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ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES

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ANALYSIS AND OPTIMIZATION OF DENSE GAS FLOWS: APPLICATION TO ORGANIC RANKINE CYCLES TURBINES ( analysis-and-optimization-dense-gas-flows-application-to-org )

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3. Optimization tool 3.1. Genetic Algorithms Genetic algorithms have been successfully applied for some time now to shape optimization in aeronautics [73][74][75][76]; in spite of their cost, they have proved their interest with respect to gradient-based methods because of their high flexibility (stemming from the fact they only require values of the objective function(s) to efficiently explore the parameters space in search of an optimum), and also because of their ability to find global optima of multi-modal problems. Moreover, so-called Pareto-type genetic algorithms are of particular interest for multi-objective optimization since they provide, after only a few generations, a set of non-dominated solutions. On the contrary, a conventional gradient- based method needs several independent runs to achieve similar results [76][77]. The MOGA (Multi-objective Genetic Algorithm) is also well suited to the solution of multi- objective problems, such as multi-point performance improvement for a lifting airfoil. The MOGA applied in this study is the Non-Dominated Sorting Algorithm (NGSA) proposed by Srinivas and Deb [78]. At a given generation number, all individuals in the population are ranked according to non-domination criteria that allow to take into account in a simultaneous way a set of objective functions. The set of individuals that dominate all the other members of the population without dominating each other is designated as front of rank 1; the set of dominant individuals in the population deprived from the members of rank 1 form the front of rank 2, and so forth until the whole population is classified into a series of dominance fronts. The individuals scattered along the front of rank 1 are assigned the same pseudo-fitness function, arbitrarily fixed to unity, since they are equally well- adapted and therefore should be given the same potential of reproduction. However, in order to favor the population diversity along the front, the pseudo-fitness value is decreased for individuals located in crowded areas of the front: practically, the initial uniform value of the pseudo-fitness function is divided by a number strictly larger than unity for individuals with neighbors within a prescribed distance. Next, the smallest value of the modified pseudo-fitness function obtained for individuals belonging to the front of rank 1 is decreased from a small number ε and assigned to all members of the front of rank 2; next this uniform value is then itself modified as previously explained in order to 41

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