Optimization techniques global minima

The multiple-minimum problem is a severe handicap of many large-scale optimization applications. The state of the art today is such that for reasonable small problems (30 variables or less) suitable algorithms exist for finding all local minima for linear and nonlinear functions. For larger problems, however, many trials are generally required to find local minima, and finding the global minimum cannot be ensured. These features have prompted research in conformational-search techniques independent of, or in combination with, minimization.26... 

An optimal control strategy for batch processes using particle swam optimisation (PSO) and stacked neural networks is presented in this paper. Stacked neural networks are used to improve model generalisation capability, as well as provide model prediction confidence bounds. In order to improve the reliability of the calculated optimal control policy, an additional term is introduced in the optimisation objective function to penalise wide model prediction confidence bounds. PSO can cope with multiple local minima and could generally find the global minimum. Application to a simulated fed-batch process demonstrates that the proposed technique is very effective. 

As noted earlier in chapter 1 of this book, simulated annealing is a powerful optimization technique that attempts to find a global minimum of a function using concepts borrowed from Statistical Mechanics. Although it was first described in its entirety by Kirkpatrick et al.(1983), significant portions of the method were described as early as 1953 by Metropolis et al. (1953). 

Recent advances in experimental techniques at the nanoscale and in high throughput experimentation (HTE) provide either information with unprecedented spatiotemporal resolution or massive data. Extraction of information from such data is also an optimization problem that is often referred to as reverse engineering. Here one bypasses the question of which are the actual kinetics giving rise to the experimental structures, i.e., how do these structures form and whether they are metastable or not, and simply focuses on determining these structures from data. Therefore, forward nonequilibrium KMC simulation is not carried out. Instead, MC is merely used as an efficient global minimum search (optimization) method [note that the term reverse MC (RMC) is also often employed] to determine structures consistent with experimental data. 

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