ELEKTROTEHNI ˇ SKI VESTNIK 90(1-2): 45–50, 2023
ORIGINAL SCIENTIFIC PAPER
A Nature-Inspired Implementation of the Computer
Opponent in the Arcade Computer Game of Darts
Nina Tovornik, Iztok Fister Jr., Vili Podgorelec, Lucija Brezoˇ cnik
University of Maribor, Faculty of Electrical Engineering and Computer Science, Intelligent Systems Laboratory
Koroˇ ska cesta 46, 2000 Maribor, Slovenia
E-mail: nina.tovornik1@student.um.si, iztok.fister1@um.si, vili.podgorelec@um.si, lucija.brezocnik@um.si
Abstract. Some three billion people play video games worldwide, which makes the video games industry an
integral part of modern life. Such demand requires game developers to provide increasingly more complex
games. Lately, to tackle the problem, many researchers have utilized approaches inspired by the Darwinian
theory of biological evolution. The paper presents an overview of optimization techniques and their use in
game development, and proposes a method for the computer opponent in the game of darts. Using the proposed
computer opponent, the effect of different difficulty levels on its performance is shown.
Keywords: Evolutionary Algorithms, Genetic Algorithms, Swarm Intelligence, Computer game of darts, Unity
game engine
Implementacija raˇ cunalniˇ skega nasprotnika v
arkadni raˇ cunalniˇ ski igri pikado po vzoru
algoritmov iz narave
Pribliˇ zno tri milijarde ljudi po vsem svetu igra video
igre, zato lahko industrijo video iger umestimo med
sestavne dele sodobnega ˇ zivljenja. Toda takˇ sen izkazani
interes od razvijalcev iger zahteva, da zagotavljajo vedno
zapletenejˇ se igre. V zadnjem ˇ casu so mnogi razisko-
valci za reˇ sevanje tega problema uporabili pristope, ki
jih je navdihnila Darwinova teorija bioloˇ ske evolucije.
Poslediˇ cno je v ˇ clanku najprej predstavljen pregled
optimizacijskih tehnik in njihova uporaba pri razvoju
iger. Sledi predstavitev predlagane metode za razvoj
raˇ cunalniˇ skega nasprotnika pri igri pikada in prikaz tega,
kako uporaba razliˇ cnih teˇ zavnostnih stopenj vpliva na
njegovo delovanje.
1 INTRODUCTION
In the latest report by Newzoo [1], the leader in video
games and gamer data, it is shown that some three billion
people worldwide play video games. That means that
some 37% of the world population consists of gamers.
Consequently, along with the positive growth trend, we
can undoubtedly say that the video games industry is an
integral part of modern life.
With the increasing complexity of the game develop-
ment, and, consequently, games themselves, researchers
and developers started to utilize different Artificial In-
telligence techniques in game development. Because of
Received 19 December 2022
Accepted 10 February 2023
the immense amount of algorithms in this field, we will
limit ourselves only to those inspired by the Darwinian
theory of biological evolution [2]–[6].
The focus of our paper is on the use of evolutionary
approaches in computer games. The goal is to present
their functionality in developing an arcade computer
game of darts [7]. The main contributions of the paper
are:
• a novel method is proposed for the computer op-
ponent in the arcade computer game of darts;
• the effect of different difficulty levels of the pro-
posed computer opponent on its performance is
evaluated.
2 NATURE-INSPIRED ALGORITHMS IN
COMPUTER GAMES
Nature is our most valuable asset. It’s our first teacher
and continues to teach, surprise, and inspire us to this
day. It offers us a daily insight into its ecosystem,
which is precisely what inspires scientists worldwide to
create inventions that simplify and improve the lives of
humanity.
Solutions inspired by the nature behavior can be
seen in various engineering fields, such as Medicine,
Robotics, Software Engineering, and Machine Learn-
ing [8]–[12]. Lately, a concept inspired by nature has
also been introduced to the computer game development,
mainly through Evolutionary Algorithms (EAs).
The EAs dynamic follows the basic principle of
the Darwin theory of evolution [13]–[16]. The idea is
based on the concept that only the most successful or
fittest individuals from a population survive, while the

46 TOVORNIK, FISTER JR., PODGORELEC, BREZO
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CNIK
others are removed from the population. Therefore, only
the strong ones that adapt well to their environment
reproduce. EA uses three main operators, i.e., selection,
mutation, and crossover [9], [17]. The EAs subfields
include:
• Genetic Algorithms (GA),
• Genetic Programming (GP),
• Evolutionary Strategies (ES),
• Evolutionary Programming (EP), and
• Differential Evolution (DE).
The focus of the paper is on GA due to the concept of
operations that it offers.
3 GENETIC ALGORITHM
GAs are one of the most general approaches to solutions
optimization, as they provide the most straightforward
mapping from the natural process of evolution to a
computer system. GA is capable of finding solutions to
complex problems, and is, at the same time, relatively
easy to use. Therefore, it can be used for various
optimization problems [9].
The GA structure and operations follow the pseu-
docode in Algorithm 1.
Algorithm 1 Genetic Algorithm pseudocode.
1: Create a random population of individuals and name
it rand pop.
2: while termination condition not met do
3: Create a new population of individuals
new pop;
4: while new pop is empty do
5: Select two individuals from rand pop,
preferably those that have a greater prob-
ability of higher fitness function.
6: Cross these individuals to create a new
generation.
7: end while
8: Let each individual in new pop have a ran-
dom chance to mutate.
9: Replace rand pop with new pop.
10: end while
11: For a solution, select the individual with the
highest fitness function fromnew pop.
4 PROPOSED METHOD
The pseudocode presented in Algorithm 1 represents the
basis for developing a computer opponent. The main
character in the game of darts is the target. The computer
moves its target randomly across the playing area, i.e.,
the dartboard. If the target is positioned at good coor-
dinates for shooting arrows, it will give the computer
opponent higher points and a higher chance of winning.
Therefore, with each generation, the coordinates that
demonstrate the upgraded position of the target are
improved. In a certain way, those coordinates represent
the area limit of the target movement.
Therefore, the task of the proposed computer oppo-
nent is crosshair aiming. The current position of the
crosshair can be presented mathematically with Eq. 1
A = (x
1
,y
1
,z
1
) (1)
and can move (up, down, left, and right) in the
following manner:
f(x) =
   B = (0,y
2
, 0) if x = 0
B = (0,− y
2
, 0) if x = 3
B = (x
2
, 0, 0) if x = 2
B = (− x
2
, 0, 0) if x = 1
(2)
where:
B - movement of the crosshair.
The new position is then calculated as:
AB =(x
2
− x
1
,y
2
− y
1
, 0− z
1
)
|AB| =
p
(x
2
− x
1
)
2
, (y
2
− y
1
)
2
, (− z
1
)
2
(3)
With every round in the game (after the last shot of an
arrow), the computer-released arrows are collected and
saved in a directory. That represents our population of
individuals. Besides collecting arrows at the end of each
computer round, we also start running our GA algorithm.
First, we begin by carrying out the selection in GA. We
find the best arrow collected up from the directory. The
current best has the highest fitness function, or, in other
words, it is the arrow that carries the highest points.
After that, we crossover and mutate the fittest arrow with
each of the three currently released arrows to get a new
generation. More specifically, we crossover and mutate
the coordinates from the fittest arrow and the coordinates
from the presently shot arrows, in order to get a new
generation.
Algorithm 2 gives an overview of the implementa-
tion of GAs and shows how selection, crossover, and
mutation are used to create new generations. The new
generations give us the coordinates for the limits of the
computer target.
When creating a new generation, we assign it to a
random operation. Therefore, the crossing takes place
so that some coordinates from the released arrows are
preserved and some are changed. For example, the
x-coordinate of the released arrow is preserved, and
the y-coordinate of the fittest arrow replaces the y-
coordinate. A new generation is created in such manner.
Afterward, the new generation replaces the previous one

A NATURE-INSPIRED IMPLEMENTATION OF THE COMPUTER OPPONENT IN THE ARCADE COMPUTER GAME OF DARTS 47
and becomes our current generation to be used in the
game.
As a result, the current generation represents the re-
set limits that define new and upgraded coordinates of
limits for the computer target. In theory, the higher the
number of the new generations, the more accurate the
target is, and the closer the computer opponent can get to
scoring higher and higher points. So, the newly released
arrows will carry a higher fitness function value.
Algorithm 2 Genetic Algorithm used in the game of
darts.
1: Create a population that holds all the so far released
arrows and name it arrow pop.
2: Get a population of the currently released arrows
and name it curr pop.
3: Create a population of coordinates that represents
limits and name it curr limits.
4: Find the current highest points from thearrow pop
- the currently best-valued fitness function, and call
it the fittest.
5: while termination condition not met do
6: Cross the x and y coordinates of the arrows
from curr pop with the x and y coordinates
of the fittest so that a new generation is cre-
ated. Name the new generationnew limits;
7: Let each individual in curr pop have a
random chance to mutate.
8: Replace curr limits with new limits.
9: end while
10: Use population of new limits to achieve
better results for the movement of the target.
When approaching the end of the game, we reach a
situation where we can no longer rely only upon GA.
For example, if a computer opponent has only five points
to nullify, but it would be throwing at the maximum of
points, such as 60, or even 25 points, it would have little
to no chance of winning.
Therefore, we choose a different approach and de-
velop a hybrid algorithm combining GA concepts with
an Ant Colony Algorithm (ACO). The ACO technique
is a widely used metaheuristic based on Swarm Intelli-
gence [18].
Due to the possibility of a rapid reduction of the
current points that the computer opponent must nullify,
we execute a hybrid algorithm after each throw of an
arrow (not after the whole round). So, the updated
coordinates instruct the target precisely where to shoot
next in order to win. Thus, the game introduces a hybrid
algorithm after the computer opponent is left with sixty
or fewer points to nullify.
In the hybrid algorithm operation, the best results,
i.e. the released arrow with the most points, are no
longer important. Instead, the released arrows that carry
the closest points to the currently remaining points of
the computer opponent come to the forefront. Now, the
closest arrows carry the higher fitness function.
Algorithm 3 shows that, in each iteration, an arrow,
is selected with points that are equal to or smaller, but
the closest to the current computer points. Based on
the selected or the fittest arrow, itsx and y-coordinates
are used to create a new generation. Therefore, ACO
is included in the selecting part of the hybrid algorithm,
and GA is included in the crossover and mutation, which
are the same as in Algorithm 2.
Algorithm 3 Use of the Hybrid algorithm in the game
of darts.
1: Create a population that holds all the so far released
arrows and name it arrow pop.
2: Get a population of the currently released arrows
and name it curr pop.
3: Create a population of coordinates that represents
limits and name it curr limits.
4: Find the currently best valued fitness function of an
arrow from the arrow pop, which points are equal
or smaller, but the closest to the current points that
the computer opponent must nullify.
5: while termination condition not met do
6: Cross the x and y coordinates of the arrows
from curr pop with the x and y coordinates
of the fittest so that a new generation is cre-
ated. Name the new generationnew limits;
7: Let each individual in curr pop have a
random chance to mutate.
8: Replace curr limits with new limits.
9: end while
10: Use population of new limits to achieve
better results for the movement of the target.
To make the game more interesting we make the
computer opponent smarter in order to challenge the
player. To accomplish this, we introduce three difficulty
levels or game modes, e.g., easy, normal, and hard. The
player can choose the preferred game mode in the game
menu, as shown in Figure 1.
The development and operation mentioned above rep-
resent an easy mode. The main difference between the
easy and normal modes is in the directory. In addition
to collecting the computer arrows, the normal mode also
collects the player arrows. In theory, such circumstances
give the computer the ability to learn faster.
Nonetheless, our goal is to develop a hard mode
that would be able to make the computer opponent
learn fastest. Therefore, the hard mode contains all the
attributes from the previously mentioned modes. Addi-
tionally, the hard mode also follows the direction arrow
developed to make the game of darts more challenging
to play. The direction arrow rotates its position on the

48 TOVORNIK, FISTER JR., PODGORELEC, BREZO
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CNIK
y-coordinate constantly. When the arrow of the player or
the computer opponent is released, the current position
of the direction arrow is added to the y-coordinate of
the released arrow. So, players must pay extra attention
to it. That is why the hard mode tracks the direction
arrow current position carefully and fires arrows when
the condition is the most suitable.
The easy and normal modes do not consider the
direction arrow rotating position. Because of that, the
two game modes are more likely to miss the desired
points their target is leading them to. In general, this
means that the hard mode should be more precise and
narrow regarding firing its arrows than the other two
game modes.
5 RESULTS
The game of darts is implemented using the Unity game
engine [19] and written in the C# programming lan-
guage. The Blender tool [20] is used to render all objects
of the game, i.e., dartboard, arrows, and scoreboard.
For the experiment, twenty measures are taken at
each difficulty level. Though the differences between
difficulty levels are minor, different results are obtained.
For a better presentation of the played games at all
levels, their average performance is shown in Figure 2.
The graph shows that the average game in the hard game
mode is the most successful.
Based on the results, the average number is calculated
of the newly created generations needed to finish the
game in a particular game mode. The average number
of the generations needed for the:
• easy mode is 40;
• normal mode is 29, and
• hard mode is only 26.
The results confirm that the computer opponent in
the hard mode learns the fastest. The easy and normal
modes are left to chance at times resulting in the so-
called anomalies due to ignoring the direction arrow.
Occasionally, this coincidence leads them either to very
good or very bad results.
Undoubtedly, incorporating the player data of released
arrows in the collected-arrows directory gives the normal
and hard modes a significant advantage over the easy
mode.
Figure 3 shows the differences between the game
difficulty levels. The games played in each game mode
and the number of newly created generations needed to
win the game are shown. Their results are given in four
intervals displaying the number of created generations.
The results show how many times each result is higher
or lower than the set intervals.
Therefore, we can see that the easy mode dominates
the intervals where the results are higher than the fifty
and thirty new generations that are required to win. The
Figure 1. Entry menu of the game of darts. Three images are
displayed. They show (from top to bottom) the easy game
mode (green color of the toggle switch), the normal game
mode (yellow color of the toggle switch), and the hard game
mode (red color of the toggle switch). The player can choose
either of the represented switches to be played by the computer
opponent.
easy difficulty level is represented by the yellow bars.
The hard mode, represented by the red bars, dominates
intervals that are lower than the fifty and thirty new
generations. This mode holds most of the results that
are closer to the game minimum (minimum number of
newly created generations).
Indeed, the minimum of this rate would decrease with
a larger number of experiments. However, these results
already give a very good presentation of the functioning
of individual difficulty levels.
The above experiments determine the necessary num-
ber of iterations (new generations) of self-adaptation

A NATURE-INSPIRED IMPLEMENTATION OF THE COMPUTER OPPONENT IN THE ARCADE COMPUTER GAME OF DARTS 49
Figure 2. Average game played in each game mode.
Figure 3. Interval representation of all results of the experi-
ments on the graph.
and show the improvement of the computer opponent
to win the game. The adjusting and upgrading is shown
in Figure 4.
6 CONCLUSION
This paper shows that it is irrelevant in which game
mode we play or have it played by the computer. Sooner
or later the computer opponent will win.
Using GA and ACO the computer opponent learns
independently and adapts successfully to its playing
ground.
There is still room for an improvement in the game of
darts. The conducted experiments reveal some possibil-
ities. One of the improvements can be a more accurate
releasing of arrows. A directory can be created to store
more precise coordinates of individual fields on the
dartboard to be used in a normal and hard game mode.
Thus, the normal mode would differ from the easy mode
in two ways, and the normal and hard mode would
improve the game further, as they would most likely
bring the computer opponents even better results.
Figure 4. The demonstration of playing with a computer op-
ponent in the hard game mode. The green frames in the figure
represent the computer opponent adjusting and upgrading the
coordinates to improve the limits for its target.
ACKNOWLEDGEMENT
The authors acknowledge the financial support by the
Slovenian Research Agency (Research Core Funding
No. P2-0057).
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Nina Tovornik received her B. Sc. degree from the Faculty of
Electrical Engineering and Computer Science of the University of
Maribor, Slovenia, in 2019, and her M. Sc. degree from the same
faculty in 2022. Her research interest is in intelligent game design.
Iztok Fister Jr. received his B.Sc., M.Sc., and Ph.D. degrees in
Computer Science from the University of Maribor, Slovenia. He is
currently an Assistant Professor at the University of Maribor. He has
published over 120 research papers in refereed journals, conferences,
and book chapters. His research interests include Data Mining, Per-
vasive Computing, Optimization, and Sports Science. He has acted as
a Program Committee member at some 30 international conferences
and is a member of the editorial boards of three international journals.
Vili Podgorelec is a professor of computer science at the University of
Maribor, Slovenia. His research interests include intelligent systems,
data analytics, computational intelligence, medical informatics, and
software engineering. He has been involved in many national and
international research projects, both scientific and industrial R&D
projects. He has worked as a visiting professor and/or researcher at
several universities around the world, including University of Osaka,
Japan; Federal University of Sao Paulo, Brazil; University of Nantes,
France; University of La Laguna, Spain; University of Madeira,
Portugal; University of Applied Sciences Sein¨ ajoko, Finland. He is an
author of over 70 peer-reviewed scientific journal papers, three books
and several book chapters. He has performed 15 invited talks at major
international conferences worldwide.
Lucija Brezoˇ cnik received her B.Sc. and M.Sc. degrees from the
Faculty of Electrical Engineering and Computer Science of the Uni-
versity of Maribor, Slovenia, in 2014 and 2016, respectively. She is a
teaching assistant and a Ph.D. candidate. She works on several projects
in the industry and is the author of journal papers, over 20 conference
papers, a book chapter, and is a reviewer for over 40 recognized
peer-review journals. Her research interests include machine learning,
computational intelligence, data science, swarm intelligence, software
engineering, and agile software development. She is a recipient of
several international and local awards and grants for her research
activities. She is also an IEEE Slovenia Vice-Chair.