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Designing a superstructure for parametric search for optimal search spaces in non-trivial optimization problems. (English) Zbl 1021.90027
Summary: We design a super genetic hybrid algorithm (SupprGHA), an integrated optimization system for simultaneous parametric search and nonlinear optimization. The parametric search machine is implemented as a genetic superstructure, producing tentative parameter vectors that control the ultimate optimization process. The family of parameter vectors evolves through ordinary genetic operators aimed at producing the best possible parametrization for the underlying optimization problem. In comparison to traditional genetic algorithms, the integrated superstructure involves a twofold ordering of the population of parameter vectors. The first sorting key is provided by the objective function of the optimization problem at issue. The second key is given by the total mesh time absorbed by the parametric setting. In consequence, SuperGHA is geared at solving an optimization problem, using the best feasible parametrization in terms of optimality and time absorbance. The algorithm combines features from classical nonlinear optimization methodology and evolutionary computation utilizing a powerful accelerator technique. The constrained problem can be cast into multiple representations, supporting the integration of different mathematical programming environments. We show by extensive Monte Carlo simulations that SuperGHA extracts suitable parameter vectors for fast solution of complicated nonlinear programming problems.

MSC:
90B40 Search theory
65C05 Monte Carlo methods
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