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The analysis is focused on the identification of limit cycle flow oscillations in the TALL-3D facility main heater leg using a global optimum search tool GA-NPO to find a general region in the parameter space where oscillatory behavior is expected.
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Then, nonlinear process optimization, based on finite element simulation, was conducted to obtain the optimum multi-stage deep drawing process, using a global, as well as a local, optimum search algorithm.
This method can converge to a global optimum using only the objective evaluations.
This test shows that although we cannot guarantee a global optimum using the proposed genetic algorithm (or other such metaheuristic algorithms), the optimized solution is extremely good compared to the other solutions in the search space.
Moreover, a logarithmic cooling schedule is used to ensure convergence to a global optimum.
However, the NLP algorithm used by Sigma mathematically guarantee a global optimum solution for genome abundance estimation, due to the convexity of the objective function for the MLE.
Importantly, we proved the convexity of the objective function of the MLE so that Sigma can guarantee to attain a global optimum solution using interior point non-linear programming (NLP) provided in the Ipopt library (Wachter and Biegler, 2006).
Genetic algorithms are search based algorithms which have higher probability of finding a global optimum as they use potential solutions and probabilistic transition rules to create a set of new solutions.
However, most researchers have formulated integrated systems as a linear programming problem using linearized electric power/gas flow models to guarantee a global optimum solution.
The suggested automated model development worked well in our hands but must be used with caution in practice as the approach is not guaranteed to find a global optimum in model space.
Hence, a local optimum of a GP problem is also a global optimum, which can always be calculated efficiently using interior-point methods [29].
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