# Pareto-Optimized AVQI Assessment of Dysphonia: A Clinical Trial Using Various Smartphones
## 3 Materials and Methods
### Calculating Required Voice Characteristics
5:Identify the Pareto optimal solutions on the Pareto front using visual inspection, clustering, or optimization algorithms, such as NSGA-II. 6:Select the Pareto optimal solution that best meets the specific needs and preferences of the AVQI assessment, considering factors such as clinical relevance, patient preference, and ease of implementation. 7:Evaluate the performance of the AVQI algorithm using validation data and feedback from clinicians and patients. 8:Fine-tune the AVQI algorithm and the Pareto optimization parameters based on the validation results and feedback. ```  
**Algorithm 7** AVQI calculation. Pareto Optimized Assessment of Impaired Voice  
Pareto optimization is a technique used to identify the optimal trade-off between multiple conflicting objectives. Let \(X\) be the set of candidate solutions, where each solution \(x\in X\) is a vector of \(n\) characteristics of voice quality, such as overall voice quality, strain, and pitch. Let \(f(x)=(f_{1}(x),f_{2}(x),\dots,f_{m}(x))\) be a vector of \(m\) objective functions that measure the performance of \(x\) in each characteristic. The Pareto front is defined as the set of nondominated solutions, i.e., those solutions that cannot be improved in any objective without worsening at least one other objective. Formally, a solution \(x_{1}\) dominates another solution \(x_{2}\) if and only if \(f_{1}(x_{1})\leq f_{1}(x_{2})\), \(f_{2}(x_{1})\leq f_{2}(x_{2})\) and \(f_{m}(x_{1})\leq f_{m}(x_{2})\) and there exists at least one objective function \(f_{j}\) such that \(f_{j}(x_{1})<f_{j}(x_{2})\). The Pareto front is the set of all nondominated solutions, i.e., \(P=\{x\in X|\forall x^{\prime}\in X,x^{\prime}\) is not dominated by \(x\}\). The Pareto optimal solution is any solution \(x^{*}\in P\) that maximizes the trade-off between the objectives, i.e., \(\forall x\in P,f(x^{*})\leq f(x)\), where \(\leq\) denotes Pareto dominance. In the context of the evaluation of impaired voice by AVQI recorded on the smartphone, Pareto optimization is used to find the best trade-off between different parameters that affect overall vocal quality, such as breathiness, roughness, strain, and pitch. The first step in Pareto optimization is to define the objectives or criteria that need to be optimized. In the case of the AVQI assessment, the objective could be to maximize overall vocal quality while minimizing breathiness, roughness, and strain. Pitch could be considered a separate objective, depending on the specific voice impairment being assessed. The next step is to generate a set of candidate solutions that represent different combinations of objectives. This is done by varying the weights or importance assigned to each objective in the AVQI algorithm. For example, increasing the weight of the overall vocal quality objective would result in a higher score for samples with better overall quality, while decreasing the weight of the breathiness objective would result in a lower score for samples with more breathiness. Once the candidate solutions are generated, Pareto optimization techniques are used to identify the optimal trade-off between the objectives as follows. Step 1: Calculate the AVQI scores for each candidate solution based on the relevant parameters. To calculate the AVQI score, we need to first define the relevant parameters that affect voice quality. These could include measures of pitch, loudness, jitter, shimmer, harmonics-to-noise ratio, and other relevant acoustic and perceptual measures. Once the parameters are defined, we can use a combination of objective and subjective methods to calculate the AVQI score. Objective methods use signal processing and machine learning techniques to analyze the acoustic properties of the voice signal and extract relevant features. These features are then combined using a mathematical model to calculate the AVQI score. Examples of objective methods include Praat software, which measures various voice parameters, and the glottal inverse filtering (GIF) method, which estimates the glottal source waveform from the speech signal.