This paper presents an innovative approach that combines optimization and simulation techniques for solving scheduling problems under uncertainty. We introduce an Opt–Sim closed-loop feedback framework (Opt–Sim) based on a sliding-window method, where a simulation model is used for evaluating the optimized solution with inherent uncertainties for scheduling activities. The specific problem tackled in this paper, refers to the airport capacity management under uncertainty, and the Opt–Sim framework is applied to a real case study (Paris Charles de Gaulle Airport, France). Different implementations of the Opt–Sim framework were tested based on: parameters for driving the Opt–Sim algorithmic framework and parameters for riving the optimization search algorithm. Results show that, by applying the Opt–Sim framework, potential aircraft conflicts could be reduced up to 57% over the non-optimized scenario. The proposed optimization framework is general enough so that different optimization resolution methods and simulation paradigms can be implemented for solving scheduling problems in several other fields.
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We present a simple analytical formalism based on the Lorentz-Scherrer equation and Bernoulli statistics for estimating the fraction of crystallites (and the associated uncertainty parameters) contributing to all finite Bragg peaks of a typical powder pattern obtained from a static polycrystalline sample. We test and validate this formalism using numerical simulations, and show that they can be applied to experiments using monochromatic or polychromatic (pink-beam) radiation. Our results show that enhancing the sampling efficiency of a given powder diffraction experiment for such samples requires optimizing the sum of the multiplicities of reflections included in the pattern along with the wavelength used in acquiring the pattern. Utilizing these equations in planning powder diffraction experiments for sampling efficiency is also discussed.
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