A hybrid algorithm using genetic algorithm and gradient-based algorithm for iterative microwave inverse scattering

Abstract

In this paper, we present a hybrid of genetic and gradient-based algorilhms, which eflciently find the global optimum without getting stuck at local minima, for iterative microwave inverse scattering(lM1S). It utilizes the global convergence of genetic algorithm(GA) and fine local tunability of gradient-based algorithm through alternation so as to $nd optimum or near-optimum in reasonable computation time. We also propose a new crossover, or 2N-parent parameter-wise crossover(N is the number of parameter) so that GA gives a faster convergence. Experimental results show that the hybrid algorithm can provide better performance eficiently. In the microwave inverse scattering, diffraction topography with the Born approximation gives an efficient reconstruction of a weak scatterer and inversion scheme with the moment method[7] in the reverse sequence may be used for a stsong scatterer[3]. Duect moment method inversion, however, suffers from the ill-posedness in the sense that a small error or noise in the measured scattered fields occurs a large error in the reconstructed profde when the total number of cells of the scatterer is larger than that of the effective propagating modes. To use the number of effective propagating modes equal to or larger than that of the cells, one may use the iterative method with the multiple incident plane waves for microwave inverse scattering of a strong scatterer[6]. An IMIS becomes a parameter optimization problem where the cost function is defined as the sum of the squared magnitudes of the difference between the measured and the calculated scattered fields from the assumed set of dielectric profile by the moment method with the multiple incidences. IMIS using the Levenberg-Marquardt Algorithm(LMA) which is one of the gradient-based Optimization algorithms gives rather limited success in the reconstruction of the large scatterer because it converges to the dielectric profile conespading to the local minimum of the cost function and has initial assumed profile dependency[6]. GA[2], a stochastic optimization algorithm having easy hybridization capability can be a candidate to overcome such local minima problem. However, GA inherently takes a long time to converge because of lack of fine local tunability although it has the advantage of not getting stuck in local minimaE83. Therefore, a hybrid search algorithm utilizing respective advantages of GA and LMA may thus be very useful when landscape on parameter space is very complex like MIS. In the hybrid algorithm, LMA can be used as the fie tuning method with GA used to escape from local minima. Additionally a new crossover, 2N-parent parameter-wise crossover(N iequals the number of parameter), is also proposed so as to increase convergence rate of GA, which eventually can reduce the total computation time. This paper describes the development of such hybrid algorithm, and examines its performance on several IMIS test problems.