Numerical Optimization Algorithm Research Articles

Well control optimization in waterflooding using genetic algorithm coupled with Artificial Neural Networks

Optimum well controls to maximize net present value (NPV) in a waterflooding operation are often obtained from an iterative process of employing numerical reservoir simulation and optimization algorithms. It is often challenging to implement gradient-based optimization algorithms because of the large number of variables and the complexities to embed the optimization algorithm in the simulator solving workflow. Approaches based on repeated model evaluation are easier to implement but are often time-consuming and computationally expensive.

Explicit-by-Implicit Treatment of Natural Orbital Occupations Using First- and Second-Order Optimization Algorithms: A Comparative Study.

To address the convergence issues in the natural occupation optimization of reduced density matrix functional theory (RDMFT), we recently proposed the explicit-by-implicit (EBI) idea to handle the ensemble N-representability constraint (Yao et al. J. Phys. Chem. Lett. 2021, 12, 6788). This work continues to focus on these issues that can affect the reliability of the electronic structure description in RDMFT; further explores the combination of EBI, as well as the (augmented) Lagrangian methods (both LM and ALM), with both first- and second-order numerical optimization algorithms; and carefully evaluates their performances in natural occupation optimizations of various systems, including strongly correlated systems and large molecules. By comparing both converged energies and elapsed times, it can be seen that the LM and ALM have serious convergence issues for systems of different sizes. In contrast, the optimizations of EBI can converge to better energies with fewer iterations. However, due to the local convergence nature of the Newton's Method (NM) algorithm, EBI@NM still suffers from the local minimum issue for both strongly correlated systems and large molecules. Overall, the combination of EBI with the simple first-order algorithm of gradient descent (GD), namely EBI@GD, consistently provides the lowest converged energies for different types of systems, with the lowest computational scaling. These tests demonstrate the advantages of EBI in the calculations of transition states, strongly correlated systems, and large molecules. Meanwhile, the insights gained from this work are helpful to further develop more efficient algorithms for RDMFT.

Optimal Design and Experiment of Manipulator for Camellia Pollen Picking

In this paper, a four-degree-of-freedom camellia-pollen-picking manipulator is proposed and designed. It can solve the problem of having no mechanized equipment for picking camellia pollen in agricultural machinery as the labor intensity of manual pollen extraction is high. To make the manipulator reach the target space quickly and efficiently, a structural-parameter-optimization method that reduces the working space to a more versatile cube is proposed. The numerical optimization algorithm is used to calculate the optimization result. Through the static analysis of the manipulator, the stability of the manipulator structure is verified. The working space of the manipulator is simulated and analyzed, and the simulation results are further verified by experiments. This research provides reliable technical support for the structural optimization, manufacturing, and intelligent upgrading of the camellia-pollen-picking robot.

Discrete Hyperparameter Optimization Model Based on Skewed Distribution

As for the machine learning algorithm, one of the main factors restricting its further large-scale application is the value of hyperparameter. Therefore, researchers have done a lot of original numerical optimization algorithms to ensure the validity of hyperparameter selection. Based on previous studies, this study innovatively puts forward a model generated using skewed distribution (gamma distribution) as hyperparameter fitting and combines the Bayesian estimation method and Gauss hypergeometric function to propose a mathematically optimal solution for discrete hyperparameter selection. The results show that under strict mathematical conditions, the value of discrete hyperparameters can be given a reasonable expected value. This heuristic parameter adjustment method based on prior conditions can improve the accuracy of some traditional models in experiments and then improve the application value of models. At the same time, through the empirical study of relevant datasets, the effectiveness of the parameter adjustment strategy proposed in this study is further proved.

A balanced butterfly optimization algorithm for numerical optimization and feature selection

Butterfly optimization algorithm (BOA) is a relatively novel optimization technique for solving function optimization as well as real-world applications. However, the paramount challenge in BOA is that it is prone to stagnation in local optima. The purpose of this study is to balance the exploration and exploitation abilities of BOA when two new strategies are introduced. The dynamic inertia weight based on Logistic model as the first strategy is introduced to modify the position updating equation. Another strategy is the opposition-based learning. A new variant of BOA called BBOA based on these two strategies is proposed. Ten widely used benchmark test functions and 30 complex benchmarks from CEC 2014 are selected to verify the effectiveness of BBOA. The used benchmark problems are composed of unimodal, multimodal, rotated, shifted, hybrid and composite functions. The experimental results and analysis show that the proposed BBOA has better exploration ability than the conventional BOA when solving different characteristics functions. Finally, BBOA is applied to solve three real-world engineering applications and sixteen feature selection problems. The results demonstrate that BBOA can outperform other competitors in terms of the accuracy of solution on constrained engineering design and feature selection problems.

Organ-based estimation and minimization of clinician's X-ray dose.

Hybrid surgeries, allowing real-time visualization of patient inner anatomy, are possible through the use of intraoperative X-ray imaging. However, the intensive use of X-rays can have undesired consequences for the clinicians or the patient in the operating room (OR). In this paper, we provide a tool to visualize the X-rays and to optimally place protective shields in the hybrid operating room to reduce the clinician's dose according to their most sensitive body parts. We first acquire measurements in a hybrid operating room with dosimeters placed at different locations on a mannequin simulating a clinician. We demonstrate that a small displacement of a protective shield has significant consequences on the dose received by a clinician. Then, we reproduce the scene virtually and use Monte Carlo simulations to estimate the dose received by the clinician. Finally, we optimally place protective shields with a Nelder-Mead-based numerical optimization algorithm. The results show a high sensitivity of the clinician's dose to protective shield placement. Numerical optimization of the shields' placement can help to reduce the dose and show a decrease between 79 and 89% of the exposition when comparing no external shield protection and our optimal external shield position. Our work can help to raise awareness of the risks induced by X-rays during intraoperative surgery and reduce the dose received by the clinicians. In future work, our approach can be linked with human pose estimation algorithms to trace surgeons' moves, estimate dynamically the dose and summarize it in a surgical report, giving the dose for important organs.

Optimization of the efficiency of large deployable reflectors by measuring the error around the feed

Large Deployable Reflector (LDR) systems are commonly used as mesh reflectors for large aperture space antennas in aerospace applications since they provide affordability while guaranteeing at the same time a high gain and a high directivity. To improve the surface accuracy several methods have been studied, most of which measure the distance between the cable-net system that forms the reflector surface and the desired paraboloid. In this paper we want to improve the reflector’s ability to convey a greater concentration of reflected rays in the direction of the feed. To deal with this issue, a numerical optimization algorithm has been proposed, both in the case of prime-focus reflector and with offset. During the explanation of the algorithm, numerical examples will be reported, thus demonstrating the goodness of the algorithm, and its effectiveness will also be demonstrated using the Monte Carlo method.

DeepRS: A Library of Recommendation Algorithms Based on Deep Learning

In recent years, recommendation systems have become more complex with increasing research on user preferences. Recommendation algorithm based on deep learning has attracted a lot of attention from researchers in academia and industry, and many new algorithm models are proposed every year. Researchers often need to implement the proposed model to compare the results, which is a great challenge. Even if some papers provide source code, there are a variety of programming languages or deep learning frameworks, and it is not easy to compare the results in the different frameworks. In view of the lack of easily extensible deep learning-based recommendation algorithm libraries, based on the common analysis of deep learning algorithms in attention factorization machine (AFM), neural factorization machine (NFM), deep factorization machine (DeepFM) and deep cross-network (DCN), a recommendation algorithm library based on deep learning (DeepRS for short) is designed and implemented. It consists of three levels: framework level, abstract level and algorithm level. The framework level adopts the Tensorflow open source framework, which provides interfaces, such as automatic differentiation, tensor computing, GPU computing, and numerical optimization algorithms. The abstraction level uses the interface of the framework level to realize the embedding layer (EL), the full connection layer (FCL), the multi-layer perceptron layer (MLPL), the prediction layer (PL), the factorization machine layer (FML), the attention network layer (ANL), the cross-layer (CL) and the cross-network layer (CNL). The algorithm level implements the deep learning-based recommendation algorithms, such as AFM, NFM, DeepFM and DCN, on the basis of the abstraction level and the framework level. Experiments show that the proposed algorithm library has good scalability, ease of use and correctness.

A modified model parametrization algorithm for solving a special type of heat and mass transfer systems

A new method for solving nonlinear heat and mass transfer design tasks was considered. Systems using the Number of Transfer Units (NTU) method are a special type of mathematical model of heat and mass exchangers. It was observed, that the NTU models in a form of differential-algebraic equations (DAEs) cannot be directly solved with higher values of NTU. The requirements for consistent initial conditions, as well as numerical limitations of DAEs solvers, result, that the solution to the considered design problems that cannot be obtained by a classical direct shooting procedure. To overcome the presented difficulties, the αDAE model optimization algorithm was adjusted for solving NTU-based models. The new approach consists of 3 main steps: 1) task discretization by a multiple-shooting approach, 2) design an appropriate function fNTU(α) to effectively influence the variability of the state variables described by dynamical relations, 3) the iterative numerical optimization algorithm for the new parametrized system. Moreover, computations can be performed by a chosen numerical optimization approach, which can be communicated with an available outer procedure for solving differential-algebraic equations. The presented algorithm was implemented and applied to solve the design task with the NTU model of a counter-flow exchanger. The new approach was used to modify the system dynamics to influence the difficulty of the considered problem. Finally, the presented method enabled failure-free numerical computations for the higher values of the NTU parameter.

RELIABILITY BASED DESIGN OF GEOTECHNICAL SYSTEMS BASED ON A DECOUPLED RELIABILITY ANALYSIS AND OPTIMIZATION APPROACH

Reliability-based design intends to design an engineering system subject to probabilistic design constraints. This paper presents a reliability design optimization approach of geotechnical engineering problems based on a decoupled reliability analysis and optimization concept. Geotechnical and foundation systems involve considerable uncertainties in soil properties, loading conditions, and inadequate site characterization. A traditional reliability design optimization method, such as the reliability index approach, requires a double-loop optimization structure, since reliability analysis is implemented for constraint function evaluation using a numerical optimization algorithm. The decoupled approach separates the reliability analyses of the constraint functions from the design optimization loop. An adaptive metamodeling method is proposed to create approximate functions of the reliability indices, so that the reliability design optimization is performed using the approximate functions of the reliability constraints. Radial basis functions are implemented to build the metamodels. To progressively improve the accuracy of predicting the reliability indices, an adaptive sampling technique is employed, so that new samples are added using the optimal points found in previous design iterations. Numerical examples are solved and presented, and the proposed design approach works well. It is shown to be a useful alternative for solving reliability-based design of geotechnical and foundation systems.

Model predictive control stabilization of a power system including a wind power plant

The conventional generators are equipped with power system stabilizers (PSS) to damp oscillations that follow disturbances. The inclusion of renewable energy sources within the existing power systems requires further investigations to enhance the performance of PSS. Several control strategies have been being used to design the PSS. In this paper, model predictive control (MPC) is investigated to be used as a PSS. It uses numerical optimization algorithms to get an optimal control output considering the system’s constraints. Therefore, It is designed and applied to a multi-machine power system with a wind power plant (WPP). Three disturbances are used to test the controllers including three-phase fault, transmission line outage, and voltage reference sudden change. MATLAB/SIMULINK is used in the simulation. Then, the results are compared to conventional multi-band controller (MB) and linear quadratic regulator (LQR). MPC shows efficient performance in handling the constraints and damping types of oscillations with the existence of the WPP in the case of partial power-sharing.

Multi-strategy adaptive cuckoo search algorithm for numerical optimization

Multi-strategy adaptive cuckoo search algorithm for numerical optimization

A novel differential dynamic gradient descent optimization algorithm for resource allocation and offloading in the COMEC system

The multiuser cooperative offloading mobile edge computing (COMEC) system has attracted much attention because it can realize delay-sensitive tasks. However, in the coupling optimization of offloading decision and resource allocation, the existing numerical optimization algorithms are difficult to obtain high-quality optimization solutions. In this paper, we propose a differential dynamic gradient descent (DDGD) optimization algorithm to solve the above optimization problems. DDGD algorithm decomposes the constrained NP-hard optimization problem into two network layers and integrates the constraint function into a larger end-to-end training network. These two-layer networks encode the dependencies and optimization constraints between parameter hidden states, which cannot be captured by a numerical optimization model or a full connection layer neural network. Because the ring learning and self-repeating learning architecture are adopted and the information is stored in the differential dynamics network, the proposed algorithm can achieve better and more intelligent decision-making in searching the solution trajectory without setting accurate parameters in advance and reduce the complexity of the network. We show that compared with the baseline method, the DDGD method has superior optimization performance in the energy consumption optimization of COMEC.

An algorithm to design a stabilizing feedback controller for linear delay systems via Parseval ’s theorem

We investigate feedback stabilization problems of a linear delay system. When the unstable characteristic roots of the system are far from the imaginary axis, the discretization of the system results in a large error. In this case, it is difficult to seek stabilizing control laws via the algorithm by Hu and Hu, (2020). To avoid the discretization of unstable differential equations, a modified state equation is constructed through a shifting parameter such that the equation is asymptotically stable. Then, based on the modified state equation and Parseval’s theorem, a numerical optimization algorithm is provided to design a stabilizing controller. Meanwhile, we compare the presented algorithm with those in the literature. Finally, numerical examples show that the presented algorithm in this paper is efficient.

RELIABILITY BASED DESIGN OF GEOTECHNICAL SYSTEMS BASED ON A DECOUPLED RELIABILITY ANALYSIS AND OPTIMIZATION APPROACH

Reliability-based design intends to design an engineering system subject to probabilistic design constraints. This paper presents a reliability design optimization approach of geotechnical engineering problems based on a decoupled reliability analysis and optimization concept. Geotechnical and foundation systems involve considerable uncertainties in soil properties, loading conditions, and inadequate site characterization. A traditional reliability design optimization method, such as the reliability index approach, requires a double-loop optimization structure, since reliability analysis is implemented for constraint function evaluation using a numerical optimization algorithm. The decoupled approach separates the reliability analyses of the constraint functions from the design optimization loop. An adaptive metamodeling method is proposed to create approximate functions of the reliability indices, so that the reliability design optimization is performed using the approximate functions of the reliability constraints. Radial basis functions are implemented to build the metamodels. To progressively improve the accuracy of predicting the reliability indices, an adaptive sampling technique is employed, so that new samples are added using the optimal points found in previous design iterations. Numerical examples are solved and presented, and the proposed design approach works well. It is shown to be a useful alternative for solving reliability-based design of geotechnical and foundation systems.

The design of an open-source carbonate reservoir model

This work presents a new open-source carbonate reservoir case study, the COSTA model, that uniquely considers significant uncertainties inherent to carbonate reservoirs, providing a far more challenging and realistic benchmarking test for a range of geo-energy applications. The COSTA field is large, with many wells and large associated volumes. The dataset embeds many interacting geological and petrophysical uncertainties in an ensemble of model concepts with realistic geological and model complexity levels and varying production profiles. The resulting number of different models and long run times creates a more demanding computational challenge than current benchmarking models. The COSTA model takes inspiration from the shelf-to-basin geological setting of the Upper Kharaib Member (Early Cretaceous), one of the most prolific aggradational parasequence carbonate formations sets in the world. The dataset is based on 43 wells and the corresponding fully anonymised data from the northeastern part of the Rub Al Khali basin, a sub-basin of the wider Arabian Basin. Our model encapsulates the large-scale geological setting and reservoir heterogeneities found across the shelf-to-basin profile, into one single model, for geological modelling and reservoir simulation studies. The result of this research is a semi-synthetic but geologically realistic suite of carbonate reservoir models that capture a wide range of geological, petrophysical, and geomodelling uncertainties and that can be history-matched against an undisclosed, synthetic ‘truth case’. The models and dataset are made available as open-source to analyse several issues related to testing new numerical algorithms for geological modelling, uncertainty quantification, reservoir simulation, history matching, optimization and machine learning. Supplementary material: supplementary data associated with this article can be found in the data repository for the COSTA model available at https://doi.org/10.17861/6e36e28d-50d9-4e31-9790-18db4bce6e5d and supplementary material is available at https://doi.org/10.6084/m9.figshare.c.5823571

Tracking and Regret Bounds for Online Zeroth-Order Euclidean and Riemannian Optimization

We study numerical optimization algorithms that use zeroth-order information to minimize time-varying geodesically convex cost functions on Riemannian manifolds. In the Euclidean setting, zeroth-order algorithms have received a lot of attention in both the time-varying and time-invariant cases. However, the extension to Riemannian manifolds is much less developed. We focus on Hadamard manifolds, which are a special class of Riemannian manifolds with global nonpositive curvature that offer convenient grounds for the generalization of convexity notions. Specifically, we derive bounds on the expected instantaneous tracking error, and we provide algorithm parameter values that minimize the algorithm's performance. Our results illustrate how the manifold geometry in terms of the sectional curvature affects these bounds. Additionally, we provide dynamic regret bounds for this online optimization setting. To the best of our knowledge, these are the first regret bounds even for the Euclidean version of the problem. Lastly, via numerical simulations, we demonstrate the applicability of our algorithm on an online Karcher mean problem.

Optimization of the biological valve appliance prosthetic heart valve

Highlights. With the use of numerical optimization algorithms, it is possible to qualitatively improve the performance (closing) of the leaflet apparatus of the heart valve prosthesis. Changing the length of the free edge of the lealflet of the prosthesis does not reduce the von Misess stress amplitude and does not change the nature of its distribution on the diagrams.Aim. Numerical study of the stress-strain state of a clinical heart valve prosthesis from the point of view of the impact of physiological loads and determination of ways to optimize the geometry of the biological leaflet apparatus.Methods. The object of study was a three-dimensional model of the UniLine (NeoCor, Russia) clinical prosthesis of the heart valve, size 23 mm, as well as four modifications focused on changing the length of the free edge. The study was carried out using the finite element method with imitation of the full cycle of operation of the leaflet apparatus under physiological conditions (pressure, heart rate). The parameters for the analysis were the qualitative and quantitative characteristics of the stress-strain state of the work of the five studied geometries.Results. It is shown that high stress areas are concentrated in two zones peripheral and free edges, regardless of the geometry. However, quantitatively, the von Mises stress amplitudes differed between the studied models. For example, the leaf shape, conventionally designated as “–10” degrees, demonstrated the smallest amplitude of this indicator relative to the original unmodified leaf model, thus reducing by a maximum of 18.8%. However, for the closed state, this model, on the contrary, showed an increase in the voltage index relative to the initial one by 8.3%. Other modification options showed similar trends.Conclusion. It is shown that despite the initial premise for optimizing the leaflet apparatus – reducing the length of the free edge and eliminating deformations of the closed state, the proposed geometry options did not significantly change the stress distribution map in the material, and also did not allow to significantly reduce the amplitudes of this parameter. Presumably, options for modifying the geometry and/or properties (rigidity, mobility) of another important component of the bioprosthesis, the support frame, which, in addition to the bearing function, provides damping of the hydrodynamic impact on the leaf due to some of its mobility, may become more promising.

Параметрическая оптимизация модального регулятора с ограничениями на основе метода роя частиц

The key to increasing the efficient functioning of automatic control systems for technical facilities and processes in various areas of industry is the optimal setting of the state feedback controller parameters, for instance, so as to minimize the duration of transient processes or achieve the minimum value of the integral control quality assessment. The optimization problem is solved for an integrand of a kind that ensures that the integral assessment better expresses the quality of control. At the same time, the control quality indicators are in a rather complex relation to the set parameters of the controller, which greatly complicates the analytical synthesis procedure. Numerical optimization algorithms differ in the way the adjustable parameters are changed, the most effective being those that achieve the result in a shorter computational time. Aim. The goal is to obtain the optimal parameter values for a state feedback controller with an integral component and limitations for continuous linear stationary systems based on the stochastic metaheuristic particle swarm method. Materials and methods. The modern theory of automatic control, swarm intelligence are used to solve the problem of optimizing the parameters of the state feedback controller and controlling technical systems. Results. The process of parametric optimization of a constrained state feedback controller using the particle swarm method for a one-dimensional controlled object is described. The results of simulation using the method of direct enumeration of the controller parameters and the particle swarm method are described and compared. Conclusion. The results of numerical studies allow us to conclude that the developed algorithm for particle swarm parametric optimization of a constrained state feedback controller is highly accurate and fast.

A hybrid approach based on simulation, optimization, and estimation of conjunctive use of surface water and groundwater resources.

Due to limited groundwater resources in arid and semi-arid areas, conjunctive use of surface water and groundwater is becoming increasingly important. In view of this, there are needs to improve the methods for conjunctive use of surface and groundwater. Using numerical models, optimization algorithms, and machine learning, we created a new comprehensive methodological structure for optimal allocation of surface and groundwater resources and optimal extraction of groundwater. The surface and groundwater system was simulated by MODFLOW to reflect groundwater transport and aquifer conditions. The important Marvdasht aquifer in the south of Iran was used as an experimental study area to test the methodology. In this context, we developed an optimal conjunctive exploitation model for dry and wet years using two new evolutionary algorithms, i.e., whale optimization algorithm (WOA) and firefly algorithm (FA). These were used in combination with the group method of data handling (GMDH) and least squares support vector machine (LS-SVM) to estimate sustainable groundwater withdrawal. The results show that the FA is more efficient in calculating optimal conjunctive water supply so that about 61% of water needs were met in the worst scenario for surface water resources, while it was 52% using the WOA. By applying the optimal conjunctive model during the simulation period, the groundwater level increased by about 0.4 and 0.55m using the WOA and FA, respectively. The results of Taylor's diagram, box plot diagram, and rock diagram with error evaluation criteria, i.e., root mean square error (RMSE), mean absolute error (MAE), and Nash-Sutcliffe efficiency (NSE), showed that the GMDH (RMSE = 6.04 MCM, MAE = 3.89 MCM, and NSE = 0.99) was slightly better than LS-SVM (RMSE = 6.36 MCM, MAE = 4.50 MCM, and NSE = 0.98) to estimate optimal groundwater use. The results show that machine learning models are cost- and time-effective solutions to estimate optimal exploitation of groundwater resources in complex combined surface and groundwater supply problems. The methodology can be used to better estimate sustainable exploitation of groundwater resources by water resources managers.