scholarly journals Lp-Norm Inversion of Gravity Data Using Adaptive Differential Evolution

2021 ◽  
Vol 11 (14) ◽  
pp. 6485
Author(s):  
Tao Song ◽  
Xing Hu ◽  
Wei Du ◽  
Lianzheng Cheng ◽  
Tiaojie Xiao ◽  
...  
Keyword(s):  
Differential Evolution ◽  
Density Distribution ◽  
Gravity Data ◽  
Physical Property ◽  
Gravity Anomalies ◽  
Property Distribution ◽  
Regularization Term ◽  
Lp Norm ◽  
De Algorithm ◽  
Mutation Strategy

As a popular population based heuristic evolutionary algorithm, differential evolution (DE) has been widely applied in various science and engineering problems. Similar to other global nonlinear algorithms, such as genetic algorithm, simulated annealing, particle swarm optimization, etc., the DE algorithm is mostly applied to resolve the parametric inverse problem, but has few applications in physical property inversion. According to our knowledge, this is the first time DE has been applied in obtaining the physical property distribution of gravity data due to causative sources embedded in the subsurface. In this work, the search direction of DE is guided by better vectors, enhancing the exploration efficiency of the mutation strategy. Besides, to reduce the over-stochastic of the DE algorithm, the perturbation directions in mutation operations are smoothed by using a weighted moving average smoothing technique, and the Lp-norm regularization term is implemented to sharpen the boundary of density distribution. Meanwhile, in the search process of DE, the effect of Lp-norm regularization term is controlled in an adaptive manner, which can always have an impact on the data misfit function. In the synthetic anomaly case, both noise-free and noisy data sets are considered. For the field case, gravity anomalies originating from the Shihe iron ore deposit in China were inverted and interpreted. The reconstructed density distribution is in good agreement with the one obtained by drill-hole information. Based on the tests in the present study, one can conclude that the Lp-norm inversion using DE is a useful tool for physical property distribution using gravity anomalies.

scholarly journals Data Clustering based on Modified Differential Evolution and Quasi-Opposition-based Learning

2020 ◽  
Vol 13 (6) ◽  
pp. 168-178
Author(s):  
Pyae Cho ◽  
◽  
Thi Nyunt ◽  
Keyword(s):  
Differential Evolution ◽  
Heuristic Search ◽  
Clustering Algorithm ◽  
Population Based ◽  
Initial Population ◽  
Local Optima ◽  
Opposition Based Learning ◽  
De Algorithm ◽  
Mutation Strategy

Differential Evolution (DE) has become an advanced, robust, and proficient alternative technique for clustering on account of their population-based stochastic and heuristic search manners. Balancing better the exploitation and exploration power of the DE algorithm is important because this ability influences the performance of the algorithm. Besides, keeping superior solutions for the initial population raises the probability of finding better solutions and the rate of convergence. In this paper, an enhanced DE algorithm is introduced for clustering to offer better cluster solutions with faster convergence. The proposed algorithm performs a modified mutation strategy to improve the DE’s search behavior and exploits Quasi-Opposition-based Learning (QBL) to choose fitter initial solutions. This mutation strategy that uses the best solution as a target solution and applies three differentials contributes to avoiding local optima trap and slow convergence. The QBL based initialization method also contributes to increasing the quality of the clustering results and convergence rate. The experimental analysis was conducted on seven real datasets from the UCI repository to evaluate the performance of the proposed clustering algorithm. The obtained results showed that the proposed algorithm achieves more compact clusters and stable solutions than the competing conventional DE variants. Moreover, the performance of the proposed algorithm was compared with the existing state of the art clustering techniques based on DE. The corresponding results also pointed out that the proposed algorithm is comparable to other DE based clustering approaches in terms of the value of the objective functions. Therefore, the proposed algorithm can be regarded as an efficient clustering tool.

scholarly journals Effect of Strategy Adaptation on Differential Evolution in Presence and Absence of Parameter Adaptation: An Investigation

2018 ◽  
Vol 8 (3) ◽  
pp. 211-235 ◽  
Author(s):  
Deepak Dawar ◽  
Simone A. Ludwig
Keyword(s):  
Differential Evolution ◽  
Control Mechanisms ◽  
Control Parameters ◽  
Parameter Adaptation ◽  
Strategy Adaptation ◽  
Adaptive Parameter ◽  
De Algorithm ◽  
Mutation Strategy ◽  
Presence And Absence ◽  
The Impact

AbstractDifferential Evolution (DE) is a simple, yet highly competitive real parameter optimizer in the family of evolutionary algorithms. A significant contribution of its robust performance is attributed to its control parameters, and mutation strategy employed, proper settings of which, generally lead to good solutions. Finding the best parameters for a given problem through the trial and error method is time consuming, and sometimes impractical. This calls for the development of adaptive parameter control mechanisms. In this work, we investigate the impact and efficacy of adapting mutation strategies with or without adapting the control parameters, and report the plausibility of this scheme. Backed with empirical evidence from this and previous works, we first build a case for strategy adaptation in the presence as well as in the absence of parameter adaptation. Afterwards, we propose a new mutation strategy, and an adaptive variant SA-SHADE which is based on a recently proposed self-adaptive memory based variant of Differential evolution, SHADE. We report the performance of SA-SHADE on 28 benchmark functions of varying complexity, and compare it with the classic DE algorithm (DE/Rand/1/bin), and other state-of-the-art adaptive DE variants including CoDE, EPSDE, JADE, and SHADE itself. Our results show that adaptation of mutation strategy improves the performance of DE in both presence, and absence of control parameter adaptation, and should thus be employed frequently.

Uncertainty analysis of 3D potential-field deterministic inversion using mixed Lp norms

Geophysics ◽  
2021 ◽  
pp. 1-103
Author(s):  
Xiaolong Wei ◽  
Jiajia Sun
Keyword(s):  
Uncertainty Analysis ◽  
Potential Field ◽  
Physical Property ◽  
Uniqueness Problem ◽  
Data Set ◽  
Regularization Term ◽  
Lp Norm ◽  
Box Plots ◽  
Model Features ◽  
Field Inversion

The non-uniqueness problem in geophysical inversion, especially potential-field inversion, is widely recognized. It is argued that uncertainty analysis of a recovered model should be as important as finding an optimal model. However, quantifying uncertainty still remains challenging, especially for 3D inversions in both deterministic and Bayesian frameworks. Our objective is to develop an efficient method to empirically quantify the uncertainty of the physical property models recovered from 3D potential-field inversion. We worked in a deterministic framework where an objective function consisting of a data misfit term and a regularization term is minimized. We performed inversions using a mixed Lp-norm formulation where various combinations of L p (0 <= p <= 2) norms can be implemented on different components of the regularization term. Specifically, we randomly sampled the p-norm values in multiple times, and generated a large and diverse sequence of physical property models that all reproduce the observed geophysical data equally well. This suite of models offers practical insights into the uncertainty of the recovered model features. We quantified the uncertainty through calculation of standard deviations and interquartile range, as well as visualizations in box plots and histograms. The numerical results for a realistic synthetic density model created based on a ring-shaped igneous intrusive body quantitatively illustrate uncertainty reduction due to different amounts of prior information imposed on inversions. We also applied the method to a field data set over the Decorah area in the northeastern Iowa. We adopted an acceptance-rejection strategy to generate 31 equivalent models based on which the uncertainties of the inverted models as well as the volume and mass estimates are quantified.

Compact gravity inversion

Geophysics ◽  
1983 ◽  
Vol 48 (6) ◽  
pp. 713-721 ◽  
Author(s):  
B. J. Last ◽  
K. Kubik
Keyword(s):  
Density Distribution ◽  
Gravity Data ◽  
Gravity Anomalies ◽  
Complete Separation ◽  
Gravity Inversion ◽  
Dimensional Model ◽  
Regular Array ◽  
Anomalous Density ◽  
Inversion Procedure ◽  
New Criterion

We present a new criterion for the inversion of gravity data. The principle employed is to minimize the volume of the causative body, which is equivalent to maximizing its compactness. The anomalous density distribution is obtained using an iterative technique which is numerically stable and rapidly convergent. The principle can also be adapted to include modeling of gravity anomalies by single‐density sources. The advantage of this approach is that desirable geologic characteristics are automatically incorporated into the model with a minimum of subjective judgments on the part of the interpreter. The treatment of noise in the data fits naturally into the formulation of the inversion procedure. The method is illustrated by the inversion of noise‐free and noisy data generated from a two‐dimensional model consisting of a regular array of identical rectangular blocks whose densities can be individually specified. In every case the algorithm successfully recovers the correct density distribution from the data. In the case of noise‐contaminated data, a complete separation of the noise from the signal is achieved. The practical effectiveness of the method is demonstrated by the inversion of published gravity data. The results obtained are compared with existing models and with available drilling information.

scholarly journals Maximum Power Point Tracking Technology of Photovoltaic Array under Partial Shading Based On Adaptive Improved Differential Evolution Algorithm

Energies ◽  
2020 ◽  
Vol 13 (5) ◽  
pp. 1254
Author(s):  
Peng Zhang ◽  
Huibin Sui
Keyword(s):  
Differential Evolution ◽  
Maximum Power Point Tracking ◽  
Maximum Power ◽  
Maximum Power Point ◽  
Partial Shading ◽  
Point Tracking ◽  
De Algorithm ◽  
Power Point Tracking ◽  
Mutation Strategy ◽  
Power Point

In the case of partial shading conditions, there will be more than one maximum power point (MPP) in photovoltaic (PV) array. The traditional maximum power point tracking (MPPT) methods are easy to get in the local maximum power point (LMPP) and fail. Based on the standard differential evolution (DE) algorithm, the mutation strategy, scaling factor F, and cross factor CR of the algorithm are optimized. Also, the population position variance δ 2 is used to prevent falling into LMPP. Finally, the conditions for algorithm termination and restart are set. It is verified by simulation that the method has fast convergence speed, high accuracy, and can adapt well to changes in the external environment. The improved DE algorithm has a great advantage in MPPT.

A new differential evolution algorithm with a combined mutation strategy for optimum synthesis of path-generating four-bar mechanisms

2016 ◽  
Vol 231 (14) ◽  
pp. 2690-2705 ◽  
Author(s):  
WY Lin ◽  
KM Hsiao
Keyword(s):  
Differential Evolution ◽  
Synthesis Method ◽  
Differential Evolution Algorithm ◽  
Population Diversity ◽  
Dimensional Synthesis ◽  
Solution Quality ◽  
De Algorithm ◽  
Mutation Operators ◽  
Mutation Strategy ◽  
Solution Accuracy

A one-phase synthesis method using heuristic optimization algorithms can solve the dimensional synthesis problems of path-generating four-bar mechanisms. However, due to the difficulty of the problem itself, there is still room for improvement in solution accuracy and reliability. Therefore, in this study, a new differential evolution (DE) algorithm with a combined mutation strategy, termed the combined-mutation differential evolution (CMDE) algorithm, is proposed to improve the solution quality. In the combined mutation strategy, the DE/best/1 operator and the DE/current-to-best/1 operator are respectively executed on some superior parents and some mediocre parents, and the DE/rand/1 operator is executed on the other inferior parents. Furthermore, the individuals participating in the three mutation operators are randomly selected from the entire set of parents. The proposed CMDE algorithm with the three different search modes possesses better population diversity as well as search ability than the DE algorithm. The effectiveness of the proposed CMDE algorithm is demonstrated using five representative problems. Findings show a marked improvement in solution accuracy and reliability. The most accurate results are obtained with an approximate combination ratio for the three mutation operators.

scholarly journals lp Norm Smooth Inversion of Magnetic Anomaly Based on Improved Adaptive Differential Evolution

2021 ◽  
Vol 11 (3) ◽  
pp. 1072
Author(s):  
Wei Du ◽  
Lianzheng Cheng ◽  
Yuanfang Li
Keyword(s):  
Differential Evolution ◽  
Magnetic Anomaly ◽  
Ore Deposits ◽  
Parametric Estimation ◽  
Source Distribution ◽  
Average Technique ◽  
Lp Norm ◽  
Magnetic Inversion ◽  
Adaptive Differential Evolution ◽  
Mutation Strategy

Due to the approved applicability of differential evolution (DE) in geophysical problems, the algorithm has been widely concerned. The DE algorithms are mostly applied to solve the geophysical parametric estimation based on specific models, but they are rarely used in solving the physical property inverse problem of geophysical data. In this paper, an improved adaptive differential evolution is proposed to solve the lp norm magnetic inversion of 2D data, in which the perturbation direction in the mutation strategy is smoothed by using the moving average technique. Besides, a new way of updating the regularization coefficient is introduced to balance the effect of the model constraint adaptively. The inversion results of synthetic models demonstrate that the presented method can obtain a smoother solution and delineate the distributions of abnormal bodies better. In the field example of Zaohuoxi iron ore deposits in China, the reconstructed magnetic source distribution is in good agreement with the one inferred from drilling information. The result shows that the proposed method offers a valuable tool for magnetic anomaly inversion.

scholarly journals An Enhancing Differential Evolution Algorithm with a Rank-Up Selection: RUSDE

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 569
Author(s):  
Kai Zhang ◽  
Yicheng Yu
Keyword(s):  
Differential Evolution ◽  
Optimization Problem ◽  
Differential Evolution Algorithm ◽  
Iteration Process ◽  
Excellent Performance ◽  
De Algorithm ◽  
Current Population ◽  
Mutation Strategy ◽  
Evolution Algorithm ◽  
Better Than

Recently, the differential evolution (DE) algorithm has been widely used to solve many practical problems. However, DE may suffer from stagnation problems in the iteration process. Thus, we propose an enhancing differential evolution with a rank-up selection, named RUSDE. First, the rank-up individuals in the current population are selected and stored into a new archive; second, a debating mutation strategy is adopted in terms of the updating status of the current population to decide the parent’s selection. Both of the two methods can improve the performance of DE. We conducted numerical experiments based on various functions from CEC 2014, where the results demonstrated excellent performance of this algorithm. Furthermore, this algorithm is applied to the real-world optimization problem of the four-bar linkages, where the results show that the performance of RUSDE is better than other algorithms.

3-Dimensional Inversion for Gravity Anomaly Calculation in Complex Geologic Region

2014 ◽  
Vol 962-965 ◽  
pp. 238-241 ◽  
Author(s):  
Gui Ju Wu ◽  
Hui Liu ◽  
Zheng Bo Zou ◽  
Guang Liang Yang ◽  
Chong Yang Shen
Keyword(s):  
Gravity Anomaly ◽  
Gravity Data ◽  
Active Faults ◽  
Physical Property ◽  
Gravity Anomalies ◽  
Research Area ◽  
Fault Zones ◽  
Longmenshan Fault Zone ◽  
3 Dimensional ◽  
Longmenshan Fault

In the gravity anomaly dectection and the inversion of physical property, the parameters can reflect the characters and details of source. At the same time, it can enhance the resolution of the source. In this paper, gravity data from global 1-minute grids are applied to inverse the structure of Longmenshan fault zone, other small faluts, several active faults and geological stratum, the research area where is complex geologic region. The main goal of this paper is an attempt to interpret the gravity anomalies of faults in the Longmenshan Fault zones.

scholarly journals Dual Mutations Collaboration Mechanism with Elites Guiding and Inferiors Eliminating Techniques for Differential Evolution

2021 ◽  
Author(s):  
Libao Deng ◽  
Chunlei Li ◽  
Haili Sun ◽  
Liyan Qiao ◽  
Xiaodong Miao
Keyword(s):  
Differential Evolution ◽  
Optimization Problems ◽  
Evaluation Process ◽  
Distribution Model ◽  
Fitness Evaluation ◽  
De Algorithm ◽  
Mutation Strategy ◽  
Base Vector ◽  
The Difference ◽  
Mutation Strategies

Abstract Differential Evolution (DE) is a powerful evolutionary algorithm for global optimization problems. Generally, appropriate mutation strategies and proper equilibrium between global exploration and local exploitation are significant to the performance of DE. From this consideration, in this paper, we present a novel DE variant, abbreviated to DMIE-DE, to further enhance the optimization capacity of DE by developing a dual mutations collaboration mechanism with elites guiding and inferiors eliminating techniques. More specifically, an explorative mutation strategy DE/current-to-embest with an elite individual serving as part of the difference vector and an exploitative mutation strategy DE/ebest-to-rand with selecting an elite individual as the base vector are employed simultaneously to achieve the balance between local and global performance of the whole population instead of only one mutation strategy in classical DE algorithm. The control parameters F and CR for above mutation strategies are updated adaptively to supplement the optimization ability of DMIE-DE based on a rational probability distribution model and the successful experience from the previous iterations. Moreover, an inferior solutions eliminating technique is embedded to enhance the convergence speed and compensate cost of the fitness evaluation times during the evaluation process. To evaluate the performance of DMIE-DE, experiments are conducted by comparing with five state-of-the-art DE variants on solving 29 test functions in CEC2017 benchmark set. The experimental results indicate that the performance of DMIE-DE is significantly better than, or at least comparable to the considered DE variants.

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