Test Problems Research Articles

Detecting bubbles via FDR and FNR based on calibrated p-values

Detecting bubbles in asset prices is still an open question that has attracted considerable attention in recent years. This paper improves the bubble detection and dating approaches developed in recent years by Phillips and co-authors, proposing to assess the plausibility of its outcomes via the false discovery rate (FDR) and the false non-discovery rate (FNR) based on calibrated p-values. Calibrating p-values of unit root tests, applied sequentially to detect bubbles, allows recovery of their super-uniformity property, which is crucial for a valid implementation of the inferential procedure. The paper also develops original self-calibrated versions of both FDR and FNR for the specific problem of bubble testing. Calibrated p-values are implemented in an online false discovery-based approach which monitors bubbles in real time. The effectiveness of the proposed methods is investigated via a simulation study and an empirical application.

A novel energy-bounded Boussinesq model and a well balanced and stable numerical discretisation

Many Boussinesq models suffer from nonlinear instabilities, especially in the context of rapid variations in the bed topography. In this work, a Boussinesq system is put forward which is derived in such a way as to be both linearly and nonlinearly energy-stable.The proposed system is designed to be robust for coastal simulations with sharply varying bathymetric features while maintaining the dispersive accuracy at any constant depth. For constant bathymetries, the system has the same linear dispersion relation as Peregrine's system ([22]). Furthermore, the system transitions smoothly to the shallow-water system as the depth goes to zero.In the one-dimensional case, we design a stable finite-volume scheme and demonstrate its robustness, accuracy and stability under grid refinement in a suite of test problems including Dingemans's wave experiment.Finally, we generalise the system to the two-dimensional case.

A local differential quadrature method for the generalized nonlinear Schrödinger (GNLS) equation

A local differential quadrature method based on Fourier series expansion numerically solves the generalized nonlinear Schrodinger equation. For time integration, a Runge-Kutta fourth-order method is used. Matrix stability analysis is used to examine the method's stability. Three test problems involving the motion of a single solitary wave, the interaction of two solitary waves, and a solution that blows up in finite time, respectively, demonstrate the accuracy and efficiency of the provided method. Finally, the numerical results obtained from the presented method are compared with the exact solution and those obtained in earlier works available in the literature.

Solving higher dimensional expensive black box global optimization problems using sparse directional search on surrogates

We present a new algorithm Directional Optimization Search with Surrogate (DOSS), for optimizing problems with box constraints and a computationally expensive black-box objective function. DOSS is a radial basis function (RBF) based method that mainly focuses on higher dimensional and computationally expensive objective functions that can be multimodal. DOSS introduces three new techniques not previously used in earlier RBF algorithms, including using a combination of the coordinates knowledge level, fewer initial sampling points, and the surrogate’s gradient information. Numerical results on a test set including 14 test problems with 36, 48, and 60 dimensions show that DOSS outperforms two recently published algorithms RBFOpt and TuRBO, and earlier RBF algorithms such as DYCORS. TuRBO is a Gaussian process based optimization algorithm, which outperformed earlier state-of-the-art methods. DOSS algorithm also has a good performance on real-world optimization problems, including robot pushing and rover trajectory planning problems. Almost sure convergence for the DOSS algorithm is also proven in this paper. An implementation of DOSS is available at https://doi.org/10.5281/zenodo.13731558.

Optimization of the electric vehicle charging strategy problem for sustainable intercity travels with multiple refueling stops

Electric vehicle (EV) drivers considering long-distance trips still face range anxiety due to the limited range of EVs and the scarcity of charging stations. Thus, it becomes important to ensure the feasibility of the selected route and determine an optimal charging strategy. As a crucial aspect of decision support for EV drivers, this study proposes a mixed integer linear programming (MILP) approach for the EV charging strategy problem (EVCSP), incorporating a piecewise linear approximation technique to address the challenges posed by nonlinear charging times. The proposed optimization model, namely CSPM determines where, when, and how much to charge an EV for a specified route to minimize travel time and cost. The solution time of large-scale test problems and a case study on Türkiye reveal the robustness and reliability of the CSPM. Furthermore, two multi-objective optimization methods (the weighted sum and the lexicographic method) are applied to the case study, and the results are analyzed. The results indicate that the travel cost is more sensitive to the selected charging strategy, with a range of 46.09 % across the applied charging strategies, whereas travel time remains more resilient, with a maximum fluctuation of 19.77 %. A comparative analysis with a full charging strategy reveals that the CSPM reduces the travel time by 60.1 % and improves the cost efficiency by 105.72 %.

Optimising seismic imaging design parameters via bilevel learning

Abstract Full waveform inversion (FWI) is a standard algorithm in seismic imaging. It solves the inverse problem of computing a model of the physical properties of the earth’s subsurface by minimising the misfit between actual measurements of scattered seismic waves and numerical predictions of these, with the latter obtained by solving the (forward) wave equation. The implementation of FWI requires the a priori choice of a number of ‘design parameters’, such as the positions of sensors for the actual measurements and one (or more) regularisation weights. In this paper we describe a novel algorithm for determining these design parameters automatically from a set of training images, using a (supervised) bilevel learning approach. In our algorithm, the upper level objective function measures the quality of the reconstructions of the training images, where the reconstructions are obtained by solving the lower level optimisation problem—in this case FWI. Our algorithm employs (variants of) the BFGS quasi-Newton method to perform the optimisation at each level, and thus requires the repeated solution of the forward problem—here taken to be the Helmholtz equation. This paper focuses on the implementation of the algorithm. The novel contributions are: (i) an adjoint-state method for the efficient computation of the upper-level gradient; (ii) a complexity analysis for the bilevel algorithm, which counts the number of Helmholtz solves needed and shows this number is independent of the number of design parameters optimised; (iii) an effective preconditioning strategy for iteratively solving the linear systems required at each step of the bilevel algorithm; (iv) a smoothed extraction process for point values of the discretised wavefield, necessary for ensuring a smooth upper level objective function. The algorithm also uses an extension to the bilevel setting of classical frequency-continuation strategies, helping avoid convergence to spurious stationary points. The advantage of our algorithm is demonstrated on a problem derived from the standard Marmousi test problem.

Алгоритм для численного решения диффузионно-реакционно-дрейфового уравнения с дробной производной по времени и координате

<p>The paper is devoted to the construction and program implementation of the computational algorithm for modeling a process of diffusion-drift nature based on the fractional diffusion approach. The mathematical model is formulated as an initial-boundary value problem for the time-space fractional diffusion-drift equation in a limited domain. Time and space fractional derivatives are considered in the sense of Caputo and Riemann – Liouville, respectively. A modified implicit finite-difference scheme is constructed. The concept of the considered mathematical problem provides an example of a deterministic model of the charging process of dielectric materials. An application program has been developed that implements the constructed numerical algorithm. The results were verified using the example of solving a test problem.</p>

A boundary-type algorithm based on the discrete ordinates for neutron transport equation

The spatial distribution of neutron flux in the core of a nuclear reactor plays a crucial role in ensuring nuclear safety. It can be determined by solving the neutron transport equation, where computational resource consumption is gradually receiving more attention, especially in problems with multiple reflective boundary conditions. It is common practice to assume initial boundary values in one angular direction to obtain a global solution, and then use reflective boundary conditions to solve for the other directions, iterating until convergence. However, this approach has the drawback of requiring the global solution, and each iteration necessitates storing the neutron flux values, consuming time and storage space. In order to address this issue, this paper proposes a precise and efficient boundary-type method, the Half Boundary Method (HBM). This method establishes relationships between adjacent node values through integration and mathematical deduction, ultimately obtaining the relationship among any node and the boundary values in any direction. As a result, iteration is only required for boundary values, reducing the iteration amount and thus saving time and storage space. Using the discrete ordinate (SN) method for angular discretization and HBM for spatial discretization, this paper solved the steady-state neutron transport equation for two-dimensional systems modeled with Cartesian geometry. The method is validated using several benchmark problems, including the 2D ISSA benchmark, the 2D mono-group k-eigenvalue problem and BWR rod bundle test problem. All of these problems demonstrate good results and effectively reduced computational time.

A new solution approach to proportion delayed and heat like fractional partial differential equations

The importance of fractional partial differential equations (FPDEs) may be observed in many fields of science and engineering. On the same hand their solutions and the approaches for the same are also very important to notice due to the effectiveness of the methods and accuracy of the results. This work discusses the diverse estimated analytic description of fractional partial differential equations (with proportion delay and heat like equation), applying the Iterative Laplace Transform Method. The specified method represents a significant advancement in the tool case of applied mathematicians and scientists. Its ability to efficiently and accurately solve complex differential equations, especially FPDEs. Here in this work, the solution of four test problems of FPDEs related to proportion delay and heat like equations is obtained for testing the validity and asset of the Iterative Laplace Transform Method. Further their numerical and graphical interpretations are also mentioned.

An adaptive interval many-objective evolutionary algorithm with information entropy dominance

Interval many-objective optimization problems (IMaOPs) involve more than three conflicting objectives with interval parameters. Various real-world applications under uncertainty can be modeled as IMaOPs to solve, so effectively handling IMaOPs is crucial for solving practical problems. This paper proposes an adaptive interval many-objective evolutionary algorithm with information entropy dominance (IMEA-IED) to tackle IMaOPs. Firstly, an interval dominance method based on information entropy is proposed to adaptively compare intervals. This method constructs convergence entropy and uncertainty entropy related to interval features and innovatively introduces the idea of using global information to regulate the direction of local interval comparison. Corresponding interval confidence levels are designed for different directions. Additionally, a novel niche strategy is designed through interval population partitioning. This strategy introduces a crowding distance increment for improved subpopulation comparison and employs an updated reference vector method to adjust the search regions for empty subpopulations. The IMEA-IED is compared with seven interval optimization algorithms on 60 interval test problems and a practical application. Empirical results affirm the superior performance of our proposed algorithm in tackling IMaOPs.

A comparative study of evolutionary algorithms and particle swarm optimization approaches for constrained multi-objective optimization problems

Many real-world optimization problems contain multiple conflicting objectives as well as additional problem constraints. These problems are referred to as constrained multi-objective optimization problems (CMOPs). Many meta-heuristics for solving CMOPs, called constrained multi-objective meta-heuristics (CMOMHs) have been introduced in the literature, including those using particle swarm optimization (PSO)(Kennedy and Eberhart, 1995), genetic algorithms (GAs)(Man et al., 1996), and differential evolution (DE)(Storn and Price, 1997). CMOMHs can be grouped into four different classes: classic CMOMHs, co-evolutionary approaches, multi-stage approaches, and multi-tasking approaches. An extensive comparative study of twenty different CMOMHs on a wide variety of test problems, including real-world CMOPs in the fields of science and engineering, is conducted. A multi-swarm PSO approach called constrained multi-guide particle swarm optimization (ConMGPSO) is introduced and compared to the best-performing previous approaches according to the comparative study. The performance of each algorithm was found to be problem dependent, however the best overall approaches were ConMGPSO, paired-offspring constrained evolutionary algorithm (POCEA)(He et al., 2021), adaptive non-dominated sorting genetic algorithm III (A-NSGA-III)(Jain and Deb, 2014), and constrained multi-objective framework using Q-learning and evolutionary multi-tasking (CMOQLMT)(Ming and Gong, 2023). ConMGPSO and POCEA had the best performance on the CF benchmark set, which contains examples of bi-objective and tri-objective CMOPs with disconnected CPOFs. The CMOQLMT approach had the best performance on the DAS-CMOP benchmark set, which contain additional difficulty in terms of feasibility-, convergence-, and diversity-hardness. For the selected real-world CMOPs, A-NSGA-III had the best performance overall. ConMGPSO was shown to have the best performance on the process, design, and synthesis problems, and had competitive performance for the power system optimization problems.

Gradient-enhanced deep Gaussian processes for multifidelity modeling

Multifidelity models integrate data from multiple sources to produce a single approximator for the underlying process. Dense low-fidelity samples are used to reduce interpolation error, while sparse high-fidelity samples are used to compensate for bias or noise in the low-fidelity samples. Deep Gaussian processes (GPs) are attractive for multifidelity modeling as they are non-parametric, robust to overfitting, perform well for small datasets, and, critically, can capture nonlinear and input-dependent relationships between data of different fidelities. Many datasets naturally contain gradient data, most commonly when they are generated by computational models that have adjoint solutions or are built in automatic differentiation frameworks.Principally, this work extends deep GPs to incorporate gradient data. We demonstrate this method on an analytical test problem and two realistic aerospace problems: one focusing on a hypersonic waverider with an inviscid gas dynamics truth model and another focusing on the canonical ONERA M6 wing with a viscous Reynolds-averaged Navier-Stokes truth model.In both examples, the gradient-enhanced deep GP outperforms a gradient-enhanced linear GP model and their non-gradient-enhanced counterparts.

A reinforcement learning-based multiobjective heuristic algorithm for multiple-truck routing problems with heterogeneous drones

As a result of new technological developments, drone usage has become common in last-mile logistics activities. Owing to the limited flight range of drones, drones may service customers by using trucks as hubs. Although the truck routing problem with drones (TRP-D) has been studied frequently, studies that have addressed this problem in a multiobjective manner are rare. In this study, multiobjective TRP-D is discussed. In this problem, multiple trucks are considered. Each truck is equipped with multiple heterogeneous drones. A multiobjective mixed-integer linear programming (MILP) model is proposed. Since the problem is NP-hard, a reinforcement learning (RL)-based multiobjective heuristic algorithm is proposed to obtain solutions in large-scale cases. A three-phase heuristic feasible-solution-generation algorithm is proposed. The variable neighbourhood descent (VND) algorithm with RL is proposed as a local search algorithm for the multiobjective optimization problem. The results of the proposed heuristic algorithm are compared with the Pareto optimal solutions for small-sized test problems via the augmented ε-constraint (AUGMECON) method and the CPLEX solver. The proposed algorithm is also compared with state-of-the-art multiobjective heuristic algorithms for large-scale problems. According to the results, the proposed algorithm is an efficient multiobjective heuristic algorithm for the addressed problem.

Testing for Sufficient Follow-Up in Censored Survival Data by Using Extremes.

In survival analysis, it often happens that some individuals, referred to as cured individuals, never experience the event of interest. When analyzing time-to-event data with a cure fraction, it is crucial to check the assumption of "sufficient follow-up," which means that the right extreme of the censoring time distribution is larger than that of the survival time distribution for the noncured individuals. However, the available methods to test this assumption are limited in the literature. In this article, we study the problem of testing whether follow-up is sufficient for light-tailed distributions and develop a simple novel test. The proposed test statistic compares an estimator of the noncure proportion under sufficient follow-up to one without the assumption of sufficient follow-up. A bootstrap procedure is employed to approximate the critical values of the test. We also carry out extensive simulations to evaluate the finite sample performance of the test and illustrate the practical use with applications to leukemia and breast cancer datasets.

A-4 Step Chebyshev Based Multiderivative Direct Solver For Third Order Ordinary Differential Equations

This paper develops and examines a uniform order, 4 step block method with Chebyshev series as bases function. Collocation and interpolation technique was used to modeled implicit discrete schemes from continuous scheme to derive our block. The block method obtained was of order 4. It is consistent, zero stable and consequently zero stable. The results obtained from four test problems shown that the method converges to exact solutions and perform better than some existing methods in the literatures.

Preventing mass loss in the standard level set method: New insights from variational analyses

For decades, the computational multiphase flow community has grappled with mass loss in the level set method. Numerous solutions have been proposed, from fixing the reinitialization step to combining the level set method with other conservative schemes. However, our work reveals a more fundamental culprit: the smooth Heaviside and delta functions inherent to the standard formulation. Even if reinitialization is done exactly, i.e., the zero contour interface remains stationary, the use of smooth functions lead to violation of mass conservation. We propose a novel approach using variational analysis to incorporate a mass conservation constraint. This introduces a Lagrange multiplier that enforces overall mass balance. Notably, as the delta function sharpens, i.e., approaches the Dirac delta limit, the Lagrange multiplier approaches zero. However, the exact Lagrange multiplier method disrupts the signed distance property of the level set function. This motivates us to develop an approximate version of the Lagrange multiplier that preserves both overall mass and signed distance property of the level set function. Our framework even recovers existing mass-conserving level set methods, revealing some inconsistencies in prior analyses. We extend this approach to three-phase flows for fluid-structure interaction (FSI) simulations. We present variational equations in both immersed and non-immersed forms, demonstrating the convergence of the former formulation to the latter when the body delta function sharpens. Rigorous test problems confirm that the FSI dynamics produced by our simple, easy-to-implement immersed formulation with the approximate Lagrange multiplier method are accurate and match state-of-the-art solvers.

Numerical Study of the Reaction Diffusion Prey–Predator Model Having Holling II Increasing Function in the Predator Under Noisy Environment

The current study deals with the stochastic diffusive prey–predator model with Holling II increasing function in the predator. As it is a population dynamics its population can be affected by various factors such as disease in prey–predator species, environmental fluctuation, etc. So, the underlying model is considered under the impact of a temporal multiplicative noise. The numerical solution of the governing model is obtained by finite difference schemes. To check the accuracy of the numerical solution, the stability and consistency of the schemes in the mean square sense are derived. All the schemes are consistent with the model and von Neumann stable. Several simulations are drawn to check the efficacy of the scheme. A test problem is investigated with numerical schemes and for the different values of the parameters, 3D and 2D plots are drawn. A graphical representation of the given system is drawn which shows the behavior of both species and the efficiency of the novel schemes. Hope so, these results will motivate the researcher to consider the stochastic prey–predator model for a better understanding of the ecosystem.

Near-optimal March Tests for Three-Cell and Four-Cell Coupling Fault Models in Random-Access Memories

This research work addresses the problem of testing n×1 RAMs in which complex models of unlinked static three or four-cell coupling faults are considered. As in other works, it is assumed that only physically neighboring memory cells could be involved in a three or four-cell coupling fault. For this reason, these fault models can also be considered to be of the neighborhood pattern sensitive type. As extensions of the well-known model of all unlinked static two-cell coupling faults, the fault models we address are complex including faults sensitized by a transition write operation as well as faults sensitized by a non-transition write or a read operation. For these complex models, near-optimal multirun march tests are proposed. This optimality assessment is based on the fact that, for any group of cells corresponding to the considered fault model, the state graph is completely covered, and each arc is traversed only once, which means that the graph is of the Eulerian type. Additional write operations are only required for data background changes.

CT-Based method for determining the elastic properties of an inhomogeneous medium element

The determination of mechanical parameters is one of the relevant directions in the calculation of inhomogeneous media elements. The need to build numerical models is primarily due to the development of modern approaches to the reconstruction of materials of various composite structures. The use of computational models in clinical practice also makes it possible to study the strength characteristics of objects of biological origin, the features of which include the uniqueness of the material structural distribution. The most widespread approaches in this case are based on the use of image data. Within the framework of this work, a method for constructing an elasticity matrix based on digital twin data is presented. During the work, images with a given material structure are constructed, as well as data extraction from CT scans of full-scale samples. The averaging of mechanical parameters was performed on the basis of the finite element method for the area of square or cubic geometry defining the unit cell. The calculations performed by the proposed method showed the convergence of the method with the analytical calculation data on the example of solving test problems, and also determined the qualitative correspondence of the results to the features of the structural distribution of the material in full-scale samples. The presented homogenization method makes it possible to determine the elastic characteristics of a medium element, taking into account the inhomogeneous properties of the forming material.

Analysis of the Effectiveness of Using a High-Accuracy Numerical Algorithm in the Simulation of Two-Phase Flow Problems

The continuous technical development of weapons and ammunition, as well as the growing requirements placed on new equipment, require the use of modern tools for their designing and testing. The analysis of the operation of powder propellant systems, which is the focus of interior ballistics, requires particularly specialised tools due to the complexity of the phenomena occurring during a shot. The development of numerical methods and the increase in the computing power of modern computers have enabled the modelling and simulation of highly complex physical problems and the development of numerical schemes with a theoretically arbitrary high order of accuracy. In this study, an attempt was made to develop a one-dimensional model of two-phase flows with a high order of solution accuracy in time, based on the finite volume method. The use of a two-phase flow model in the context of interior ballistics allows, among other things, the analysis of wave phenomena occurring during firing, which is crucial for safety reasons, especially in tank guns. The developed algorithm for solving two-phase systems was checked using recognised test problems for this type of model. The results of the work will be used to develop a numerical model to solve the main problem of interior ballistics.