Stochastic Optimization Methods Research Articles

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%.

Deep Learning Models for Airport Demand Forecasting With Google Trends

Managers gain new insights into how operational benefits can be achieved. Forecasting problems for passenger flow in airports are gaining interest among marketing researchers, but comparison of stochastic optimisation methods via deep learning forecasts with search query data is not yet available in the aviation field. To fill this gap, the current study predicts the demand of Madrid airport demand with Google search query data using H2O deep learning method. The findings indicate that there is a long-term relationship between search queries and actual passenger demand. Besides, search queries “fly to madrid,” and “flights to madrid spain” were found to be the cause of the actual domestic air passenger demand in Madrid. Also, to determine the best forecasting accuracy, stochastic gradient descent (SGD) optimisers were used. Specifically, findings indicate that Adam is a better optimiser increasing forecasting accuracy for Madrid airports.

Extended Regularized Dual Averaging Methods for Stochastic Optimization

Extended Regularized Dual Averaging Methods for Stochastic Optimization

Model building of urban energy system and effect analysis of green low‐carbon transition under the background of carbon peaking and carbon neutrality

AbstractUnder the carbon peaking and carbon neutrality goals background in China, cities are the main force of energy consumption and carbon emission, and their low‐carbon transition development has become the primary task of urban planning. The transitional development of cities not only puts forward higher requirements for the output proportion of new energy, but also puts forward higher requirements for the flexibility of energy system. This paper proposes an optimization model of urban energy system considering the uncertainty output of new energy and new energy vehicles. The uncertainty and operational flexibility of electric vehicles are taken into account at the planning level by using stochastic optimization method. The model considers the expansion and retirement of new energy units and various conversion devices in urban energy system, and ensures the achievement of carbon peaking and carbon reduction goals by imposing constraints on electric vehicles. The case results show that this model can effectively improve the economy and new energy consumption rate of urban energy system, and can meet the carbon reduction demand.

Commuting-pattern-oriented stochastic optimization of electric powertrains for revealing contributions of topology modifications to the powertrain energy efficiency

The performance of an electric vehicle (EV) powertrain is greatly influenced by the design scheme, control strategy, and driving conditions. Owing to uncertainties in driving conditions and the mutual correlation between design scheme and control strategy, identifying the optimal topology and component parameters of EV powertrains for improving the energy efficiency of EVs remains a challenging task. Oriented to the commuting patterns of individuals, this paper proposes a stochastic optimization method for identifying the superior powertrain design that optimizes the expected energy economy of the EV powertrain and reduces the energy economy variability in random driving conditions. This paper also introduces a machine-learning solution to the complex mutual restrictions among design variables, control strategies, and driving conditions, which determines the feasible design space and powertrain performance. Suggested by massive validations, the stochastic optimization method reduces the expectation and deviation of the energy consumption of EV powertrains up to 12.0% and 5.6%, compared with deterministic optimization methods. Additionally, by comparative evaluation among stochastic optimal design results of different topologies, contributions of topology modifications to the energy efficiency of EV powertrains are clarified, and the superior powertrain topology is identified, which improves 17.1% expected energy economy compared with the current popular topology.

Programable structural color generation by phase-change-medium-enabled pixelated hyperbolic metamaterial

Phase-change-medium-enabled hyperbolic metamaterial structures were investigated for generating a wide range of colors by applying external electrical pulses to the embedded graphene-based micro-heater system. The stochastic particle swarm optimization method was implemented to accelerate the design process, followed by the transfer-matrix method to observe the effects of incidence polarization and angle. The results revealed a wide range of colors attainable via the constitutive properties of the designed pixels, which remains insensitive to the incidence polarization, and under a wide range of incidence angle. The investigated programable structure can find potential use in reflective displays and holographic devices for security systems.

HUB: a method to model and extract the distribution of ice nucleation temperatures from drop-freezing experiments

Abstract. The heterogeneous nucleation of ice is an important atmospheric process facilitated by a wide range of aerosols. Drop-freezing experiments are key for the determination of the ice nucleation activity of biotic and abiotic ice nucleators (INs). The results of these experiments are reported as the fraction of frozen droplets fice(T) as a function of decreasing temperature and the corresponding cumulative freezing spectra Nm(T) computed using Gabor Vali's methodology. The differential freezing spectrum nm(T) is an approximant to the underlying distribution of heterogeneous ice nucleation temperatures Pu(T) that represents the characteristic freezing temperatures of all INs in the sample. However, Nm(T) can be noisy, resulting in a differential form nm(T) that is challenging to interpret. Furthermore, there is no rigorous statistical analysis of how many droplets and dilutions are needed to obtain a well-converged nm(T) that represents the underlying distribution Pu(T). Here, we present the HUB (heterogeneous underlying-based) method and associated Python codes that model (HUB-forward code) and interpret (HUB-backward code) the results of drop-freezing experiments. HUB-forward predicts fice(T) and Nm(T) from a proposed distribution Pu(T) of IN temperatures, allowing its users to test hypotheses regarding the role of subpopulations of nuclei in freezing spectra and providing a guide for a more efficient collection of freezing data. HUB-backward uses a stochastic optimization method to compute nm(T) from either Nm(T) or fice(T). The differential spectrum computed with HUB-backward is an analytical function that can be used to reveal and characterize the underlying number of IN subpopulations of complex biological samples (e.g., ice-nucleating bacteria, fungi, pollen) and to quantify the dependence of these subpopulations on environmental variables. By delivering a way to compute the differential spectrum from drop-freezing data, and vice versa, the HUB-forward and HUB-backward codes provide a hub to connect experiments and interpretative physical quantities that can be analyzed with kinetic models and nucleation theory.

Multi-level model predictive control based multi-objective optimal energy management of integrated energy systems considering uncertainty

Integrated energy systems (IES) with renewable energy systems (RES), carbon capture systems (CCS) and energy storage systems (ESS) are considered efficient in supporting the low-carbon energy supply with both economic and environmental benefits. Effective energy management is required to ensure the economical, environmental and reliable operation of the IES. However, the optimal IES operation is considered a non-trivial task due to the renewable generation uncertainty and the optimization of multiple contradictory objectives (e.g. economic, environmental and risk costs). This paper aims to provide a multi-level optimization model for the real-time optimal IES operation consisting of RES, ESS and CCS. This work quantifies the uncertainty by the Conditional Value at Risk (CVaR) theory in the optimization model. The uncertainty is further reduced by improving the operation strategy through a model predictive control (MPC)-based method. Also, the multi-objective optimization model is adopted to minimize the economic cost, carbon dioxide emissions (CDE) and primary energy consumption (PEC) for optimal energy scheduling in the intra-day stage. Based on the result of the intra-day stage, the feedback correction model is applied to adjust the schedule to balance the difference between the forecasting and actual values. Numerical results show that the proposed solution can provide the trade-off between economical and environmental performance. Through ablation experiments, the proposed method with feedback correction can carry out demand response with lower costs, CDE and PEC. The proposed solution is further confirmed with outperformed performance compared with single-objective optimization methods and other stochastic optimization methods. In addition, a robustness analysis is conducted to quantify the benefits of RES, ESS and CCS in IES.

Energy management of an intelligent parking lot equipped with hydrogen storage systems and renewable energy sources using the stochastic p-robust optimization approach

Transportation electrification is an undeniable trend for moving towards sustainable energy systems. Therefore, electric intelligent parking lots (IPL) enhanced with renewable energy sources (RESs) and hydrogen storage systems (HSSs) play an essential role in reaching multiple techno-environmental purposes. In this regard, this paper proposes a novel energy management framework for HSS-based IPL considering risk management approach and demand response programs. The uncertainties of input parameters such as solar irradiation and its temperature, wind speed, energy tariff of the upper grid, and IPL's demand are captured into the model through two strategies; the stochastic optimization method (SOM) and the stochastic p-robust optimization approach (SPROA). The SPROA is applied to model the risk-based form of the IPL to minimize the total expected expenditure of the IPL and its maximum related regret (MRR). Finally, the proposed approach is applied to a typical IPL and the results demonstrate the effectiveness of the proposed approach for conservative operators.

Robust Multi-objective optimal dispatching model for a novel island micro energy grid incorporating biomass waste energy conversion system, desalination and power-to-hydrogen devices

To realize renewable and self-sustainable energy supply in island region, based on geographical characteristics with abundant renewable resources, an optimal model for island micro energy grid (MEG) is designed incorporating biomass waste energy conversion system (ECS), desalination, and power-to-hydrogen (BSP-MEG) Firstly, the mathematical model is designed, including models of power generators, ECS, desalination and power-to-hydrogen (P2H) devices, etc. Next, the multi-objective scheduling optimization model is designed, containing conventional scheduling model (Scheduling optimization objectives and constraints established with minimum operation and environment costs) and stochastic scheduling model (Minimum Conditional Value-at-Risk objective specific to volatility and uncertainty of renewable generations based on robust stochastic optimization method). Then, to solve the multi-objective optimization problem (MOP), a hybrid differential evolution algorithm is proposed based on local optimal and external archiving strategies. Finally, the MEG of YongXing Island is selected as an example. The results show (1) BSP-MEG effectively realized multi-energy cooperative optimization, and promote intra-day peak shaving. (2) BSP-MEG reduced operating costs, environmental costs and Conditional Value-at-Risk (CVaR) by 78.2%, 61.8% and 77.9% respectively, while curtailment rate by 25.6 to 0.9%. (3) Whether in general scenario or worst, BSP-MEG can realize self-production and self-sale of energy and material, of which risk resistance ability is better. (4) By designing local optimal and external archiving strategies, hybrid differential evolution algorithm performs better in solving complex MOP. In general, the optimization model proposed in this paper can improve the utilization of renewable resources, alleviate the shortage of fresh water, and help realize renewable and sustainable energy supply.

Full waveform inversion as training a neural network

Full waveform inversion (FWI) is usually solved as a nonlinear least-squares problem to minimize the discrepancy between the recorded signal and the synthetic data by some gradient-based optimization methods. In this paper, we investigate acoustic FWI as training a neural network. We recast the time-domain difference scheme into a forward propagation process of vanilla recurrent neural network (RNN) and then find that the parameters of RNN coincide with the physical parameters in the wave equation. As a result, the FWI problem is resolved as training such a kind of neural network. Some stochastic optimization methods such as the Adam optimizer are applied to update the model parameters. We demonstrate our method numerically with three typical models including the benchmark Marmousi model. The numerical results show that the fast convergence and good velocity inversion result can be achieved.

Three-stage coordinated operation of steel plant-based multi-energy microgrids considering carbon reduction

Steel production is one of the most energy-intensive industries on demand side. Highly distributed energy resource-penetrated multi-energy microgrids (MEMGs) with combined heat and power (CHP) units can supply both electricity and heat while the by-product coal gases during manufacturing can be reused for onsite power supply. However, there is a lack of coordination between steel production and MEMG operation, and the steelmaking process is not fully modelled. Thus, this paper proposes a three-stage coordinated operation method for steel plant-based MEMGs, aiming to minimize the total operating cost. In this method, the steel production is scheduled weekly-ahead to meet the production demand considering carbon emission reduction. Then, the CHP commitment and day-ahead energy transaction are optimized in a day-ahead stage, while the dispatchable device output and intraday energy transaction are determined hourly-ahead based on uncertainty realizations. Accordingly, the steel production is modelled as continuous and discontinuous processes in parallel or series. To tackle the uncertainty of renewable generation, a scenario-based stochastic optimization method is utilized. Moreover, different carbon prices are applied to investigate their effects on steel production. The results show that the proposed method can decrease the operating cost by 14.33% and 1.45% compared with the other two conventional methods.

Optimal multi-market scheduling of a sustainable photovoltaic-oriented distribution network hosting hydrogen vehicles and energy storages: A regret assessment optimization

One of the goals of the smart-grids is to increase the penetration of renewable energy sources like photovoltaics (PVs) and hydrogen-based resources in a controllable manner. To fully utilize these resources in smart cities, dealing with a significant amount of generation and demand uncertainty may be necessary. This article proposed a two-stage optimization procedure smart distribution grid at the city level with a high penetration of solar and hydrogen-powered cars considering the real-time and day-ahead markets. In addition to renewable resources, the proposed network also considers energy storage (ESs), generator units (GUs), and demand response programs (DRPs). In this paper, uncertainties involved in the system are modeled using a scenario-based method. Then, a regression index, so-called maximum relative regret (MRR) derived from the stochastic p-robust optimization (SPRO) method, is utilized to model the imposed regret on uncertainties. Uncertainties in the proposed system include PV generation, electricity and hydrogen demands, real-time market prices, and hydrogen-powered car behavior. The IEEE 33 bus test system has chosen to evaluate the proposed regret-based framework. The findings show that the proposed approach is well-suited to the conservative SPRO technique for the employed system, in which the projected cost of the objective function increases by just 3.40 % for a 45.42 % decrease in the MRR.

Integration of reactor network synthesis: A literature review and opportunities for future research

AbstractThe reactor network synthesis (RNS) is one of the subtopics of the chemical process synthesis, the purpose of which is to find an optimal reactor network for the specific objective function of the studied reaction system. This review discusses the principles, advantages, and disadvantages of various methods of RNS, together with the state of the research in each field. These methods could be divided into four categories: the process‐based approach (such as the attainable region, the targeting approach, and the method based on the elementary process functions), superstructure‐based approach, stochastic optimization, and parametric method. Finally, the paper discusses the existing problems of RNS in academic researches and practical applications, as well as its research directions in the future. This paper is helpful to the readers who have interests in the design and optimization of the reactor networks.

A modified approach on modeling-design-optimization procedure for cutting of pure titanium using wire electric discharge machining (WEDM)

The main goal of this study is to introduce a modified approach to the modeling-design-optimization triple procedure for cutting pure titanium. The manufacturing process is selected as wire electric discharge machining. To achieve a smooth cutting operation of the pure titanium plate (grade 2), the independent cutting parameters, peak current, pulse off time, pulse on time, spark gap voltage, wire feed, and wire tension are taken into consideration. Their effects on machining rate, surface roughness, dimensional deviation, and wire wear ratio are also examined. The mathematical model of the process is determined with the multiple nonlinear neuroregression approach. Stability study that measures the ability to realize the cutting parameters was conducted during the modeling phase. This type of step has not been used as a criterion for model determination before in modeling studies. Comparisons were accomplished with the traditional and nontraditional models, and it is shown that the nontraditional models’ accuracy was more reasonable. Besides, this study contains the design optimization of the manufacturing process parameters using modified version of different stochastic and derivative-free optimization methods: differential evaluation, random search, simulated annealing, and Nelder-Mead algorithm, (MDE, MRS, MSA and MNM) simultaneously.

Monitoring and Evaluating on Ecological Environment Quality of Tourism Areas Using Stochastic Optimization Method

Monitoring and Evaluating on Ecological Environment Quality of Tourism Areas Using Stochastic Optimization Method

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.