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Checking the difficulty of
evolutionary-generated maps in a
N-Body inspired mobile game
C. López-Rodríguez, A.J. Fernández-Leiva,
R. Lara-Cabrera, A.M. Mora, P. García-Sánchez
The N-Body Problem
• In physics, it is the problem of
predicting the individual
motions of a group of celestial
objects interacting with each
other gravitationally.
2
plus.maths.org
Youtube: phuebu1
Wikipedia
Gravityvolve
Game
• Physics-based Android game.
• A kind of ‘space golf’
In order to complete a map, the player will
have to push the particle from its initial
position until it reaches the circumference's
position.
3
Search for “GravityVolve” in Google Play
4
Gravityvolve
Game
Search for “GravityVolve” in Google Play
5
Gravityvolve
Game
Search for “GravityVolve” in Google Play
6
Evolutionary
Procedural Content Generation
• A tool for generating maps automatically.
• Depending of the chosen difficulty.
• Based on an Evolutionary Algorithm.
7
Evolutionary
Procedural Content Generation
• Algorithms that autonomously and dynamically create content
(maps, items, characters, stories).
• A creative and time-saving tool.
• A way to do adaptive (to the player) games.
• Potentially infinite games.
• The generated content always fulfils certain restrictions.
8
Evolutionary
Procedural Content Generation
• An Evolutionary Algorithm is a metaheuristic inspired in
natural evolution.
• It a population-based method.
• Optimization algorithm.
9
Evolutionary
Procedural Content Generation
Wikipedia
i  population initialization
f(x)  evaluation of individuals
Se  selection mechanism
Cr  crossover operator
Mu  mutation operator
Re  replacement policy
10
Evolutionary
Procedural Content Generation
• Individual
• Steady-state EA.
• Binary Tournament selection.
• Specific Mutation operator (random increase/decrease of coordinates, mass or angle).
• Fitness: feasible distribution, solvable map.
11
Evolutionary
Procedural Content Generation
• Crossover operator
Parents
Offspring
12
Difficulty Evaluation
• We aim to evaluate the difficulty of the generated maps.
• The player will vote (EASY, MEDIUM, HARD) after completing a map.
• With and without the help line.
• Checking the correlation  validate the PCG algorithm.
13
Difficulty Evaluation
14
Difficulty Evaluation Experiment
• 30 players / 21 maps per player.
• With and without the help line (HL).
(after one week)
• 448 votes with help line.
• 210 votes without help line.
15
Difficulty Evaluation Experiment
Voted difficulties are mainly EASY Voted difficulties become harder
16
Difficulty Evaluation Experiment
Not well adjusted in some maps (voted EASY) Voted difficulties become harder, but still not good
17
Difficulty Evaluation Experiment
Not well adjusted in most of maps Voted difficulties become harder, but still not good
18
Difficulty Evaluation Experiment
HL makes the maps easier than expected HARD difficulty has not been well adjusted
19
Difficulty Evaluation Experiment
Maps with HARD and
MEDIUM difficulty
show higher error.
HL has a big impact
on the difficulty
perception.
Blue  EASY
Red  MEDIUM
Green  HARD
EASY = 1, MEDIUM = 2, HARD = 3
20
Conclusions
• Players tend to vote mainly EASY. Most of times using the
Help Line.
• Players normally vote easier difficulty that they have felt 
shame (compromise their own ability).
• Difficulty asignment must be ‘softered’ for MEDIUM and
HARD maps.
FUTURE WORK
• The difficulty assignment method must be improved to
better fit the players’ feeling.
Thanks!
(astronomic)
Questions?
Contact info:
╺ carlillo_lopez@hotmail.com
╺ afdez@lcc.uma.es
╺ raul.lara@upm.es
╺ amorag@ugr.es
╺ pablo.garciasanchez@uca.es
21
Template from
SlidesCarnival
GravityVolve Game for Android
https://play.google.com/store/apps/details?id=com.carlos.gravityvolve&hl=es

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Checking the difficulty of evolutionary-generated maps in a N-Body inspired mobile game (OLA2020)