Stochastic Optimization Methods Research Articles

A single timescale stochastic quasi-Newton method for stochastic optimization

In this paper, we propose a single timescale stochastic quasi-Newton method for solving the stochastic optimization problems. The objective function of the problem is a composition of two smooth functions and their derivatives are not available. The algorithm sets to approximate sequences to estimate the gradient of the composite objective function and the inner function. The matrix correction parameters are given in BFGS update form for avoiding the assumption that Hessian matrix of objective is positive definite. We show the global convergence of the algorithm. The algorithm achieves the complexity to find an approximate stationary point and ensure that the expectation of the squared norm of the gradient is smaller than the given accuracy tolerance ϵ. The numerical results of nonconvex binary classification problem using the support vector machine and a multicall classification problem using neural networks are reported to show the effectiveness of the algorithm.

A mini-batch algorithm for large-scale learning problems with adaptive step size

The step size selection in stochastic optimization methods is a crucial aspect that holds significant importance in theoretical analysis and practical applications. We propose two stochastic optimization methods based on the competitive Barzilai-Borwein (BB) step size in both the inner and outer loops of the mini-batch semi-stochastic gradient descent (mS2GD) algorithm. The competitive BB step size is automatically updated using the latest and most accurate secant equation. We introduce two algorithms: mS2GD-CBB, which updates the step size in the outer loop, and mS2GD-RCBB, which updates the step size in the inner loop. We evaluate the performance of the proposed algorithms on the classical optimization problem and compare them against existing methods. Experimental results demonstrate that the methods exhibit favorable convergence properties and can effectively handle the challenges of big data arising from the fields of signal processing, statistics, and machine learning. The methods offer enhanced adaptability, flexibility, and exploration capabilities, making them promising approaches for a wide range of optimization problems.

A stochastic investment decision making method for distribution system resilience enhancement considering automation, hardening and distributed energy resources

Extreme weather events have always posed as a serious threat to the power system. In recent years the frequent occurrences of extreme events highlight the requirement for a resilient distribution system capable of maximizing load restoration under the most adverse situations. Because the requirement to reinforce the distribution system appears to be an expensive approach, it is crucial to make the proper investment decisions. In this regard, this article introduces a single-stage stochastic multi-criteria optimization method for maximizing network resilience over a series of investments while minimizing overall costs. This method conducts different categories of investments including the installation of sectionalizing switches, distributed energy resources, and hardening of overhead distribution lines. The optimization method is based on a genetic algorithm and can be used to address a large-scale network. Several numerical studies are tested on the IEEE 69-bus system to verify the effectiveness of the proposed method. The results of the investment decision-making method show the significance of combining planning and operational preparedness in distribution systems to respond to extreme weather events.

Adaptive Stochastic Optimization to Improve Protein Conformation Sampling.

We have long known that characterizing protein structures structure is key to understanding protein function. Computational approaches have largely addressed a narrow formulation of the problem, seeking to compute one native structure from an amino-acid sequence. Now AlphaFold2 is shown to be able to reveal a high-quality native structure for many proteins. However, researchers over the years have argued for broadening our view to account for the multiplicity of native structures. We now know that many protein molecules switch between different structures to regulate interactions with molecular partners in the cell. Elucidating such structures de novo is exceptionally difficult, as it requires exploration of possibly a very large structure space in search of competing, near-optimal structures. Here we report on a novel stochastic optimization method capable of revealing very different structures for a given protein from knowledge of its amino-acid sequence. The method leverages evolutionary search techniques and adapts its exploration of the search space to balance between exploration and exploitation in the presence of a computational budget. In addition to demonstrating the utility of this method for identifying multiple native structures, we additionally provide a benchmark dataset for researchers to continue work on this problem.

A Novel Chaotic Elite Adaptive Genetic Algorithm for Task Allocation of Intelligent Unmanned Wireless Sensor Networks

In recent times, the progress of Intelligent Unmanned Wireless Sensor Networks (IUWSNs) has inspired scientists to develop inventive task allocation algorithms. These efficient techniques serve as robust stochastic optimization methods, aimed at maximizing revenue for the network’s objectives. However, with the increase in sensor numbers, the computation time for addressing the challenge grows exponentially. To tackle the task allocation issue in IUWSNs, this paper introduces a novel approach: the Chaotic Elite Adaptive Genetic Algorithm (CEAGA). The optimization problem is formulated as an NP-complete integer programming challenge. Innovative elite and chaotic operators have been devised to expedite convergence and unveil the overall optimal solution. By merging the strengths of genetic algorithms with these new elite and chaotic operators, the CEAGA optimizes task allocation in IUWSNs. Through simulation experiments, we compare the CEAGA with other methods—Hybrid Genetic Algorithm (HGA), Multi-objective Binary Particle Swarm Optimization (MBPSO), and Improved Simulated Annealing (ISA)—in terms of task allocation performance. The results compellingly demonstrate that the CEAGA outperforms the other approaches in network revenue terms.

Robust multi‐echelon inventory management with multiple suppliers

AbstractWe study a periodic‐review multi‐supplier series inventory system in which the demand is restricted to partial sum uncertainty sets. We present and solve a robust rolling‐horizon model for the system. We propose an induction framework to characterize the closed‐form robust optimal solution of the problem. We show that the robust optimal policy combines the echelon base‐stock policy and a gap‐of‐echelon‐base‐stock policy for the uppermost stage and a modified echelon base‐stock policy for the other downstream stages. The policy structure is easy for the manager to understand and implement in practice. The policy parameters are directly determined by a sequence of nominal partial‐sum demands, and its computation is very effective. In addition, the policy does not rely on complete information about the demand distribution; its solution can be more robust than that of stochastic optimization methods, especially when demand is highly uncertain, and forecasting is difficult. Based on the structure of the robust optimal policy, we design two heuristic policies for the system and evaluate the policies' performance through an extensive numerical study using both synthetic and real data.

Gradient-free methods for non-smooth convex stochastic optimization with heavy-tailed noise on convex compact

Gradient-free methods for non-smooth convex stochastic optimization with heavy-tailed noise on convex compact

Comparative analyses of covariance matrix adaptation and iterative ensemble smoother on high-dimensional inverse problems in high-resolution groundwater modeling

Parameter estimation is an inverse problem which is crucial to reliable groundwater model predictions and management. Numerous techniques have been developed to address this challenging problem. This study aims to compare the performance of a stochastic optimization method, covariance matrix adaptation-evolution strategy (CMA-ES), and a data assimilation method, Levenberg-Marquardt based iterative ensemble smoother (ES-LM), on solving inverse problems in groundwater modeling. This study also presents a parallelization strategy to accelerate their implementation. The comparative analysis involves synthetic inverse problems and a real-world case study of calibrating a high-resolution groundwater model. Results from the synthetic problems suggest that both the CMA-ES and the ES-LM are able to achieve desirable data fitting, but the ES-LM generally exhibits greater efficiency than the CMA-ES. Also, with appropriate stopping criteria, both methods can perform well on propagating uncertainty of model predictions. However, both methods can underestimate the uncertainty of model parameters derived from Bayesian posterior. The underestimation is particularly pronounced by the ES-LM when using a small ensemble size, whereas uncertainty quantification by the CMA-ES is less affected by population size. Moreover, calibration of the highly parameterized groundwater model in Louisiana and Southwest Mississippi indicates that the ES-LM can outperform the CMA-ES for high-dimensional inverse problems regarding both data match and computational costs. With proper ensemble size, the two methods can produce comparable uncertainty of model parameters and predictions. This study contributes to the scientific understanding and efficient application of the CMA-ES and the ES-LM.

Cardiovascular Disorder Detection with a PSO-Optimized Bi-LSTM Recurrent Neural Network Model

The medical community is facing ever-increasing difficulties in identifying and treating cardiovascular diseases. The World Health Organization (WHO) reports that despite the availability of numerous high-priced medical remedies for persons with heart problems, CVDs continue to be the main cause of mortality globally, accounting for over 21 million deaths annually. When cardiovascular diseases are identified and treated early on, they cause far fewer deaths. Deep learning models have facilitated automated diagnostic methods for early detection of these diseases. Cardiovascular diseases often present insidious symptoms that are difficult to identify in a timely manner. Prompt diagnosis of individuals with CVD and related conditions, such as high blood pressure or high cholesterol, is crucial to initiate appropriate treatment. Recurrent neural networks (RNNs) with gated recurrent units (GRUs) have recently emerged as a more advanced variant, capable of surpassing Long Short-Term Memory (LSTM) models in several applications. When compared to LSTMs, GRUs have the advantages of faster calculation and less memory usage. When it comes to CVD prediction, the bio-inspired Particle Swarm Optimization (PSO) algorithm provides a straightforward method of getting the best possible outcomes with minimal effort. This stochastic optimization method requires neither the gradient nor any differentiated form of the objective function and emulates the behaviour and intelligence of swarms. PSO employs a swarm of agents, called particles, that navigate the search space to find the best prediction type.This study primarily focuses on predicting cardiovascular diseases using effective feature selection and classification methods. For CVD forecasting, we offer a GRU model built on recurrent neural networks and optimized with particle swarms (RNN-GRU-PSO). We find that the proposed model significantly outperforms the state-of-the-art models (98.2% accuracy in predicting cardiovascular diseases) in a head-to-head comparison.

ACFlow: An open source toolkit for analytic continuation of quantum Monte Carlo data

The purpose of analytic continuation is to establish a real frequency spectral representation of single-particle or two-particle correlation function (such as Green's function, self-energy function, spin and charge susceptibilities) from noisy data generated in finite temperature quantum Monte Carlo simulations. It requires numerical solutions of a family of Fredholm integral equations of the first kind, which is indeed a challenging task. In this paper, an open source toolkit (dubbed ACFlow) for analytic continuation of quantum Monte Carlo data is presented. We first give a short introduction to the analytic continuation problem. Next, three popular analytic continuation algorithms, including the maximum entropy method, the stochastic analytic continuation, and the stochastic optimization method, as implemented in this toolkit are reviewed. And then we elaborate on the major features, implementation details, basic usage, inputs, and outputs of this toolkit. Finally, four representative examples, including analytic continuations of Matsubara self-energy function, Matsubara and imaginary time Green's functions, and current-current correlation function, are shown to demonstrate the usefulness and flexibility of the ACFlow toolkit. Program summaryProgram Title: ACFlowCPC Library link to program files:https://doi.org/10.17632/th6w74gwjm.1Developer's repository link:https://github.com/huangli712/ACFlowLicensing provisions: GNU General Public License Version 3Programming language: JuliaNature of problem: Most of the quantum Monte Carlo methods work on imaginary axis. In order to extract physical observables and compare them with the experimental results, analytic continuation must be done in the post-processing stage to convert the quantum Monte Carlo simulated data from imaginary axis to real axis.Solution method: Three well-established analytic continuation methods, including the maximum entropy method, the stochastic analytic continuation (both A. W. Sandvik's and K. S. D. Beach's algorithms), and the stochastic optimization method, have been implemented in the ACFlow toolkit.Additional comments including restrictions and unusual features: The ACFlow toolkit is written in pure Julia language. It is highly optimized and parallelized. It can be executed interactively in a Jupyter notebook environment.

A stochastic multi-objective optimization method for railways scheduling: a NSGA-II-based hybrid approach

A stochastic multi-objective optimization method for railways scheduling: a NSGA-II-based hybrid approach

Stochastic electrical, thermal, cooling, water, and hydrogen management of integrated energy systems considering energy storage systems and demand response programs

Energy hub (EH) is a multi-energy system that combines several energy sources to increase energy supply efficiency, flexibility, and reliability. In this paper, a stochastic two-step multi-objective optimization method is proposed for multi-EH planning that focuses on economic, environmental, and security concerns. In order to meet the demands for electricity, heating, cooling, hydrogen, natural gas, and water, the proposed model includes several components, such as nonrenewable and renewable energy sources, cogeneration units, converters, and storage systems. Also, price-based demand response programs are implemented to provide demand-side flexibility for EHs. The proposed multi-objective framework investigates the total cost of the system, average reserve index (ARI), emissions of the system, and energy not supplied (ENS), simultaneously. EHs categorize their objectives into main and secondary based on priority. Since the total cost is so important, it has been recognized as the primary objective that is minimized in the first step. Also, the emissions, ENS, and ARI are the secondary objectives that are optimized in the second step simultaneously. The proposed model's efficiency is evaluated using an 18-bus test network in both summer and winter seasons. The simulation results present that the proposed model improves the emission, ARI, and ENS by 47.78 %, 53.4 %, and 23.38 % in summer seasons, respectively. And also, the multi-objective framework improves the emission, ARI, and ENS by 45.66 %, 65.84 %, and 52.56 % in winter seasons, respectively.

Stochastic optimisation-based methods for the identification of the physical parameters of a metal hydride tank

In this paper, three optimisation methods are used to determine the parameters of a commercial metal hydride hydrogen tank, considered as a grey box in which the thermophysical parameters are unknown. These parameters are essential for the development of energy management strategies and the study of tank ageing. A model of the hydride tank containing an AB5 intermetallic was developed and experimentally validated. An absorption test campaign of the studied tank was carried out to collect data necessary for the optimisation algorithms. A comparative study was carried out in accordance with the speed of convergence and precision between the three stochastic optimisation methods: Particle Swarm Optimisation (PSO), Genetic Algorithm (GA) and Differential Evolution (DE). The results of the simulation of the storage system using the parameters determined by the algorithms show a remarkably close agreement with the experimental data, with a maximum error of 2.1%.

Satisfying strict deadlines for cellular Internet of Things through hybrid multiple access

AbstractLatency‐constrained aspects of cellular Internet of Things (IoT) applications rely on Ultra‐Reliable and Low Latency Communications (URLLC), which highlight research on satisfying strict deadlines. In this study, we address the problem of latency‐constrained communications with strict deadlines under average power constraint using Hybrid Multiple Access (MA), which consists of both Orthogonal MA (OMA) and power domain Non‐Orthogonal MA (NOMA) as transmission scheme options. We aim to maximize the timely throughput, which represents the average number of successfully transmitted packets before deadline expiration, where expired packets are dropped from the buffer. We use Lyapunov stochastic optimization methods to develop a dynamic power assignment algorithm for minimizing the packet drop rate while satisfying time average power constraints. Moreover, we propose a flexible packet dropping mechanism called Early Packet Dropping (EPD) to detect likely to become expired packets and drop them immediately. Numerical results show that Hybrid MA improves the timely throughput compared to conventional OMA by up to and on average by more than . With EPD, these timely throughput gains improve to and , respectively.

Day-Ahead Distributionally Robust Optimization-Based Scheduling for Distribution Systems With Electric Vehicles

In this paper, a day-ahead optimal scheduling strategy for the DSO based on EV aggregation is proposed. Generally, the uncertain parameters of EVs, i.e., arrival and departure times as well as the charging demands, can be effectively modeled by a Gaussian mixture model (GMM) with historical charging records. The empirical data of net load error, i.e., mean values and covariance, can be obtained from historical data, while the explicit probability distribution function may not be fully known. Therefore, a distributionally robust optimization (DRO) model is formulated for the DSO to characterize the net load uncertainty. Then, an EV aggregation-based reservation capacity prearrangement method is proposed to specifically address the net load error. Next, with the reservation capacity from EVs, the DRO model is convexified by transforming into two subproblems with deterministic forms. Finally, simulation and comparison tests are conducted on the 33-bus distribution network to demonstrate that the proposed approach achieves a tradeoff between economic performance and computation efficiency compared with the scenario-based stochastic optimization method and achieves a tradeoff between operation costs and system reliability compared with the chance constraint method.

Fuzzy logic based adaptive vibration control system for structures subjected to seismic and wind loads

In this study, an attempt has been made to develop a Fuzzy Logic Multi Verse Optimal Control (FLMVOC) system as a new adaptive real-time vibration control mechanism for structures subjected to seismic excitation and wind load by utilizing the capability of the stochastic optimization method and fuzzy logic technique.The magnetorheological damper (MR) is deployed as a controllable vibration damping system in this study due to its excellent damping performance and low energy consumption. Therefore, the analytical model for the MR damper is formulated and integrated with the developed fuzzy logic optimal control (FLOC) algorithm. The story drift and absolute acceleration have been defined as the inputs of the fuzzy logic controller (FLC), while the MR commanding voltage is considered as the controller’s output. Then, the membership functions and fuzzy rule base have been formulated. To derive the optimal controller, the FLC with full parameters has been trained with multi objective multi verse algorithm (MOMVO). For this purpose, the MATLAB program and its Simulinks have been integrated and hybridised with finite element package to simulate and evaluate structure response for various input parameters.The developed FLMVOC system has been implemented in three story shear building subjected to seismic load and 60 story wind induced high rise building in order to evaluate its efficiency in diminishing the dynamic response of the structure.The result revealed that FLMVOC system successfully reduced structural drifts by 60%, 53%, and 41% under the effect of El Centro, Kobe, and Northridge earthquakes, respectively, while the floor absolute acceleration was reduced by 38%, 17%, and 10%, respectively. For the wind induced structure, the proposed system showed the ability to maintain the floor acceleration within people’s comfort criterion in addition to the reduction in story drift.

A Risk-Averse Adaptive Stochastic Optimization Method for Transactive Energy Management of a Multi-Energy Microgrid

This paper proposes a new energy management method for a multi-energy microgrid (MEMG) which supplies both electrical and thermal energies. Based on the transactive energy (TE) concept, the problem is formulated as a Stackelberg game-theoretic bi-level optimization model. The MEMG operator optimizes the energy scheduling and pricing strategies at the upper level, and the industrial, commercial and residential agents optimize their energy trading strategies at the lower level. The equivalent single-level mixed-integer linear program (MILP) reformulation is then derived for computational tractability. To coordinate the strategies made in the day-ahead and intra-day energy markets, an adaptive stochastic optimization (SO) approach is adopted, by which a day-ahead stochastic MILP and an intra-day deterministic model are formed. Furthermore, the conditional value-at-risk (CVaR) measure is incorporated in the day-ahead stage for risk aversion of the MEMG operator towards uncertainties. To solve the models, an adaptive Progressive Hedging (PH) algorithm is developed to decompose the day-ahead stochastic MILP into multiple scenario-based subproblems which can be solved in parallel, and an outer approximation (OA) algorithm is adopted in the intra-day stage to linearize the bilinear objective function. Finally, the simulation results verify the effectiveness of the proposed energy management method and the efficiency of the solution algorithms.

Risk-Aware Distributionally Robust Optimization for Mobile Edge Computation Task Offloading in the Space–Air–Ground Integrated Network

As an emerging network paradigm, the space–air–ground integrated network (SAGIN) has garnered attention from academia and industry. That is because SAGIN can implement seamless global coverage and connections among electronic devices in space, air, and ground spaces. Additionally, the shortage of computing and storage resources in mobile devices greatly impacts the quality of experiences for intelligent applications. Hence, we plan to integrate SAGIN as an abundant resource pool into mobile edge computing environments (MECs). To facilitate efficient processing, we need to solve the optimal task offloading decisions. In contrast to existing MEC task offloading solutions, we have to face some new challenges, such as the fluctuation of processing capabilities for edge computing nodes, the uncertainty of transmission latency caused by heterogeneous network protocols, the uncertain amount of uploaded tasks during a period, and so on. In this paper, we first describe the task offloading decision problem in environments characterized by these new challenges. However, we cannot use standard robust optimization and stochastic optimization methods to obtain optimal results under uncertain network environments. In this paper, we propose the ‘condition value at risk-aware distributionally robust optimization’ algorithm for task offloading, denoted as RADROO, to solve the task offloading decision problem. RADROO combines the distributionally robust optimization and the condition value at risk model to achieve optimal results. We evaluated our approach in simulated SAGIN environments, considering confidence intervals, the number of mobile task offloading instances, and various parameters. We compare our proposed RADROO algorithm with state-of-the-art algorithms, such as the standard robust optimization algorithm, the stochastic optimization algorithm, the DRO algorithm, and the Brute algorithm. The experimental results show that RADROO can achieve a sub-optimal mobile task offloading decision. Overall, RADROO is more robust than others to the new challenges mentioned above in SAGIN.

Optimal Allocation of Energy Storage Capacity in Microgrids Considering the Uncertainty of Renewable Energy Generation

The high dimensionality and uncertainty of renewable energy generation restrict the ability of the microgrid to consume renewable energy. Therefore, it is necessary to fully consider the renewable energy generation of each day and time period in a long dispatching period during the deployment of energy storage in the microgrid. To this end, a typical multi-day scenario set is used as the simulation operation scenario, and an optimal allocation method of microgrid energy storage capacity considering the uncertainty of renewable energy generation is designed. Firstly, the historical scenarios are clustered into K types of daily state types using the K-means algorithm, and the corresponding probability distribution is obtained. Secondly, the Latin hypercube sampling method is used to obtain the state type of each day in a multi-day scenario set. Then, the daily scenario generation method based on conditional generative adversarial networks is used to generate a multi-day scenario set, combining the day state type as a condition, and then the typical scenario set is obtained using scenario reduction. Furthermore, a double-layer optimization allocation model for the energy storage capacity of microgrids is constructed, in which the upper layer optimizes the energy storage allocation capacity and the lower layer optimizes the operation plans of microgrids in each typical scenario. Finally, the proposed model is solved using the PSO algorithm nested with the CPLEX solver. In the microgrid example, the proposed method reduces the expected annual total cost by 19.66% compared with the stochastic optimal allocation method that assumes the scenic power obeys a specific distribution, proving that it can better cope with the uncertainty of renewable energy generation. At the same time, the expected annual total cost is reduced by 6.99% compared with the optimal allocation method that generates typical daily scenarios based on generative adversarial networks, which proves that it can better cope with the high dimensionality of renewable energy generation.

Green supply chain management: a renewable energy planning and dynamic inventory operations for perishable products

The emergence of renewable energy microgrids (REM)-supported logistics parks reflects the urgent social requirement for sustainability facing energy crisis and climate change. Focusing on the emergency REM capacity planning and dynamic inventory operations problem for a REM-supported cold warehouse, this paper constructs a novel two-stage stochastic optimization method to comprehensively minimise long-term investment and short-term emergency operation costs of the system, while improving the resilience of energy-constrained supply chain management of perishable products. In particular, we formulate the second stage emergency operation problem as a Markov decision process that considers the interaction between energy and operational decisions constrained by intermittent of renewable energy, the randomness of the occurrence time, and the balance between power supply and temperature changes of the cold warehouse. We propose a novel two-phase PSO-based MPC algorithm to solve the entire problem. We also examine the effectiveness of our algorithm via an empirical study based on the data in East China. Nine typical scenarios clustered from the real data suggest different optimal capacity planning and operational policies. The empirical results show that it can reduce an overall 9% of operating costs on average compared to other heuristic policies. Moreover, installing REM can improve the resilience of power systems by 23% (risk impact area reduction ratio) and improve the resilience of inventory systems by 49%.