Paper: ICA model estimation using an optimized version of genetic algorithms (ICLR-2024)

Reviewer comment (Theory):
The justification and design principle of the proposed method is unclear. In addition, the reason for the performance improvement by the proposed method is also unclear.

Author response:
-	The design principle is to estimate the ICA model by optimizing the objective function through improved genetic algorithms in terms of the crossover stage of selected chromosomes to form offspring for the new generation. Improvement for GA is achieved in the crossover stage by determining the most suitable weights associated with the linear combination used for linear gene recombination method of selected chromosomes to produce new offspring, through a multilayer neural network (CMCNN algorithm).  
-	The justification is given by the computational advantages (no longer needing to apply the Lagrange multiplier method with the necessary derivatives and solving the multidimensional equation through Newton's or secant method) for determining the training rule that establishes weight vectors associated with discovering independent components.

Reviewer comment (Evaluation):
How is the computational cost of the proposed method for ICA optimization compared to other ICA algorithms?

Author response:
-	Traditional calculation costs of genetic algorithm are mitigated by using neural networks that determine improved values for linear recombination in the crossover stage, thus obtaining offspring with improved fitness function values estimating weight vectors associated with independent components.  
-	In general, the evolutionary algorithm improved by appropriate crossover regarding the offspring of the new generation and determining vectors associated with independent components has a faster convergence rate than standard methods based on Newton or secant numerical methods.

Reviewer comment (Reproducibility):
I cannot identify the role of the neural network in the proposed method. It would be better to clarify the detailed algorithm, including the input/output and training data of the neural network, and the advantages of using the neural network.

Author response:
-	The role of the neural network is to determine the optimal values for linear recombination of selected chromosomes in order to create a new generation. Using the neural network, we select the recombination weights and the most suitable chromosomes for crossover (the offspring have fitness function values from the genetic algorithm used greater than those of the best chromosomes from the previous generation).  

	The input data of the algorithm are the recorded mixed signals which are centered and whitened in the preprocessing stages. To determine each independent component, a weight vector Wi is used, which is determined by optimizing the objective function F(Wi) using an evolutionary method with genetic algorithms. The genetic algorithm used has as input prototypes of the weight vector Wi that will discover independent component i. In the evolution process, after selecting chromosomes to participate in creating offspring, in the crossover stage, a multilayer neural network algorithm is applied to weights corresponding to linear combinations used for crossing genes with real values of chromosomes. In the evolution process, the genetic algorithm after the selection of the chromosomes that will participate in the creation of offspring, in the crossover stage the multilayer neural network algorithm is applied regarding the weights corresponding to the linear combination used to cross the genes with real values of the selected chromosomes. The role of the neural network is to provide the most appropriate linear recombination weights of the genes of the selected chromosomes so that the descendants used in the genetic algorithm present improved performance of the fitness function compared to the representatives of the previous generation from the optimization genetic algorithm. The weight vectors finally obtained after optimizing the objective function with genetic algorithms are used to establish the independent components.