development

of electronic circuits. It covers the developments and

issues related to the use of Evolutionary Computing

in the design of electronic circuits (Haddow and

Tyrrell, 2018). In addition, it enables the development

of practices, methods, algorithms and software and

hardware structures that allow evolving in the design

of more robust circuits. This terminology covers a

wide field of research on the use of evolutionary

algorithms in optimization and synthesis of electronic

circuits. Another point of interest is the growing

demand for the synthesis of more complex analog

circuits, to interact with the environment, and the

need to design them more quickly for the market

(Amaral et al., 2007). This imposes more dynamic

design practices that can generate products in less and

less time (Lohn et al., 1999).

Fuzzy systems are based on fuzzy logic and are

widely used, especially in control systems and

decision support models. There are several related

applications in the literature, such as, for example, in

the area of health and the study of human locomotion,

in speech signal processing, in the recognition of

information and emotions, in economics and in

routing systems (Luca et al.,2015). Its characteristic

of expressing human inference behavior enables a

high level of understanding, being interpretability a

strong point of fuzzy systems.

Among the points usually addressed in the area of

computational intelligence, optimization stands out,

which consists of the search for the best solution for

a given problem. At this point, evolutionary

algorithms are a commonly used computational

intelligence technique due to their great search

capability. Optimization in evolutionary algorithms

consists of trying several solutions and using the

information obtained in this process in order to find

better and better solutions. Initially, the great

concentration of efforts in the optimization area

consisted in understanding, developing and applying

methods for the optimization of a single objective

function. However, most real optimization problems,

such as in electronic design or component

adjustments in electronic systems, involve multiple

objectives and one cannot apply the idea of

optimizing each objective in isolation. Each objective

has its degree of importance and often the objectives

conflict with each other (Ajith et al., 2005). In

everyday situations it is common to find contexts that

Coelho, P., M. do Amaral, J., Bacelar, Y., N. Da Rocha, E. and Bentes, M.

Evolving Analog Electronic Circuits for Fuzzy Membership Functions Generation.

DOI: 10.5220/0011549800003332

In Proceedings of the 14th International Joint Conference on Computational Intelligence (IJCCI 2022), pages 175-182

ISBN: 978-989-758-611-8; ISSN: 2184-3236

175

have different objectives. For example, in an

industrial environment, generally, the aim is to

maximize the quality of a product while the cost must

be minimized.

Currently, there are several techniques and

computational algorithms developed for application

in multi-objective optimization (MOP) problems

motivated by the vast area of application (Coello

Coello, 2013). Many researches show good results

obtained over the years in this field for example

(Fonseca et al., 1995) (Altinoz et al., 2015) (Jiang et

al., 2016). The most used methodologies include the

use of genetic algorithms and are based on the Pareto

optimality concept. Such an approach comprises a

border with several solutions considered optimal in

relation to the analyzed objectives. This methodology

is characterized by having an a-posteriori articulation,

that is, the search process is performed autonomously,

and after obtaining the solutions, an expert must make

a choice to decide which is the best solution to be used

for the problem. The process of choosing the solution

considered acceptable, with a large number of

possibilities and variables involved, is not a trivial

task and requires experience and expert knowledge.

In this way, the articulation of the designer's

preferences made a-priori, that is, before the

execution of the algorithm, and the use of a technique

capable of translating the preferences in a simpler and

more understandable way are essential.

This article deals with the design of analog

electronic circuits to generate fuzzy membership

functions, in order to modify the traditional

evaluation form of a genetic algorithm to enable the

evaluation of multiple objectives. To this end, it was

chosen to use a fuzzy system that aggregates the

various objectives (Reiser at al., 2013), (Mardani et

al., 2015). The use of fuzzy systems makes it possible

to simultaneously evaluate all objectives, integrating

user preferences in relation to each objective and each

situation. This feature is an advantage over multi-

objective methods based on Pareto optimality, as this

type of model does not require user interference to

choose the best solution at the end of the process,

since preferences are entered before evolution, in a

more efficient way, simple and interpretable, through

fuzzy logic. Thus, the evolution process is guided

towards pre-established preferences or specifications.

The purpose of this work is to study the application

of an evolutionary model, which uses genetic

algorithms with the ability to evaluate multiple

objectives based on a fuzzy system, to optimize the

values of components of analog electronic circuits to

generate fuzzy membership functions. The technique

is evaluated in a purely simulation-based

environment that is used for the design of electronic

circuits.

From the recent literature, articles dealing with the

subject stand out (Marlen et. al, 2018) and (Rojec et.

al., 2022). The first deals with the implementation of

fuzzy membership function (MF), realized as an

analog electronic hardware with memristor. The other

one proposes an evolution of analog circuits,

including their topology, for general purposes,

considering the synthesis of robust and failure-

resilient electronics.

This paper is organized in four sections. The

second section describes the basic structure of the

evolutionary environment for generating the

membership functions. Section three discusses

examples and results in connection with the

evolutionary analog circuits. Finally, section four

ends the paper with the conclusions.

2 ELECTRONIC CIRCUITS

EVOLUTION

2.1 Basic Foundations

An electronic project can be developed in an intrinsic

or extrinsic way.

In the so-called intrinsic applications, the

evaluation is performed based on the behavior of the

circuits when loaded on programmable integrated

circuits or reconfigurable platforms. In this way the

real circuit is developed, although flexibility and

experimentation possibilities are more limited.

On the other hand, extrinsic applications are those

in which circuits are evaluated through their

equivalent models. For example, a linear analog filter

can be developed using its transfer function. It is also

possible to use circuit simulators, such as Spice, in

which case the evolutions tend to become very slow.

In this paper, we opted for the extrinsic evolution

based on models of analog electronic circuits to make

the experimentation of the multi-objective evaluation

method more flexible.

Evolutionary algorithms are efficient in solving

multicriteria optimization problems. A variety of

techniques using genetic algorithms have been

developed in recent decades.

The great advantage obtained in the use of genetic

algorithms is the fact that they simultaneously

evaluate a set of possible solutions that allows finding

the total set of solutions of the Pareto frontier in a

single round of the algorithm without the need to

FCTA 2022 - 14th International Conference on Fuzzy Computation Theory and Applications

176

carry out several iterations as in the other methods

(Coello Coello, 1999).

In addition, they present ease and flexibility of

modeling, are less susceptible to non-convex and

discontinuous Pareto frontier characteristics and can

work in search spaces that are intractable by

traditional approaches.

2.2 The Evolutionary Environment

The purpose of this work is the application of a hybrid

model to enable the evolution of electronic circuits,

based on a genetic algorithm and using a fuzzy system

to evaluate multiple objectives. The traditional fitness

assessment of genetic algorithms is modified, so that

a fuzzy system is effectively responsible for the

assessment, thus being able to aggregate the different

objectives of the electronic design and generating a

fitness value for each circuit in the population.

One of the most important advantages of fuzzy

systems is interpretability. This feature makes it

possible to insert preferences and adapt the system to

different situations using a natural and easy-to-

understand language. In this way, the evolutionary

environment presents a simpler and more

interpretable way of inserting preferences and

specifications, as it uses a fuzzy system. Such

specifications are inserted before the evolution of the

circuit, that is, a-priori, ensuring that it is guided in

the desired direction, preventing the designer from

having to choose the most appropriate solution at the

end of the process. The possibility of including

possibly conflicting inputs, but resulting in a single

output that aims to meet both, is also a strong point

that allows its use in solving problems with multiple

objectives.

An implementation based purely on simulation of

circuit models was chosen, providing a flexible

environment for case studies and enabling future

applications. Thus, a method for evaluation through

fuzzy systems has become attractive for the evolution

of electronic circuits. The search capability of genetic

algorithms motivated the choice of this intelligent

technique as a basis for use in this work. A genetic

algorithm was developed capable of obtaining a

solution, that is, the developed circuit, according to

preferences established according to the different

objectives of the problem, and, for this, a fuzzy

aggregation system is used. Comparing the model

with the algorithms that use the Pareto concept, this

fact is of great importance because it prevents several

solutions from being presented for later selection of

the best among them by the designer at the end of the

process.

The methodology used in the present work allows

the evolution of electronic circuits with

characteristics to be optimized, focusing on the

adjustment of the values of the components of pre-

defined topologies and whose model is available or

can be built. Basically, an evolutionary algorithm is

used to search for the best circuit that meets the

objectives. The evolutionary algorithm used is a

genetic algorithm based on GAOT (Genetic

Algorithm Optimization Toolbox) (Houck et al.,

1996) and executed in Matlab. For the simulations,

mathematical models of the circuits were used. The

genetic algorithm used in the work follows the model

presented in Figure 1. The algorithm starts with a

population normally generated randomly, but which

can also be generated from a seed with potentially

good solutions obtained from other methods. The

traditional fitness assessment is performed from a

fitness function defined by the designer.

Figure 1: Hybrid Model with Genetic Algorithm and Fuzzy

Aggregator.

Such a function generates a scalar number for

each evaluated individual, which corresponds to the

individual's aptitude in relation to the objective

established by the defined function. In this work, the

evaluation is performed by a fuzzy system, called

fuzzy aggregator. The fuzzy aggregator system makes

it possible to evaluate all objectives simultaneously,

integrating the user's preferences and specifications in

relation to each objective and each situation, in a

natural way. Figure 2 illustrates the proposed

evaluation model.

Evolving Analog Electronic Circuits for Fuzzy Membership Functions Generation

177

Figure 2: Fitness evaluation model with aggregator system.

A general model for aggregating two objectives

was developed, which can be used as a basis for

application to any problem. The model has five

triangular membership functions uniformly

distributed within the range from 0 to 1 for the inputs,

corresponding to the variation limits of each input

that must be normalized to facilitate and generalize

the application, as shown in Figure 3.

Figure 3: Base membership functions for inputs.

The defuzzified output of the fuzzy system

represents the general fitness assessment of the

individual being evaluated. For the membership

functions of the output, the format shown in Figure 4

is used as standard, consisting of five membership

functions.

Figure 4: Base membership functions for the output.

The fuzzy aggregator system is of the Mamdani

type, characterized by being simpler and more

interpretable than TSK-type systems and all rules

have the same degree of importance, that is, a weight

equal to one. The rules of the fuzzy aggregator system

are designed to meet the problem specifications

considering each of the objectives. To exemplify the

process of creating rules, Table 1 shows basic rules

for minimizing two objectives without preference

between their minimization, that is, the minimization

of both is sought equally. Thus, when the entries

correspond to a Very Low value, they generate a Very

Good aptitude assessment. Likewise, entries with a

Very High value have a Very Bad aptitude rating.

Table 1: Base model for minimization rules.

In case where it is desired to prioritize the

minimization of one objective in relation to the other,

the rules must be modified to meet this preference.

Likewise, if the problem involves maximization, the

same rules can be used by inverting only the linguistic

terms of the antecedents, or the designer can create a

new set of rules. The operators used in the system are

the minimum and maximum operators and

defuzzification is performed using the center of

gravity method. After the evaluation of all the

individuals of the population of the current

generation, the genetic algorithm continues the

evolution process in the traditional way, until the

evaluation of the next generation, where the

evaluation process through the fuzzy aggregator

system is executed again for all the individuals, until

the stopping criterion is reached. To carry out the

evolution of circuits with multiple objectives and the

fuzzy aggregator, the project must be carried out in a

simulated environment. Figure 5 shows a block

diagram of the proposal, illustrating in general the

interconnections between the components used.

An implementation based purely on simulation of

circuit models was chosen, providing a flexible

environment for case studies and enabling future

applications. Evolutions of analog electronic circuits

in different application areas are evaluated through

computer simulations.

FCTA 2022 - 14th International Conference on Fuzzy Computation Theory and Applications

178

Figure 5: Basic Structure Used.

3 CASE STUDIES

With the great advance in research related to fuzzy

systems applications as controllers of increasingly

complex systems, it becomes interesting to enable the

production of analog circuits capable of

implementing fuzzy logic. The objective here was to

evolve the values of the components of topologies of

circuits known to perform membership functions.

3.1 Case Study 1:

S Membership Function (MF)

For the evolution of a S membership function circuit,

it is necessary a topology capable of generating at its

output a voltage similar to that shown in Figure 6.

Figure 6: Vo x Vi for the S Membership Function.

Thus, to proceed with the proposal, it was

necessary to use a circuit that behaves linearly when

its input was contained in the interval [ 1, 2 ], in

addition to providing 0V at the output when the

voltage applied to the input were at [ 0 , 1 ] and 3V in

the range [ 2 , 3]. A suitable circuit that has these

characteristics can be seen in Figure 7. One of the

objectives for the search for resistor values will be to

minimize the Root Mean Square Error (RMSE) in

relation to the straight line on figure 6, where Vi

varies from 1V to 2V. The other objective will be to

minimize the power consumption in the +3V source,

for that it is enough to maximize the value of resistor

R2, since the current supplied by the source is

inversely proportional to the value of R2.

Table 2 shows the possible values of resistors R1,

R2 and R3 as well as their ideal values, according to

the previously defined objectives.

Table 2: Range of values for Values of R1, R2, R3 and Vi

for the S Membership Function.

Parameters Range of Values

Ideal

Value

R1 1

Ω - 10

Ω 10

Ω

R2 1

Ω - 10

Ω 10

Ω

R3 1

Ω - 10

Ω 10

Ω

Vi 0V

–

3V ------

Figure 7: Selected topology for the S Membership

Function.

For this evolution, the used parameters are shown in

Table 3.

Table 3: Parameters of Genetic Algorithms.

Parameters Value

Number of Generations 100

Number of individuals

eneration 100

Crossover Probabilit

0.8

Probability of mutation 0.01

The rules were laid down so to minimize RMSE

and maximize R2. The matrix of rules is presented in

the Table 4. For the multi-objective Genetic

Algorithm with weighted aggregation, the following

fitness evaluation was adopted:

Evolving Analog Electronic Circuits for Fuzzy Membership Functions Generation

179

(1)

Table 4: Rules Matrix for S MF Circuit.

For the fuzzy aggregator system, the objectives were

normalized between 0 and 1 as follows:

(2)

(3)

Figure 8 depicts an evaluation graph of the best

individual and the average of individuals per

generation of the Multiobjective genetic algorithm

with fuzzy aggregator.

Figure 8: S MF circuit evolution.

The results of the evolutions are presented in Table 5.

Table 5: Results for the S membership function circuit.

Mono obj.

G.A.

Multi obj.

G.A.

Multi obj.

G.A. with

Fuzzy

ato

RMSE 0 0 0

R1 3,3 kΩ 8,2 kΩ 10

Ω

R2 3,3 kΩ 8,2 kΩ 10

Ω

R3 3,3 kΩ 8,2 kΩ 10

Ω

3.2 Case Study 2: Triangular

Membership Function (MF)

The triangular membership function circuit topology

should provide an output voltage relative to the input

voltage as illustrated in Figure 9.

Figure 9: Vo x Vi for the triangular MF circuit.

A suitable circuit that has these characteristics is

depicted in Figure 10.

Figure 10: Topology for the evolution of the triangular

Membership Function.

The first objective of this evolution is to minimize

the RMSE of the voltage curve given by the circuit

that generates the triangular MF in relation to the

objective function that represents the target triangular

function. The second objective is to minimize the sum

of the resistor values in the circuit. The range of each

value of the 11 resistors in the circuit are between

FCTA 2022 - 14th International Conference on Fuzzy Computation Theory and Applications

180

1kΩ and 10 kΩ. The used parameters of the GA are

the same as in case study 1.

The configuration of the fuzzy aggregator system

was similar to that used for the S MF circuit but

following the rules according to Table 1. For this

system the objectives were normalized between 0 and

1 as follows:

(4)

(5)

For the multi-objective GA with weighted

aggregation, the following aptitude assessment was

used:

(6)

The obtained results are shown in Table 6:

Table 6: Results for the triangular MF circuit.

Mono obj.

G.A.

Multi obj.

G.A.

Multi obj.

G.A. with

Fuzzy

ato

RMSE 0.16 0.21 0.13

51.7 kΩ 24.2 kΩ

9.02 kΩ

4 CONCLUSIONS

In this work, an evolutionary model was used for the

development of analog electronic circuits, which uses

a method for evaluation that considers more than one

objective and uses, for that, a process of aggregation

of objectives through a fuzzy system. This method

was called fuzzy aggregator and some circuits were

successfully evolved. The fuzzy aggregator was

applied in the evaluation process of genetic

algorithms, modifying the traditional method of these

algorithms and including, in this way, the feature of

multi-objective evaluation to such evolutionary

algorithms.

Case studies of MF circuit evolution were carried

out to analyze the effectiveness of the method. An

implementation based purely on simulation of circuit

models was chosen, providing a flexible environment

for case studies and enabling future applications.

Evolutions of analog electronic circuits are evaluated

through computer simulations. The work developed

for evolution, evaluation and implementation showed

good performance in the analyzed case studies, and

can be used as a basis for new applications and

implementations of other circuits. Compared to the

other methods studied, the evaluated method yielded

consistent results, with the advantages of inserting the

designer's preferences and specifications in a simple

and interpretable way at the beginning of the project,

in addition to not requiring the designer's

interference, either during or after the evolution

process. In this way, the work developed for the

evolution of analog electronic circuits with multi-

objective evaluation through a fuzzy system

constitutes a contribution to the design studies and

implementation of electronic systems that can be used

in several applications.

For future work, studies in different lines of action

may be suggested. It would be important to

implement the evaluation of circuits in a Spice-type

circuit simulator, thus facilitating the experimentation

and design of new circuits with models closer to the

real thing. The use of the GPGPU (General Purpose

Graphics Processing Unit) technique deserves to be

investigated because it will certainly contribute to

faster evaluations in the simulators and,

consequently, the evolved circuit will be obtained in

a shorter time. After implementing an evolutionary

platform with a Spice simulator that uses GPGPU, it

is worth investigating chromosomal representations

to enable the search for circuit topologies and not just

the values of the components.

In addition, comparisons with other algorithms

such as Coyote optimization algorithms, Particle

Swarm Optimization (PSO) (Mekhmoukh Taleb et al,

2022), Quantum Butterfly Optimization algorithm (Li

et al, 2022), etc. are anticipated possibilities in future

works.

ACKNOWLEDGEMENTS

This study was financed in part by the Coordenação

de Aperfeiçoamento de Pessoal de Nível Superior –

Brasil (CAPES) – Finance Code 001, and FAPERJ.

REFERENCES

Haddow, P. C.; Tyrrell, A. M., 2018. Evolvable Hardware

Challenges: Past, Present and the Path to a Promising

Future. Inspired by Nature, Emergence, Complexity

and Computation 28. Springer International Publishing.

Amaral, J. L. M., Amaral, J. F. M., Morin, D., Tanscheit,

R., 2007. An immune fault detection system with

automatic detector generation by genetic algorithms.

Seventh International Conference on Intelligent

Evolving Analog Electronic Circuits for Fuzzy Membership Functions Generation

181

Systems Design and Application (ISDA), 2007, p. 283

– 288.

Lohn, J. D., Colombano, S. P., 1999. A circuit

representation technique for automated circuit design.

IEEE Transactions on Evolutionary Computation, Vol.

3, No. 3, p. 205 – 219.

Luca, M., Luca, R., Bejinariu, Silviu-Ioan, Ciobanu, A.,

Paduraru, O., Zbancioc, M., Barbu, T., 2015. An

overview of several researches on fuzzy logic in

intelligent systems. 2015 International Symposium on

Signals, Circuits and Systems (ISSCS).

Ajith, A., Jain, L.C., Goldberg, R., (Eds.), 2005.

Evolutionary multiobjective optimization: theoretical

advances and applications. Springer Series on

Advanced Information and Knowledge Processing.

Coello Coello, C. A., 2013. Multi-objective evolutionary

algorithms in real-world applications: some recent

results and current challenges. Advances

inEvolutionary and Deterministic Methods for

Design, Optimization and Control in Engineering and

Sciences, Vol. 36 of the series Computational Methods

in Applied Sciences pp 3-18.

Fonseca, C. M., Fleming, P. J., 1995. Multiobjective

genetic algorithms made easy: selection, sharing and

mating restriction. First International Conference on

Genetic Algorithms in Engineering Systems:

Innovations and Applications, (Conf. Publ. No. 414).

Altinoz, O. T., Deb, K., 2015. Late parallelization and

feedback approaches for distributed computation of

evolutionary multiobjective optimization algorithms.

Second International Conference on Soft Computing

and Machine Intelligence.

Jiang, S., Yang, S., 2016. Evolutionary Dynamic

multiobjective optimization: benchmarks and algorithm

comparisons, IEEE Transactions on Cybernetics,

Volume: PP, Issue: 99, pp. 1-14.

Reiser, R. H. S., Bedregal, B., Baczyński, M., 2013.

Aggregating fuzzy implications. Information Sciences,

Volume 253, December 2013, pp. 126-146

Mardani, A., Jusoh, A., Zavadskas, E. K., 2015. Fuzzy

multiple criteria decision-making techniques and

applications – two decades review from 1994 to 2014,

Expert Systems with Applications, Volume 42, Issue 8,

pp. 4126-4148.

Marlen, A., Dorzhigulov, A., 2018. Fuzzy membership

function implementation with memristor. Computer

Science, Emerging Technologies, 1-4.

Rojec, Ž., Fajfar, I., Burmen, Á., 2022. Evolutionary

Synthesis of Failure-Resilient Analog Circuits.

Mathematics 10, no. 1: 156.

Coello Coello, C. A., 1999. A comprehensive survey of

evolutionary-based multiobjective optimization

techniques. Knowledge and Information Systems,

Volume 1, Issue 3, pp. 269–308.

Houck, C.R., Joines, J., Kay, M., 1996. A genetic algorithm

for function optimization: A Matlab implementation,

ACM Transactions on Mathematical Software.

Mekhmoukh Taleb, S., Meraihi Y., Gabis, A. B., Mirjalili,

S., Zaguia A., Ramdane-Cherif, A., 2022. Solving the

mesh router nodes placement in wireless mesh

networks using coyote optimization algorithm, IEEE

Access, vol. 10, pp. 52744-52759.

Li, M.W., Xu, D.Y., Geng, J., Hong, W.C., 2022. A ship

motion forecasting approach based on empirical mode

decomposition method hybrid deep learning network

and quantum butterfly optimization algorithm.

Nonlinear Dynamics 107, 2447–2467.

FCTA 2022 - 14th International Conference on Fuzzy Computation Theory and Applications

182