Stochastic Optimization Methods Research Articles

Competitive search algorithm: a new method for stochastic optimization

Competitive search algorithm: a new method for stochastic optimization

Rainfall retrieval algorithm for commercial microwave links: stochastic calibration

Abstract. During the last decade, rainfall monitoring using signal-level data from commercial microwave links (CMLs) in cellular communication networks has been proposed as a complementary way to estimate rainfall for large areas. Path-averaged rainfall is retrieved between the transmitting and receiving cellular antennas of a CML. One rainfall estimation algorithm for CMLs is RAINLINK, which has been employed in different regions (e.g., Brazil, Italy, the Netherlands, and Pakistan) with satisfactory results. However, the RAINLINK parameters have been calibrated for a unique optimum solution, which is inconsistent with the fact that multiple similar or equivalent solutions may exist due to uncertainties in algorithm structure, input data, and parameters. Here, we show how CML rainfall estimates can be improved by calibrating all parameters of the algorithm systematically and simultaneously with the stochastic particle swarm optimization method, which is used for the numerical maximization of the objective function. An open dataset of approximately 2800 sub-links of minimum and maximum received signal levels over 15 min intervals covering the Netherlands (∼ 35 500 km2) is employed: 12 d are used for calibration and 3 months for validation. A gauge-adjusted radar rainfall dataset is utilized as a reference. Verification of path-average daily rainfall shows a reasonable improvement for the stochastically calibrated parameters with respect to RAINLINK's default parameter settings. Results further improve when averaged over the Netherlands. Moreover, the method provides a better underpinning of the chosen parameter values and is therefore of general interest for calibration of RAINLINK's parameters for other climates and cellular communication networks.

Методика восстановления геополя на основе данных сети высокомобильных геосенсоров с использованием автоматического адаптивного метода определения параметров ядра локальной регрессии

The article deals with the matter of restoring the geofield based high-intensity spatio-temporal data streams received from a highly mobile geosensors network in real time. It includes dozen thousands of active measuring devices that measure at a frequency of up to 5 Hz and are installed on mobile platforms moving at speeds of up to 80–100 km/h. For solving this task, we propose to apply the method of local smoothing. To adapt a kernel of local regression to the conditions of a specific task, such as the features of the terrain or the simulated geofield, as well as the characteristics of the geosensor network, the authors suggested using the kernel of local regression obtained through using stochastic optimization methods. The application of genetic algorithms and the method of simulating annealing for this purpose are considered. The structure of a generalized method based on this idea is presented in the article. The results of model experiments aimed to confirm the operability of this method and those of evaluating the performance of this method in single-threaded mode are given.

Stochastic Optimization Method for Energy Storage System Configuration Considering Self-Regulation of the State of Charge

Photovoltaic (PV) power generation has developed rapidly in recent years. Owing to its volatility and intermittency, PV power generation has an impact on the power quality and operation of the power system. To mitigate the impact caused by the PV generation, an energy storage (ES) system is applied to the PV plants. The capacity configuration and control strategy based on the stochastic optimization method have become an important research topic. However, the accuracy of the probability distribution model is insufficient and a stochastic optimization method is rarely used in a control strategy. In this paper, a stochastic optimization method for the energy storage system (ESS) configuration considering the self-regulation of the battery state of charge (SoC) is proposed. Firstly, to reduce the sampling error when typical scenarios of PV power are generated, a time-divided probability distribution model of the ultra-short-term predicted error of PV power is established. On this basis, to solve the problem that SoC reaches the threshold frequently, a self-regulation model of the SoC based on multiple scenarios is established, which can regulate the SoC according to rolling PV power prediction. A stochastic optimization configuration model of the energy storage system is constructed, which can reduce the impact of PV uncertainty on the configuration result. Finally, the proposed stochastic optimization method is validated. The fitting error of the time-divided probability distribution model is 15.61% lower than that of the t-distribution. The expected revenue of the optimal configuration in this paper is 8.86% higher than the scheme with a fixed probability distribution model, and 16.87% higher than without considering the stochastic optimization method.

Fairness-Oriented Multiple RIS-Aided mmWave Transmission: Stochastic Optimization Methods

In millimeter wave (mmWave) systems, it is challenging to ensure reliable communication links due to the high sensitivity to the presence of blockages. In order to improve the robustness of mmWave systems in the presence of random blockages, we consider the deployment of multiple reconfigurable intelligent surfaces (RISs) to enhance the spatial diversity gain, and the design of robust beamforming schemes based on stochastic optimization methods that minimize the maximum outage probability among multiple users so as to ensure fairness. Under the stochastic optimization framework, we adopt the stochastic majorization–minimization (SMM) method and the stochastic successive convex approximation (SSCA) method to construct deterministic surrogate problems at each iteration, and to obtain closed-form solutions of the precoding matrix at the base station (BS) and the beamforming vectors at the RISs. Both stochastic optimization methods are proved to converge to the set of stationary points of the original stochastic problems. Simulation results show that the proposed robust beamforming for RIS-aided systems can effectively compensate for the performance loss caused by the presence of random blockages, especially when the blockage probability is high.

An Augmented Lagrangian Deep Learning Method for Variational Problems with Essential Boundary Conditions

This paper is concerned with a novel deep learning method for variational problems with essential boundary conditions. To this end, we first reformulate the original problem into a minimax problem corresponding to a feasible augmented Lagrangian, which can be solved by the augmented Lagrangian method in an infinite dimensional setting. Based on this, by expressing the primal and dual variables with two individual deep neural network functions, we present an augmented Lagrangian deep learning method for which the parameters are trained by the stochastic optimization method together with a projection technique. Compared to the traditional penalty method, the new method admits two main advantages: i) the choice of the penalty parameter is flexible and robust, and ii) the numerical solution is more accurate in the same magnitude of computational cost. As typical applications, we apply the new approach to solve elliptic problems and (nonlinear) eigenvalue problems with essential boundary conditions, and numerical experiments are presented to show the effectiveness of the new method.

Statistical Parametric Design of a Controller in the Stabilization Loop of a Single Axis Gyro-Stabilized Platform Using Stochastic Global Optimization Methods

Statistical Parametric Design of a Controller in the Stabilization Loop of a Single Axis Gyro-Stabilized Platform Using Stochastic Global Optimization Methods

The Two-Stage PI2 Control Strategy

PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> is a stochastic optimal control method generally regarded as a reinforcement learning algorithm. Recent work, however, suggests that the reinforcement learning aspect of PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> actually appears when optimizing feedforward controls which will lead to optimal closed-loop performance once combined with feedback controls. These feedbacks are necessary to achieve the predicted performance, yet have been largely neglected in the literature and applications due to their complexity. In this letter, we show that the feedbacks actually take a simple-to-implement form for a wide range of system dynamics, paving way for future research and applications of PI <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> . The correctness of the results is demonstrated through numerical simulations.

Open-Circuit Fault Diagnosis of NPC Inverter Based on Improved 1-D CNN Network

With the increasing popularization of a three-level neutral point clamped (NPC) inverter, realizing an accurate and fast fault diagnosis is also required. However, most methods are either not accurate enough or require a long period of time to collect signals as input. To compensate for these drawbacks, a novel 1-D convolution neural network (CNN) with the improved stochastic gradient optimization method is proposed in this article. First, the input data are segmented to ensure that the fault diagnosis can be completed if the current of a period is collected at any time in a period. Then, the feature of the waveform is extracted by the proposed network. In the meantime, the improved Adamod (IAdamod) method is implemented to better adaptively adjust the learning rate during the training process. Specifically, the learning rate is bigger at the beginning and smaller at the end. Finally, the classifier softmax is used for classification. The experimental results demonstrate the effectiveness of the proposed method in detecting and locating the faulty devices, which has shown that it perfectly realizes the fault diagnosis with 100% accuracy and can be diagnosed online with the time of less than 0.25 ms, far less than one cycle. The proposed method is also compared the traditional methods, and shows a better performance both in speed and accuracy, the loss can be less than 0.5 in iteration 220 and achieve zero in 1000.

A multi-objective computation offloading algorithm in MEC environments

Mobile edge computing (MEC) is able to provide cloud computing capabilities at network edges by offloading computation tasks to MEC servers deployed in proximity of edge nodes. Therefore, how to make offloading decision for mobile users has become a critical issue. In this paper, we propose a multi-objective computation offloading algorithm combining multi-objective evolutionary algorithm based on decomposition (MOEA/D) with invasive weed optimisation (IWO) and differential evolution (DE). Considering that IWO is a numerical stochastic optimisation method imitating weeds, behaviour in nature and enjoys great robustness, we further improve its searching abilities. In order to reduce computing time, single-object problems can be clustered into several groups in which only one problem can be optimised by IWO and others are optimised by DE. Experimental results show the competitive performance of our proposed algorithm for computation offloading in MEC environments.

A comparative study of Gaussian process regression with other three machine learning approaches in the performance prediction of centrifugal pump

Accurate prediction of performance indices using impeller parameters is of great importance for the initial and optimal design of centrifugal pump. In this study, a kernel-based non-parametric machine learning method named with Gaussian process regression (GPR) was proposed, with the purpose of predicting the performance of centrifugal pump with less effort based on available impeller parameters. Nine impeller parameters were defined as model inputs, and the pump performance indices, that is, the head and efficiency, were determined as model outputs. The applicability of three widely used nonlinear kernel functions of GPR including squared exponential (SE), rational quadratic (RQ) and Matern5/2 was investigated, and it was found by comparing with the experimental data that the SE kernel function is more suitable to capture the relationship between impeller parameters and performance indices because of the highest R square and the lowest values of max absolute relative error (MARE), mean absolute proportional error (MAPE), and root mean square error (RMSE). In addition, the results predicted by GPR with SE kernel function were compared with the results given by other three machine learning models. The comparison shows that the GPR with SE kernel function is more accurate and robust than other models in centrifugal pump performance prediction, and its prediction errors and uncertainties are both acceptable in terms of engineering applications. The GPR method is less costly in the performance prediction of centrifugal pump with sufficient accuracy, which can be further used to effectively assist the design and manufacture of centrifugal pump and to speed up the optimization design process of impeller coupled with stochastic optimization methods.

Improving Sample Average Approximation Using Distributional Robustness

Sample average approximation is a popular approach to solving stochastic optimization problems. It has been widely observed that some form of robustification of these problems often improves the out-of-sample performance of the solution estimators. In estimation problems, this improvement boils down to a trade-off between the opposing effects of bias and shrinkage. This paper aims to characterize the features of more general optimization problems that exhibit this behaviour when a distributionally robust version of the sample average approximation problem is used. The paper restricts attention to quadratic problems for which sample average approximation solutions are unbiased and shows that expected out-of-sample performance can be calculated for small amounts of robustification and depends on the type of distributionally robust model used and properties of the underlying ground-truth probability distribution of random variables. The paper was written as part of a New Zealand funded research project that aimed to improve stochastic optimization methods in the electric power industry. The authors of the paper have worked together in this domain for the past 25 years.

Innovative Reactive Distillation Process for the Sustainable Purification of Lactic Acid

Lactic acid is commonly used in a wide range of fields, such as cosmetics, pharmaceutical products, chemistry, and food. During recent years, its use for new applications, such as the production of biodegradable and biocompatible polymers, green solvents, and oxygenated chemicals, have received considerable attention. However, the relatively high production cost of lactic acid hinders many large-scale applications. It is necessary to develop more efficient methods of separation and purification to cheapen lactic acid production processes. The main objective of this study is to investigate the use of process intensification, particularly the reactive distillation process, for a sustainable purification of lactic acid. To do so, there have been proposed, on the one hand, four intensified alternatives in which synthesis and design are based on thermal couplings and, on the other hand, three alternatives looking for water mass integration. Design and optimization of those modified configurations are carried out employing a stochastic optimization method, using as objective functions some metrics associated with the concept of sustainability (economics, environmental, and inherent safety indexes). A study on the dynamic performance of the configurations through the use of singular value decomposition is carried out in a complementary way. The results in the first redesign stage show improvements in all performance indexes. However, a great difference between the implementation of a thermal coupling that substitutes a condenser instead of a reboiler has been identified. The best scheme, based on a sustainability framework, resulted in a modified process, including a dividing wall column-based scheme.

Affine-arithmetic-based microgrid interval optimization considering uncertainty and battery energy storage system degradation

Microgrids can effectively integrate renewable energy sources (RESs) and provide power for local customers. However, uncertainties of RESs and loads pose challenges to microgrid operation. The traditional point optimization method is unrealistic, and the widely used stochastic optimization (SO) method is time-consuming. Besides, battery energy storage systems (BESSs) are critical dispatchable devices to alleviate adverse effects of uncertainty, so an accurate nonlinear degradation cost model of BESSs should also be proposed. To handle such problems, the paper proposes an affine–arithmetic (AA)-based microgrid interval optimization (IO) method considering uncertainty and BESS degradation. First, the AA theory is introduced to model the RES and load variation ranges as intervals and calculate the interval uncertainty. Then, a nonlinear BESS degradation cost model is proposed, which can assess battery degradation costs considering different charging and discharging behaviors. The nondominated sorting genetic algorithm-II (NSGA-II) is employed to solve the proposed microgrid IO framework. For validation, the proposed IO method was compared with the point optimization method and SO method under various uncertainty realizations in a modified IEEE 33 bus system. The simulation results indicated the effectiveness of the proposed IO method in terms of an equilibrium between the simulation time and optimization performance.

Hierarchical stochastic scheduling of multi-community integrated energy systems in uncertain environments via Stackelberg game

An operating entity utilizing community-integrated energy systems with a large number of small-scale distributed energy sources can easily trade with existing distribution markets. To solve the energy management and pricing problem of multi-community integrated energy systems (MCIESs) with multi-energy interaction, this study investigated a hierarchical stochastic optimal scheduling method for uncertain environments. To handle multiple uncertainties, a Wasserstein generative adversarial network with a gradient penalty was used to generate renewable scenarios, and the Kmeans++ clustering algorithm was employed to generate typical scenarios. A Stackelberg-based hierarchical stochastic schedule with an integrated demand response was constructed, where the MCIES operator acted as the leader pursuing the maximum net profit by setting energy prices, while the building users were followers who adjusted their energy consumption plans to minimize their total costs. Finally, a distributed iterative solution method based on a metaheuristic was designed. The effectiveness of the proposed method was verified using practical examples.

Stochastic inversion of magnetotelluric data using deep reinforcement learning

We have adopted a new tool to invert magnetotelluric data for the 1D model based on deep Q-networks (DQN), which works as a stochastic optimization method. By transforming the inversion problem into a Markov decision process, the tool learns by trial and error to find the optimal path for updating the model to fit the observed data. The DQN method converges to the target through different paths (e.g., Bayesian or other stochastic methods) and can partially provide the probability distribution of the inversion results, which can be used for uncertainty estimation. The DQN search space gradually decreases as the learning experience progresses, accelerating the single inversion and approximating the optimal result. To check the effectiveness of the DQN inversion, the five- and eight-layer models were separately designed to test the robustness of the DQN for the initial model and the noise level. A further comparison with Occam’s method and the Bayesian method indicated that our DQN obtained more robust inversion results for data contaminated by different noise levels. The inversion results with the survey data from Zhagaitunuoergong area, Inner Mongolia, China, well reveals the shape of the interface basement.

Stochastic Bayesian optimization for predicting borderline knock

Engine knock is an undesirable combustion that could damage the engine mechanically. On the other hand, it is often desired to operate the engine close to its borderline knock limit to optimize combustion efficiency. Traditionally, borderline knock limit is detected by sweeping tests of related control parameters for the worst knock, which is expensive and time consuming, and also, the detected borderline knock limit is often used as a feedforward control without considering its stochastic characteristics without compensating current engine operational condition and type of fuel used. In this paper, stochastic Bayesian optimization method is used to obtain a tradeoff between stochastic knock intensity and fuel economy. The log-nominal distribution of knock intensity signal is converted to Gaussian one using a proposed map to satisfy the assumption for Kriging model development. Both deterministic and stochastic Kriging surrogate models are developed based on test data using the Bayesian iterative optimization process. This study focuses on optimizing two competing objectives, knock intensity and indicated specific fuel consumption using two control parameters: spark and intake valve timings. Test results at two different operation conditions show that the proposed learning algorithm not only reduces required time and cost for predicting knock borderline but also provides control parameters, based on trained surrogate models and the corresponding Pareto front, with the best fuel economy possible.

Optimal operational strategy for a future electricity and hydrogen supply system in a residential area

This study introduces a novel framework of an electricity and hydrogen supply system integrating with a photovoltaic power station for a residential area. The non-residential parts including the power grid and non-residential vehicles are added to ensure power balance and bring benefits, respectively. The optimal operational strategy of the proposed framework with considering uncertainties is proposed. The objective function minimizes the expected operational cost (EOC) by reducing the imported electricity from the power grid and increasing exported electricity/hydrogen to non-residential vehicles. Additionally, the demand response program (DRP) is applied in the residential load to achieve operational cost reduction. The uncertainties are modeled via various scenarios by using scenario-based stochastic optimization method. Notably, existing research for similar frameworks both lacks the consideration of uncertainties and DRP, and fails to distinguish the residential and non-residential vehicles with different charging behaviors. The results indicate that 1) The feasibility of the proposed framework is validated which can ensure the power balance of the residential area and reduce the operational cost. 2) The EOC is reduced when considering DRP.

A modified genetic algorithm for system optimization

PurposeIn this paper, the previously developed idea of generalized optimization of circuits for deterministic methods has been extended to genetic algorithm (GA) to demonstrate new possibilities for solving an optimization problem that enhance accuracy and significantly reduce computing time.Design/methodology/approachThe disadvantages of GAs are premature convergence to local minima and an increase in the computer operation time when setting a sufficiently high accuracy for obtaining the minimum. The idea of generalized optimization of circuits, previously developed for the methods of deterministic optimization, is built into the GA and allows one to implement various optimization strategies based on GA. The shape of the fitness function, as well as the length and structure of the chromosomes, is determined by a control vector artificially introduced within the framework of generalized optimization. This study found that changing the control vector that determines the method for calculating the fitness function makes it possible to bypass local minima and find the global minimum with high accuracy and a significant reduction in central processing unit (CPU) time.FindingsThe structure of the control vector is found, which makes it possible to reduce the CPU time by several orders of magnitude and increase the accuracy of the optimization process compared with the traditional approach for GAs.Originality/valueIt was demonstrated that incorporating the idea of generalized optimization into the body of a stochastic optimization method leads to qualitatively new properties of the optimization process, increasing the accuracy and minimizing the CPU time.

Robust energy management for an on-grid hybrid hydrogen refueling and battery swapping station based on renewable energy

The potential of renewable energy should be fully exploited in the transportation sector to achieve a cleaner production. Therefore, this paper proposes an on-grid hybrid hydrogen refueling and battery swapping station powered by wind energy. This novel concept can promote the development of low-carbon emission vehicles including hydrogen-based vehicle and battery electric vehicle. During the daily operation of the station, the multiple uncertainties may lead to a higher operational cost. To address this problem, a hybrid stochastic/distributionally robust optimization method is proposed to handle different uncertainties for the energy management problem. The first type of uncertainties can be depicted by a certain distribution, i.e. electricity price and wind power, which is processed by a stochastic optimization method. The second type of uncertainties is associated with human behaviors and is difficult to find its probability distribution, i.e. the hydrogen demand of hydrogen-based vehicles, so the second type is processed by a distributionally robust optimization method. The overall objective is to minimize the total operational cost of the station, which also considers the battery swapping station overstock punishment. Because a reasonable battery swapping scheduling can reduce the waiting time of users and operational cost of the station. The results indicate that the proposed method can effectively address the conservatism of solutions as its total operational cost is 4.4% lower than that of the hybrid stochastic/robust optimization method under a high confidence level.