The paper discusses the complex, agent-oriented hierarchic memetic strategy (HMS) dedicated to solving inverse parametric problems. The strategy goes beyond the idea of two-phase global optimization algorithms. The global search performed by a tree of dependent demes is dynamically alternated with local, steepest descent searches. The strategy offers exceptionally low computational costs, mainly because the direct solver accuracy (performed by the hp-adaptive finite element method) is dynamically adjusted for each inverse search step. The computational cost is further decreased by the strategy employed for solution inter-processing and fitness deterioration. The HMS efficiency is compared with the results of a standard evolutionary technique, as well as with the multi-start strategy on benchmarks that exhibit typical inverse problems' difficulties. Finally, an HMS application to a real-life engineering problem leading to the identification of oil deposits by inverting magnetotelluric measurements is presented. The HMS applicability to the inversion of magnetotelluric data is also mathematically verified.

Abstract. The paper introduces a stochastic model for a class of population-based global optimization meta-heuristics, that generalizes existing models in the following ways. First of all, an individual becomes an active software agent characterized by the constant genotype and the meme that may change during the optimization process. Second, the model embraces the asynchronous processing of agent's actions. Third, we consider a vast variety of possible actions that include the conventional mixing operations (e.g. mutation, cloning, crossover) as well as migrations among demes and local optimization methods. Despite the fact that the model fits many popular algorithms and strategies (e.g. genetic algorithms with tournament selection) it is mainly devoted to study memetic algorithms.The model is composed of two parts: EMAS architecture (data structures and management strategies) allowing to define the space of states and the framework for stochastic agent actions and the stationary Markov chain described in terms of this architecture. The probability transition function has been obtained and the Markov kernels for sample actions have been computed.The obtained theoretical results are helpful for studying metaheuristics conforming to the EMAS architecture. The designed synchronization allows the safe, coarse-grained parallel implementation and its effective, sub-optimal scheduling in a distributed computer environment. The proved strong ergodicity of the finite state Markov chain results in the asymptotic stochastic guarantee of success, which in turn imposes the liveness of a studied metaheuristic. The Markov chain delivers the sampling measure at an arbitrary step of computations, which allows further asymptotic studies, e.g. on various kinds of the stochastic convergence.

No abstract

This paper focuses on the application of hp hierarchic genetic strategy (hp–HGS) for solution of a challenging problem, the inversion of 3D direct current (DC) resistivity logging measurements. The problem under consideration has been formulated as the global optimization one, for which the objective function (misfit between computed and reference data) exhibits multiple minima. In this paper, we consider the extension of the hp–HGS strategy, namely we couple the hp–HGS algorithm with a gradient based optimization method for a local search. Forward simulations are performed with a self-adaptive hp finite element method, hp–FEM. The computational cost of misfit evaluation by hp–FEM depends strongly on the assumed accuracy. This accuracy is adapted to the tree of populations generated by the hp–HGS algorithm, which makes the global phase significantly cheaper. Moreover, tree structure of demes as well as branch reduction and conditional sprouting mechanism reduces the number of expensive local searches up to the number of minima to be recognized. The common (direct and inverse) accuracy control, crucial for the hp–HGS efficiency, has been motivated by precise mathematical considerations. Numerical results demonstrate the suitability of the proposed method for the inversion of 3D DC resistivity logging measurements.

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.