Index Information Algorithm with Local Tuning for Solving Multidimensional Global Optimization Problems with Multiextremal Constraints

Multidimensional optimization problems where the objective function and the constraints are multiextremal non-differentiable Lipschitz functions (with unknown Lipschitz constants) and the feasible region is a finite collection of robust nonconvex subregions are considered. Both the objective function and the constraints may be partially defined. To solve such problems an algorithm is proposed, that uses Peano space-filling curves and the index scheme to reduce the original problem to a H\"{o}lder one-dimensional one. Local tuning on the behaviour of the objective function and constraints is used during the work of the global optimization procedure in order to accelerate the search. The method neither uses penalty coefficients nor additional variables. Convergence conditions are established. Numerical experiments confirm the good performance of the technique.Comment: 29 pages, 5 figure

Freeze-drying modeling and monitoring using a new neuro-evolutive technique

This paper is focused on the design of a black-box model for the process of freeze-drying of pharmaceuticals. A new methodology based on a self-adaptive differential evolution scheme is combined with a back-propagation algorithm, as local search method, for the simultaneous structural and parametric optimization of the model represented by a neural network. Using the model of the freeze-drying process, both the temperature and the residual ice content in the product vs. time can be determine off-line, given the values of the operating conditions (the temperature of the heating shelf and the pressure in the drying chamber). This makes possible to understand if the maximum temperature allowed by the product is trespassed and when the sublimation drying is complete, thus providing a valuable tool for recipe design and optimization. Besides, the black box model can be applied to monitor the freeze-drying process: in this case, the measurement of product temperature is used as input variable of the neural network in order to provide in-line estimation of the state of the product (temperature and residual amount of ice). Various examples are presented and discussed, thus pointing out the strength of the too