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A QC procedure is considered to be optimum when it minimizes (or maximizes) a context specific objective function. The objective function depends on the probabilities for error detection and for false rejection. The probabilities for error detection and for false rejection depend on the parameters of the QC procedure (1) and on the probability density function of the error in the process.
In general, we can not use algebraic methods to optimize the QC procedures. Usage of enumerative methods would be very tedious, especially with multi-rule procedures, as the number of the points of the parameter space to be searched grows exponentially with the number of the parameters to be optimized. Optimization methods based on the genetic algorithms (GAs) offer an appealing alternative as they are robust search algorithms, that do not require knowledge of the objective function and search through large spaces quickly. GAs have been derived from the processes of the molecular biology of the gene and the evolution of life. Their operators, cross-over, mutation, and reproduction, are isomorphic with the synonymous biological processes. GAs have been used to solve a variety of complex optimization problems. Furthermore, the complexity of the design process of novel QC procedures is obviously greater than the complexity of the optimization of predefined ones. The classifier systems and the genetic programming paradigm have shown us that GAs can be used for tasks as complex as the program induction.
In fact, since 1993, GAs have been successfully used to optimize and to design novel QC procedures, as it is described in (
--Aristides T. Hatjimihail, MD, PhD, ath@hcsl.com
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