Explainable Decision Support Modelling Based on Multi-Layer FCM

with Multi-Objective Optimization Characteristics: The Case of the

Microservices Adoption Problem

Andreas Christoforou

and Andreas S. Andreou

Department of Electrical Engineering, Computer Engineering and Informatics,

Cyprus University of Technology, Limassol, Cyprus

Keywords:

Multi-Layer Fuzzy Cognitive Maps, Explainable Decision Support, Multi-Objective Optimization, Microser-

vices Adoption.

Abstract:

The tremendous progress in the ﬁeld of artiﬁcial and computational intelligence has enabled the application of

relevant techniques to a wide range of human life aspects. However, these techniques appear in their majority

incompetent to allow users to explain and understand their decisions. This paper introduces an enhanced, ex-

plainable decision support approach using a promising graph-based computational intelligent model, namely

Multi-Layer Fuzzy Cognitive Maps (MLFCM). MLFCM have evolved over the last two decades into a ﬂexi-

ble and powerful tool that enables the execution of simulation scenarios to facilitate decision support in highly

complex environments. The proposed enhancement of MLFCM revolves around their integration with Multi-

Objective Evolutionary Algorithms that allows executing simulations with multiple conﬂicting targets and then

analyzing the values and relationships of the participating nodes. The applicability of the enhanced MLFCM is

demonstrated through a case-study on adopting microservices. Microservices have been considered as one of

the most promising alternatives to software development nowadays. Nevertheless, their adoption often stum-

bles on various factors such as security, exit policy, effectiveness, etc. In this context, the factors contributing

to Microservices adoption are assessed, analyzed and modeled via MLFCM using a series of real-world and

synthetic scenarios that yielded quite promising results.

1 INTRODUCTION

Nowadays, the ever-increasing use of intelligent

decision-making methods in complex problem do-

mains plays a vital role in everyday human life. At

the same time, trust and transparency are becoming

essential for such kinds of approaches, and this un-

derlines the importance and need for techniques that

humans can interpret (Gunning and Aha, 2019). Mod-

els with enhanced explainable abilities can deliver re-

sults through a transparent process that allows one to

understand how the system decides, predicts, and per-

forms its operations.

While the models and techniques that aim to de-

liver predictions with high accuracy and support a de-

cision efﬁciently become more complex, the develop-

ment of transparent versions becomes more complex

(Meske and Bunde, 2020). Towards delivering a suf-

https://orcid.org/0000-0001-5598-8894

https://orcid.org/0000-0001-7104-2097

ﬁcient model with enhanced explainable and analysis

features, this work introduces a new computational

intelligence process involving Multi-objective opti-

mization characteristics. The applicability and perfor-

mance of the proposed model are tested and demon-

strated on a complex decision problem related to the

adoption of microservices architecture.

Software microservice architectures are consid-

ered nowadays one of the most successful approaches

for the development of cloud-native applications, of-

fering a plethora of small, autonomous, and collab-

orative services, which are easy to understand, de-

ploy, and scale. Nevertheless, there is yet no consen-

sus between the industry and academia on the critical

and decisive factors that would enable a global ac-

ceptance and adoption of this new paradigm (Woot-

ton, 2014). In addition, since such architectures are

highly complex and are described by multiple, often

conﬂicting factors, the majority of the software devel-

opment organizations are not ready to fully exploit the

beneﬁts of microservices, while adapting their pro-

Christoforou, A. and Andreou, A.

Explainable Decision Support Modelling Based on Multi-Layer FCM with Multi-Objective Optimization Characteristics: The Case of the Microservices Adoption Problem.

DOI: 10.5220/0011681000003393

In Proceedings of the 15th International Conference on Agents and Artiﬁcial Intelligence (ICAART 2023) - Volume 3, pages 413-420

ISBN: 978-989-758-623-1; ISSN: 2184-433X

 2023 by SCITEPRESS – Science and Technology Publications, Lda. Under CC license (CC BY-NC-ND 4.0)

413

cesses to this new environment is a tedious task (Bal-

alaie et al., 2016). The present paper builds upon

and extends previous works on the topic that utilized

MLFCMs (Mateou and Andreou, 2005) and Geneti-

cally Evolved MLFCMs (Christoforou et al., 2022) to

offer a novel decision and analysis model comprising

the key factors to consider for adopting a microser-

vice architecture using a multi-objective approach. So

far the relevant literature reports hybrid MLFCM-GA

forms and execution strategies that allow perform-

ing only single target optimization. This is consid-

ered as a weakness of the hybrid model as it is of-

ten desired that multiple factors are considered for

optimization. This is addressed in this paper which

proposes an extension of the MLFCM structure with

Multi-Objective Evolutionary Algorithms (MOEA).

The hybrid MOEA-MLFCM model allows for the ex-

ecution of simulations with multiple, often conﬂicting

targets and the analysis of the activation levels and re-

lationships of the participating nodes.

The main contributions of this paper are the

following: (i) Extension and enhancement of the

MLFCM model with multi-objective capabilities

which opens new ground for the study and simula-

tion of different scenarios that involve achieving si-

multaneously conﬂicting targets. This allows a deeper

and more precise deﬁnition of the critical factors that

affect the decision of microservices adoption, along

with their importance and interrelationship. (ii) Re-

visit of the problem of supporting the decision for

migrating to microservices architecture under a new,

multi-objective prism. As will be shown later, the

new multi-objective MLFCM model allows to deﬁne

more than one objective reﬂecting the important fac-

tors affecting the ﬁnal decision, set up different sim-

ulation scenaria with multiple objectives which relate

to the major concerns or drivers against or in favor

of adopting microservices respectively. (iii) Prelimi-

nary investigation and comparison between the results

achieved when coupling MLFCM with known and

widely used MOEA over the problem of adopting mi-

croservices as a new software development paradigm.

The above contributions of this paper essentially con-

stitute the most signiﬁcant differences to similar at-

tempts reported in literature in the past, which also

differentiate the type of experiments executed and the

results yielded and interpreted.

The rest of the paper is organised as follows: Sec-

tion 2 outlines related work on the topic, while sec-

tion 3 presents brieﬂy the technical background be-

hind FCM and MLFCM. Section4 describes the pro-

posed approach for integrating MLFCM with MOEA,

while Section 5 demonstrates its application on mod-

eling the decision for adopting microservices as the

architecture for developing software and discusses the

results obtained. Finally, Section6 concludes the pa-

per and suggests some future research steps.

2 RELATED WORK

The integration of FCM models with evolutionary

techniques and methodologies has been used during

the last two decades, mostly to address some FCM

shortcomings and extend their application. The ﬁrst

attempt to use an evolutionary approach with a FCM

and deliver a hybrid model is reported in (Koulouri-

otis et al., 2001). The authors in this work adopted

an evolution strategy to estimate the cause-effect rela-

tionships among the concepts of the maps.

The authors in (Andreou et al., 2003) introduced

a genetically evolved FCM model aiming to adjust

the weights of the interrelations between the nodes to

meet the objectives after a strategic change. A novel

approach for the automatic construction of FCM mod-

els from historical data was introduced in (Stach et al.,

2005). Through a comparative analysis, the authors

in (Froelich and Juszczuk, 2009) showed how and

to what extent evolutionary learning methods may

outperform the corresponding adaptive ones. The

research work of (Pedrycz, 2010) utilised Particle

Swarm Optimization (PSO) to identify and calibrate

the causal relationships between the nodes of the

map. A decomposed learning scheme was proposed

in (Chen et al., 2015) based on Swarm Intelligence

to adjust gene regulatory networks. A new Structure

Optimization Genetic Algorithm (SOGA) for FCMs

learning is presented in (Poczeta et al., 2015) aiming

to simplify complex FCM models and reduce their

size by selecting the most important concepts and

connections between them. The development of an

evolutionary approach for FCM learning is introduced

in (Poczeta et al., 2019) to reduce the number of con-

cepts of the map, as well as to determine the weights

of the connections between them.

One can easily observe that the majority of the rel-

evant research uses evolutionary approaches to calcu-

late the weights of the causal relationships between

the concepts of the map under study targeting par-

ticular objectives. In addition, very few of them uti-

lize evolutionary algorithms to identify the proper set

of concepts and initial activation levels so that the

model can deliver the best possible output. Although

the approaches mentioned above exhibit high perfor-

mance on the target they are designed for, by calculat-

ing the inter-correlations in a somewhat random way

they practically remove the most signiﬁcant advan-

tages of the model, which are the transparency and

ICAART 2023 - 15th International Conference on Agents and Artiﬁcial Intelligence

414

the reasoning process. This weakness is tackled by

the approach proposed in this paper through the evo-

lution (optimization) of the model’s initial activation

levels, something that preserves its reasoning capabil-

ities and explainability.

3 TECHNICAL BACKGROUND

Fuzzy Cognitive Maps (FCMs) are computationally

intelligent, soft computing tools that combine ele-

ments of fuzzy logic and neural networks (Kosko,

1992). FCMs are easy to construct and comprehend,

and straightforward to execute. In essence, a FCM is a

directed graph with nodes that represent concepts in a

domain and weighted edges that describe the various

causal relationships that exist among these concepts –

either positive or negative. The capabilities of FCMs

are enhanced by fuzzy logic, which deﬁnes both the

type of representation of the causal relationships be-

tween the concepts and the strength of presence of

each concept in the problem dealt. Causal relation-

ships are deﬁned as numerical values in the interval

[−1,+1]. A value w

i j

> 0 means that a positive in-

terrelation exists between concepts C

and C

, that is,

an increase or decrease of the C

value causes an in-

crease or decrease of C

respectively. Inversely, when

i j

< 0 there is a negative interrelation between con-

cepts C

and C

. Finally, if w

i j

= 0 then there is no

relationship between concepts C

and C

. Naturally,

the higher the number of nodes and relationships, the

higher the complexity of the resulting map. A nu-

meric activation level AL (or activation value) per

concept denotes the strength of its presence in the

problem domain. Activation levels are represented

as a vector the elements of which take values in the

interval [−1,1] or [0, 1], depending on the modelling

scheme followed. The map is initialized with a set of

activation levels which represent a particular situation

or problem in hand, and then it is executed on a series

of discrete steps. Equation 1 describes the update rule

initially proposed by Kosko, which calculates the to-

tal causal input for node A

at a given iteration (t + 1)

based on the inﬂuence it receives from all other nodes

that are connected to it (also known as feeders or

sources) at the previous iteration.

t+1

= f

∑

j=1,i6= j

(1)

Similarly to neural networks, four transfer func-

tions are widely used in FCMs (Bueno and Salmeron,

2009): (a) sigmoid, (b) hyperbolic tangent, (c) step

and (d) threshold linear. Generally, most of the

studies that use FCMs for decision making (includ-

ing ours) use the unipolar sigmoid function, which

exhibits the highest predictive capacity among all.

FCMs that use sigmoid functions are also called sig-

moid FCMs.

The iterative execution of the map (i.e., the ap-

plication of the transfer function over the concepts) is

terminated when the model for a number of iterations:

(1) is stabilised at an equilibrium state, (2) exhibits

oscillating behavior, or (3) exhibits chaotic behavior.

The former two cases allow for inference, while the

third case suggests that the model should be revisited.

For inference purposes, the ﬁnal activation value of

the central concept of the model is interpreted in the

context of the problem.

In the case of complex and multifaceted concepts

then it comes into the picture the notion of Multi-

Layer Fuzzy Cognitive Maps (MLFCM) (Mateou and

Andreou, 2005). A MLFCM is essentially a hierarchi-

cal tree structure, with the upper levels (parents) be-

ing composed of other nodes at the lower level (chil-

dren). Thus, several “local” sub-FCMs are formed.

The traversing algorithm of the MLFCM adopted in

this paper is the one proposed in (Mateou et al., 2008)

which starts from the root FCM and follows a depth-

ﬁrst search approach, computes the activation level of

a leaf sub-FCM for only one iteration and transfers

its value back to the parent sub-FCM. Then the exe-

cution of this sub-FCM is performed for one iteration

and its activation level is transferred again back to its

parent FCM and so on. The process for one iteration

ends when the root sub-FCM completes the calcula-

tion of the new activation level of all of the nodes it

comprises.

4 MULTI-OBJECTIVE

OPTIMIZATION IN MLFCM

As previously mentioned, this paper addresses a sig-

niﬁcant challenge in modeling problems with the use

of MLFCM, that is, the inability to execute what-if

scenarios with multiple, conﬂicting objectives. These

scenarios essentially reﬂect hypothetical cases inves-

tigated in a simulated environment which focus on

multiple concepts of the map at different levels of the

hierarchy and with different impact on the ﬁnal out-

put. Therefore, the main contribution of this paper

may be summarized to the integration of MLFCM

with different Multi-Objective approaches. In this

context, a multi-objective engine is developed to serve

the dynamic analysis of MLFCM, that is, the analy-

sis of the model’s behavior under execution, which

utilizes various well-known Multi-Objective Evolu-

Explainable Decision Support Modelling Based on Multi-Layer FCM with Multi-Objective Optimization Characteristics: The Case of the

Microservices Adoption Problem

415

tionary Algorithms (MOEA), such as the NSGAII,

GDE3, OMOPSO and SPEA2, that are then used

to execute scenarios with multi-objective targets and

compare the outputs of the map. The results are as-

sessed in terms of demonstrating the applicability of

the MOEA and proving the signiﬁcant enhancement

of MLFCM models.

Problems that require the optimization of multiple

criteria at the same time, need to use multi-objective

evolutionary algorithms where the goal is to ﬁnd the

best solution by optimizing a set of objective func-

tions. In case of conﬂicting or competing objectives,

a multi-objective evolutionary algorithm typically de-

livers a set of optimal solutions instead of a single

one. This set of optimal solutions is called Pareto op-

timal set (or Pareto front) and contains those solutions

that are not dominated by any other solution yielded

during evolution. Each optimal solution constitutes

a speciﬁc balance between the objectives under op-

timization, where any improvement in one of them

leads to worsening the other. Therefore, a decision-

maker is provided with the set of optimal solutions

and is supported to decide which values of the deci-

sion variables are most suited based on the targets and

the requirements of his application.

A Multi-objective optimization (MOO) problem

can be mathematically expressed using the equation:

min/max f

(x), f

(x),..., f

(x),x ∈ U, (2)

where x is solution, n is the number of objective func-

tions, U is feasible set, f

(x) is the n

h objective func-

tion and min/max is combined objects operations.

The proposed approach of integrating and execut-

ing an MOEA with an MLFCM model relies on a

step-wise process as follows:

Step 1: Identify the decisive nodes in the map

that were revealed through its static analysis; Step

2: Deﬁne the decisive nodes or nodes of interest af-

ter consulting domain experts and decision-makers;

Step 3: Execute the resulting model utilizing a se-

lected set of MOEA under different initial conﬁgu-

rations; Step 4: Evaluate the resulting solutions and

assess whether objectives are conﬂicting (set of solu-

tions diverse) or synergistic (very few solutions); Step

5: Identify which algorithm provides the best values

for the objectives-concepts.

In the context of the proposed approach, the can-

didate solutions, or the decision variables, are the

activation values of all nodes participating in the

MLFCM. The objectives reﬂect the ﬁnal activation

values of two or more nodes for which we target par-

ticular equilibrium values.

Four well-known and widespread MOEAs were

selected, aiming to assess their ability to pro-

vide solutions coupled with an MLFCM: The Non-

dominated Sorting Genetic Algorithm II (NSGA-

II) (Deb et al., 2002), the Generalized Differen-

tial Evolution 3 (GDE3) (Kukkonen and Lampinen,

2005), the Strength Pareto Evolutionary Algorithm

2 (SPEA2) (Zitzler et al., 2001) and the Opti-

mized Multi-Objective Particle Swarm Optimization

(OMOPSO) (Sierra and Coello Coello, 2005).

5 MODELING THE

MICROSERVICES ADOPTION

DECISION PROBLEM WITH

MO-MLFCM

As mentioned above, the case study used in this pa-

per to demonstrate the applicability and efﬁciency of

the Multi-Objective MLFCM is related to the adop-

tion of microservices architecture as a paradigm for

software development. This problem is quite complex

and challenging, and was ﬁrst addressed in (Christo-

forou et al., 2022) where the authors reported also the

use of a framework introduced in (Christoforou and

Andreou, 2017) to analyse the behavior of a MLFCM

and reveal its hidden features and dynamics. This

analysis is divided into two steps: The ﬁrst provides

information about the structure of the map and is

called static analysis, while the second is called dy-

namic and it essentially executes the MLFCM model

with different what-if scenarios (i.e. initial activation

level values) and investigates the results produced.

The dynamic analysis was extended in (Christoforou

et al., 2022) with the integration of a Genetic Al-

gorithm (GA) able to produce a set of near-optimal

solutions in the form of initial activation values tar-

geting particular ﬁnal activation values. It should

be noted that the GA integration targeted a single-

objective optimization and therefore it was quite difﬁ-

cult, if not impossible, to reach to solutions involving

more than one objective, and in particular when the

objectives set are conﬂicting (see also (Christoforou

et al., 2022)). This paper follows the same approach

for the static and dynamic analysis of MLFCM, with

the latter being enhanced with multi-objective (MO)

optimization capabilities. In this context, the integra-

tion of MLFCM with known MO algorithms will be

described in terms of traversing of the map and devel-

opment of the solution space. Below we provide the

main ﬁndings of the static and dynamic analysis per-

formed on the MLFCM model depicted in Figure 1,

which comprises the concepts listed in Table 1.

The static analysis uses notions and metrics from

graph theory to draw meaningful conclusions about

the structure of a MLFCM model. The results are

ICAART 2023 - 15th International Conference on Agents and Artiﬁcial Intelligence

416

Figure 1: The MLFCM model for the Microservice Archi-

tecture adoption problem.

provided in Tables 2 and 3. Table 2 presents the

corresponding metrics and measurements about the

model’s complexity and tendency for each subFCM.

The Complexity indicator consists of Density, the

number of nodes and interactions, and Depth the num-

ber of layers. The Tendency indicator takes into

account the number of positive or negative cycles

formed in a (sub)FCM and checks their balance; if the

number of positive cycles is substantially higher com-

pared to that of negative then the map exhibits a pos-

itive tendency (i.e. a small increase in any node leads

the central concept of interest to increase as well) and

vice-versa. Table 3 lists metrics and measurements

that describe the impact of each participating node on

the model (calculated incoming (in-value) and outgo-

ing (out-value) weight, and number of incoming (in-

degree) and outgoing (out-degree) edges).

A series of experimental runs (simulations) was

then performed by setting different concepts of the

model under study as objective functions (dynamic

analysis). Each algorithm was run ten times for

5000 ﬁtness evaluations (FE) and concluded with a

Pareto near-optimal solution. For the performance

comparison between the selected MOEAs, two in-

dicators were utilized, the HyperVolume (HV) (Zit-

zler and Thiele, 1999) and the Inverted Generational

Distance (IGD) (Van Veldhuizen and Lamont, 2000).

These two quality indicators were selected to assist

in comparing the four MOEAs with respect to per-

formance and scalability, given the metrics’ ability to

assess both convergence and diversity (uniformity and

spread) of the algorithms. Speciﬁcally, the HV indica-

tor assesses the volume covered by the non-dominated

solutions of a Pareto front in the objective space.

Table 1: Concepts related to the decision of adopting mi-

croservice architecture and their groupings (FCMs) - Cen-

tral concept of each FCM in bold.

No. FCM Concept Name

C1 1, 2 Governance

C2 1, 3 Infrastructure and Manage-

ment Services

C3 1 Maintainability and Evolvability

C4 1 Operational Complexity

C5 1 Business Complexity

C6 1 Reliability

C7 1 Security

C8 1, 4 Cost

C9 1, 5 Design

C10 1, 6 DevOps

C11 1 Data Migration

C12 2 Decentralized Governance

C13 2 Data Governance

C14 3 Containerization

C15 3 Scalability/Elasticity

C16 3 Monitoring

C17 3 Serverless Architecture

C18 4 Migration Cost

C19 4 Operations Cost

C20 5 Design For Failure

C21 5 Granularity and Bounded Context

C22 5 Service Contracts

C23 5 Communication Model

C24 5 Decentralization

C25 6 Organization Culture

C26 6 Skilled and Educated DevOps

Teams

C27 6 Tool Support

C28 6 Continues Activities

C29 6 Automated Tasks

C30 6 Information Sharing

C31 1 Microservices Adoption

Table 2: Complexity static measurements.

FCM Layer Density Cycles+ Cycles-

1 1 0.72 64642 65900

2 2 1 5 0

3 2 1 68 16

4 2 1 5 0

5 2 1 409 0

6 2 1 2365 0

Therefore, the larger the volume covered by the so-

lutions generated in a run, the higher the HV value,

which indicates a better performance. The IGD indi-

cator assesses how far the elements of the true Pareto

front (reference data in our case) are from the non-

dominated points of an approximation Pareto front.

Therefore, the greater the extent of the true Pareto

Explainable Decision Support Modelling Based on Multi-Layer FCM with Multi-Objective Optimization Characteristics: The Case of the

Microservices Adoption Problem

417

Table 3: Strength indicators for the top level FCM.

Node deg

tot

(i) val

tot

(i) Cycles+ Cycles-

C1 18 8.4 56703 57479

C2 16 7.2 53897 54464

C3 18 8.5 56149 57610

C4 18 8.7 56724 57633

C5 9 4.5 30705 31338

C6 18 7 56355 58002

C7 18 7.8 56445 57912

C8 11 6.3 0 0

C9 18 9.6 57279 58307

C10 16 7.5 54070 55041

C11 19 5.6 58390 59921

C31 11 6.7 0 0

front that is covered by the non dominated points gen-

erated by a run in the objective space, the lower the

IGD value, which denotes better performance.

All of the parameters in the algorithms used were

selected considering that decision variables take real

values ranging between 0 and 1. The overall im-

plementation utilized the Platypus

, a Python-based

multi-objective optimization algorithms library.

Among a series of executions that were per-

formed, two indicative simulations were selected and

presented below. In the ﬁrst case, consultation with

domain experts and decision-makers indicated Mi-

croservices adoption and Security as the factors to

take part in the objective functions. These concepts

were considered interesting by the experts to study

together and test how they may be related since se-

curity is a common concern of companies moving to

developing software with microservices. Therefore,

the model was executed targeting to identify solutions

for maximizing both objectives. The resulting two

dimensional Pareto fronts for each algorithm are de-

picted in Figure 2.

Table 4: Hypervolume and IGD mean values from a series

of 12 executions for the ﬁrst optimization case.

GDE3 NSGAII OMOPSO SPEA2

HV 0.8870 0.8856 0.8743 0.8803

IGD 0.5121 0.5189 0.7270 0.5134

The HV and IGD values of 12 executions (out of

100 repetitions) calculated for these series of simula-

tions and their corresponding means are listed in Ta-

ble 4. It is clear from HV and IGD that all algorithms

perform quite well, with GDE3 appearing slightly su-

perior than the rest in both metrics. It is also interest-

ing to note that NSGAII and GDE3 reach multiple and

diverse solutions, followed by SPEA2. OMOPSO, on

https://github.com/Project-Platypus/Platypus

Figure 2: Pareto front for Microservices adoption (x-axes)

and Security (y-axes) objectives. (a) NSGAII, (b) GDE3,

the other hand, ﬁnds only one dominant solution with

both objectives set to values very near to their desired

maximums. We should also note here the existence

of multiple solutions that span a range of values for

the Security concept. This suggests that Security is

not the most decisive factor contributing in favor or

against Microservices adoption since the maximum

values for the latter are also achieved with lower val-

ues of the former.

To check whether there is a statistically signiﬁcant

difference between the four algorithms, the Wilcoxon

singed-rank test (Rey and Neuh

auser, 2011) was ap-

plied on both performance indicators HV and IGD.

The null hypothesis (H0) initially set is that the two

compared samples are equal. The calculation of the

p − value, which indicates the level of signiﬁcance,

for HV and IGD is listed in Table 5. Based on the cal-

culated p − values, in the case HV, the null hypothe-

sis is rejected (p < 0.05) in all pairs of algorithms but

NSGAII and OMOPSO. Similarly, when examining

IGD it is not clear whether there is statistically sig-

niﬁcant difference between the algorithms except for

the pairs GDE3-OMOPSO, NSGAII-OMOPSO and

OMOPSO-SPEA2. Therefore, we may assume with-

out loss of generalization that all algorithms perform

well, but GDE3 stands out with signiﬁcant statistical

difference.

The second case explores the solutions delivered

by the model considering three objectives, the Mi-

croservices adoption, which is the central concept

of interest, the Security as the main concern of the

decision-maker, and the Operational Complexity as

one of the most decisive concepts based on the static

ICAART 2023 - 15th International Conference on Agents and Artiﬁcial Intelligence

418

Table 5: Pairwise comparison for HV and IGD indicators

for the ﬁrst optimization case.

NSGAII OMOPSO SPEA2

Hypervolume

GDE3 0.002 0.002 0.002

NSGAII 0.770 0.002

OMOPSO 0.002

IGD

GDE3 0.193 0.002 0.131

NSGAII 0.002 0.160

OMOPSO 0.002

Figure 3: Pareto front for Microservices adoption (z-axes),

Security (x-axes) and Operational complexity objectives (y-

axes). (a) NSGAII, (b) GDE3, (c) OMOPSO, (d) SPEA2.

analysis (Table 3). The Microservices adoption and

Security objectives were set to be maximized, while

the Operational complexity was set to be minimized.

The three-dimensional Pareto fronts that emerged

from the above executions are depicted in Figure 3.

The calculations of the two performance indicators

for the second series of simulations are listed in Ta-

ble 6.

Table 6: Hypervolume and IGD mean values from a series

of 12 executions for the second optimization case.

GDE3 NSGAII OMOPSO SPEA2

HV 0.7880 0.7774 0.8012 0.6991

IGD 0.5121 0.5189 0.7270 0.5134

The results suggest again that the algorithms per-

form well and manage to ﬁnd solutions despite the

fact that the problem is now harder than the ﬁrst case.

The diversity of the solutions is now evident for all

algorithms, while GDE3 seems again superior than

the rest of the algorithms in terms of both the HV

and the IGD metrics. According to the Wilcoxon

test, the null hypothesis for the HV values may be re-

jected for all pairs of algorithms except for NSGAII-

OMOPSO. In the case of IGD, the null hypothesis

can not be rejected for the pairs NSGAII-OMOPSO,

GDE3-NSGAII and GDE3-OMOPSO. Therefore, it

seems that GDE3 again performs best, with slight dif-

ferences compared to the rest of the algorithms.

Table 7: Pairwise comparison for HV and IGD indicators

for the second optimization case.

NSGAII OMOPSO SPEA2

Hypervolume

GDE3 0.002 0.002 0.002

NSGAII 0.770 0.002

OMOPSO 0.002

IGD

GDE3 0.084 0.084 0.002

NSGAII 0.084 0.002

OMOPSO 0.004

Overall, the experimental process described in this

section demonstrated that all of the multi-objective

algorithms utilized have managed to ﬁnd good solu-

tions and that GDE3 appears to be slightly superior.

It should be noted that the theory of multi-objective

optimization in the case of MLFCM is somewhat dis-

turbed by the fact that the complexity of the relation-

ships between the nodes does not allow for a clear

separation of the conﬂicting nodes. This means that

there are paths in the model that could be visited that

are not easy to deﬁne a-priori and these alternative

routes in some cases give birth to solutions that are

not necessarily conﬂicting, as in the ﬁrst case of the

experimental process. Therefore, one thing that the

model calls for further analysis and investigation is

the number and type of individual solutions, as well

as the different forms of conﬂicting or not objectives.

This assessment reveals also the complexity of the op-

timization scenario in cases in which the set of solu-

tions is not so rich and vice-versa.

6 CONCLUSIONS

This paper proposed an enhanced form of explain-

able decision support modelling based on Multi-

Layer Fuzzy Cognitive Maps (MLFCM) and Multi-

Objective Evolutionary Algorithms (MOEA). The

case of a complex decision problem related to the

adoption of microservices architecture was addressed

to show the applicability and effectiveness of the pro-

posed model using four well known and effective

MO approaches, namely NSGAII, OMOPSO, GDE3

and SPEA2. Two MO scenarios were developed and

tested, the ﬁrst involving two and the second three ob-

Explainable Decision Support Modelling Based on Multi-Layer FCM with Multi-Objective Optimization Characteristics: The Case of the

Microservices Adoption Problem

419

jectives, which were formed with the aid of domain

experts. The results suggested that the proposed inte-

grated MOEA-MLFCM successfully managed to cap-

ture the dynamics behind the decision for migrating to

microservices.

Future research will concentrate on the following:

First, more objectives and scenarios will be investi-

gated so as to form a more complete experimental pic-

ture in terms of factors and inter-dependencies. Sec-

ond, automation of the selection of the most appropri-

ate MOEA will be pursued for each multi-objective

scenario formed in each problem dealt.

REFERENCES

Andreou, A., Mateou, N., and Zombanakis, G. A. (2003).

Evolutionary fuzzy cognitive maps: A hybrid system

for crisis management and political decision making.

Balalaie, A., Heydarnoori, A., and Jamshidi, P. (2016). Mi-

croservices architecture enables devops: Migration to

a cloud-native architecture. IEEE Software, 33(3):42–

52.

Bueno, S. and Salmeron, J. L. (2009). Benchmarking main

activation functions in fuzzy cognitive maps. Expert

Systems with Applications, 36(3):5221–5229.

Chen, Y., Mazlack, L. J., Minai, A. A., and Lu, L. J. (2015).

Inferring causal networks using fuzzy cognitive maps

and evolutionary algorithms with application to gene

regulatory network reconstruction. Applied Soft Com-

puting, 37:667–679.

Christoforou, A. and Andreou, A. S. (2017). A framework

for static and dynamic analysis of multi-layer fuzzy

cognitive maps. Neurocomputing, 232:133–145.

Christoforou, A., Andreou, A. S., Garriga, M., and

Baresi, L. (2022). Adopting microservice architec-

ture: A decision support model based on genetically

evolved multi-layer fcm. Applied Soft Computing,

114:108066.

Deb, K., Pratap, A., Agarwal, S., and Meyarivan, T. (2002).

A fast and elitist multiobjective genetic algorithm:

Nsga-ii. IEEE transactions on evolutionary compu-

tation, 6(2):182–197.

Froelich, W. and Juszczuk, P. (2009). Predictive capabilities

of adaptive and evolutionary fuzzy cognitive maps-a

comparative study. In Intelligent systems for knowl-

edge management, pages 153–174. Springer.

Gunning, D. and Aha, D. (2019). Darpa’s explainable

artiﬁcial intelligence (xai) program. AI magazine,

40(2):44–58.

Kosko, B. (1992). Neural networks and fuzzy systems:

a dynamical systems approach to machine intelli-

gence/book and disk. Vol. 1Prentice hall.

Koulouriotis, D., Diakoulakis, I., and Emiris, D. (2001).

Learning fuzzy cognitive maps using evolution strate-

gies: a novel schema for modeling and simulating

high-level behavior. In Proceedings of the 2001

Congress on Evolutionary Computation (IEEE Cat.

No. 01TH8546), volume 1, pages 364–371. IEEE.

Kukkonen, S. and Lampinen, J. (2005). Gde3: The third

evolution step of generalized differential evolution.

In 2005 IEEE congress on evolutionary computation,

volume 1, pages 443–450. IEEE.

Mateou, N., Andreou, A. S., and Stylianou, C. (2008).

A new traversing and execution algorithm for multi-

layered fuzzy cognitive maps. In 2008 IEEE Inter-

national Conference on Fuzzy Systems (IEEE World

Congress on Computational Intelligence), pages

2216–2223. IEEE.

Mateou, N. H. and Andreou, A. S. (2005). Tree-structured

multi-layer fuzzy cognitive maps for modelling large

scale, complex problems. In International Conference

on Intelligent Agents, Web Technologies and Internet

Commerce, volume 2, pages 131–139. IEEE.

Meske, C. and Bunde, E. (2020). Transparency and trust in

human-ai-interaction: The role of model-agnostic ex-

planations in computer vision-based decision support.

In International Conference on Human-Computer In-

teraction, pages 54–69. Springer.

Pedrycz, W. (2010). The design of cognitive maps: A

study in synergy of granular computing and evolution-

ary optimization. Expert systems with applications,

37(10):7288–7294.

Poczeta, K., Kubu

s, Ł., and Yastrebov, A. (2019). Analysis

of an evolutionary algorithm for complex fuzzy cog-

nitive map learning based on graph theory metrics and

output concepts. Biosystems, 179:39–47.

Poczeta, K., Yastrebov, A., and Papageorgiou, E. I. (2015).

Learning fuzzy cognitive maps using structure opti-

mization genetic algorithm. In 2015 federated con-

ference on computer science and information systems

(FedCSIS), pages 547–554. IEEE.

Rey, D. and Neuh

auser, M. (2011). Wilcoxon-signed-rank

test.

Sierra, M. R. and Coello Coello, C. A. (2005). Improving

pso-based multi-objective optimization using crowd-

ing, mutation and dominance. In International con-

ference on evolutionary multi-criterion optimization,

pages 505–519. Springer.

Stach, W., Kurgan, L., Pedrycz, W., and Reformat, M.

(2005). Genetic learning of fuzzy cognitive maps.

Fuzzy sets and systems, 153(3):371–401.

Van Veldhuizen, D. A. and Lamont, G. B. (2000). Multiob-

jective evolutionary algorithms: Analyzing the state-

of-the-art. Evolutionary computation, 8(2):125–147.

Wootton, B. (2014). Microservices: a deﬁnition of this new

architectural term. Retrieved from:.

Zitzler, E., Laumanns, M., and Thiele, L. (2001). Spea2:

Improving the strength pareto evolutionary algorithm.

TIK-report, 103.

Zitzler, E. and Thiele, L. (1999). Multiobjective evolu-

tionary algorithms: a comparative case study and the

strength pareto approach. IEEE transactions on Evo-

lutionary Computation, 3(4):257–271.

ICAART 2023 - 15th International Conference on Agents and Artiﬁcial Intelligence

420