Improve Solution Accuracy Research Articles

Extension of Radiative Transfer Coherent Backscattering RT-CB code to dense discrete random media

The Radiative transfer coherent backscattering (RT-CB) code is extended to apply to dense discrete random media of optically soft spherical particles. This is achieved by utilizing the well-known static-structure-factor (SSF) correction derived from the Percus–Yevick approximation for sticky-hard-sphere (SHS) pair correlation function. The code is verified against the numerically exact electromagnetic method for small spherical media consisting of submicrometer-sized icy particles at optical wavelengths. The SSF-corrected RT-CB method significantly improves solution accuracy, and the solution agrees well with the numerically exact solution when the packing density is less than 20% and particles are optically soft, i.e., the refractive index of particles is close to that of the background medium.

Dispersion Analysis of Three-Dimensional Elastic Wave Propagation in Transversely Isotropic Media Using Optimally Blended Spectral-Element Method

The accuracy of the optimally blended spectral-element method for wave propagation in a homogeneous transversely isotropic elastic medium was investigated. A nonstandard quadrature rule obtained by combining Gauss quadrature rule and Gauss–Lobatto–Legendre quadrature rule was used to compute elementary matrixes. The mass and stiffness matrixes were represented as the triple tensor-product of elementary matrixes as second-order tensors. The solution of the eigenvalue problem representing the semidiscretized version of elastic wave equation for plane harmonic wave propagation was obtained using the Rayleigh quotient approximation technique. The resulting eigenvalues subsequently were used to estimate the phase and group velocity of three bulk waves. The variations of the errors in these velocities of the bulk waves with the number of grid points per wavelength were depicted graphically. These variations were shown for different polynomial orders and various angles of deviation from the symmetry axis. The effect of a change in the order of time discretization on error variation also was shown. The solution obtained by the optimally blended spectral-element method was found to be more accurate than that from the classical spectral-element method for low-order polynomials. The improvement in solution accuracy was demonstrated through dispersion analysis.

A mutually embedded perception model for solar corona

ABSTRACTThis paper proposes a new mutually embedded perception model (MEPM) based on the 3D magnetohydrodynamic (MHD) equations of the solar wind plasma to reconstruct the structure of the solar corona. The goal is to embed the physics-based information and gradient into solar wind parameters data through the neural network and leverage the adaptive procedures to improve solution accuracy. The loss term proportional to the divergence is directly introduced to force a divergence-free solution. The established MEPM displays almost the same results as the exact solution for an artificial 3D analytic problem and the Parker solar wind for 1D steady Parker flow with the corresponding boundary conditions. The MEPM can well capture the solar coronal leading structures, recover the results of the traditional numerical schemes, and be consistent with the observations with CR 2068 as an example. When supplementary data (from the results of the MHD simulation or empirical models) are used, the modeled results improve. This implies that in situ satellite observations as supplementary data can be incorporated into the model in the same way.

A total energy-based adaptive mesh refinement technique for the simulation of compressible flow

In this paper, an adaptive mesh refinement technique is presented for simulation of compressible flows, which can effectively refine the mesh in the regions with shock waves and vortices. The present approach uses the total energy per unit volume as an indicator to capture the shock waves and vortical structures. In the approach, an h-refinement strategy is adopted. To save the computational effort, the flow variables on the new mesh are obtained from the previous step by interpolation, which ensures that the problem is always solved on the refined mesh. Both inviscid and viscous compressible flows are considered in this work. Their governing equations are, respectively, Euler equations and Navier–Stokes equations associated with the implementation of the Spalart–Allmaras turbulence model. The cell-centered finite volume method and Jameson scheme are chosen to carry out spatial discretization, and the five-stage Runge–Kutta scheme is applied to discretize the temporal derivative. The present approach is applied to simulate three test problems for its validation. Numerical results show that it can effectively capture the shock waves and vortices with improvement in solution accuracy.

Deep neural network method for solving the fractional Burgers-type equations with conformable derivative

In this article, we introduce the modified physics-informed neural network (PINN) method for finding data-driven solutions of three classes of time-fractional Burgers-type equations under the conformable sense. Since conformable derivative satisfies the chain rule, automatic differentiation can be applied to compute it directly to avoid truncation and other numerical discretization. In addition, the locally adaptive activation function and two effective weighting strategies are introduced to improve solution accuracy. As a result, three numerical examples indicate that the modified PINN method gives an efficient and reliable solution.

Multi-Strategy Improved Flamingo Search Algorithm for Global Optimization

To overcome the limitations of the Flamingo Search Algorithm (FSA), such as a tendency to converge on local optima and improve solution accuracy, we present an improved algorithm known as the Multi-Strategy Improved Flamingo Search Algorithm (IFSA). The IFSA utilizes a cube chaotic mapping strategy to generate initial populations, which enhances the quality of the initial solution set. Moreover, the information feedback model strategy is improved to dynamically adjust the model based on the current fitness value, which enhances the information exchange between populations and the search capability of the algorithm itself. In addition, we introduce the Random Opposition Learning and Elite Position Greedy Selection strategies to constantly retain superior individuals while also reducing the probability of the algorithm falling into a local optimum, thereby further enhancing the convergence of the algorithm. We evaluate the performance of the IFSA using 23 benchmark functions and verify its optimization using the Wilcoxon rank-sum test. The compared experiment results indicate that the proposed IFSA can obtain higher convergence accuracy and better exploration abilities. It also provides a new optimization algorithm for solving complex optimization problems.

Electric Fences for Dockless Bike-Sharing Systems: An Electric Fence-Planning Framework for a Dockless Bike-Sharing System Based on a Land Parcel Subdivision and Regional Coverage Maximization

Dockless bike sharing (DBS) is convenient for bike users because it can solve their last-mile problems. However, dockless bikes that are disorderly parked in public spaces can disturb normal traffic. In planning electric fences for DBS systems, the maximum coverage location problem (MCLP) identifies locations suitable for electric fences. However, the MCLP model ignores the regional boundaries of bike use and causes substantial errors in coverage assessments. In this article, we present a novel framework for planning electric fences, accounting for both trip distribution and area shapes. We first introduce a dynamic land parcel subdivision algorithm, which can reasonably divide the city into fine-scale regions concerning the distributions of spatial parking demands. Then, we formulate the electric fence-planning problem as a regional coverage maximization problem. We develop an accelerated maximum coverage model with complementary coverage (MCMCC) to locate electric fence areas, which can improve solution accuracy and reliability. The DBS data of Shenzhen, China, are used to validate the framework. The study findings indicate that MCMCC produces more robust and accurate results than the MCLP model because the planning solutions are not affected by changes in the shapes and sizes of the regions. The framework can also automatically and accurately determine electric fence capacities and locations.

High-Resolution Reconstruction of FMT Based on Elastic Net Optimized by Relaxed ADMM.

Fluorescence Molecular Tomography (FMT), providing thethree-dimensional fluorescent distribution information of specific molecular probes in tumors, is widely applied to detect in vivo tumors. However, the ill-posedness of reconstruction greatly affects the resolution of FMT. Traditional methods have introduced different regularization terms to solve this problem, but there are still challenges for the high-resolution reconstruction of small tumors under complex conditions. In this paper, we proposed an elastic net method optimized by the relaxed Alternating Direction Method of Multipliers (EN-RADMM) to improve the reconstruction resolution for small tumors. The objective function consisted of the Least-Square term and elastic net regularization. Relaxation, equivalent deformation directing at ill-posed equations, and LU decomposition were applied to accelerate algorithm convergence and improve solution accuracy. Thereby, the light from small tumors can be precisely reconstructed. We designed a series of digital tumor models with different distances, sizes, and shapes to verify the performance of EN-RADMM, and utilized the real glioma-bearing mouse models to further verify its feasibility and accuracy. The simulation results demonstrated that EN-RADMM can achieve significantly higher resolution and reconstruction accuracy of morphology and position with less time compared with other advanced methods. Furthermore, in vivo experiments proved the broad prospect of EN-RADMM in pre-clinical application of FMT reconstruction.

Creep modeling of composite materials based on improved gene expression programming

In this article, a new method for creep modeling and performance prediction of composite materials is presented. Since Findley power-law model is usually suitable for studying one-dimensional time-dependent creep of materials under low stress, an intelligent computing method is utilized to derive three temperature-related sub-functions, the creep model as a function of time and temperature is established. In order to accelerate convergence rate and improve solution accuracy, an improved gene expression programming (IGEP) algorithm is proposed by adopting the probability-based population initialization and semi-elite roulette selection strategy. Based on short-term creep data at seven temperatures, a bivariate creep model with certain physical significance is developed. At fixed temperature, the univariate creep model is acquired. R2, RMSE, MAE, RRSE statistical metrics are used to verify the validity of the developed model by comparison with viscoelastic models. Shift factor is solved by Arrhenius equation. The creep master curve is derived from time–temperature superposition model, and evaluated by Burgers, Findley and HKK models. R-square of IGEP model is above 0.98 that is better than classical models. Moreover, the model is utilized to predict creep values at t = 1000 h. Compared with experimental values, the relative errors are within 5.2%. The results show that the improved algorithm can establish effective models that accurately predict the long-term creep performance of composites.

A second-order modular grad-div stabilized scheme for the Darcy–Brinkman model

In this article, a fully discrete modular grad-div stabilized finite element scheme for the Darcy–Brinkman equations are considered. This fully discrete scheme includes two steps: the first step is a combination of a mixed finite element approximation for space discretization, the second-order backward differentiation formula for temporal discretization, and extrapolated treatments in linearization for the nonlinear terms. Then, in the second step, a modular grad-div stabilized technique is applied, which can improve solution accuracy without increasing computational time for large stabilized parameters. Moreover, we show that the scheme is unconditionally stable and convergent with second-order accuracy with respect to time step. Finally, several numerical examples are provided to support the derived theoretical results, and demonstrate the efficiency of the presented scheme.

Improved Black Widow Spider Optimization Algorithm Integrating Multiple Strategies.

The black widow spider optimization algorithm (BWOA) had the problems of slow convergence speed and easily to falling into local optimum mode. To address these problems, this paper proposes a multi-strategy black widow spider optimization algorithm (IBWOA). First, Gauss chaotic mapping is introduced to initialize the population to ensure the diversity of the algorithm at the initial stage. Then, the sine cosine strategy is introduced to perturb the individuals during iteration to improve the global search ability of the algorithm. In addition, the elite opposition-based learning strategy is introduced to improve convergence speed of algorithm. Finally, the mutation method of the differential evolution algorithm is integrated to reorganize the individuals with poor fitness values. Through the analysis of the optimization results of 13 benchmark test functions and a part of CEC2017 test functions, the effectiveness and rationality of each improved strategy are verified. Moreover, it shows that the proposed algorithm has significant improvement in solution accuracy, performance and convergence speed compared with other algorithms. Furthermore, the IBWOA algorithm is used to solve six practical constrained engineering problems. The results show that the IBWOA has excellent optimization ability and scalability.

Performance enhancement of UPQC based on optimized GBSSA hybrid fuzzy controller with EPLL

In this research, UPQC (Unified Power Quality Conditioner) with optimized hybrid fuzzy controller based GBSSA (Gaussian Barebone Salp Swarm Algorithm) with EPLL (Enhanced Phase Locked Loop) have been proposed for power quality enhancement in power distribution networks. Using the proposed method, the difficulties in major of the power distribution system networks can be solved, related to power quality issues. GBSSA has been employed in this research, to improve solution accuracy and optimization efficiency. Given that, it is permissible to add some extra time cost to acquire a better solution, based on the Non-Free Lunch (NFL) theory, and that the time consumption of function evaluation is rather large, when addressing actual optimization problems, the extra time consumption can be overlooked to some extent. The EPLL control method improves the standard PLL, by reducing its fundamental flaw, which is the occurrence of main frequency errors, as well as double frequency errors. It controls the DC-bus voltage of unified power quality conditioners, during supply voltage and load voltage turbulences. The proposed UPQC control technique has been found to be resilient, to a variety of source and load perturbations, including unbalanced, transient distorted supply, voltage sag, unbalanced load and voltage swell. The proposed optimized GBSSA hybrid fuzzy controller with EPLL has been proven to be more effective in reducing the THD (Total Harmonic Distortion) to 3.22%. Moreover, comparative analysis with a conventional TSF-PLL has been performed with that of Takagi-Sugeno fuzzy controller and implemented using MATLAB (MATrix Laboratory).

Information-decision searching algorithm: Theory and applications for solving engineering optimization problems

The nature of the real-world problem is multi-modal and multidimensional. This paper proposes a novel metaheuristic algorithm based on social behaviors of people acquiring favorable information, which is the society-based metaheuristic optimization mechanism, called the Information-Decision Search Algorithm(IDSE), aiming to provide a new optimization technology for solving real-world optimization problems. This optimization technology proposes special searching mechanisms of delivery behavior, approaching behavior, inheritance behavior, mutation behavior, interaction, and learning behavior, establishing corresponding mathematical models to develop an efficient optimization framework for solving constrained optimization. The performance of the proposed algorithm and 10 state-of-the-art optimizers is evaluated on 46 benchmarks, including convergence, solution accuracy, robustness, diversity, significance, and the dimensional-scalability on CEC 2017 benchmarks (50 Dim and 100 Dim). The statistical results suggest, with the dimensionality of the problem variable increasing, the computing efficiency of the proposed optimization technology keeps on the highest level at all times. The low-rank feature for IDSE on 46 benchmarks emphasizes the selective priority in solving the same optimization problem. In addition, IDSE also considers 7 real-world engineering problems. The comparison results suggest that IDSE is superior to competitive algorithms in improving solution accuracy and reducing optimization costs, indicating the significant performance for solving constraint optimization.

Improved moth flame optimization algorithm based on opposition-based learning and Lévy flight distribution for parameter estimation of solar module

An enhanced version of the moth flame optimization algorithm is proposed in this paper for rapid and precise parameter extraction of solar cells. The proposed OBLVMFO algorithm’s novelty lies primarily in the improved search strategies, where two modifications are proposed to maintain a proper balance between exploration and exploitation. Firstly, an opposition-based learning mechanism is employed to initialize the search population for the purpose of enhancing the global search. Secondly, Lévy flight distribution is used to prevent the stagnation of solutions in local minima. The implementation of intelligent rules such as OBL and Lévy flight distribution significantly improves the performance of the standard MFO. The developed OBLVMFO performed adequately and is reliable in terms of RMSE compared to other methodologies such as MFO, ALO, SCA, MRFO, and WOA. The best optimized value of RMSE achieved by OBLVMFO is 6.060E−04, 1.3600E−05, and 7.0001E−06 for STE 4/100 (polycrystalline), LSM 20 (monocrystalline), and SS2018P (polycrystalline) PV modules, respectively. The experiments performed on the benchmark test function revealed that the OBLVMFO has a 61% faster convergence speed than the standard version of MFO, which improves solution accuracy. In addition to this, two non-parametric tests: Friedman ranking and Wilcoxon rank sum are performed for the validation.

Incorporation of anisotropic scattering into the method of characteristics

In this study, we incorporate an anisotropic scattering scheme involving spherical harmonics into the method of characteristics (MOC). The neutron transport solution in a light water reactor can be significantly improved because of the impact of an anisotropic scattering source with the MOC flat source approximation. Several problems are selected to verify the proposed scheme and investigate its effects and accuracy. The MOC anisotropic scattering source is based on the expansion of spherical harmonics with Legendre polynomial functions. The angular flux, scattering source, and cross section are expanded in terms of the surface spherical harmonics. Later, the polynomial is expanded to achieve the odd and even parity of the source components. Ultimately, the MOC angular and scalar fluxes are calculated from a combination of two sources. This paper presents various numerical examples that represent the hot and cold conditions of a reactor core with boron concentration, burnable absorbers, and control rod materials, with and without a reflector or baffle. Moreover, a small critical core problem is considered which involves significant neutron leakage at room temperature. We demonstrate that an anisotropic scattering source significantly improves solution accuracy for the small core high-leakage problem, as well as for practical large core analyses.

Adaptive backtracking search optimization algorithm with a dual-learning strategy for dynamic economic dispatch with valve-point effects

Dynamic economic dispatch with valve-point effect (DED_vpe) is a dynamic nonlinear high-dimensional optimization problem with non-smooth and non-convex characteristics. Meta-heuristic methods have become the mainstream for solving the DED_vpe problem. However, most of these methods only focus on minimizing the generation costs and ignore the algorithmic robustness. In this paper, an adaptive backtracking search optimization algorithm with a dual-learning strategy (DABSA) is proposed for solving the DED_vpe problem. In DABSA, a dual-learning strategy (DL) based on the current and historical optimal individuals is developed to update each individual. This updating strategy helps DABSA improve solution accuracy and overcome premature convergence. In addition, an adaptive parameter control mechanism (APC), which can automatically adjust parameter ‘mixrate’ value according to the current iteration number, is presented. To handle the system constraints, a ‘repair + penalty’ constraints-handling approach is employed to lead non-feasible solutions towards the feasible region quickly. The performance of DABSA is assessed by testing on four DED problems containing 5, 10 and 30 units. The experimental results show that DABSA is very competitive compared with reported representative methods in yielding low fuel costs along with high robustness.

An Amalgamated Heap and Jellyfish Optimizer for economic dispatch in Combined heat and power systems including N-1 Unit outages

One of the critical optimization issues in the economic management of power and heat systems is the Combined heat and power economic dispatch (CHPED). The valve-point effects of thermal units as well as the interdependency of CHP outputs make the nonlinearity and non-convexity in optimization and dispatch models. A novel Amalgamated Heap-based and JellyFish Optimizer (AHJFO) is proposed, in this paper, to improve the efficiency of two newly developed techniques, Heap-based Optimizer (HO) and Jellyfish Optimizer (JFO). The proposed AHJFO incorporates an adjustment strategy function (ASF) to increase the explorative characteristic at the beginning of iterations by upgrading the produced solutions using HO. Further, as iterations go, it improves the exploitative characteristic by expanding the created solutions using JFO. The proposed AHJFO provides higher effectiveness compared to HO and JFO to obtain the solution of CHPED problem for medium 24 and large 96-unit systems. The simulation results show that the proposed AHJFO based on ASF aids in the avoidance of premature convergence and improves solution accuracy. Besides, the proposed AHJFO is successfully applied to the CHPED issue involving (N-1) unit outages. A re-dispatch strategy based on AHJFO is presented and the impact of outages of all units is analyzed after (N-1) unit outages. Also, further applications of the proposed AHJFO for ED problem are carried out with/without additional constraint models of power flow considering the IEEE 30-bus system. The simulation results show the superiority of the proposed AHJFO compared to HO, JFO and other algorithms for solving the CHPED and ED issues. Moreover, feasibility study is demonstrated of the solutions obtained for the CHPED and ED issues with additional constraint models.

Ray effects mitigation using the Monte Carlo first collision source method and application to the Kobayashi benchmark problems

The problem of ray effects, arising in the calculation of local source problems with low scattering media, have been perplexing the discrete ordinates (SN) method. Conventionally, the first collision source technique based on deterministic methods is used to remedy ray effects. In this paper, we investigate a technique based on Monte Carlo method to calculate first collision source distributions and consequently mitigate the ray effects. The Monte Carlo first collision source (MC-FCS) method has been implemented into the three-dimensional (3D) parallel SN transport code Marvin. The 3D Kobayashi benchmark problems were used to systematically verify effectiveness of the MC-FCS solver and to evaluate its computational efficiency. Numerical results show that: the MC-FCS solver has been correctly implemented; the MC-FCS method is highly effective in remedying ray effects; and computational efficiency of MC-FCS is acceptable, especially considering the great improvement in solution accuracy it can bring.

Application research of a new neighbourhood structure with adaptive genetic algorithm for job shop scheduling problem

The job shop scheduling problem (JSSP) is to find the optimal jobs sequence to optimise one or more performance indicators and makespan is the most common optimisation target. In solving NP-hard problems such as JSSPs by genetic algorithm (GA), trapping in local extremum, low search efficiency and instability are often encountered, especially unable to find the optimisation direction. To restrain this condition, a new neighbourhood structure with adaptive GA was put forward. The crossover probability (Pc) and mutation probability (Pm) can be adjusted in nonlinear and adaptive based on the dispersion of the fitness of population in the evolution. The idle time before critical operations can be made full use of through the multi-operations combination and adjustment. To research the performance of the proposed method in solving JSSPs, a detailed application scheme was given out for the process of it. In the solving scheme, the chromosome active decoding algorithm with the objective function of maximum makespan was proposed. From the results of testing of 28 JSSP benchmark instances in 3 adaptive strategies and 3 neighbourhood strategies, the new neighbourhood structure with adaptive GA has been significant improvement in solution accuracy and convergence efficiency.

Households, auctioneers, and aggregation

We examine aggregation in the neoclassical growth model with aggregate shocks and uninsurable employment risk, as well as related environments. We introduce a Walrasian auctioneer whose job is to report to households all possible state-contingent future prices. Households take these as given when forming expectations and making optimal consumption/savings decisions, and the auctioneer adjusts her forecasts until markets clear. This natural dichotomy between the households and the auctioneer allows us to study each problem in isolation as well as to discuss the intersection. On the household side, we separate an explicit expression for the linear permanent income component of savings from a well-behaved nonlinear adjustment arising from precautionary behavior and incomplete markets. Equipped with this decomposition, we then study how economies aggregate in the presence of various auctioneer types that are popular in the literature. The steady-state auctioneer of Huggett (1997) and Aiyagari (1994) offers a paper-and-pencil analysis of aggregation that provides a bound on more complex environments. We provide an economic interpretation of the regression coefficients and explain the lack of time variation in the auctioneer of Krusell and Smith (1998). We also introduce a new numerical method which uses the empirical distribution of auctioneer forecasts to substantially improve solution accuracy in cases where the standard coefficient of determination and other well-known statistics prove to be misleading.