Using Meta-heuristics to Optimize the Parameterization of Algorithms in

Simulation Models

Chabi Babatounde

, Bastien Poggi

, Thierry Antoine-Santoni

and Antoine Aiello

Universit

e de Corse, UMR CNRS 6134, Science Pour l’Environnement, Corte, France

Universit

e de Corse, UMS CNRS 3514, STELLA MARE, Biguglia, France

Keywords:

Meta-heuristics, Optimization, Algorithm, Modeling and Simulation.

Abstract:

The research topic of the laboratory Science Pour l’Environnement (SPE) and the laboratory STELLA MARE

of Universit

e de Corse, focus on solving the environmental problems of our time. Various research teams focus

their work on modeling and simulation of complex systems and behavioral modeling of species. Generally, in

this modeling process (abstractions from the real world), we observe that the parameterization of the models is

usually very tedious, carried out in an empirical or intuitive way based on assumptions speciﬁc to each modeler.

There are also several modeling techniques which are generally parameterized intuitively and empirically. We

have therefore proposed an approach to optimize the parameterization of models based on the algorithms of

these models. This approach uses meta-heuristics, a class of optimization algorithms inspired by nature for

which we obtain remarkable results. The use of meta-heuristics in this approach is justiﬁed by the nature of the

problem to be solved. Indeed, the parameterization of models can be considered as a complex problem with a

very large solution space that needs to be explored in an intelligent way. The risk of a combinatorial explosion

is also very high because of the number of variables to be optimized. The advantage of this approach that we

propose is that it allows an evolutive optimization of the model parameterization as the data arrives. For the

validation of this approach, we used simulated data from a theoretical model. The validation of this theoretical

model opens possibilities of applications on real world models.

1 INTRODUCTION

The evolution of human activities and demograph-

ics in recent centuries have brought about several

changes on the planet, with the result that a large

number of species are in danger of extinction, even

though they have a major ecological and economic

impact. It is in this context that the SPE Laboratory

and the STELLA MARE platform have been work-

ing since their creation to develop strategies to ensure

the restoration and maintenance of Corsica’s ﬁshing

resources. With the democratization of the Internet of

Things in recent years (Dave, 2011), large volumes of

data have been collected on species of interest in order

to understand their behavior and model them (Schichl,

2004); (Wong and Ming, 2019), in order to make pre-

dictions. There are various modeling approaches in

the literature (Yin and McKay2, 2018); (Sharma and

Sharma, 2014a); (Zeigler, 2017) that produce accept-

able results, but the conﬁguration of these methods

is generally very tedious and performed intuitively,

based on assumptions speciﬁc to each expert. Since

there is precisely no exact knowledge about the sys-

tem to be modeled and the knowledge of the experts

is limited, biases may be introduced. Based on this

observation, our research focuses on reﬁning the con-

ﬁguration of the models by adding a layer of opti-

mization by meta-heuristics. The present work has

consisted in using meta-heuristic optimization to im-

prove the quality of simulations through intelligent

model parameterization. The implementation of this

approach allows to take in input datasets and the algo-

rithm of the model to be conﬁgured to produce after

processing, an optimal parameterization. The advan-

tage of such an approach is that it is scalable and al-

lows a dynamic reﬁnement of the model as new data

is received.

In the Section 2 of this paper, we present the works

related to our work, and in the section 3, we review

the general concepts related to optimization and meta-

heuristics. We then present the approach we pro-

pose for the optimization of model parameterization

as well as the different variants of algorithms imple-

mented in Section 5.

Babatounde, C., Poggi, B., Antoine-Santoni, T. and Aiello, A.

Using Meta-heuristics to Optimize the Parameterization of Algorithms in Simulation Models.

DOI: 10.5220/0010508102150223

In Proceedings of the 11th International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH 2021), pages 215-223

ISBN: 978-989-758-528-9

215

2 RELATED WORK

Over the last twenty years, it has become increas-

ingly common to see a particular emphasis on opti-

mization in modeling and simulation work; (Sharma

and Sharma, 2014b); (Allegrini et al., 2015); (Hut-

terer, 2010).Today, it is almost impossible to see any

modeling work that does not involve optimization, be-

cause the ultimate goal of modeling is to get as close

as possible to the real system, which means solving

optimization problems at several levels, such as de-

termining the optimal structure and the optimal pa-

rameters of the model. When we consider the param-

eterization of models, optimization methods are much

more used in the design of behavioral models than in

phenomenological models. This is mainly due to the

fact that for phenomenological models, the relation-

ships that rule the system to be modeled are known,

contrary to behavioral models where it is necessary

to ﬁnd relationships that link the inputs and outputs

of the system. The main methods used for this type

of problem are automatic programming and artiﬁcial

neural networks. Automatic programming started in

the 90’s with genetic algorithms (genetic program-

ming) (Koza, 1992). With the evolution of comput-

ers and the availability of more computing power,

meta-heuristics started to be more and more present

in the world of modeling and automatic programming

in particular. New meta-heuristics were appeared but

they focus much more on the generation of models

than on their reﬁnement. It is this reﬁnement that

we ﬁnd in machine learning models and more specif-

ically in artiﬁcial neural networks under different an-

gles: optimization of weights, network architecture,

activation nodes, learning parameters, learning envi-

ronment, etc. (Gandomi, 2013). The advantage of

meta-heuristics in this process over ”classical” gradi-

ent descent methods is that meta-heuristics can over-

come limitations related mainly to blocking in the lo-

cal extrema (Ojha et al., 2017).

3 OPTIMIZATION PROBLEM

AND META-HEURISTICS

An optimization problem is deﬁned by its dimension

n ∈ N, its set of variables {x

, x

, ..., x

} denoted S,

a set of constraints C and a goal function f : S 7→ R.

Solving an optimization problem consists in ﬁnding

the optimal values of x

, x

, ... and x

which min-

imise or maximise the objective function on C. Meta-

heuristics are used to ﬁnd these optimal values. Meta-

heuristics (Tarraq, 2021); (Abdel-Basset et al., 2018);

(Glover and S

orensen, 2015); (Xin-She, 2014); (Xin-

She, 2011); (Lee and El-Sharkawi, 2008), also called

”nature-inspired methods” form a class of optimiza-

tion methods which are based on probabilistic and

random reasoning and allow the resolution of prob-

lems for which ”classical” optimization methods also

called ”deterministic methods” (Moxnes, 2015) do

not allow results to be obtained. Meta- heuristics are

based on an iterative process which allows conver-

gence towards the solution. In other words, a meta-

heuristic starts from one or more solutions which it

improves around two central concepts: diversiﬁcation

and intensiﬁcation. Diversiﬁcation makes it possible

to search in the research space for areas where solu-

tions could be found and intensiﬁcation makes it pos-

sible to improve the solutions found in the identiﬁed

areas. A multitude of algorithms and implementations

of meta-heuristics can be found in the literature. As

far as they are concerned, the development of these

algorithms goes through ﬁve (05) generic phases that

are executed in an iterative manner until a solution is

found or one of the stopping conditions is satisﬁed

as shown in Figure 1 which presents these different

phases.

Figure 1: Meta-heuristics execution phases (Poggi, 2014).

There are several meta-heuristic P’s in the liter-

ature. In order to make a performance comparison

between the meta-heuristics we will focus on the two

most intuitive and which are inspired by the animal

kingdom. These are the genetic algorithm and the im-

mune algorithm.

3.1 Genetic Algorithms

Genetic algorithms (Sopov, 2017); (Oltean, 2005)

(McCall, 2005); (Wong and Ming, 2019) are opti-

mization algorithms based on analogies of genetics

and natural evolution (selection, cross-breeding, mu-

tations). Table 1 presents the analogy between the

concepts of genetics and genetic algorithms. A ge-

netic algorithm searches for the extrema of a deﬁned

function in a data space. The behaviour of a ge-

netic algorithm is described by Algorithm 1. It be-

gins by randomly generating a population of individ-

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216

uals. Then, in order to move on to the next genera-

tion, three main operations inspired by natural evolu-

tion are applied, which are repeated for all individuals

in the population.

• Selection: Couples of parents P1 and P2 are se-

lected according to their adaptation to the problem

to be solved.

• Cross-breeding: Each pair of parents (P

, P

i+1

)

selected is crossed to produce pairs of

children(C

i+1

). There are various cross-

ing techniques. It can be for example an exchange

of variables between parents (P

and P

with

respective genomes {22, 25} and {12, 15} give

children C

and C

with respective genomes

{22, 15} et {12, 25}).

It is also possible to make a combination of each

variable from each parent according to a random

constant α with α ∈ [0, 1]. In this case, parents

and P

give children C

with the genome

{22α + 12(1 − α), 25α + 15(1 − α)} and C

with

the genome {22(1 − α) + 12α, 25(1 − α) + 15α}

• Mutation: There are several mutation techniques

in the literature and they are generally based on

probabilistic approaches. The children (C

i+1

)

and individuals who have been mutated are then

evaluated before being included in the new popu-

lation.

Algorithm 1: Genetic algorithms.

population = generatePopulation( );

evaluate(population);

while Not(Solution found OR stop condition)

for i ← 1 to populationSize do

parents = selectParents(population) ;

children = crossBreeding(parents) ;

children = mutate(children) ;

evaluate(population) ;

population = update(children) ;

return (solution) ;

3.2 Immune Algorithm

Immune algorithm (Darmoul, 2010); (Zhang, 2011)

is based on the way the body’s immune system de-

fends itself against foreign bodies. Indeed, to de-

fend the organism, the immune system is capable of

creating a very wide variety of cells and molecules

that can speciﬁcally recognize and eliminate a large

number of foreign invaders. This ability to recognize

an ”aggressor” is used here to recognize solutions to

the optimization problem. There are several types of

immune algorithms. For this study, we use the

CLONALG type immune algorithm (Sharma and

Sharma, 2011). Table 2 presents the analogy made

between the immune system of organisms and the im-

mune algorithm of CLONALG type. Like the im-

mune system of organisms, at the beginning of the

process, a set of antibodies is generated. Each anti-

body of the immune system thus formed is evaluated

and standardized. Then, an iterative process begins

that leads to the solution. With each iteration, a quan-

tity of solutions (antibodies) is produced and evolved.

The evolution of the solutions in this algorithm, as

with an immune system, is based on a principle of

cloning and mutation. A solution better adapted to the

problem will be much more cloned than a less adapted

solution.

Similarly, a less suitable solution will undergo a

greater change than a more suitable solution. As the

optimization variables in our case are real, the mu-

tation of a solution will consist in incrementing or

decrementing the value of one or more variables. This

technique allows convergence towards the desired so-

lution. A phase which particularly inﬂuences this al-

gorithm on its performance is the cloning phase. To

determine the clonnig rate (quantity of clones pro-

duced), several approaches exist:

• The Probabilistic Approach: This approach al-

lows the rate to be determined in proportion to

the adjustment according to equation 1. When the

number obtained is not an integer, it is rounded.

clones = antibodies ∗

adaptation

(1)

• The Empirical Approach: Using data collected

from several experiments with our algorithm, we

manage to deﬁne a relation between a score at-

tributed to the solution and the number of clones.

• The Stochastic Approach: The number of muta-

tions and clones is set randomly within a prede-

ﬁned interval.

The process of an immune algorithm is described

in Algorithm 2. Figure 2 illustrates the steps of an

immune algorithm in the search for the value 10.

By exploring these few meta-heuristic algorithms,

we realize the interest of their use for complex prob-

lems, which is in adequacy with our problem of ”in-

telligent” parameterization of simulation models. To

this end, the approach we propose is presented in Sec-

tion 4.

Using Meta-heuristics to Optimize the Parameterization of Algorithms in Simulation Models

217

Table 1: Analogy between genetics, genetic algorithm and optimization.

Genetic Genetic algorithm Optimization

Set genome possible Set of possible genes Search space

Individual Coded solution Solution

Genome Details of a solution Values of each parameter

Adaptation Fitness Adaptation

Natural selection Random selection Diversiﬁcation

Genetic mutation Value change Diversiﬁcation

Table 2: Analogy between Genetics, Immune Algorithm and optimization.

Immune system Immune Algorithm Optimization

All possible antibodies All possible solutions Search space

Antibody Coded solution Solution

Cell receptor Details of a solution Values of each parameter

Adaptation Fitness Adaptation

Figure 2: Searching for the value 10 by an immune algorithm.

Algorithm 2: Immune Algorithm.

immuneSystem = randomlyGenerated( );

evaluate(immuneSystem);

normalize(immuneSystem) ;

while Not(Solution found OR stop condition)

clones = createClones(immuneSystem) ;

clones = mutate(clones) ;

evaluate(clones) ;

nomarlize(clones) ;

newAntibodies = generateNewClones() ;

evaluate(newAntibodies) ;

nomarlize(newAntibodies) ;

immuneSystem = merge(clones,

newAntibodies, immuneSystem) ;

return (solution) ;

4 PROPOSED APPROACH

We propose an architecture allowing to optimise the

parameterization of the algorithms implemented in

the models. Figure 3 presents the different compo-

nents of this proposed architecture and the way they

communicate.

4.1 Global Architecture

The proposed architecture for algorithm optimization

is composed of four main entities:

• The Optimizer: It leads the optimization process.

It contains the execution logic and behaves like a

scheduler by choosing the order of execution of

each task. Its role is mainly to choose an opti-

mization algorithm and to parameterize it for the

optimization process.

• Meta-heuristics: This entity can be considered

as a library of meta-heuristics. It implements and

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218

Figure 3: Proposed architecture.

makes available meta-heuristics for the process of

optimization.

• The Simulator: The simulator, allows to produce

for each solution obtained, the corresponding data

set. This phase is essential to evaluate the solution

obtained.

• The Viewer: It allows to visually render the

dataset, the algorithm to be optimized as well as

the evolution of the process.

All these entities cooperate together to ﬁnd a solu-

tion in the following way: The model to be optimized

and the reference dataset are passed to the optimizer,

which guides the optimization process. It chooses the

meta-heuristics and parameters for the optimization.

During the iterative process, the meta-heuristics will

collaborate with the simulator to evaluate each solu-

tion obtained and move towards the optimal solution.

At the end of the optimization process, the solution

and the process metrics are sent back to the optimizer

where the solution is rendered in the format speciﬁed

by the user. It should be noted that throughout this

process, the viewer is used to display the algorithm,

the simulation results and the evolution of the solu-

tions obtained.

4.2 Abstraction

We have given our own representation for some enti-

ties to facilitate data exchange between the elements.

This is mainly the model and the solution. We will

illustrate each element with simple examples to facil-

itate understanding.

The model to be optimized is deﬁned by an al-

gorithm (a logical instruction sequence) characterized

by its variables and operations to be executed. In our

proposed approach, we then represent a model like a

graph. Each node of the graph represents an action or

a phase in the execution of the algorithm. The way

the nodes are linked deﬁnes the way the algorithm is

executed. To illustrate this, let’s consider the algo-

rithm 3 which is a simple algorithm that calculates

the remaining energy in a system up to t = 100. The

corresponding representation is given in Figure 4.

Algorithm 3: Example of a model algorithm.

energy = 100 ;

t = 0 ;

running cost = 5;

cost at rest = 2;

while t ≤ 100 do

if running == True then

energy = energy - running cost ;

else

energy = energy - cost at rest ;

t = t + 1 ;

Figure 4: Representation of algorithm 3.

4.3 Meta-heuristics Implementation

For this ﬁrst implementation, we are focusing on

the genetic algorithm and the Immune algorithm of

CLONALG type in order to carry out performance

comparisons. In accordance with the concepts spe-

ciﬁc to each of these algorithms (presented in sec-

Using Meta-heuristics to Optimize the Parameterization of Algorithms in Simulation Models

219

tion 3), their implementation in the context of the ap-

proach complies with the following rules: For the ge-

netic algorithm, we have:

• Encoding: All the parameters of the solution are

converted to standardized binary form (IEEE754)

and concatenated.

• Cross-breeding Operator: We make a crossover

by exchanging between the solutions. This ex-

change consists in randomly deﬁning the number

of crossings (Xin-She, 2014) as well as the points

where to realize them.

• Mutation Operator: A sufﬁciently large α value

(0.95) is set at the beginning of the optimization.

At each crossover, a value θ ∈ [0, 1] is generated.

If θ > α then a mutation occurs. Otherwise noth-

ing is changed

On the side of the CLONALG type Immune algo-

rithm, the speciﬁcity was to implement the three ap-

proaches presented in Section 3.2 in order to deter-

mine the number of clones to be generated. This al-

lows to vary the search method.

4.4 Solutions Evaluation

The adaptation of a solution is measured by the dif-

ference between the produced values and the awaited

values. Several methods exist in the literature (Lee

and El-Sharkawi, 2008); (Shtovba, 2005)to measure

this difference. In this work, we use the root mean

square error because it is simple to implement and ex-

plicit. Equation 2 then becomes the cost function to

be minimized during the optimization process.

(x,y)

∑

i=1

((x

− x

)

+ (y

− y

)

) (2)

With (x

, y

) the coordinates of point i in the data set

and (x

, y

) the coordinates of point in the simulation

result. The higher the G value, the less suitable the

solution.

5 ARCHITECTURE VALIDATION

5.1 Validation Model

The validation process of the proposed approach con-

sisted in using data obtained by simulating a model to

ﬁnd the parameterization used for the conﬁguration of

the model, or an optimal parameterization. We base

our tests on a conceptual animal species model that

can be updated to be closer to a real-world animal

species. The choice of this model type is explained

by an exact knowledge of the awaited behaviour. This

behaviour is deﬁned over one hundred (100) units of

time where each interval corresponds to behavioural

functions. Each of the behavioural functions is also

deﬁned by a set of speciﬁc operations that vary the

position of the subject and the level of energy it uses.

The variation in position and level of energy is a func-

tion of several constants that characterize each be-

havioural function. It is these constants that must be

optimized, and in the case of the model, there are ten

(10). The data set produced by the model is a col-

lection of positions and the amount of energy at each

instant. Table 3 shows the distribution of behavioural

functions by time interval and deﬁnes the associated

position and energy variation functions. The task will

be to ﬁnd the optimal values for the constants ε

, G

, Y

, G

, X

, Y

, G

, X

and Y

and Ye that give the

closest possible output to the trajectory and the value

of the energy in the reference data set.

By representing this algorithm in graph form, we

obtain Figure 5.

Figure 5: Graphical representation of the model (variables

to be optimized in red).

5.2 Experimental Results

A series of ﬁfty (50) tests were carried out with

the data obtained by simulating the model presented

in Section 5.1. The experimental conditions are

recorded in Table 4 and Table 6. The Table 6 show

one of the results obtained during the series of tests.

Figures 6, 7 and 8 show the state of the solutions

obtained at different phases of the optimization pro-

cess in relation to the awaited result. On the side of

trajectory and energy, a large gap between the awaited

solution and the solution obtained at the ﬁrst iteration

can be seen (Figure 6). At the halfway point (Fig-

ure 7), the gap between the obtained trajectory and

the expected trajectory is considerably is. But on the

other hand about the energy, the difference is created

even more. This could be explained by the fact that

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220

Table 3: Distribution of behaviours by time slot.

Time interval (t) Behaviour Equation

t = 0 Initialization











ε = ε

x = 10

y = 0

t ∈]0, 30] The subject is at rest : sleeping











= ε

t−1

+ G

= x

t−1

+ X

cos(t)

= y

t−1

t ∈]30, 50] The subject is wandering around : wandering











= ε

t−1

− G

= (x

t−1

)

= y

t−1

sin(t) −Y

t ∈]50, 80] The subject is feeding : Eating











= ε

t−1

+ G

= x

t−1

= y

t−1

t ∈]80, 100] The subject is wandering around : wandering











= ε

t−1

− G

= (x

t−1

)

= y

t−1

sin(t) −Y

Table 4: Experimental conditions.

Maximum Iteration 500

Variables to be optimized 10

Population size 100

Cross-breeding ratio (Genetic algorithm) 60%

Table 5: Computer used.

Brand DELL

Model Latitude 5480

RAM 16 Go

Processor Intel i57300HQ

CPU 2.500GHz x 4

Operating system Ubuntu 20.04.1

Table 6: An example of the results obtained during the ex-

periments.

found before the last iteration No

Iteration of the solution 421

Adaptation of the solution 99.7862

Adaptation of the worst solution 100.1378

the variables which intervene in the deﬁnition of the

trajectory are close to an optimal value, which is not

the case for the energy side. At the end of the pro-

cess, the solution obtained gives a result very similar

to that of the dataset. In two out of ﬁfty tests, we ob-

tained exactly the awaited path, i.e. a solution with an

adaptation equal to zero, which shows that we were

managing to converge towards a solution we were ex-

pecting. This is also shown in Figures 9. We can see

that very quickly we converge towards a solution and

that over the iterations, the entire population is also

greatly improved. This can be explained by the stabi-

lization of the population around an optimal solution.

The performance of each meta-heuristic is recorded

in Table 7 and clearly reveals the superiority of the

genetic algorithm over the immune algorithm for this

type of problem. The performances of the genetic al-

gorithm outshines the immune algorithm, with solu-

tions found faster in less time with lower adaptation.

6 CONCLUSION AND

PERSPECTIVES

In this paper, we have done preliminary work on

the optimization of the parameterization of simulation

models using meta-heuristics. We have observed that

meta-heuristics allow us to have good results with a

certain number of variables to be optimized within an

acceptable period of time. However, interesting per-

spectives are contemplated and will be the subject of

future work. At ﬁrst, the architecture will be used to

optimize the parameterization of other types of mod-

els, in particular machine learning models. Futher, the

performance of this architecture and the algorithms

implemented will be studied in order to improve the

choice of parameters and to deﬁne the types of prob-

lems for which the use of such an architecture is suit-

able.

Using Meta-heuristics to Optimize the Parameterization of Algorithms in Simulation Models

221

Table 7: Performance of each meta heuristic.

Meta-heuristics solution with adaptation ≤ 200 Execution time average Adaptation average

Genetic algorithm 42 out of 50 921 seconds 63.11389372

Immune algorithm 37 out of 50 1453 seconds 97.19834646

Figure 6: Comparison between the solution obtained at the beginning and the awaited one.

Figure 7: Comparison between the solution obtained at mid-term and the awaited one.

Figure 8: Comparison between the obtained solution and the awaited one.

Figure 9: Evolution of the average adaptation of the population.

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222

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