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of GA using binary encoding. An extension of the epistasis concept to real encoding has been proposed by Rochet in [59], but it has not found application in practice. An alternative measure of GA-hardness well suited for real encoding, is fitness distance correlation (FDC), introduced by Jones in [60]. FDC is a statistical correlation between the fitness of strings encoding a given shape and the distance of these strings to the nearest global optimum. In spite of these attempts, developing a general theory that explains the behavior of a GA and that is able to predict how it will perform on different problems remains extremely difficult. In [61] Naudts introduced a measure, called the site-wise optimization measure, which suffers less from a number of problems encountered with the two known measures (epistasis variance and fitness distance correlation). The measure is based on an algorithmically defined property of the fitness landscape. This effort does not lead to a successful GA-hardness measure, however. A second possible cause of GA- hardness is the fact that a GA sometimes has to traverse a large part of the search space before it can reach the optimum of a function. For this aspect in [62] and in [61] an approach based on the construction of so-called “long path” is proposed. One necessary component is the ability to create what it is called a controlled path: a fitness function which leads a GA through successive areas of the search space. For BZT-flow optimization problems, a marked sensitivity of GA convergence to the starting population and solution parameters such as flow Mach number and thermodynamic operating conditions has been observed [48][57]. In order to better understand this phenomenon, a systematic study of GA convergence for both perfect and dense gas flows at different operating conditions has been made by Cinnella&Congedo in [48] and in [57]. This study shows that the greatest convergence difficulties are encountered for optimization problems such that airfoil shapes close to the optimum generate flow-fields characterized by extremely weak shocks. This is particularly true for flows of BZT gases, whose peculiar property is to give rise to flow discontinuities much weaker than those characterizing perfect-gas flows. To reduce this difficulty to converge, a very efficient objective-function evaluation procedure based on Richardson extrapolation is proposed by Cinnella&Congedo in [57]. This procedure is explained in 3.3.2, and the main results will be presented in 4.5. 30PDF Image | ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES
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