## Abstract

Purpose

– The paper aims to present a new methodology for hybrid genetic algorithms (GA) in the solution of electromagnetic optimization problems.

Design/methodology/approach

– This methodology can be seen as a local search operator which uses local quadratic approximations for each objective and constraint function in the problem. In the local search phase, these approximations define an associated local search problem that is efficiently solved using a formulation based on linear matrix inequalities.

Findings

– The paper illustrates the proposed methodology comparing the performance of the hybrid GA against the basic GA in two analytical problems and in the well‐known TEAM benchmark Problem 22. For the analytical problems, 30 independent runs for each algorithm were considered whereas for Problem 22, ten independent runs for each algorithm were taken.

Research limitations/implications

– For the analytical problems, the hybrid GA enhanced both the convergence speed, in terms of the number of function evaluations, and the accuracy of the final result. For Problem 22, the hybrid GA was able to reach a better solution, with a better value of the standard deviation with less CPU time.

Practical implications

– The paper could be useful both for device designers and researchers involved optimization in computational electromagnetics.

Originality/value

– The hybrid GA proposed enhanced the convergence speed, in terms of the number of function evaluations, representing a faster and robust algorithm for practical optimization problems.

– The paper aims to present a new methodology for hybrid genetic algorithms (GA) in the solution of electromagnetic optimization problems.

Design/methodology/approach

– This methodology can be seen as a local search operator which uses local quadratic approximations for each objective and constraint function in the problem. In the local search phase, these approximations define an associated local search problem that is efficiently solved using a formulation based on linear matrix inequalities.

Findings

– The paper illustrates the proposed methodology comparing the performance of the hybrid GA against the basic GA in two analytical problems and in the well‐known TEAM benchmark Problem 22. For the analytical problems, 30 independent runs for each algorithm were considered whereas for Problem 22, ten independent runs for each algorithm were taken.

Research limitations/implications

– For the analytical problems, the hybrid GA enhanced both the convergence speed, in terms of the number of function evaluations, and the accuracy of the final result. For Problem 22, the hybrid GA was able to reach a better solution, with a better value of the standard deviation with less CPU time.

Practical implications

– The paper could be useful both for device designers and researchers involved optimization in computational electromagnetics.

Originality/value

– The hybrid GA proposed enhanced the convergence speed, in terms of the number of function evaluations, representing a faster and robust algorithm for practical optimization problems.

Original language | English |
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Pages (from-to) | 773-787 |

Number of pages | 15 |

Journal | COMPEL - The international journal for computation and mathematics in electrical and electronic engineering |

DOIs | |

Publication status | Published - 2007 |

## Keywords

- algorithmic languages
- approximation theory
- optimization techniques
- electromagnetism