Stochastic Optimization Methods Research Articles

A new uncertain remanufacturing scheduling model with rework risk using hybrid optimization algorithm.

As a resource-conserving and environmentally friendly manufacturing paradigm, remanufacturing with the potential to realize sustainability in production has been extensively investigated. Scheduling plays a significant role in achieving the remanufacturing benefits. However, the remanufacturing process involves intricate uncertainties because it takes end-of-life products with different qualities as workblanks, which increases the risk of rework and complicates remanufacturing scheduling. Though the traditional stochastic optimization methods or fuzzy theory have been employed to address uncertainties in the remanufacturing scheduling problem, they are constrained with the limited historical data which renders it difficult to describe uncertainties accurately and intuitively. Therefore, a new uncertain remanufacturing scheduling model with rework risk is proposed, in which the interval grey numbers are applied to describe the uncertainty clearly and consider the rework risk in remanufacturing process. To solve this model, a hybrid optimization algorithm that combines differential evolution and particle swarm optimization algorithms through an efficient representation scheme is proposed. Besides, this algorithm integrates multiple improvements to maintain the diversity of the population and enhance its performance. Simulation experiments are conducted on 18 sets of instances with different scales, and the results demonstrated that the proposed algorithm obtains a better optimal solution than other baseline algorithms on 17 sets of instances. The main finding of this study is providing a new method for solving uncertain remanufacturing scheduling problem with rework risk practically and effectively.

Systematically improvable mean-field variational ansatz for strongly correlated systems: Application to the Hubbard model

A systematically improvable wave function is proposed for the numerical solution of strongly correlated systems. With a stochastic optimization method, based on the auxiliary field quantum Monte Carlo technique, an effective temperature ${T}_{\mathrm{eff}}$ is defined, probing the distance of the ground-state properties of the model in the thermodynamic limit from the ones of the proposed correlated mean-field ansatz. In this way, their uncertainties from the unbiased zero temperature limit may be estimated by simple and stable extrapolations well before the so-called sign problem gets prohibitive. At finite ${T}_{\mathrm{eff}}$, the convergence of the energy to the thermodynamic limit is indeed shown to already be possible in the Hubbard model for relatively small square lattices with linear dimension $L\ensuremath{\simeq}10$, thanks to appropriate averages over several twisted boundary conditions. Within the estimated energy accuracy of the proposed variational ansatz, two clear phases are identified, as the energy is lowered by spontaneously breaking some symmetries satisfied by the Hubbard Hamiltonian: (a) a stripe phase where both spin and translation symmetries are broken and (b) a strong coupling $d$-wave superconducting phase when the particle number is not conserved and global $U(1)$ symmetry is broken. On the other hand, the symmetric phase is stable in a wide region at large doping and small coupling.

Adaptive sampling quasi-Newton methods for zeroth-order stochastic optimization

Adaptive sampling quasi-Newton methods for zeroth-order stochastic optimization

Simultaneous UAV having actively sweep angle morphing wing and flight control system design

PurposeThe purpose of this paper is to improve autonomous flight performance of an unmanned aerial vehicle (UAV) having actively sweep angle morphing wing using simultaneous UAV and flight control system (FCS) design.Design/methodology/approachAn UAV is remanufactured in the ISTE Unmanned Aerial Vehicle Laboratory. Its wing sweep angle can vary actively during flight. FCS parameters and wing sweep angle are simultaneously designed to optimize autonomous flight performance index using a stochastic optimization method called as simultaneous perturbation stochastic approximation (SPSA). Results obtained are applied for flight simulations.FindingsUsing simultaneous design process of an UAV having actively sweep angle morphing wing and FCS design, autonomous flight performance index is maximized.Research limitations/implicationsAuthorization of Directorate General of Civil Aviation in Turkey is crucial for real-time UAV flights.Practical implicationsSimultaneous UAV having actively sweep angle morphing wing and FCS design process is so beneficial for recovering UAV autonomous flight performance index.Social implicationsSimultaneous UAV having actively sweep angle morphing wing and FCS design process achieves confidence, high autonomous performance index and simple service demands of UAV operators.Originality/valueComposing a novel approach to improve autonomous flight performance index (e.g. less settling and rise time, less overshoot meanwhile trajectory tracking) of an UAV and creating an original procedure carrying out simultaneous UAV having actively sweep angle morphing wing and FCS design idea.

Simultaneous design of morphing hexarotor and autopilot system by using deep neural network and SPSA

Purpose The purpose of this paper is to optimize the simultaneous flight performance of a hexarotor unmanned aerial vehicle (UAV) by using simultaneous perturbation stochastic approximation (i.e. SPSA), deep neural network and proportional integral derivative (i.e. PID) according to varying arm length (i.e. morphing). Design/methodology/approach In this paper, proper PID gain coefficients and morphing ratio were obtained using the stochastic optimization method, also known as SPSA to maximize flight efficiency. Because it is difficult to establish an analytical connection between the morphing ratio and hexarotor moments of inertia, the deep neural network was used to obtain the moments of inertia according to the morphing ratio. By using SPSA and deep neural network, the best performance indexes were obtained and both longitudinal and lateral flight simulations were performed with the obtained data. Findings With SPSA, the best PID coefficients and morphing ratio are obtained for both longitudinal and lateral flight. Because the hexarotor solid body model changes according to the morphing ratio, the moment of inertia values used in the simulations also change. According to the morphing ratio, the moment of inertia values was obtained with the deep neural network over a created data set. Research limitations/implications It takes a long time to obtain the morphing ratio suitable for the hexarotor model and the PID gain coefficients suitable for this morphing ratio. However, this situation can be overcome with the proposed SPSA. In addition, it takes a long time to obtain the appropriate moments of inertia according to the morphing ratio. However, in this case, it was overcome using the deep neural network. Practical implications Determining the morphing ratio and PID gain coefficients using the optimization method, as well as determining the moments of inertia using the deep neural network, is very useful as it can increase the efficiency of hexarotor flight and flight efficiently with different arm lengths. With the proposed method, the hexarotor design performance criteria (i.e. rise time, settling time and overshoot) values were significantly improved compared to similar studies. Social implications Determining the hexarotor flight parameters using SPSA and deep neural network provides advantages in terms of time, cost and applicability. Originality/value The hexarotor flight efficiency is improved with the proposed SPSA and deep neural network approaches. In addition, the desired flight parameters can be obtained more quickly and reliably with the proposed approaches. The design performance criteria were also improved, enabling the hexarotor UAV to follow the given trajectory in the best way and providing convenience for end users. SPSA was preferred because it converged faster than other methods. While other methods perform 2n operations per iteration, SPSA only performs two operations. To obtain the moment of inertia, many physical parameter values of the UAV are required in the existing methods. In the proposed method, by creating a date set, only arm length and moment of inertia were estimated without the need to obtain physical parameters with the deep neural network structure.

Stochastic Optimization and Sensitivity Analysis of the Combined Negative Stiffness Damped Outrigger and Conventional Damped Outrigger Systems Subjected to Nonstationary Seismic Excitation

In recent years, various kinds of damped outrigger systems, particularly with the negative stiffness devices, have been shown to effectively suppress excessive vibration induced by earthquake and wind. To gain insight into such systems, this paper proposes a stochastic optimization method to investigate optimal configurations of combined negative stiffness damped outriggers (NSDOs) and conventional damped outriggers (CDOs) subjected to nonstationary stochastic seismic excitation. The simplified analysis model of various combinations of damped outriggers is developed, and the state-space representation of outrigger systems is then formulated. The nonstationary seismic excitation is modeled as a uniformly modulated stationary Gaussian process with a time-modulating function following Clough–Penzien spectrum, and combining equations of motions of outrigger systems and seismic excitation gives rise to the augmented state-space representation of structure-damper-excitation and subsequently the differential Lyapunov equation. The optimal designs of damped outriggers are defined via the solution of the differential Lyapunov equation. The multiobjective optimization with Pareto optimal fronts is adopted to deal with conflicting objectives between harmful interstory drift and floor absolute acceleration. The sensitivity of negative stiffness devices on optimal objectives is also investigated. The optimal designs are further examined under real typical and near-fault earthquake records. The results demonstrate the efficacy of the proposed method and provide insight into the systems subjected to nonstationary seismic excitation. While the purely NSDO systems could have better performance with adequate negative stiffness devices, the proposed combined NSDO and CDO systems prove to be more effective with limited negative stiffness devices and thus provide more design flexibilities tailored to different application situations.

A new approach to training neural networks using natural gradient descent with momentum based on Dirichlet distributions

In this paper, we propose a natural gradient descent algorithm with momentum based on Dirichlet distributions to speed up the training of neural networks. This approach takes into account not only the direction of the gradients, but also the convexity of the minimized function, which significantly accelerates the process of searching for the extremes. Calculations of natural gradients based on Dirichlet distributions are presented, with the proposed approach introduced into an error backpropagation scheme. The results of image recognition and time series forecasting during the experiments show that the proposed approach gives higher accuracy and does not require a large number of iterations to minimize loss functions compared to the methods of stochastic gradient descent, adaptive moment estimation and adaptive parameter-wise diagonal quasi-Newton method for nonconvex stochastic optimization.

Stabilizing the training of deep neural networks using Adam optimization and gradient clipping

The field of neural network training and optimization has seen significant advancements in recent years, with new techniques and algorithms being proposed to improve the efficiency and effectiveness of training. In this paper, we review several key optimization techniques and their impact on training neural networks, with a focus on long-term dependencies and the difficulties that can arise during training. We begin by discussing the challenges of learning long-term dependencies with gradient descent, as highlighted in the 1994 paper by Bengio et al. We then introduce Adam, a method for stochastic optimization proposed by Kingma and Ba in 2014. We also explore the difficulties of training recurrent neural networks, as discussed in the 2013 paper by Pascanu, Mikolov, and Bengio. We also review recent advances in optimization techniques such as Convergence of Adam and Beyond by Jianmin et al. (2017), Yogi by Dong et al. (2018), AdaBound by Zhang et al. (2018) and On the Variance of the Adaptive Learning Rate and Beyond by Liu et al. (2019). We will highlight the advantages and disadvantages of each technique and discuss their potential impact on the field. Overall, this paper provides a comprehensive overview of recent advancements in neural network optimization and their implications for training and performance. Keywords: Deep neural networks, optimization, Adam, gradient clipping, training, stabilization, overfitting, generalization, recurrent neural networks, non-convex loss landscapes.

Resonant mode coupling approximation for calculation of optical spectra of stacked photonic crystal slabs. Part I

We develop the resonant mode coupling approximation to calculate the optical spectra of a stack of two photonic crystal slabs in terms of the scattering matrix. The method is based on the derivation of input and output resonant vectors in each slab in terms of the Fourier modal method in the scattering matrix form. We show that using the resonant mode coupling approximation of the scattering matrices of the upper and lower slabs, one can construct the total scattering matrix of the stack. The formation of the resonant output and input vectors of the stacked system is rigorously derived by means of an effective Hamiltonian. We demonstrate that the proposed procedure dramatically decreases the computation time without sufficient loss of accuracy. We believe that the proposed technique can be a powerful tool for fast-solving inverse scattering problems using stochastic optimization methods such as genetic algorithms or machine learning.

A data-driven multi-stage stochastic robust optimization model for dynamic optimal power flow problem

The uncertainty caused by the distributed generations(DG) with inconspicuous patterns has been an essential subject in the optimization scheduling for the distribution network. We propose a novel data-driven approach to deal with the dynamic optimal power flow(DOPF) problem which contains uncertain variables with their unknown probability distribution. The data-driven model is made to learn the joint probability distribution of the uncertain variables and use robust optimization(RO) to solve the multi-stage stochastic linear DOPF by averaging the worst case from each uncertainty set. In contrast to the motivation for traditional RO to find solutions that perform well on the worst-case realization, our proposed approach adds robustness to the historical data as a tool to avoid overfitting as the number of data points tends to infinity. The application verification for the AC OPF problem is presented for the IEEE-33 system. The simulation verifies the feasibility and robustness of the proposed approach and its results are compared with those of other data-driven stochastic optimization methods. We prove that the proposed approach can effectively solve the overvoltage problem caused by the high permeability of photovoltaic generation and achieve a better out-of-sample performance guarantee, and also has obvious economic advantages over other data-driven methods.

CoolMomentum-SPGD Algorithm for Wavefront Sensor-Less Adaptive Optics Systems

Instead of acquiring the previous aberrations of an optical wavefront with a sensor, wavefront sensor-less (WFSless) adaptive optics (AO) systems compensate for wavefront distortion by optimizing the performance metric directly. The stochastic parallel gradient descent (SPGD) algorithm is pervasively adopted to achieve performance metric optimization. In this work, we incorporate CoolMomentum, a method for stochastic optimization by Langevin dynamics with simulated annealing, into SPGD. Numerical simulations reveal that, compared with the state-of-the-art SPGD variant, the proposed CoolMomentum-SPGD algorithm achieves better convergence speed under various atmospheric turbulence conditions while requiring only two tunable parameters.

PV Inverter Reliability Constrained Volt/Var Control With Power Smoothing via a Convex-Concave Programming Method

Intensive use of photovoltaic (PV) inverter in the volt/var control (VVC) methods in active distribution networks can impair inverter reliability. This article proposes a PV inverter reliability-constrained (PiReCon-) VVC method with a power smoothing scheme under uncertainties. First, considering impacts on inverter reliability, new reliability constraints are developed with a power smoothing factor to constrict inverter apparent power variation. Second, a new VVC optimization model is proposed with the reliability constraints, which minimizes power losses by optimizing both inverter var output and PV curtailment. Uncertainties of PV generation and loads are fully considered and addressed via a stochastic optimization method. Third, this article develops a penalty convex-concave programming method to effectively tackle nonconvexity of the proposed optimization model. The proposed PiReCon-VVC method is tested on a 33-bus distribution network, and simulation results verify its high efficiency in both minimizing the power losses and enhancing the PV inverter reliability.

ACO-Inspired Load Balancing Strategy for Cloud-Based Data Centre with燩redictive Machine Learning Approach

Virtual Machines are the core of cloud computing and are utilized to get the benefits of cloud computing. Other essential features include portability, recovery after failure, and, most importantly, creating the core mechanism for load balancing. Several study results have been reported in enhancing load-balancing systems employing stochastic or biogenetic optimization methods. It examines the underlying issues with load balancing and the limitations of present load balance genetic optimization approaches. They are criticized for using higher-order probability distributions, more complicated solution search spaces, and adding factors to improve decision-making skills. Thus, this paper explores the possibility of summarizing load characteristics. Second, this study offers an improved prediction technique for pheromone level prediction over other typical genetic optimization methods during load balancing. It also uses web-based third-party cloud service providers to test and validate the principles provided in this study. It also reduces VM migrations, time complexity, and service level agreements compared to other parallel standard approaches.

Tri-Level Multi-Energy System Planning Method for Zero Energy Buildings Considering Long- and Short-Term Uncertainties

To effectively supply the multi-energy loads and achieve the annual zero energy targets of zero energy buildings (ZEBs) throughout the planning horizon, this paper proposes a tri-level multi-energy system planning method for ZEBs considering both long- and short-term uncertainties. In the upper level, the optimal goal is to obtain an optimal device sizing scheme within the electric-thermal-hydrogen integrated multi-energy system (EHT-MES). The middle and lower levels tackle the long-term temperature change and short-term source-load uncertainties separately. For the former, a set of representative scenarios that include typical and extreme weather conditions are generated from the future temperature forecast dataset, and an ambiguous set is utilized to model the uncertain probability distributions of the scenario set. For the latter, to guarantee the reliable and economic operation of ZEBs under different seasonal-daily patterns, a hybrid stochastic and robust optimization (HSRO) method is applied to deal with short-term uncertainties from solar radiation, wind output, outdoor temperature, electric loads, and hot water loads. A reformulation method is proposed to transform the multi-level coupling planning model into an equivalent and tractable form, and an improved column-and-constraint generation (C&CG) algorithm is developed to solve the recast model. Simulation results verify the effectiveness of the proposed planning method in deploying ZEBs’ multi-energy devices and immunizing against multiple timescale uncertainties.

Separation of the roots of the systems of nonlinear equations. Stochastic approach

The work is devoted to the actual problem of separating the roots of nonlinear systems of equations in the case of many variables. The well-known method of reducing the problem of solving the system to an equivalent extremal problem, which is supposed to be solved by one of the methods of stochastic optimization. The annealing simulation modeling method and its modification are chosen, which are especially interesting in that they allow efficient implementation on quantum computers. Since quantum ccomputers based on simulated annealing demonstrate quantum superiority, the results obtained can be useful in solving systems of equations on these computing systems.

Applying a stochastic quasi-Newton optimizer to least-squares reverse time migration

As we keep moving towards large-scale 3D datasets, inversions based on the wave equation, such as least-squares reverse time migration (LSRTM), must rapidly converge to reduce the computational burden and deliver its well-known advantages, compensating the illumination and providing accurate amplitudes. For that, we explore stochastic optimization methods for LSRTM beyond the minibatch stochastic gradient descent (SGD), considered the state of the art in large-scale machine learning problems. We apply a second-order stochastic method to the LSRTM problem, that uses a quasi-Newton approach, known as the Sum of Functions Optimizer (SFO) algorithm. This method also works well with minibatches of data and has shown good performance on optimization of multi-layer neural networks. It can maintain computational tractability and limit memory requirements even for high dimensional optimization problems. As typical for quasi-Newton methods no adjustment of hyperparameters is required. On our experiments presented here, using synthetic data, we demonstrated that the SFO algorithm shows better results and faster convergence than the minibatch SGD.

Discrete Stochastic Optimization for Public Health Interventions with Constraints

Many public health threats exist, motivating the need to find optimal intervention strategies. Given the stochastic nature of the threats (e.g., the spread of pandemic influenza, the occurrence of drug overdoses, and the prevalence of alcohol-related threats), deterministic optimization approaches may be inappropriate. In this paper, we implement a stochastic optimization method to address aspects of the 2009 H1N1 and the COVID-19 pandemics, with the spread of disease modeled by the open-source Monte Carlo simulations, FluTE, and Covasim, respectively. Without testing every possible option, the objective of the optimization is to determine the best combination of intervention strategies so as to result in minimal economic loss to society. To reach our objective, this application-oriented paper uses the discrete simultaneous perturbation stochastic approximation method (DSPSA), a recursive simulation-based optimization algorithm, to update the input parameters in the disease simulation software so that the output iteratively approaches minimal economic loss. Assuming that the simulation models for the spread of disease (FluTE for H1N1 and Covasim for COVID-19 in our case) are accurate representations for the population being studied, the simulation-based strategy we present provides decision makers a powerful tool to mitigate potential human and economic losses from any epidemic. The basic approach is also applicable in other public health problems, such as opioid abuse and drunk driving.

Distributionally Robust Unit Commitment with N-k Security Criterion and Operational Flexibility of CSP

In order to reduce the conservatism of the robust optimization method and the complexity of the stochastic optimization method and to enhance the ability of power systems to deal with occasional line fault disturbance, this paper proposes a distributionally robust unit commitment (DRUC) model with concentrating solar power (CSP) operational flexibility and N-k safety criterion under distributed uncertainty. According to the limited historical sample data, under the condition of satisfying a certain confidence level, based on the imprecise Dirichlet model (IDM), an ambiguity set is constructed to describe the uncertainty of transmission line fault probability. Through the identification of the worst probability distribution in the ambiguity set, the adaptive robust optimal scheduling problem is transformed into a two-stage robust optimization decision model under the condition of deterministic probability distribution. The CSP flexibility column and constraint generation (C&CG) algorithm is used to process the model and the main problem and subproblem are solved by using the Big-M method, linearization technique, and duality principle. Then, a mixed integer linear programming problem (MILP) model is obtained, which effectively reduces the difficulty of solving the model. Finally, case studies on the IEEE 14 bus system and the IEEE 118 bus system demonstrate the efficiency of the proposed method, such as enhancing the ability of power systems to cope with occasional line fault disturbances and reducing the conservatism of the robust optimization method.

LSOS: Line-search second-order stochastic optimization methods for nonconvex finite sums

We develop a line-search second-order algorithmic framework for minimizing finite sums. We do not make any convexity assumptions, but require the terms of the sum to be continuously differentiable and have Lipschitz-continuous gradients. The methods fitting into this framework combine line searches and suitably decaying step lengths. A key issue is a two-step sampling at each iteration, which allows us to control the error present in the line-search procedure. Stationarity of limit points is proved in the almost-sure sense, while almost-sure convergence of the sequence of approximations to the solution holds with the additional hypothesis that the functions are strongly convex. Numerical experiments, including comparisons with state-of-the art stochastic optimization methods, show the efficiency of our approach.

Identification of Soil Mechanical Parameters by Inverse Analysis Using Stochastic Methods

Abstract The mechanical parameters of the soil that must be introduced into geotechnical calculations, in particular those carried out by the Finite Element Method, are often poorly understood. The search for the numerical values of these parameters so that the models best reflect the observed reality constitutes the inverse analysis approach. In this article, we are interested in the identification of the mechanical parameters of the soil based on the principle of inverse analysis using the two methods of stochastic optimization, the genetic algorithm and the hybrid genetic algorithm with Tabu search. Soil behavior is represented by the constitutive soil Mohr-Coulomb model. The identification relates to the following two parameters: The shear modulus (G) and the friction angle (φ). The validation of these two stochastic optimization methods is done on the experimental sheet pile wall of Hochstetten in Germany. The results obtained by applying the genetic algorithm method and the hybrid genetic algorithm method for the identification of the two Mohr-Coulomb parameters (G, φ) show that the hybridization process of the genetic algorithm combined with the Tabu search method accelerated the convergence of the algorithm to the exact solution of the problem whereas the genetic algorithm alone takes a much longer computation time to reach the exact solution of the problem.