hp-HGS strategy for inverse 3D DC resistivity logging measurement simulations

In this paper we present a twin adaptive strategy hp-HGS for solving inverse problems related to 3D DC borehole resistivity measurement simulations. The term "simulation of measurements" is widely used by the geophysical community. A quantity of interest, voltage, is measured at a receiver electrode located in the logging instrument. We use the self-adaptive goal-oriented hp-Finite Element Method (hp-FEM) computer simulations of the process of measurements in deviated wells (when the angle between the borehole and formation layers are < 90 deg). We also employ the hierarchical genetic search (HGS) algorithm to solve the inverse problem. Each individual in the population represents a single configuration of the formation layers. The evaluation of the individual is performed by solving the direct problem by means of the hp-FEM algorithm and by comparison with measured logging curve. We conclude the paper with some discussion on the parallelization of the algorithm. © 2012 Published by Elsevier Ltd

A hybrid method for inversion of 3D DC resistivity logging measurements

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

Multi-objective hierarchic memetic solver for inverse parametric problems

We propose a multi-objective approach for solving challenging inverse parametric problems. The objectives are misfits for several physical descriptions of a phenomenon under consideration, whereas their domain is a common set of admissible parameters. The resulting Pareto set, or parameters close to it, constitute various alternatives of minimizing individual misfits. A special type of selection applied to the memetic solution of the multi-objective problem narrows the set of alternatives to the ones that are sufficiently coherent. The proposed strategy is exemplified by solving a real-world engineering problem consisting of the magnetotelluric measurement inversion that leads to identification of oil deposits located about 3 km under the Earth's surface, where two misfit functions are related to distinct frequencies of the electric and magnetic waves

A multi-objective memetic inverse solver reinforced by local optimization methods

We propose a new memetic strategy that can solve the multi-physics, complex inverse problems, formulated as the multi-objective optimization ones, in which objectives are misfits between the measured and simulated states of various governing processes. The multi-deme structure of the strategy allows for both, intensive, relatively cheap exploration with a moderate accuracy and more accurate search many regions of Pareto set in parallel. The special type of selection operator prefers the coherent alternative solutions, eliminating artifacts appearing in the particular processes. The additional accuracy increment is obtained by the parallel convex searches applied to the local scalarizations of the misfit vector. The strategy is dedicated for solving ill-conditioned problems, for which inverting the single physical process can lead to the ambiguous results. The skill of the selection in artifact elimination is shown on the benchmark problem, while the whole strategy was applied for identification of oil deposits, where the misfits are related to various frequencies of the magnetic and electric waves of the magnetotelluric measurement

Recognizing Sets in Evolutionary Multiobjective Optimization

Among Evolutionary Multiobjective Optimization Algorithms (EMOA) there are many which find only Paretooptimal solutions. These may not be enough in case of multimodal problems and non-connected Pareto fronts, where more information about the shape of the landscape is required. We propose a Multiobjective Clustered Evolutionary Strategy (MCES) which combines a hierarchic genetic algorithm consisting of multiple populations with EMOA rank selection. In the next stage, the genetic sample is clustered to recognize regions with high density of individuals. These regions are occupied by solutions from the neighborhood of the Pareto set. We discuss genetic algorithms with heuristic and the concept of well-tuning which allows for theoretical verification of the presented strategy. Numerical results begin with one example of clustering in a single-objective benchmark problem. Afterwards, we give an illustration of the EMOA rank selection in a simple two-criteria minimization problem and provide results of the simulation of MCES for multimodal, multi-connected example. The strategy copes with multimodal problems without losing local solutions and gives better insight into the shape of the evolutionary landscape. What is more, the stability of solutions in MCES may be analyzed analytically

Memetic Algorithms for Business Analytics and Data Science: A Brief Survey

This chapter reviews applications of Memetic Algorithms in the areas of business analytics and data science. This approach originates from the need to address optimization problems that involve combinatorial search processes. Some of these problems were from the area of operations research, management science, artificial intelligence and machine learning. The methodology has developed considerably since its beginnings and now is being applied to a large number of problem domains. This work gives a historical timeline of events to explain the current developments and, as a survey, gives emphasis to the large number of applications in business and consumer analytics that were published between January 2014 and May 2018