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.

Understanding measure-driven algorithms solving irreversibly ill-conditioned problems

“…The broad review of stochastic, population-based methods of solving global optimization problems in continuous domains involving multiple local minimizers is reported in Pardalos and Romeijn handbook [36], while the population-based methods dedicated to the ill-conditioned multimodal global optimization problems was discusses in the Preuss book [39]. The information about some specialized strategies (HGS, HMS, CGS and EMAS) can be found in our former papers [4,6,13,17,47,50,53,[55][56][57]64].…”

“…The HMS is a complex stochastic strategy consisting of a multi-deme evolutionary algorithm and other accuracyboosting, time-saving and knowledge-extracting techniques, such as gradient-based local optimization methods, dynamic accuracy adjustment, sample clustering and additional evolutionary components equipped with a MWS operator aimed at the discovery of insensitivity regions in the objective function landscape (see e.g. [47,57] and the references therein).…”

Using Covariance Matrix Adaptation Evolutionary Strategy to boost the search accuracy in hierarchic memetic computations

“…Additionally, it is equipped with a multiwinner selection operator for the objective plateau discovery, cf. [17,21,22]. In this paper, we focus on the evolutionary core of HMS that was its straightforward predecessor and has been developed under its own name, i.e., Hierarchic Genetic Strategy (HGS), cf.…”

“…• EA equipped with the multi-winner selection [21] and the local objective approximation [22], if the insensitivity regions have to be determined.…”

“…The final solutions to the whole strategy are then discovered by the leaf demes. For the full description of the HGS and the HMS we refer the reader to papers [23,24,17,21,25,22].…”