Knowing every single component of a given biological sys- tem is not enough to understand the complexity of the system but rather it becomes crucial to understand how these com- ponents interact with each others. It is not only important the knowledge of genes and proteins, but also knowing their structures and primarily the laws and parameters governing their dynamics, which is often unknown and impossible to measure directly. The Gene Regulatory Networks explain ex- actly how a genomic sequence encodes the regulation of ex- pression of sets of genes, which progressively generate de- velopmental patterns, and execute the construction of multi- ple states of differentiation. Their main aim is to represent the regulation rules underlying the gene expression. In this work we have designed the CMA-ES algorithm to infer the parameters in the S-system model of a gene regulatory net- work. This model is a well-known mathematical framework whose structure is rich enough to capture many relevant bi- ological details, and it can model more complicated genetic network behaviour. CMA-ES has been compared against 7 state-of-the-art algorithms to evaluate its efficiency and its ro- bustness. From a general point of view, it seems clear how CMA-ES is able to estimate in a better way the target pa- rameters with respect to the state-of-the-art methods, either in terms of success rate or in terms of Euclidean distance. Fi- nally, this research paper includes a study on the convergence of CMA-ES through Time-To-Target plots, which are a way to characterize the running time of stochastic algorithms; and a global sensitivity analysis method, the Morris algorithm.
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