# Synthesis of Non-Linguistic Utterances for Sound Design Support Using a Genetic Algorithm
## 2 NLU Generation Using GA and Valence and Arousal Model
### Genetic Algorithm (GA) Methodology
This is followed by a dense fully connected layer containing 90 neurons and using the rectified linear activation function. Following this dense layer, a batch normalization layer and a dropout layer are included to reduce over-fitting. The same over-fitting precautions are added after the following dense layer containing 180 neurons and using a rectified linear activation function. Finally, a single output layer using a linear activation function is used to predict a continuous variable. Training loss is measured using mean squared error (MSE) and the Adam optimizer. The neural network was trained using 10-fold cross-validation and achieved an average mean absolute error (MAE) of 0.136 and an average correlation between predicted and actual rating values of 0.725. An MAE of 0.136 represents less than one rating point difference on the original 5-point rating scale used to rate the sounds for the training data. The correlation value when considered for the fold size of 3000/10 = 300 results in a \(p\)-value for significance of <0.00001. The training loss and validation loss decreased steadily, and minimal over-fitting was observed. The neural network is applied to the GA to automatically evaluate the fitness of individuals through successive generations. The GA starts with a population of randomly generated individuals. A population size of 400 is selected to ensure genetic variation. The fitness of the population of individuals is evaluated in a batch by the trained neural network. The GA then selects parents from the population based on the tournament selection method with a tournament size of 16, chosen to strike a balance between promoting fit individuals and maintaining some level of genetic diversity in the mating pools [26]. Once the mating pool is populated with parents equal to the population size, the parents are chosen at random to reproduce in pairs using the two-point crossover method followed by a mutation step which applies mutation according to a probability of  
\[\frac{1}{\text{genotype\_length}}\times 2 \tag{1}\]  
As shown by [27], higher rates of mutation (above 0.05) result in the search becoming too random, while a convention is also to use [28],  
\[\frac{1}{\text{genotype\_length}} \tag{2}\]  
which was multiplied by 2 to increase the chances of mutation while staying under 0.05. Once a new population is produced, it replaces the old population and the process repeats until convergence is reached, the fitness of successive populations stops improving or changing significantly, and a suitable amount of genetic diversity or sample space has been explored, at which point the GA is manually stopped. After the GA has finished, binary strings are used to generate and save MIDI files, which are converted to WAV files to be used as sounds. The sounds are input into the random forest model which was trained on 560 NLU sounds extracted from movies, TV shows, and video games [15], to obtain valence and arousal inferences. Audio features, openSMILE LLDs [29], are extracted from the sounds, and the data are used by the random forest model to infer the valence and arousal of the sounds. Finally, the valence and arousal inferences of the sounds used in the experiment are compared to the human ratings of valence and arousal of the same sounds.