Approximating landscape insensitivity regions in solving ill-conditioned inverse problems

Abstract

Solving ill-posed continuous, global optimization problems is challenging. No well-established methods are available to handle the objective intensity that appears when studying the inversion of non-invasive tumor tissue diagnosis or geophysical applications. The paper presents a complex metaheuristic method that identifies regions of objective function’s insensitivity (plateaus). It is composed of a multi-deme hierarchic memetic strategy coupled with random sample clustering, cluster integration, and a special kind of local evolution processes using the multiwinner selection that allows to breed the demes to cover each plateau separately. The final phase consists in a smooth local objective approximation which determines the shape of the plateaus by analyzing the objective level sets. We test the method on benchmarks with multiple non-convex plateaus and in an actual geophysical application of magnetotelluric data inversion.