Stochastic Optimization Approach Research Articles

P-robust energy management of a multi-energy microgrid enabled with energy conversions under various uncertainties

Given the optimistic future of hydrogen energy in transition toward a low-carbon society, hydrogen subsystem and its role in the optimal energy management of multi-energy microgrids (MEMG) should be considered. Uncertainties of hydrogen vehicles (HVs), demands, wind turbine (WT) and photovoltaic (PV) power output, and prices associated within MEMG can impose regret to the optimality of solution. In this study, a stochastic p-robust optimization approach is developed to cope with uncertainties and obtain an optimal solution for the proposed MEMG while satisfying a robustness criterion. The proposed MEMG considers different energy conversions including power to hydrogen (P2H), hydrogen to power (H2P), hydrogen to gas (H2G), gas to power (G2P) and gas to power and heat (G2He). Additional energy transactions with the external electricity grid as well as liquified natural gas (LNG) are considered and application of renewables and hydrogen storage system (HSS) towards a sustainable isolated MEMG is investigated via the ϵ-constraint approach. The effectiveness and applicability of the proposed approach is evaluated on a case study and results verify that the proposed MEMG is scheduled to be robust and obtain the maximum profit.

A Computational Framework for Preserving Privacy and Maintaining Utility of Geographically Aggregated Data: A Stochastic Spatial Optimization Approach

Geographically aggregated data are often considered to be safe because information can be published by group as population counts rather than by individual. Identifiable information about individuals can still be disclosed when using such data, however. Conventional methods for protecting privacy, such as data swapping, often lack transparency because they do not quantify the reduction in disclosure risk. Recent methods, such as those based on differential privacy, could significantly compromise data utility by introducing excessive error. We develop a methodological framework to address the issues of privacy protection for geographically aggregated data while preserving data utility. In this framework, individuals at high risk of disclosure are moved to other locations to protect their privacy. Two spatial optimization models are developed to optimize these moves by maximizing privacy protection while maintaining data utility. The first model relocates all at-risk individuals while minimizing the error (hence maximizing the utility). The second model assumes a budget that specifies the maximum error to be introduced and maximizes the number of at-risk individuals being relocated within the error budget. Computational experiments performed on a synthetic population data set of two counties of Ohio indicate that the proposed models are effective and efficient in balancing data utility and privacy protection for real-world applications.

Coupled oxygen desorption and structural reconstruction accompanying reduction of copper oxide.

Understanding structural transformation and phase transition accompanying reactions in a solid as a catalyst or oxygen carrier is important to the design and optimization of many catalytic or chemical looping reaction processes. Herein, we combined density functional theory calculation with the stochastic surface walking global optimization approach to track the structural transformation accompanying the reduction of CuO upon releasing oxygen. We then used machine learning (ML) methods to correlate the structural properties of CuOx with varying x. By decomposing a reduction step into oxygen detachment and structural reconstruction, we identified two types of pathways: (1) uniform reduction with minimal structural changes; (2) segregated reduction with significant reconstruction. The results of ML analysis showed that the most important feature is the radial distribution functions of Cu-O at a percentage of oxygen vacancy [C(OV)] < 50% and Cu-Cu at C(OV) > 50% for CuOx formation. These features reflect the underlying physicochemical origin, i.e., Cu-O breaking and Cu-Cu formation in the respective stage of reduction. Phase diagram analysis indicates that CuO will be reduced to Cu2O under a typical oxygen uncoupling condition. This work demonstrates the complexity of solid structural transformation and the potential of ML methods in studying solid state materials involved in many chemical processes.

Guest Editorial Special Issue on Evolutionary Computer Vision

Evolutionary Computer Vision (ECV) is at the intersection of two major research fields of artificial intelligence: 1) computer vision (CV) and 2) evolutionary computation (EC). This special issue brings an overview of state-of-the-art contributions to the latest research and development in the discipline. CV includes methods for acquiring, processing, analyzing, and understanding images. The aim is to design computational models of human and animal perception. ECV is an interdisciplinary research area where analytical methods combined with powerful stochastic optimization and metaheuristic approaches produced human-competitive results. From an engineering standpoint, ECV aims to design software and hardware solutions useful for solving challenging CV problems. From a scientific viewpoint, the goal is to enhance our current understanding of visual processing in nature and replicate this within a seeing machine. ECV is a well-established research discipline as evolutionary algorithms are more efficient than classical optimization approaches for the discontinuous, nondifferentiable, multimodal, and noisy search, optimization, and learning problems arising in many CV tasks. EC has also demonstrated its ability as a robust approach to cope with the fundamental steps of image processing, image analysis, and image understanding included in the CV pipeline (e.g., restoration, segmentation, registration, classification, reconstruction, or tracking).

Energy management and operational planning of renewable energy resources-based microgrid with energy saving

• Proposing an environmental/economic model for optimal energy management. • Considering renewable energy resources in the presence of Photovoltaic and battery. • Presenting Hybrid Whale and Pattern Search Algorithm for optimizing Micro-grid. • Reporting superior solutions in Short-Term Scheduling and Micro-grid Energy Management. Energy resource scheduling is one of the major problems in power systems. This issue has become even more significant as renewable sources with intermittent power output are becoming more and more prevalent. Due to their low environmental impact and low operating costs, renewable energy sources (RESs) have attracted interest. The excess power generated by such generation methods may be a negative that affects power systems, hence issues relating to such systems should be properly handled. The optimal operation of a microgrid (MG) with several distributed generation (DG) units and uncertain behavior of RESs is suggested in this research using a stochastic optimization approach. So, for an MG fitted with a solar photovoltaic (PV) unit, this research proposes a day-ahead scheduling paradigm. In this regard, the effects of various climatic circumstances on the power production of the PV unit and the optimal scheduling of the MG have been examined in this research. In order to achieve this, statistics on solar irradiance were extracted from four distinct days from each of the four seasons. The single-objective optimization framework used to design the scheduling problem states that the objective function should be to minimize the total operating cost across the scheduling period. The aforementioned day-ahead scheduling problem can be solved by the "hybrid whale optimization algorithm and pattern search (HWOA-PS)” optimization algorithm, while both renewable and nonrenewable generating units, as well as an energy storage system are present. In order to confirm the higher performance of the recommended approach, a thorough comparison between the Hybrid WOA-PS algorithm and a few well-known optimization algorithms has also been conducted.

Scalable Orthonormal Projective NMF via Diversified Stochastic Optimization.

The increasing availability of large-scale neuroimaging initiatives opens exciting opportunities for discovery science of human brain structure and function. Data-driven techniques, such as Orthonormal Projective Non-negative Matrix Factorization (opNMF), are well positioned to explore multivariate relationships in big data towards uncovering brain organization. opNMF enjoys advantageous interpretability and reproducibility compared to commonly used matrix factorization methods like Principal Component Analysis (PCA) and Independent Component Analysis (ICA), which led to its wide adoption in clinical computational neuroscience. However, applying opNMF in large-scale cohort studies is hindered by its limited scalability caused by its accompanying computational complexity. In this work, we address the computational challenges of opNMF using a stochastic optimization approach that learns over mini-batches of the data. Additionally, we diversify the stochastic batches via repulsive point processes, which reduce redundancy in the mini-batches and in turn lead to lower variance in the updates. We validated our framework on gray matter tissue density maps estimated from 1000 subjects part of the Open Access Series of Imaging (OASIS) dataset. We demonstrated that operations over mini-batches of data yield significant reduction in computational cost. Importantly, we showed that our novel optimization does not compromise the accuracy or interpretability of factors when compared to standard opNMF. The proposed model enables new investigations of brain structure using big neuroimaging data that could improve our understanding of brain structure in health and disease.

Optimal assets allocation and benefit adjustment strategy with longevity risk for target benefit pension plans

&lt;p style='text-indent:20px;'&gt;This paper studies the optimal investment choices and benefit adjustment strategy for a target benefit plan (TBP) with stochastic mortality force. The pension fund is invested in a risk-free asset, a stock, and a longevity-linked asset, as a derivative of the mortality force. Using the stochastic optimal control approach, we obtain closed-form solutions for optimal portfolio choices and benefit adjustment strategy in the financial market with or without the longevity-linked asset, which minimize the combination of benefit gap from the target level and pension plan's discontinuity risk. Numerical analysis is provided to show the effects of parameters on the optimal strategies.&lt;/p&gt;

A novel Bayesian approach for multi-objective stochastic simulation optimization

Multi-objective stochastic simulation optimization plays an important role in designing complex engineering systems. To identify optimal solutions via simulations, Bayesian optimization, which utilizes metamodels and an acquisition function to determine the next design point, has been popular in machine learning. However, studies on Bayesian optimization of multi-objective stochastic simulation are limited and can give undesired performances in terms of convergence and diversity metrics. Moreover, direct extension of Bayesian optimization algorithms of deterministic responses is unrealistic as stochastic responses are observed with heterogeneous noise. To handle these issues, we propose a novel framework for Bayesian optimization of multiple stochastic responses. Stochastic kriging metamodels are constructed independently for multiple stochastic responses considering heterogeneous simulation noise. To remove undesired effects of random simulation noise on comparing solutions, quantiles of stochastic kriging metamodels are employed to define the Pareto dominance. Acquisition functions are proposed by integrating the hypervolume-based and probability-of-improvement (PoI)-based acquisition functions from deterministic multi-objective optimization with typical acquisition functions from univariate stochastic response optimization. This not only enhances the convergence and diversity of Pareto-optimal solutions but also properly handles heterogeneous noise. Exact calculation formulas of the proposed algorithms are further developed. Typical numerical cases and two engineering examples (a rocket injector design example and a real inventory design scenario) demonstrate that the proposed algorithms give better Pareto-optimal solutions of which the proximity to true Pareto fronts and the diversity are improved.

An optimal real-time pricing strategy for aggregating distributed generation and battery storage systems in energy communities: A stochastic bilevel optimization approach

The expansion of distributed electricity generation and the increasing capacity of installed battery storage systems at the community level have posed challenges to efficient technical and economic operation of the power systems. With advances in smart-grid infrastructure, many innovative demand response business models have sought to tackle these challenges, while creating financial benefits for the participating actors. In this context, we propose an optimal real-time pricing (ORTP) approach for the aggregation of distributed energy resources within energy communities. We formulate the interaction between a community-owned profit-maximizing aggregator and the users (consumers with electricity generation and storage potential, known as “prosumagers”, and electric vehicles) as a stochastic bilevel disjunctive program. To solve the problem efficiently, we offer a novel solution algorithm, which applies a linear quasi-relaxation approach and an innovative dynamic partitioning technique. We introduce benchmark tariffs and solution algorithms and assess the performance of the proposed pricing strategy and solution algorithm in four case studies. Our results show that the ORTP strategy increases community welfare while providing useful grid services. Furthermore, our findings reveal the superior computational efficiency of our proposed solution algorithm in comparison to benchmark algorithms.

A novel stochastic model for flexible unit commitment of off-grid microgrids

This work proposes a novel two stage stochastic optimization approach for the Energy Management System (EMS) of MicroGrids (MG). It combines the scenario-based uncertainty characterization with the use of piecewise affine correction rules for the recourse decision. These rules are used by the EMS to set the commitment status of the programmable generators and to correct the storage management as a function of the realization of the uncertainty, measured in real-time. The novel stochastic model is integrated in a hierarchical EMS, based on two control layers: the first one employs the proposed stochastic approach to determine the daily strategic scheduling of the MG, and the second layer optimizes the real-time dispatch.. The proposed EMS is applied to a real-world case study of a rural MG. Results indicate that the proposed EMS outperforms state-of-the-art optimization approaches in terms ofservice reliability (99.8%) and fuel efficiency. Moreover, rolling horizon simulations of the proposed stochastic model showed 100% reliability, and 30% of fuel cost savings with respects to state-of-the-art methods. The novel EMS is then deployed on a laboratory-scale microgrid (Multi-Goods MicroGrid Laboratory, MG2lab), demonstrating secure and economic operations. A comparative analysis is made with respect to deterministic and standard stochastic two-stage approaches; the proposed solution outperforms the other models during real operations, with savings of fuel cost up to almost 10%.

Robust design optimization for enhancing delamination resistance of composites

AbstractRecent developments in the field of computational modeling of fracture have opened up possibilities for designing structures against failure. A special case, called interfacial fracture or delamination, can occur in loaded composite structures where two or more materials are bonded together at comparatively weak interfaces. Due to the potential crack growth along these interfaces, the structural problem suffers from snap‐back/snap‐through instabilities and bifurcations with respect to the model parameters, leading to noisy and discontinuous responses. For such a case, the design optimization problem for a selected quantity of interest is ill‐posed, since small variations in the design parameters can lead to large jumps in the structural response. To this end, this article presents a stochastic optimization approach to maximize delamination resistance that is less sensitive to small perturbations of the design and thereby leads to a robust solution. To overcome the intractability of Monte Carlo methods for estimating the expected value of the expensive‐to‐evaluate response function, a global, piecewise‐constant surrogate is constructed based on nearest‐neighbor interpolation that is iteratively refined during the optimization run. We found that by taking a large stochastic region at the beginning of the optimization and gradually reducing it to the desired one can help overcome poor local optima. Our results demonstrate the effectiveness of the proposed framework using an example of shape optimization of hard inclusions embedded in a double‐cantilever beam, which significantly enhances delamination resistance.

Clustering and Stochastic Simulation Optimization for Outpatient Chemotherapy Appointment Planning and Scheduling.

Outpatient Chemotherapy Appointment (OCA) planning and scheduling is a process of distributing appointments to available days and times to be handled by various resources through a multi-stage process. Proper OCAs planning and scheduling results in minimizing the length of stay of patients and staff overtime. The integrated consideration of the available capacity, resources planning, scheduling policy, drug preparation requirements, and resources-to-patients assignment can improve the Outpatient Chemotherapy Process's (OCP's) overall performance due to interdependencies. However, developing a comprehensive and stochastic decision support system in the OCP environment is complex. Thus, the multi-stages of OCP, stochastic durations, probability of uncertain events occurrence, patterns of patient arrivals, acuity levels of nurses, demand variety, and complex patient pathways are rarely addressed together. Therefore, this paper proposes a clustering and stochastic optimization methodology to handle the various challenges of OCA planning and scheduling. A Stochastic Discrete Simulation-Based Multi-Objective Optimization (SDSMO) model is developed and linked to clustering algorithms using an iterative sequential approach. The experimental results indicate the positive effect of clustering similar appointments on the performance measures and the computational time. The developed cluster-based stochastic optimization approaches showed superior performance compared with baseline and sequencing heuristics using data from a real Outpatient Chemotherapy Center (OCC).

Itô-theory-based multi-time scale dispatch approach for cascade hydropower-photovoltaic complementary system

The complementary operation of cascade hydropower (CHP) and photovoltaic (PV) can increase the integration of PV power and has become a trend in modern power systems. However, the randomness and variability of PV power output might cause challenges in precisely tracking the submitted generation plan of the CHP-PV complementary system. The safety and stability of the receiving-end power grid might deteriorate. In this paper, a multi-time scale dispatch framework with day-ahead and intra-day dispatch is established for the CHP-PV complementary system to address the PV uncertainties. The day-ahead dispatch is employed to provide reliable reference results and sufficient adjustment reservations for the intra-day dispatch. An Itô-theory-based stochastic optimization (ITB-SO) approach is proposed for the intra-day dispatch by modeling the PV prediction error with stochastic differential equations (SDE). The SDE model can be embedded into the ITB-SO approach without scenario generation, and thus computational burden can be significantly reduced compared with scenario-based methods. A complementary system in southwest China is chosen as a detailed case study. The simulation results demonstrate that real-time random PV fluctuations could be compensated by adjusting CHPs. Meanwhile, the target water level of cascade reservoirs can be tracked under the proposed approach.

Reliability-Based Expansion Planning Studies of Active Distribution Networks With Multiagents

In this paper, a multi-agent framework is proposed to address the expansion planning problem in a restructured active distribution network. In this framework, the objective and techno-economic constraints of participating agents are addressed in the expansion planning of power network and DER assets as well as the network and DERs optimal operation management. The agents include distributed generator owners and load aggregators which participate along with the distribution network operator (DNO) in the active distribution network planning. The proposed framework is formulated as a bi-level optimization problem with multi-lower levels in which the DNO optimizes the network expansion planning and operation in the upper level where the network reliability is also modeled. In the lower level problems, other participating agents optimize the expansion planning and operation of their assets. The model addresses the optimal operation of resources by clearing the local energy market. The uncertainties in the upper and the lower level problems are effectively addressed using a stochastic adaptive robust optimization approach. The proposed model is implemented on the 54-bus and 138-bus distribution networks and the results demonstrate the effectiveness and scalability of the proposed framework.

A stochastic optimization approach for staff scheduling decisions at inpatient units

AbstractThis paper describes a solution approach for stochastic multi‐resource multi‐patient staff scheduling problems in inpatient units. Our solution approach has four steps. First, we classify patients into a number of groups with similar care‐provider requirements. Second, a predictive Markov model captures patients' flow in the inpatient unit and provides a prediction of the number of patients of each group in the future. This predictive model allows us to generate a potentially large set of possible system utilization scenarios over the planning horizon. Third, a mixed‐integer programming model with an expected value objective function seeks to minimize the expected over‐staffing and under‐staffing costs across all possible scenarios. Lastly, we use simulation to sample system utilization scenarios and the sample average approximation method to find a reliable and generalizable solution to the model across all possible scenarios. We evaluate the performance of the proposed solution using real data from the Children's Hospital of Eastern Ontario's inpatient mental health unit. The results show that the proposed approach significantly decreases the expected cost of the schedules in comparison to the traditional approaches.

A stochastic approach to dynamic participation in energy communities

With energy communities and local electricity markets on the rise, the possibilities for prosumers to be actively involved in the energy system increase, creating more complex settings for energy communities. This paper addresses the following research question: Does having knowledge about the future development in energy communities help make better decisions selecting new participants than without consideration of any future developments? Each year, the community is faced with the exit of existing members and a portfolio of possible new entrants with different characteristics. For this purpose, a bi-level optimization model for dynamic participation in local energy communities with peer-to-peer electricity trading, which is able to select the most suitable new entrants based on the preferences of the members of the original community, is extended to a stochastic dynamic program. The community wants to plan a few years ahead, which includes the following uncertainties: (i) which members leave after each period, and (ii) which are the potential new members willing to join the community. This paper’s contribution is a stochastic optimization approach to evaluate possible future developments and scenarios. The focus lies on the contractual design between the energy community and new entrants; the model calculates the duration of contracts endogenously. The results show a sample energy community’s decision-making process over a horizon of several years, comparing the stochastic approach with a simple deterministic alternative solution.

Designing sustainable closed-loop supply chain network with considering spot-to-point inflation and carbon emission policies: A case study

This paper uses a fuzzy robust stochastic optimization (FRSO) approach and a new hybrid algorithm of genetic algorithm (GA) and multi-choice goal programming with Utility Function (MCGP-UF) to minimize environmental impacts (EI) while maximizing net present value (NPV) and social impacts (SI) in a sustainable closed-loop supply chain (SCLSC) in a case study has been proposed under hybrid uncertainty with considering spot-to-point inflation (STPI). The resulting mixed-integer linear programming (MILP) model has been applied to the electronic industry. The proposed model is evaluated in several experiments and discussed in different scenarios to prove the efficiency and performance comparison and validation of the proposed method. The results of this study double the share of the article (i) Effective improvement of the obtained solutions by reducing the solution time by 25% showed that the proposed method can be responsible for large-scale problems. (ii) Sensitivity analysis on parameters such as demand, inflation, costs, and capacity showed which scenario has the most impact on the strategic and tactical decisions of companies.

Long-Term Bifurcation and Stochastic Optimal Control of a Triple-Delayed Ebola Virus Model with Vaccination and Quarantine Strategies

Despite its high mortality rate of approximately 90%, the Ebola virus disease (EVD) has not received enough attention in terms of in-depth research. This illness has been responsible for over 40 years of epidemics throughout Central Africa. However, during 2014–2015, the Ebola-driven epidemic in West Africa became, and remains, the deadliest to date. Thus, Ebola has been declared one of the major public health issues. This paper aims at exploring the effects of external fluctuations on the prevalence of the Ebola virus. We begin by proposing a sophisticated biological system that takes into account vaccination and quarantine strategies as well as the effect of time lags. Due to some external perturbations, we extend our model to the probabilistic formulation with white noises. The perturbed model takes the form of a system of stochastic differential equations. Based on some non-standard analytical techniques, we demonstrate two main approach properties: intensity and elimination of Ebola virus. To better understand the impact of applied strategies, we deal with the stochastic control optimization approach by using some advanced theories. All of this theoretical arsenal has been numerically confirmed by employing some real statistical data of Ebola virus. Finally, we mention that this work could be a rich basis for further investigations aimed at understanding the complexity of Ebola virus propagation at pathophysiological and mathematics levels.

Cellular-Connected Multi-UAV MEC Networks: An Online Stochastic Optimization Approach

In this paper, we consider a mobile edge computing (MEC) network where multiple cellular-connected unmanned aerial vehicles (UAVs) can offload their computation tasks to multiple ground base stations (GBSs). In practice, the UAVs are generally unable to master stochastic information of task arrival and channel changes in advance, which may cause a severe issue in terms of energy consumption. Therefore, we formulate a stochastic optimization problem with the goal of minimizing the average weighted sum energy consumption, by jointly optimizing UAV-GBS associations, communication and computation resource allocation, and three-dimensional (3D) UAV trajectories, during which a velocity-triggered penalty term (VTPT) is designed to suppress a large amount of the energy consumption of the UAVs. To handle the stochastic problem, we propose an online resource allocation and trajectory optimization algorithm with outer and inner structures. The outer structure transforms the original problem to a deterministic one by applying the Lyapunov-based optimization framework. The inner structure solves the obtained deterministic problem via the Lagrange duality method and the successive convex approximation technique, based on the block coordinate descent framework. Numerical results demonstrate that: 1) VTPT dramatically decreases the UAVs’ energy consumption, and 2) the proposed algorithm not only reduces the energy consumption but also ensures the computation queue stability compared with other benchmark schemes.

Integration of stochastic and robust optimization techniques into DEA model for more accurate and reliable efficiency estimation

Efficiency assessment is vital to assessing decision-making units (DMUs) in numerous sectors. DEA is a prominent non-parametric efficiency assessment tool. Traditional DEA models assume deterministic inputs and outputs, ignoring real-world uncertainties and variability. To improve efficiency estimation, stochastic and robust optimization approaches can be integrated into DEA models. To improve efficiency estimation, we present a stochastic and robust optimization framework incorporating DEA. Probabilistic inputs and outputs allow stochastic optimization to account for uncertainty. The model can capture data variability and create stochastic DMU efficiency scores by adding probability distributions. For data uncertainties and outliers, the DEA model uses robust optimization. Robust optimization considers worst-case scenarios and minimizes extreme observations on efficiency estimation. This makes efficiency scores more resilient to data outliers and noise. DEA models benefit from stochastic and resilient optimization. First, considering data uncertainties and fluctuations improves DMU efficiency representation. Second, eliminating outliers and extreme observations improves efficiency estimation. Third, efficiency scores help decision-makers make better, more informed choices. A case study in a specific industry shows the framework's efficacy. We compare classic and integrated stochastic-robust DEA model outcomes. The integrated model provides more accurate and dependable efficiency estimates, helping decision-makers understand DMU performance. DEA models with stochastic and resilient optimization increase efficiency estimation. By considering uncertainties and outliers, this paradigm helps decision-makers evaluate DMUs in many sectors more accurately and reliably.