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Abstract Differential evolution (DE) is one of the most efficient evolution algorithms (ES) for dealing with nonlinear, complicated and difficult global optimization problems. The main contribution of this paper can be summarized in three directions: Firstly, a novel crossover rate (CR) generation scheme based on the zscore value of fitness, named fcr, is introduced. For a minimization problem, the proposed CR generation strategy always assigns a smaller CR value to individual with smaller fitness value. Therefore, the parameters of individuals with better fitness are inherited by their offspring with high probability. In the second direction, the control parameters are adjusted by unused bimodal settings in which each parameter setting is selected according to the evolution status of individual. The third direction of our work is introducing the L1 norm distance as the weights for updating the mean value of crossover rate and scale factor. Theoretically, compared with L2 norm, L1-norm is more efficient to suppress outliers in the difference vector. These modifications are first integrated with the mutation strategy of JADE, then a modified version, named JADEfcr, is proposed. In addition, to improve the optimization ability further, another variant LJADEfcr by using a linear population reduction mechanism is considered. So as to confirm and examine the performance of JADEfcr and LJADEfcr, numerical experiments are conducted on 29 optimization problems defined by CEC2017 benchmark. For JADEfcr, its experimental results are made a comparison with twelve state-of-the-art algorithms. The comparative study demonstrates that in terms of robustness, stability and solution quality, JADEfcr are better and highly competitive with these well-known algorithms. For LJADEfcr, its results are compared with JADEfcr and other nine powerful algorithms including four recent algorithms and five top algorithms on CEC2017 competition. Experimental results indicate that LJADEfcr is superior and statistically competitive with these excellent algorithms in terms of robustness, stability and the quality of the obtained solutions.

In recent decades, differential evolution (DE) has been employed to address a diverse range of nonlinear, nondifferentiable, and nonconvex optimization problems. In this study, we introduce an enhanced adaptive differential evolution algorithm to address the inversion problem associated with magnetic data. The primary objective of the inversion process is to minimize the discrepancy between observed data and predicted data derived from the inverted model. So, the contributions of this paper include the following two points. First, a new mechanism for generating crossover rate (CR) is proposed, which tends to reduce the CR values corresponding to vectors with better objective function values. Second, a new mutation strategy with direction information is proposed to expedite convergence. Additionally, modifications were made to the adjustment of the regularization factor to prevent it from becoming too minimal, thereby preserving its efficacy. The proposed algorithm is validated through synthetic models and a field example. Results from synthetic models demonstrate that our method is superior to and competitive with the original adaptive DE in both solution quality and convergence velocity. For the field example, the Inverted models align closely with the drill-well information.

Differential evolution (DE) is a stochastic optimization technique that imitates the evolution process in nature. This paper uses an improved adaptive differential evolution to solve gravity inversion with multiplicative regularization. Compared with additive regularization, the advantage of multiplicative regularization is that it does not require the regularization parameter in the search process. The contributions in this paper mainly focus on two aspects: accelerating the convergence speed of adaptive DE and balancing the effect of model and data misfits in the objective function. The effectiveness of the proposed inversion method is verified by synthetic and field cases. For the synthetic cases, it is concluded that, based on the obtained results and analysis, the presented DE method is superior and competitive with its original version. Additionally, the designed parameter adaptation for multiplicative regularization is useful for trading off the effect of data and model misfits. For the field cases, two successful applications from China were conducted, and the obtained density source distributions were in accordance with those obtained from drilling wells. The synthetic and practical examples demonstrate that high-quality inversion results can be obtained using improved adaptive differential evolution and multiplicative regularization.

As a powerful optimization algorithm for solving nonlinear, complex and tough global optimization problems, differential evolution (DE) has been widely applied in various science and engineering fields. In this article, considering that the evolution direction of each individual is not fully exploited to guide the search process in most DE algorithms, a new DE variant (named ADEwSE), which incorporates the successful experience of evolved individuals into classic “current-to-pbest/1” mutation strategy to reduce the randomness of search direction, is proposed. Moreover, crossover matrix sorting scheme based on real crossover rate, opposition learning of crossover rate and adaptive adjustment of top p% values are combined with the new mutation strategy to improve the global search ability. In addition, to improve the searching ability of ADEwSE further, an ADEwSE variant by introducing the linear reduction of population size is proposed. In order to verify and analyze the performance of ADEwSE, numerical experiments on a set of 29 test problems from CEC2017 benchmark for 30, 50 and 100 dimensions are executed. And the experimental results are compared with that of 21 state-of-art DE-based algorithms. Comparative analysis indicates that the ADEwSE and its improved version are competitive with these state-of-art DE variants in terms of solution quality obtained.

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.

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.