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1.
Methods Mol Biol ; 2847: 95-108, 2025.
Article in English | MEDLINE | ID: mdl-39312138

ABSTRACT

Ribonucleic acid (RNA) design is the inverse of RNA folding. RNA folding aims to identify the most likely secondary structure into which a given strand of nucleotides will fold. RNA design algorithms, on the other hand, attempt to design a strand of nucleotides that will fold into a specified secondary structure. Despite the apparent NP-hard nature of RNA design, promising results can be achieved when formulated as a combinatorial optimization problem and approached with simple heuristics. The main focus of this paper is to describe an RNA design algorithm based on simulated annealing. Additionally, noteworthy features and results will be presented herein.


Subject(s)
Algorithms , Nucleic Acid Conformation , RNA Folding , RNA , RNA/chemistry , RNA/genetics , Software , Computational Biology/methods , Computer Simulation
2.
Sci Rep ; 14(1): 23568, 2024 Oct 09.
Article in English | MEDLINE | ID: mdl-39384628

ABSTRACT

The multivariable process plays a significant role in industrial applications, and designing a controller for the Multi-Input Multi-Output process is challenging due to dynamic process changes and interactions between system variables. Traditionally, the PI family of controllers has been used for its simple design, easy tuning, and quick deployment. However, these processes require complex control actions due to multiple loops in process plants. Thus, this paper proposes an Iterative Learning Controller Dead-time compensating PI, which utilizes the newly developed hybrid Simulated Annealing-Ant Lion Optimization algorithm for Single-Input Single-Output process simulation and real-time experimentation on the Quadruple Tank System. To validate the effectiveness of the developed controller, Machine Learning techniques such as regression and ensemble trees are used to accurately predict the actual system response using error values from respective processes. The simulation and experimental results demonstrate that the proposed controller achieved better performance. The regression and ensemble tree algorithm models effectively predicted the actual response. The obtained data shows that the proposed controller improved system stability and robustness by minimizing nearly half of the overshoot and improving settling time, with an average of 29.9596% faster than the other controller in the SISO process and 14.6116% in the MIMO process.

3.
Article in English | MEDLINE | ID: mdl-39392585

ABSTRACT

In this paper we develop a new multi-objective simulated annealing (MOSA) algorithm to generate optimal testing protocols for infectious diseases, using the COVID-19 pandemic as our context. A SEIR (susceptible-exposed-infected-recovered) epidemiological model is embedded as the computational platform for our MOSA algorithm to optimize testing protocols for screening across three joint objectives: minimum cost of test materials, minimum total infections over the testing horizon, and minimum number of false negatives over the horizon. We demonstrate the application of this optimization tool to recommend screening protocols for K-12 school districts in the U.S. State of North Carolina. Our approach is scalable by population coverage and can be employed at the level of individual school districts or regional collections of districts, individual schools or collections of schools across a district, business sites, or nursing homes, among other congregate settings where individuals may be screened prior to gaining entry to the site. The algorithm can be solved two ways, generating either independent optimal protocols across individual testing locations, or a common protocol covering all locations in the collection of testing sites. Our findings can be used to inform policy decisions to guide the development of effective testing strategies for controlling the spread of COVID-19 or other pandemic diseases in a wide range of congregate settings across various geographic regions.

4.
BMC Health Serv Res ; 24(1): 1167, 2024 Oct 04.
Article in English | MEDLINE | ID: mdl-39363315

ABSTRACT

BACKGROUND AND AIM: China has used traditional Chinese medicine (TCM) to treat diseases for more than 2000 years. Traditionally, TCMs in medicine cabinets are arranged alphabetically or on the basis of experience, but this arrangement greatly affects dispensing efficiency. However, owing to the unique properties and qualities of TCM, very few automatic approaches or systems have specifically addressed TCM dispensing problems. Therefore, it is necessary to establish a method of optimizing the traditional Chinese medicine placement scheme (TCMPS) via computer algorithms to improve the work efficiency of pharmacists. METHODS: A prescription dataset from a hospital in 2022 was obtained, and the association rule algorithm (ARA) was used to calculate the frequency of use for each type of TCM and the associations between different types of TCMs. On the basis of these association and frequency data, the optimal TCMPS was calculated using the simulated annealing algorithm (SAA) and then verified using the prescription dataset from 2023. RESULTS: A total of 10,601 prescriptions were collected in 2022, involving 360 different TCMs, and each prescription contained an average of 9.485 TCMs, with Danggui (3628) being the most frequently used. When the threshold of support was set to 0.05 and the confidence was set to 0.8, 78 couplet medicines used in orthopedics clinics were found through ARA. When the threshold value of support was set to 0, the confidence was set to 0, and the rule length was 2, a total of 129,240 rules were obtained, indicating support between all pairwise TCMs. The TCMPS, calculated using SAA, had a correlation sum of 14.183 and a distance sum of 3.292. The TCMPS was verified using a prescription dataset from 2023 and theoretically improved the dispensing efficiency of pharmacists by approximately 50%. CONCLUSIONS: In this study, the ARA and SAA were successfully applied to pharmacies for the first time, and the optimal TCMPS was calculated. This approach not only significantly improves the dispensing efficiency of pharmacists and reduces patient waiting time but also enhances the quality of medical services and patient satisfaction, and provides a valuable reference for the development of smart medicine.


Subject(s)
Algorithms , Medicine, Chinese Traditional , Medicine, Chinese Traditional/methods , Humans , China , Pharmacy Service, Hospital , Drugs, Chinese Herbal/standards , Drugs, Chinese Herbal/therapeutic use , Drug Prescriptions/statistics & numerical data , Drug Prescriptions/standards
5.
Nutrients ; 16(18)2024 Sep 15.
Article in English | MEDLINE | ID: mdl-39339715

ABSTRACT

BACKGROUND/OBJECTIVE: Nutritionists play a crucial role in guiding individuals toward healthier lifestyles through personalized meal planning; however, this task involves navigating a complex web of factors, including health conditions, dietary restrictions, cultural preferences, and socioeconomic constraints. The Analytic Hierarchy Process (AHP) offers a valuable framework for structuring these multi-faceted decisions but inconsistencies can hinder its effectiveness in pairwise comparisons. METHODS: This paper proposes a novel hybrid Particle Swarm Optimization-Simulated Annealing (PSO-SA) algorithm to refine inconsistent AHP weight matrices, ensuring a consistent and accurate representation of the nutritionist's expertise and client preferences. Our approach merges PSO's global search capabilities with SA's local search precision, striking an optimal balance between exploration and exploitation. RESULTS: We demonstrate the practical utility of our algorithm through real-world use cases involving personalized meal planning for individuals with specific dietary needs and preferences. Results showcase the algorithm's efficiency in achieving consistency and surpassing standard PSO accuracy. CONCLUSION: By integrating the PSO-SA algorithm into a mobile app, we empower nutritionists with an advanced decision-making tool for creating tailored meal plans that promote healthier dietary choices and improved client outcomes. This research represents a significant advancement in multi-criteria decision-making for nutrition, offering a robust solution to the inconsistency challenge in AHP and paving the way for more effective and personalized dietary interventions.


Subject(s)
Algorithms , Meals , Humans , Decision Making , Diet, Healthy/methods , Nutritionists , Mobile Applications , Menu Planning
6.
Bioengineering (Basel) ; 11(9)2024 Sep 06.
Article in English | MEDLINE | ID: mdl-39329639

ABSTRACT

Dipole localization, a fundamental challenge in electromagnetic source imaging, inherently constitutes an optimization problem aimed at solving the inverse problem of electric current source estimation within the human brain. The accuracy of dipole localization algorithms is contingent upon the complexity of the forward model, often referred to as the head model, and the signal-to-noise ratio (SNR) of measurements. In scenarios characterized by low SNR, often corresponding to deep-seated sources, existing optimization techniques struggle to converge to global minima, thereby leading to the localization of dipoles at erroneous positions, far from their true locations. This study presents a novel hybrid algorithm that combines simulated annealing with the traditional quasi-Newton optimization method, tailored to address the inherent limitations of dipole localization under low-SNR conditions. Using a realistic head model for both electroencephalography (EEG) and magnetoencephalography (MEG), it is demonstrated that this novel hybrid algorithm enables significant improvements of up to 45% in dipole localization accuracy compared to the often-used dipole scanning and gradient descent techniques. Localization improvements are not only found for single dipoles but also in two-dipole-source scenarios, where sources are proximal to each other. The novel methodology presented in this work could be useful in various applications of clinical neuroimaging, particularly in cases where recordings are noisy or sources are located deep within the brain.

7.
Bioengineering (Basel) ; 11(9)2024 Sep 11.
Article in English | MEDLINE | ID: mdl-39329650

ABSTRACT

The aim of this study was to improve the diagnostic ability of fall risk classifiers using a Bayesian approach and the Simulated Annealing (SA) algorithm. A total of 47 features from 181 records (40 Center of Pressure (CoP) indices and 7 patient descriptive variables) were analyzed. The wrapper method of feature selection using the SA algorithm was applied to optimize the cost function based on the difference of the mean minus the standard deviation of the Area Under the Curve (AUC) of the fall risk classifiers across multiple dimensions. A stratified 60-20-20% hold-out method was used for train, test, and validation sets, respectively. The results showed that although the highest performance was observed with 31 features (0.815 ± 0.110), lower variability and higher explainability were achieved with only 15 features (0.780 ± 0.055). These findings suggest that the SA algorithm is a valuable tool for feature selection for acceptable fall risk diagnosis. This method offers an alternative or complementary resource in situations where clinical tools are difficult to apply.

8.
Adv Mater ; 36(40): e2410191, 2024 Oct.
Article in English | MEDLINE | ID: mdl-39194394

ABSTRACT

Due to its area and energy efficiency, a memristive crossbar array (CBA) has been extensively studied for various combinatorial optimization applications, from network problems to circuit design. However, conventional approaches include heavily burdening software fine-tuning for the annealing process. Instead, this study introduces the "in-materia annealing" method, where the inter-layer interference of vertically stacked memristive CBA is utilized as an annealing method. When mapping combinatorial optimization problems into the configuration layer of the CBA, exponentially decaying annealing profiles are generated in nearby noise layers. Moreover, in-materia annealing profiles can be controlled by changing compliance current, read voltage, and read pulse width. Therefore, the annealing profiles can be arbitrarily controlled and generated individually for each cell, providing rich noise sources to solve the problem efficiently. Consequently, the experimental and simulation of Max-Cut and weighted Max-Cut problems achieve notable results with the minimum software burden.

9.
Article in English | MEDLINE | ID: mdl-39138745

ABSTRACT

The issue of left against medical advice (LAMA) patients is common in today's emergency departments (EDs). This issue represents a medico-legal risk and may result in potential readmission, mortality, or revenue loss. Thus, understanding the factors that cause patients to "leave against medical advice" is vital to mitigate and potentially eliminate these adverse outcomes. This paper proposes a framework for studying the factors that affect LAMA in EDs. The framework integrates machine learning, metaheuristic optimization, and model interpretation techniques. Metaheuristic optimization is used for hyperparameter optimization-one of the main challenges of machine learning model development. Adaptive tabu simulated annealing (ATSA) metaheuristic algorithm is utilized for optimizing the parameters of extreme gradient boosting (XGB). The optimized XGB models are used to predict the LAMA outcomes for patients under treatment in ED. The designed algorithms are trained and tested using four data groups which are created using feature selection. The model with the best predictive performance is then interpreted using the SHaply Additive exPlanations (SHAP) method. The results show that best model has an area under the curve (AUC) and sensitivity of 76% and 82%, respectively. The best model was explained using SHAP method.

10.
PeerJ Comput Sci ; 10: e2176, 2024.
Article in English | MEDLINE | ID: mdl-39145221

ABSTRACT

In the context of the 5G network, the proliferation of access devices results in heightened network traffic and shifts in traffic patterns, and network intrusion detection faces greater challenges. A feature selection algorithm is proposed for network intrusion detection systems that uses an improved binary pigeon-inspired optimizer (SABPIO) algorithm to tackle the challenges posed by the high dimensionality and complexity of network traffic, resulting in complex models, reduced accuracy, and longer detection times. First, the raw dataset is pre-processed by uniquely one-hot encoded and standardized. Next, feature selection is performed using SABPIO, which employs simulated annealing and the population decay factor to identify the most relevant subset of features for subsequent review and evaluation. Finally, the selected subset of features is fed into decision trees and random forest classifiers to evaluate the effectiveness of SABPIO. The proposed algorithm has been validated through experimentation on three publicly available datasets: UNSW-NB15, NLS-KDD, and CIC-IDS-2017. The experimental findings demonstrate that SABPIO identifies the most indicative subset of features through rational computation. This method significantly abbreviates the system's training duration, enhances detection rates, and compared to the use of all features, minimally reduces the training and testing times by factors of 3.2 and 0.3, respectively. Furthermore, it enhances the F1-score of the feature subset selected by CPIO and Boost algorithms when compared to CPIO and XGBoost, resulting in improvements ranging from 1.21% to 2.19%, and 1.79% to 4.52%.

11.
Sensors (Basel) ; 24(16)2024 Aug 15.
Article in English | MEDLINE | ID: mdl-39204978

ABSTRACT

In recent years, single-source-data-based deep learning methods have made considerable strides in the field of fault diagnosis. Nevertheless, the extraction of useful information from multi-source data remains a challenge. In this paper, we propose a novel approach called the Genetic Simulated Annealing Optimization (GASA) method with a multi-source data convolutional neural network (MSCNN) for the fault diagnosis of rolling bearing. This method aims to identify bearing faults more accurately and make full use of multi-source data. Initially, the bearing vibration signal is transformed into a time-frequency graph using the continuous wavelet transform (CWT) and the signal is integrated with the motor current signal and fed into the network model. Then, a GASA-MSCNN fault diagnosis method is established to better capture the crucial information within the signal and identify various bearing health conditions. Finally, a rolling bearing dataset under different noisy environments is employed to validate the robustness of the proposed model. The experimental results demonstrate that the proposed method is capable of accurately identifying various types of rolling bearing faults, with an accuracy rate reaching up to 98% or higher even in variable noise environments. The experiments reveal that the new method significantly improves fault detection accuracy.

12.
Environ Sci Technol ; 58(31): 13726-13736, 2024 Aug 06.
Article in English | MEDLINE | ID: mdl-39047191

ABSTRACT

With the rapid depletion of phosphate rocks and increasing agricultural demand, establishing a phosphorus (P) flow "loop" rather than a one-way trajectory between cropland and urban areas was imperative. Recovering P from municipal wastewater stood as a viable strategy to mitigate reliance on traditional P-containing chemical fertilizer. This study analyzed the intricate relationships between the potentials of P recovery from municipal wastewater and the P demand of croplands in the populated Yangtze River Delta (YRD), China. An indicator of the P vehicle transport distance was constructed and calculated to estimate the potential to recover and reuse P in agriculture, applying the simulated annealing (SA) algorithm and road networks obtained from OpenStreetMap (OSM). The results indicated that, on a regional scale, recovered P from municipal wastewater could fulfill 14.0% of the cropland P demands in the YRD, with a median P vehicle transport distance of 3.1 km/Mg of P. Notably, the P vehicle transport distance varied largely depending upon the cropland distributions, road density, and P recovery potential from municipal wastewater. The novel methodology developed here determined the optimal transportation routes for P recovery from wastewater treatment plants (WWTPs) to cropland, which played a crucial role in refining the wastewater management strategies aligned with the United Nations Sustainable Development Goals.


Subject(s)
Phosphorus , Rivers , Wastewater , Wastewater/chemistry , China , Rivers/chemistry , Agriculture
13.
Acta Pharm Sin B ; 14(7): 3086-3109, 2024 Jul.
Article in English | MEDLINE | ID: mdl-39027234

ABSTRACT

Multifunctional therapeutics have emerged as a solution to the constraints imposed by drugs with singular or insufficient therapeutic effects. The primary challenge is to integrate diverse pharmacophores within a single-molecule framework. To address this, we introduced DeepSA, a novel edit-based generative framework that utilizes deep simulated annealing for the modification of articaine, a well-known local anesthetic. DeepSA integrates deep neural networks into metaheuristics, effectively constraining molecular space during compound generation. This framework employs a sophisticated objective function that accounts for scaffold preservation, anti-inflammatory properties, and covalent constraints. Through a sequence of local editing to navigate the molecular space, DeepSA successfully identified AT-17, a derivative exhibiting potent analgesic properties and significant anti-inflammatory activity in various animal models. Mechanistic insights into AT-17 revealed its dual mode of action: selective inhibition of NaV1.7 and 1.8 channels, contributing to its prolonged local anesthetic effects, and suppression of inflammatory mediators via modulation of the NLRP3 inflammasome pathway. These findings not only highlight the efficacy of AT-17 as a multifunctional drug candidate but also highlight the potential of DeepSA in facilitating AI-enhanced drug discovery, particularly within stringent chemical constraints.

14.
Sci Rep ; 14(1): 13330, 2024 Jun 10.
Article in English | MEDLINE | ID: mdl-38858453

ABSTRACT

Non-renewable energy sources, including fossil fuels, are a type of energy whose consumption rate far exceeds its natural production rate. Therefore, non-renewable resources will be exhausted if alternative energy is not fully developed, leading to an energy crisis in the near future. In this paper, a mathematical model has been proposed for the design of the biomass supply chain of field residues that includes several fields where residue is transferred to hubs after collecting the residue in the hub, the residue is transferred to reactors. In reactors, the residue is converted into gas, which is transferred to condenser and transformers, converted into electricity and sent to demand points through the network. In this paper, the criteria of stability and disturbance were considered, which have been less discussed in related research, and the purpose of the proposed model was to maximize the profit from the sale of energy, including the selling price minus the costs. Genetic algorithm (GA) and simulated annealing (SA) algorithm have been used to solve the model. Then, to prove the complexity of the problem, different and random examples have been presented in different dimensions of the problem. Also, the efficiency of the algorithm in small and large dimensions was proved by comparing GA and SA due to the low deviation of the solutions and the methods used have provided acceptable results suitable for all decision-makers. Also, the effectiveness of the algorithm in small and large dimensions is proven by comparing the genetic algorithm and simulated annealing, and the genetic algorithm's values are better, considering the deviation of 2.9%.and have provided solution methods suitable for all decision makers.

15.
Heliyon ; 10(9): e29958, 2024 May 15.
Article in English | MEDLINE | ID: mdl-38694131

ABSTRACT

This paper studies a variant of the Pollution Traveling Salesman Problem (PTSP) focused on fuel consumption and pollution emissions (PTSPC). The PTSPC generalizes the well-known Traveling Salesman Problem (TSP), classified as NP-Hard. In the PTSPC, a vehicle must deliver a load to each customer through a Hamiltonian cycle, minimizing an objective function that considers the speed of each edge, the mass of the truck, the mass of the load pending delivery, and the distance traveled. We have proposed a three-phase algorithm for the PTSPC. The first phase solves the Traveling Salesman Problem (TSP) exactly with a time limit and heuristically using a Nearest Neighborhood Search approach. This phase considers the constraints associated with the PTSPC by using commercial software. In the second phase, both the obtained solutions and their inverse sequences from the initial phase undergo enhancement utilizing metaheuristic algorithms tailored for the PTSPC. These algorithms include Variable Neighborhood Search (VNS), Tabu Search (TS), and Simulated Annealing (SA). Subsequently, for the third phase, the best solution identified in the second phase-determined by having the minimum value by the PTSPC objective function-is subjected to resolution by a mathematical model designed for the PTSPC, considering the heuristic emphasis of commercial software. The efficiency of the former algorithm has been validated through experimentation involving the adaptation of instances from the Pollution Routing Problem (PRP) to the PTSPC. This approach demonstrates the capacity to yield high-quality solutions within acceptable computing times.

16.
Am Stat ; 78(1): 76-87, 2024.
Article in English | MEDLINE | ID: mdl-38680760

ABSTRACT

The use of simulation-based sensitivity analyses is fundamental for evaluating and comparing candidate designs of future clinical trials. In this context, sensitivity analyses are especially useful to assess the dependence of important design operating characteristics with respect to various unknown parameters. Typical examples of operating characteristics include the likelihood of detecting treatment effects and the average study duration, which depend on parameters that are unknown until after the onset of the clinical study, such as the distributions of the primary outcomes and patient profiles. Two crucial components of sensitivity analyses are (i) the choice of a set of plausible simulation scenarios and (ii) the list of operating characteristics of interest. We propose a new approach for choosing the set of scenarios to be included in a sensitivity analysis. We maximize a utility criterion that formalizes whether a specific set of sensitivity scenarios is adequate to summarize how the operating characteristics of the trial design vary across plausible values of the unknown parameters. Then, we use optimization techniques to select the best set of simulation scenarios (according to the criteria specified by the investigator) to exemplify the operating characteristics of the trial design. We illustrate our proposal in three trial designs.

17.
Sci Rep ; 14(1): 7637, 2024 Apr 01.
Article in English | MEDLINE | ID: mdl-38561394

ABSTRACT

Rapid placement of electric vehicle charging stations (EVCSs) is essential for the transportation industry in response to the growing electric vehicle (EV) fleet. The widespread usage of EVs is an essential strategy for reducing greenhouse gas emissions from traditional vehicles. The focus of this study is the challenge of smoothly integrating Plug-in EV Charging Stations (PEVCS) into distribution networks, especially when distributed photovoltaic (PV) systems are involved. A hybrid Genetic Algorithm and Simulated Annealing method (GA-SAA) are used in the research to strategically find the optimal locations for PEVCS in order to overcome this integration difficulty. This paper investigates PV system situations, presenting the problem as a multicriteria task with two primary objectives: reducing power losses and maintaining acceptable voltage levels. By optimizing the placement of EVCS and balancing their integration with distributed generation, this approach enhances the sustainability and reliability of distribution networks.

18.
Methods Mol Biol ; 2795: 247-261, 2024.
Article in English | MEDLINE | ID: mdl-38594544

ABSTRACT

Increased day lengths and warm conditions inversely affect plant growth by directly modulating nuclear phyB, ELF3, and COP1 levels. Quantitative measures of the hypocotyl length have been key to gaining a deeper understanding of this complex regulatory network, while similar quantitative data are the foundation for many studies in plant biology. Here, we explore the application of mathematical modeling, specifically ordinary differential equations (ODEs), to understand plant responses to these environmental cues. We provide a comprehensive guide to constructing, simulating, and fitting these models to data, using the law of mass action to study the evolution of molecular species. The fundamental principles of these models are introduced, highlighting their utility in deciphering complex plant physiological interactions and testing hypotheses. This brief introduction will not allow experimentalists without a mathematical background to run their own simulations overnight, but it will help them grasp modeling principles and communicate with more theory-inclined colleagues.


Subject(s)
Models, Theoretical , Vernalization , Plants , Hypocotyl/physiology
19.
Sensors (Basel) ; 24(6)2024 Mar 14.
Article in English | MEDLINE | ID: mdl-38544119

ABSTRACT

The total focusing method (TFM) is often considered to be the 'gold standard' for ultrasonic imaging in the field of nondestructive testing. The use of matrix phased arrays as probes allows for high-resolution volumetric TFM imaging. Conventional TFM imaging involves the use of full matrix capture (FMC) for ultrasonic signals acquisition, but in the case of a matrix phased array, this approach is associated with a huge volume of data to be acquired and processed. This severely limits the frame rate of volumetric imaging with 2D probes and necessitates the use of high-end equipment. Thus, the aim of this research was to develop a novel design method for determining the optimal sparse 2D probe configuration for specific conditions of ultrasonic imaging. The developed approach is based on simulated annealing and involves implementing the solution of the sparse matrix phased array layout optimization problem. In order to implement simulated annealing for the aforementioned task, its parameters were set, the acceptance function was introduced, and the approaches were proposed to compute beam directivity diagrams of sparse matrix phased arrays in TFM imaging. Experimental studies have shown that the proposed approach provides high-quality volumetric imaging with a decrease in data volume of up to 84% compared to that obtained using the FMC data acquisition method.

20.
Sci Rep ; 14(1): 5240, 2024 Mar 04.
Article in English | MEDLINE | ID: mdl-38438454

ABSTRACT

Geophysical inversion usually involves ill-posed problem. Regularization is the most commonly used method to mitigate this problem. There are many regularization parameter selection methods, among which the adaptive regularization method can automatically update parameters during iteration, reducing the difficulty of parameter selection. Therefore, it is widely used in linear inversion. However, there are very few studies on the use of adaptive regularization methods in stochastic optimization algorithms. The biggest difficulty is that in stochastic optimization algorithms, the search direction of any iteration is completely random. Data fitting term and stabilizing term vary in a wide range, making it difficult for traditional methods to work. In this paper, we consider the contributions of the data fitting term and the stabilizing term in the objective function and give an improved adaptive regularization method for very fast simulated annealing (VFSA) inversion for transient electromagnetic (TEM) data. The optimized method adjusts the two terms dynamically to make them in balance. We have designed several numerical experiments, and the experimental results demonstrate that the method in this paper not only accelerates the convergence, but also the inversion results are very little affected by the initial regularization parameter. Finally, we apply this method to field data, and the inversion results show very good agreements with nearby borehole data.

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