Dynamic Optimization of Xylitol Production Using Legendre-Based Control Parameterization

This paper presents an improved methodology for optimizing the fed-batch fermentation process of xylitol production, aiming to maximize the final concentration in a bioreactor co-fed with xylose and glucose. Xylitol is a valuable sugar alcohol widely used in the food and pharmaceutical industries, and its microbial production requires precise control over substrate feeding strategies. The proposed technique employs Legendre polynomials to parameterize two control actions (the feeding rates of glucose and xylose), and it uses a hybrid optimization algorithm combining Monte Carlo sampling with genetic algorithms for coefficient selection. Unlike traditional optimization approaches based on piecewise parameterization, which produce discontinuous control profiles and require post-processing, this method generates smooth profiles directly applicable to real systems. Additionally, it significantly reduces mathematical complexity compared to strategies that combine Fourier series with orthonormal polynomials while maintaining similar optimization results. The methodology achieves good results in xylitol production using only eight parameters, compared to at least twenty in other approaches. This dimensionality reduction improves the robustness of the optimization by decreasing the likelihood of convergence to local optima while also reducing the computational cost and enhancing feasibility for implementation. The results highlight the potential of this strategy as a practical and efficient tool for optimizing nonlinear multivariable bioprocesses.