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By Daniel P. Raymer
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Extra info for Enhancing Aircraft Conceptual Design Using Multidisciplinary Optimization
It is also useful for classes of problems with a large number of design variables, where traditional optimizers may simply be incapable of finding any usable solution. An advantage of Genetic and Evolutionary Algorithms is their ability to incorporate noncontinuous (discrete, or integer) variables such as number of engines in an optimization with continuous variables such as wing sweep. This is difficult to do with derivative-base optimization methods and generally has to be “faked” by what amounts to duplicate optimizations, one for each potential value of every discrete variable.
In the military terminology of the day such planning was known as “programming”, and since the equations were linearized, this became known as "Linear Programming" (not to be confused with computer programming, which didn’t exist at that time). A key aspect of linear programming is its ability to deal with constraint functions independent of the objective function. Linear programming has become widespread in its usage, especially for business decision making. The Kuhn-Tucker Theorem (Albert Tucker and Harold Kuhn) of 1950 is considered to have launched the modern field of nonlinear programming (although it was apparently defined twice previously, by William Karush in 1939 and by Fritz John in 1948).
For each step of the iteration, the number of system analyses required is at least one more than the number of design variables. Also, the difference between the “real world” and the linear assumption of the method requires that the solution found for each iteration be kept fairly close to the values of the parameters used in determining the slopes, which increases the number of steps required and introduces error. 2 Implicit Function Theorem The Implicit Function Theorem differentiates the various governing equations to obtain sensitivity equations.
Enhancing Aircraft Conceptual Design Using Multidisciplinary Optimization by Daniel P. Raymer