# Procedural Video Game Scene Generation by Genetic and Neutrosophic WASPAS Algorithms

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## Abstract

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## 1. Introduction

## 2. Related Work

## 3. Scene Layout Modeling and Optimization Algorithm

#### 3.1. Game Scene Encoding Modeling

- Player (number 0)—represents the starting position of the subject, which is intended to play the game;
- Exit (number 1)—marks the location that the player should reach to finish the game;
- Empty space (number 2)—traversable and empty space, which can be used to navigate by the player;
- Wall (number 3)—object that blocks player navigation;
- Hazzard or enemy (number 4)—a traversable object, which is dangerous for the player;
- Collectible (number 5)—a desirable object that can be collected by the player;
- Ground—this object is not encoded in the chromosome matrix but is used during the 3D projection visualization step as a floor layer.

#### 3.2. Game Scene Procedural Generation Criteria List

- Symmetry calculation for aesthetic purposes. The chromosome grid is crossed with a horizontal and vertical slice to form 4 smaller 5 × 5 grids. Each object is checked to determine if it has an identical vertically and horizontally symmetrically matching object (Figure 2 and Figure 3) in the 5 × 5 grid. The final results are calculated by dividing the symmetrical matches by the maximal possible matches (each object has two matching objects with touching 5 × 5 grids) (1). x and y represent the size of the grid, s is a binary value, the value of which is 0 if the object does not have a matching pair. Each object is measured twice for each axis.

- Balance criteria for aesthetic purposes. Calculate how close to 50% is the ratio between empty game object count and total object count (Figure 4).

- Distance between player and exit game objects. x and y represent the coordinates of the player and exit (4). This rule makes sure that the player can see as much of the generated scene as possible while traveling to the exit point;

- The safe zone criteria calculate the amount of Hazzard-type objects in a defined square around the Player and divide the result by the total area of this square (5).

- Scan the chromosome grid and check if Player object exists;
- Scan chromosome grid and check if an exit object exists;
- Pathfinding algorithm to check if there is a passable way between Player and Exit.

#### 3.3. Application of WASPAS-SVNS in Genetic Algorithm

- Combining criteria evaluation data into matrix $X$ where one dimension represents the index of a chromosome, and another dimension represents the index of the criteria (6);$$X=\left[\begin{array}{cccc}{x}_{11}& {x}_{12}& \cdots & {x}_{1n}\\ {x}_{21}& {x}_{22}& \cdots & {x}_{2n}\\ \vdots & \vdots & \ddots & \vdots \\ {x}_{m1}& {x}_{m2}& \cdots & {x}_{mn}\end{array}\right]$$
- The original algorithm normalizes the data here, inside the WASPAS-SVNS algorithm, but for the iterative process it does not work because the local min–max and global min–max values are not the same, so we need to define boundaries before this step [33]. Normalization is made in the criteria functions to fit in the range of 0 to 1 (7). $v$ represents current criteria value and ${v}_{max}$ is the highest possible value for that criterion for the selected matrix size. ${\tilde{x}}_{ij}$ is a normalized index ij criteria value of matrix $X$;$${\tilde{x}}_{ij}=\frac{v}{{v}_{max}}$$
- Neutrosophication step. In this step, we convert results from our normalized criteria function results into neutrosophic sets. The neutrosophic set consists of three numbers: truth (t), intermediary (i), and falsehood (f). For this, we map criteria results with neutrosophic numbers, but we do a linear conversion as even the slightest non-proportional shifts can make a huge error in the long evolutionary run. N represents a neutrosophic number and S represents a scalar number (8);$$N\left(t,i,f\right)=\{\begin{array}{c}S\\ 1-S\\ 1-S\end{array}$$
- Sum of the total relative importance of the alternative (single evolutionary iteration chromosome);
- Total relative importance of the product of the alternative;
- A joint generalized criterion for the ranking alternatives (step 4 and step 5) (9);$${\tilde{Q}}_{i}=0.5{\tilde{Q}}_{i}^{\left(1\right)}+0.5{\tilde{Q}}_{i}^{\left(2\right)}$$
- Neutrosophic numbers (truth, intermediacy, and falsehood) are converted to scalar numbers using this formula and then used for chromosome evaluation in the genetic algorithm (10);$$S\left({\tilde{Q}}_{i}\right)=\frac{3+{t}_{i}-2{i}_{i}-{f}_{i}}{4}$$

#### 3.4. Proposed Extension of Genetic Algorithm

Algorithm 1. Genetic algorithm. |

InitializeRandomPopulation: DoFullEvolution: for amountOfEvolutionCycles CalculateAllCriteria for populationSizeValidation PlayerExists ExitExists PathBetweenPlayer-ExitExists Symetry EmptySpaceBalance Player-ExitDistance SafeZone FindUnderperformersAndPerformers for populationSize calculateFitnessWASPAS-SVNS EvolveUnderperformersWithGeneticAlgorithm DrawGrid(best fitness): |

## 4. Results

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

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**Figure 14.**Symmetry and empty space balance. The numbers ‘1’ and ‘2’ represent the corresponding symmetrical objects. ‘50%’ represents the balance between the number of objects and the empty space.

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Petrovas, A.; Bausys, R.
Procedural Video Game Scene Generation by Genetic and Neutrosophic WASPAS Algorithms. *Appl. Sci.* **2022**, *12*, 772.
https://doi.org/10.3390/app12020772

**AMA Style**

Petrovas A, Bausys R.
Procedural Video Game Scene Generation by Genetic and Neutrosophic WASPAS Algorithms. *Applied Sciences*. 2022; 12(2):772.
https://doi.org/10.3390/app12020772

**Chicago/Turabian Style**

Petrovas, Aurimas, and Romualdas Bausys.
2022. "Procedural Video Game Scene Generation by Genetic and Neutrosophic WASPAS Algorithms" *Applied Sciences* 12, no. 2: 772.
https://doi.org/10.3390/app12020772