Numerical Optimization Method Research Articles

Research of nonstationary dynamic models of the organizational and technological process of railway transport technical vehicles repair

The problems of analytical and computer research of dynamic models of repair and operation of technical vehicles used in railway transport are among the urgent problems related to ensuring safety and stability of traffic, with the development of digital twins and the improvement of monitoring and diagnostic systems. The analysis of models described by various types of multidimensional nonlinear differential equations requires the use of modern methods of dynamical systems theory, numerical optimization and computer algebra. The purpose of the article is to conduct a qualitative and numerical analysis of mathematical models of organizational and technological processes (OTP) in railway transport, as well as the synthesis of new controlled OTP models. Nonstationary generalizations of a two-dimensional dynamic model describing the repair process of railway transport equipment are proposed. Various cases of using constant and time-dependent parameters are considered. The case of linear and exponential dependences of parameters on time is studied. For the studied models, trajectories are obtained taking into account the variation of constant parameters and taking into account the choice of parametric dependencies, a comparative analysis of the results is presented. The formulation of the problem of optimal control of the number of repaired and repaired railway wagons is proposed. Promising methods for solving this problem using numerical optimization methods, including those inspired by nature, are described. The results can be used in the tasks of constructing and analyzing mathematical models of dynamic systems, in the tasks of numerical modeling of transport systems and technological processes, in the tasks of optimizing the number of vehicles and improving the transportation process, as well as in the tasks of creating digital counterparts in the transport industry.

Vertical Parking Trajectory Planning With the Combination of Numerical Optimization Method and Gradient Lifting Decision Tree

Vertical Parking Trajectory Planning With the Combination of Numerical Optimization Method and Gradient Lifting Decision Tree

Hyper-Heuristic Approach for Tuning Parameter Adaptation in Differential Evolution

Differential evolution (DE) is one of the most promising black-box numerical optimization methods. However, DE algorithms suffer from the problem of control parameter settings. Various adaptation methods have been proposed, with success history-based adaptation being the most popular. However, hand-crafted designs are known to suffer from human perception bias. In this study, our aim is to design automatically a parameter adaptation method for DE with the use of the hyper-heuristic approach. In particular, we consider the adaptation of scaling factor F, which is the most sensitive parameter of DE algorithms. In order to propose a flexible approach, a Taylor series expansion is used to represent the dependence between the success rate of the algorithm during its run and the scaling factor value. Moreover, two Taylor series are used for the mean of the random distribution for sampling F and its standard deviation. Unlike most studies, the Student’s t distribution is applied, and the number of degrees of freedom is also tuned. As a tuning method, another DE algorithm is used. The experiments performed on a recently proposed L-NTADE algorithm and two benchmark sets, CEC 2017 and CEC 2022, show that there is a relatively simple adaptation technique with the scaling factor changing between 0.4 and 0.6, which enables us to achieve high performance in most scenarios. It is shown that the automatically designed heuristic can be efficiently approximated by two simple equations, without a loss of efficiency.

Application to optimize the geometry of a parallel kinematics sun tracker

A detailed description is made of a software application that is designed to optimize a sun-tracker mechanism. It takes the main characteristics of any given installation site into account: geographical coordinates, inclination and orientation of the assembly platform. The desired result is a low-cost mechanism, which will have minimum-length construction elements, which will maximize coverage, and which will furthermore have the most energy efficient configuration. A multi-objective optimization technique (MOEAs) and numerical methods have successfully been applied to achieve these design objectives. In addition, the most computationally efficient kinematic model for the mechanism is analysed.

A sequential sampling-based Bayesian numerical method for reliability-based design optimization

For efficiently solving the Reliability-Based Design Optimization (RBDO) problem with multi-modal, highly nonlinear and expensive-to-evaluate limit state functions (LSFs), a sequential sampling-based Bayesian active learning method is developed in this work. The penalty function method is embedded to transform the constrained optimization problem into a non-constrained one to reduce the model complexity. The proposed method for solving RBDO problems starts by training a Gaussian process (GP) model, in the augmented space of random and design variables. It is then based on an efficient sampling scheme for simulating the GP model, the adaptive Bayesian optimization (BO) and Bayesian reliability analysis (BRA) procedures are combined in a collaborative way for sequentially producing the joint training points. BO driven by expected improvement (EI) function is used for inferring the global optimum in the design space with global convergence, and the BRA equipped with U function is implemented for inferring the failure probabilities at the identified design points with the desired accuracy. The superiority of the proposed method is demonstrated with two numerical and two real-world engineering examples.

Load balance -aware dynamic cloud-edge-end collaborative offloading strategy.

Cloud-edge-end (CEE) computing is a hybrid computing paradigm that converges the principles of edge and cloud computing. In the design of CEE systems, a crucial challenge is to develop efficient offloading strategies to achieve the collaboration of edge and cloud offloading. Although CEE offloading problems have been widely studied under various backgrounds and methodologies, load balance, which is an indispensable scheme in CEE systems to ensure the full utilization of edge resources, is still a factor that has not yet been accounted for. To fill this research gap, we are devoted to developing a dynamic load balance -aware CEE offloading strategy. First, we propose a load evolution model to characterize the influences of offloading strategies on the system load dynamics and, on this basis, establish a latency model as a performance metric of different offloading strategies. Then, we formulate an optimal control model to seek the optimal offloading strategy that minimizes the latency. Second, we analyze the feasibility of typical optimal control numerical methods in solving our proposed model, and develop a numerical method based on the framework of genetic algorithm. Third, through a series of numerical experiments, we verify our proposed method. Results show that our method is effective.

Study on the Solution and Variation Law of Diffusion Coefficient Based on the Numerical Simulation Optimization Method.

Since the diffusion coefficient is a key parameter to characterize the diffusion rate of methane molecules, its measurement and solution have always been a research hotspot. The diffusion coefficient is normally solved through analytical solutions of theoretical models, which is complex and poorly applicable. In comparison, the numerical simulation optimization method can seek a solution easily and quickly, providing a clue for solving such problem. In this paper, first, gas desorption experiments were conducted on coal samples with different initial gas equilibrium pressures, coal particle sizes, and metamorphic degrees. Combined with existing theoretical models, the numerical simulation optimization method was adopted to solve the diffusion coefficient of the coal particle. Furthermore, the applicability and advantages of the numerical simulation optimization method were discussed. Finally, the variation law of the diffusion coefficients was analyzed. The results demonstrate that the numerical simulation optimization method can not only solve the diffusion coefficient easily and quickly but also reveal the law of diffusion concentration with time. The d values between the solution results and the experimental data under different conditions are all smaller than 0.2, which proves the effectiveness and accuracy of the simulation optimization method. The diffusion coefficient of gas from coal particles is unrelated to the initial gas equilibrium pressure, yet it has a Z-shaped relationship with the coal particle size and a V-shaped relationship with the metamorphic degree.

Design and Optimization of Heatsink for an Active CPU Cooler using Numerical Simulations

Heat generation in CPUs with high computing performance has been a very serious issue that deteriorates their performance. To ensure that CPUs operate at their maximum potential, it is essential to maintain their temperature below 80 °C. Forced convection coolers comprising of a heatsink and fan are considered the most effective means of satisfying operating temperature requirements for a CPU in order to ensure its maximum performance. A heatsink design paired with a fan with airflow speed of 80 cubic feet per minute (CFM) for a CPU Cooler targeted at CPUs with maximum heat generation of 380 watts operating in ambient temperature of 25 °C, is developed using numerical methods of Computational Fluid Dynamics (CFD) and topology optimization using ANSYS Mechanical and ANSYS Fluent. Various fin profiles, fin arrangements, fin numbers and heatsink materials are comparatively analyzed. The best results from the comparative analyses are combined to present a base design capable of keeping the CPU temperature below 80 °C, which is the requirement for ensuring maximum computing performance. A 30 fin heatsink with covered rectangular plate fins in an arc-shaped placement configuration is determined to provide the maximum cooling performance. In materials, Silicon Carbide resulted in the lowest CPU temperature of 78°C, followed by copper at 84 °C. Silicon Carbide heatsink successfully managed to satisfy the requirements for maximum CPU performance. Copper heatsink is unlikely to cause CPU failure, but it fails to meet conditions for maximum CPU performance. In addition, this base design is then optimized for material cost reduction using topology optimization which resulted in 13% reduction in material cost with a negligible cooling performance reduction of only 0.32%. The overall design of the cooler can be improved by incorporating fan design and various CPU load conditions into the design parameters in future research.

Designing Porous Structure with Optimized Topology using Machine Learning

Biomedical engineering relies on topology optimization to refine material distribution, crucial for lightweight, high-performance prostheses and orthoses. Advanced manufacturing techniques like additive manufacturing can then be used to create these intricate designs layer by layer, ensuring precision and customization. However, conventional numerical simulation-based topology optimization methods can be time-consuming and resource-intensive, especially as the design domain expands. To overcome this issue, machine learning models are investigated for their ability to perform topology optimization. The results indicate a significant decrease in computation time, along with comparable optimization performance to conventional methods.

Definition of information in computer science

Purpose of this study is to formulate a working definition of information to meet the needs of computer science. There is currently no strict definition of this term. There is a methodological contradiction: the development and application of information technologies requires accuracy and rigor, but at the same time the development is based on a vague, intuitive concept. Materials and methods. The materials for the study are existing classical approaches to understanding information, and the main method is the analysis of these approaches. The proposed definition is constructed taking into account two mathematical transformations: the selection of a certain subset and the mapping between sets. To formalize the allocation procedure, it is used apparatus of fuzzy sets. Results. A definition of information is proposed as the result of a mapping in which the selection of a subset from a set of prototypes leads to the selection of a corresponding subset from a set of images. The selected subset can be understood as fuzzy, then an equivalent definition of information is acceptable as a result of mapping, in which an increase in the heterogeneity of the distribution of the presence indicator on the set of prototypes leads to an increase in the heterogeneity of the distribution of the corresponding indicator on the set of images. The essence of the new definition is demonstrated using models of population dynamics in discrete time. The significance of the proposed approach for information technology is revealed using the example of the numerical method of multi-extremal optimization. It is shown that the proposed definition makes it possible to formulate effective stopping conditions for the numerical method of stochastic optimization, which guarantees the receipt of a given amount of information. Conclusion. The proposed understanding of information allows us to overcome the shortcomings of previous approaches to understanding the essence of information, retains all the advantages of the classical approach and is consistent with other well-known approaches in the field of computer science. This definition can be used to improve numerical optimization methods, as well as other information technology tools.

Transient freeform thermal metamaterials via inverse-design

Thermal metamaterials have gained significant interest because of their unconventionally tailored properties. Analytical transformation optics and numerical optimization method dealing with structural parameters have motivated unique and beneficial potential applications for thermal management. Nevertheless, analytical design methods are expected to possess and complex artificial mathematical derivation. Moreover, a self-driven standard strategy that meets the demands of different design requirements is unavailable. Herein, we report an inverse-design strategy using topology optimization for freeform thermal metamaterials in a transient state. The design of thermal metamaterials in transient state is converted to an inverse heat conduction problem, in which the sensitivity analysis and the adjoint problem are defined over the strong-form. The thermal conductivity and volumetric heat capacity of thermal metadevices are evolved simultaneously relying on the conjugate gradient method. Thermal metadevices with irregular shapes are specifically designed to verify the feasibility and universality of the paradigm. This study constructs a standard programmable design strategy for transient freeform thermal metamaterials and further suggests conducting more explorations in other Laplace fields, such as DC and magnetostatics.

A monotone numerical integration method for mean–variance portfolio optimization under jump-diffusion models

We develop a highly efficient, easy-to-implement, and strictly monotone numerical integration method for Mean-Variance (MV) portfolio optimization. This method proves very efficient in realistic contexts, which involve jump-diffusion dynamics of the underlying controlled processes, discrete rebalancing, and the application of investment constraints, namely no-bankruptcy and leverage.A crucial element of the MV portfolio optimization formulation over each rebalancing interval is a convolution integral, which involves a conditional density of the logarithm of the amount invested in the risky asset. Using a known closed-form expression for the Fourier transform of this conditional density, we derive an infinite series representation for the conditional density where each term is strictly positive and explicitly computable. As a result, the convolution integral can be readily approximated through a monotone integration scheme, such as a composite quadrature rule typically available in most programming languages. The computational complexity of our proposed method is an order of magnitude lower than that of existing monotone finite difference methods. To further enhance efficiency, we propose an implementation of this monotone integration scheme via Fast Fourier Transforms, exploiting the Toeplitz matrix structure.The proposed monotone numerical integration scheme is proven to be both ℓ∞-stable and pointwise consistent, and we rigorously establish its pointwise convergence to the unique solution of the MV portfolio optimization problem. We also intuitively demonstrate that, as the rebalancing time interval approaches zero, the proposed scheme converges to a continuously observed impulse control formulation for MV optimization expressed as a Hamilton–Jacobi–Bellman Quasi-Variational Inequality. Numerical results show remarkable agreement with benchmark solutions obtained through finite differences and Monte Carlo simulation, underscoring the effectiveness of our approach.

SuperAdjoint: Super-resolution neural networks in adjoint-based error estimation

Numerical simulations and optimisation methods, such as mesh adaptation, rely on the accurate and inexpensive use of error estimation methods. Adjoint-based error estimation is the most accurate method, and generally the most costly. A strong contributor to this cost is the need to compute a higher resolution adjoint solution. Here, it is proposed to use super-resolution neural networks to super-resolve a fine adjoint solution from a lower-cost coarse adjoint solution: a superAdjoint. The method is compared to reference error estimators on an unsteady Burgers’ equation using the method of manufactured solutions. Two forms of the superAdjoint were implemented, a twice and a four times refining super-resolution neural network. These were used to demonstrate both the computational cost reduction and the potential for the reduction of the storage footprint of the primal problem. The first, referred to as 2×CNN, was able to reconstruct the spatially enriched adjoint solution, thus providing a robust and inexpensive local output error. The second, the 4×CNN, was able to demonstrate the reconstruction ability of super-resolution neural networks for higher upscaling factors. This was leveraged in order to subsample the primal solution in space, thus reducing substantially the storage footprint of the discrete primal solution. Both superAdjoints could achieve the desired level of accuracy when compared to the reconstruction of the refined adjoint-based error estimate. Moreover, superAdjoint was shown to be able to generalise to a new QoI that was untrained for. This gives great confidence in the use of super-resolution neural networks for the reduction of both computational cost and storage requirements of adjoint-based error estimation, and goal-oriented mesh adaptation.

CFD based aerodynamic optimization design

The CFD technology based on the N-S equation plays an extremely important role in the detailed aerodynamic shape design of the complex surface of civil aircraft. In this paper, a consistent parameterization method, response surface model and numerical optimization method are used to conclude the optimization design. The aerodynamic optimization based on CFD, the commonly used CFD methods and free-form surface modeling technology are studied, and the challenges faced in the process of aerodynamic shape optimization of civil aircraft are analyzed. The adoption of a genetic algorithm based on the response surface increases the effectiveness of the entire optimization process.The results show that the adopted design method is effective in solving the problem of complex shape optimization using computationally expensive CFD codes. The advantage of the proposed method is that it can flexibly shape the wing body design and can quickly respond to changes in design requirements during the design process; the proposed method can be used in the design of a wider range of complex aerodynamic shapes.

Applications of artificial intelligence in power system operation, control and planning: a review

Abstract As different artificial intelligence (AI) techniques continue to evolve, power systems are undergoing significant technological changes with the primary goal of reducing computational time, decreasing utility and consumer costs and ensuring the reliable operation of an electrical power system. AI techniques compute large amounts of data at a faster speed than numerical optimization methods with higher processing speeds. With these features, AI techniques can further automate and increase the performance of power systems. This paper presents a comprehensive overview of diverse AI techniques that can be applied in power system operation, control and planning, aiming to facilitate their various applications. We explained how AI can be used to resolve system frequency changes, maintain the voltage profile to minimize transmission losses, reduce the fault rate and minimize reactive current in distributed systems to increase the power factor and improve the voltage profile.

A technique for modeling and optimizing the design of wave energy conversion devices

With the continuous development of society and the economy, energy shortages have become increasingly prominent. As an important marine renewable energy source, wave energy holds significant theoretical significance due to its widespread distribution and vast storage potential. In this paper, we employ differential equation theory, numerical optimization methods, and optimization techniques to model and design algorithms for investigating the energy conversion mechanisms of wave energy devices. Due to the complex situation, we decided to simplify that into two scenarios. As to the first scenario, the essence of energy output in wave energy devices lies in the relative velocity between the floater and the oscillator. Firstly, the product of the damping force and the instantaneous relative velocity is integrated over time and divided by the period to obtain the average output power. Maximizing the average output power, with the damping coefficient as the decision variable, establishes a nonlinear optimization model. Secondly, a stepwise optimization approach is applied to control the damping coefficient, resulting in optimal damping coefficients of 33600, . Finally, a genetic algorithm is employed to validate the results as to the next scenario. After adding rotational dampers and torsion springs to the wave energy device, the relative velocity and relative angular velocity between the floater and the oscillator jointly contribute to energy output. The objective is to maximize the sum of the average output power of linear dampers and rotational dampers. The decision variables are the linear damping coefficient and the rotational damping coefficient. A nonlinear optimization model is established. A stepwise optimization approach is applied to optimize both types of coefficients, and the results are validated using a genetic algorithm. The optimal solution is found to have a linear damping coefficient of 60135.7781 N·s/m and a rotational damping coefficient of 4244.90358 N·s·m for the rotational dampers.

Quadratic Programming for Continuous Control of Safety-Critical Multiagent Systems Under Uncertainty

This paper studies the control problem for safety-critical multi-agent systems based on quadratic programming (QP). Each controlled agent is modeled as a cascade connection of an integrator and an uncertain nonlinear actuation system. In particular, the integrator represents the position-velocity relation, and the actuation system describes the dynamic response of the actual velocity to the velocity reference signal. The notion of input-to-output stability (IOS) is employed to characterize the essential velocity-tracking capability of the actuation system. The standard QP algorithms for collision avoidance may be infeasible due to uncertain actuator dynamics. Even if feasible, the solutions may be non-Lipschitz because of possible violation of the full rank condition of the active constraints. Also, the interaction between the controlled integrator and the uncertain actuator dynamics may lead to significant robustness issues. Based on the current development of nonlinear control theory and numerical optimization methods, this paper first contributes a new feasible-set reshaping technique and a refined QP algorithm for feasibility, robustness, and local Lipschitz continuity. Then, we present a nonlinear small-gain analysis to handle the inherent interaction for guaranteed safety of the closed-loop multi-agent system. The proposed method is illustrated by numerical simulation and a physical experiment.

Calibration of Viscous Damping–Stiffness Control Force in Active and Semi-Active Tuned Mass Dampers for Reduction of Harmonic Vibrations

Tuned mass dampers (TMDs) are commonly used to mitigate vibrations in civil structures. There is a growing demand for new solutions that offer similar effectiveness as TMDs but with reduced mass. In this context, this paper investigates active (ATMD) and semi-active (STMD) tuned mass dampers with relative displacement and velocity feedback. The control force of the ATMD is assumed to be the sum of viscous damping and either positive or negative stiffness forces. This control force is calibrated for a specific parameter K such that the effectiveness of the ATMD in reducing harmonic vibrations matches that of the TMD with K times larger mass. The optimal calibration is derived based on the mathematical reformulation of an existing optimal acceleration feedback control algorithm. The control approach for the ATMD is then applied to the STMD. Subsequently, the sub-optimal STMD is analyzed, with a focus on its limitations arising from the clipping of active forces. Finally, the paper presents a calibration of the STMD using a numerical optimization method. It is demonstrated that the maximum achievable performance of the numerically optimized STMD matches that of the TMD with three times larger mass.

An iso-contour method for automated fiber placement optimization of composite structures

A new method for numerical optimization of fiber-steered composites is presented, which allows to control efficiently and effectively the curvature of the fibers of single- or multi-layer composite structures. It is based on the introduction of an artificial surface defined and controlled by a relatively small number of control points, which is optimized to identify optimal fiber orientations varying smoothly over the panels. Curvature constraints like the maximum fiber curvature constraint, MFCC, or the average fiber curvature constraint, AFCC, are respected explicitly by the method to ensure manufacturability of the composite component. Three validation cases are regarded where results of the unconstrained case are compared to those of established methods to illustrate the validity of the new approach. They are complemented by results considering curvature constraints showing that optimal structures depend strongly on the chosen curvature thresholds. Finally, a rib optimization of a wingbox structure is realized as a more complex case.

Adjoint-Based Design Optimization of a Volute for a Radial Compressor

Numerical optimization methods are widely used for designing turbomachinery components due to the cost and time savings they can provide. In the available literature, the shape optimization of radial compressors mainly focuses on improving the impeller alone. However, it is well-established knowledge that the volute plays a key role in the overall performance of the compressor. The aim of the present paper is to perform an adjoint-based optimization of a volute that is designed for the SRV2-O compressor. The CAD model was first created by using the parametrization of 33 design parameters. Then, a butterfly topology was applied to mesh the computational domain with a multi-block structured grid, and an elliptic smoothing procedure was used to improve the quality of the fluid grid. A steady-state RANS CFD solver with a Spalart-Allmaras turbulence model was used to solve the Navier–Stokes equations, and then the flow sensitivities were computed with an adjoint solver. The objective function consists of minimizing the loss coefficient of the volute. The optimization is performed to obtain an improved design with a 14% loss reduction. A detailed flow and design analysis is carried out to highlight the loss reduction mechanisms, followed by the optimizer. Finally, the compressor map of the full stage is compared between the baseline and the optimized volute from the CFD simulations using a mixing plane interface. This research demonstrates the successful use of a gradient-based optimization technique to improve the volute of a radial compressor and opens the door towards simultaneously optimizing the wheel and the volute.