Two-stage Optimization Framework Research Articles

Design and characterization of effective solar cells

We propose a two-stage multi-objective optimization framework for full scheme solar cell structure design and characterization, cost minimization and quantum efficiency maximization. We evaluated structures of 15 different cell designs simulated by varying material types and photodiode doping strategies. At first, non-dominated sorting genetic algorithm II (NSGA-II) produced Pareto-optimal-solutions sets for respective cell designs. Then, on investigating quantum efficiencies of all cell designs produced by NSGA-II, we applied a new multi-objective optimization algorithm II (OptIA-II) to discover the Pareto fronts of select (three) best cell designs. Our designed OptIA-II algorithm improved the quantum efficiencies of all select cell designs and reduced their fabrication costs. We observed that the cell design comprising an optimally doped zinc-oxide-based transparent conductive oxide (TCO) layer and rough silver back reflector (BR) offered a quantum efficiency (Q_e) of 0.6031. Overall, this paper provides a full characterization of cell structure designs. It derives relationship between quantum efficiency, Q_e of a cell with its TCO layer’s doping methods and TCO and BR layer’s material types. Our solar cells design characterization enables us to perform a cost-benefit analysis of solar cells usage in real-world applications.

A two-stage design optimization framework for multifield origami-inspired structures

Different types of active materials have been used to actuate origami-inspired self-folding structures. To model the highly nonlinear deformation and material responses, as well as the coupled field equations and boundary conditions of such structures, high-fidelity models such as finite element (FE) models are needed but usually computationally expensive, which makes optimization intractable. In this paper, a computationally efficient two-stage optimization framework is developed as a systematic method for the multi-objective designs of such multifield self-folding structures where the deformations are concentrated in crease-like areas, active and passive materials are assumed to behave linearly, and low- and high-fidelity models of the structures can be developed. In Stage 1, low-fidelity models are used to determine the topology of the structure. At the end of Stage 1, a distance measure [Formula: see text] is applied as the metric to determine the best design, which then serves as the baseline design in Stage 2. In Stage 2, designs are further optimized from the baseline design with greatly reduced computing time compared to a full FEA-based topology optimization. The design framework is first described in a general formulation. To demonstrate its efficacy, this framework is implemented in two case studies, namely, a three-finger soft gripper actuated using a PVDF-based terpolymer, and a 3D multifield example actuated using both the terpolymer and a magneto-active elastomer, where the key steps are elaborated in detail, including the variable filter, metrics to select the best design, determination of design domains, and material conversion methods from low- to high-fidelity models. In this paper, analytical models and rigid body dynamic models are developed as the low-fidelity models for the terpolymer- and MAE-based actuations, respectively, and the FE model of the MAE-based actuation is generalized from previous work. Additional generalizable techniques to further reduce the computational cost are elaborated. As a result, designs with better overall performance than the baseline design were achieved at the end of Stage 2 with computing times of 15 days for the gripper and 9 days for the multifield example, which would rather be over 3 and 2 months for full FEA-based optimizations, respectively. Tradeoffs between the competing design objectives were achieved. In both case studies, the efficacy and computational efficiency of the two-stage optimization framework are successfully demonstrated.

Robust Spacecraft Guidance Around Small Bodies Under Uncertainty: Stochastic Optimal Control Approach

Dynamical environments around small celestial bodies are complex and uncertain, leading to highly perturbed, uncertain orbital motions in their proximity. Under such complexity and uncertainty, mission designers need to plan robust guidance and control of the spacecraft orbit to meet some requirements derived from their mission objectives such as precise science observation campaigns. To develop a robust planner for spacecraft guidance under uncertainty, this paper presents a stochastic optimal control approach to design robust guidance policies that minimize the expected control effort while ensuring the requirement satisfaction with a user-defined confidence level, i.e., chance constraints. The solution method is formulated as a two-stage optimization framework that consists of a convex programming stage, followed by a nonlinear programming stage. The developed framework is applied to a small-body global-mapping scenario on a science orbit around asteroid Bennu, demonstrating the robustness of the optimized guidance policies; the stochastic orbital states are controlled to meet science requirements to 99.9% confidence over 31 days with minimum control cost. Although the developed framework is demonstrated in a small-body global-mapping scenario, it is independent from specific equations of motion, and hence applicable to other proximity operation scenarios as well.

Two-Timescale Uplink Channel Estimation for Dual-Hop MIMO Relay Multi-User Systems

Multiple-input multiple-output (MIMO) relay systems have received great attention for the development of future wireless networks, since they can be invoked for improving system capacity and extending the coverage area. Considering the fixed base station (BS) and relay station (RS) and the highly mobile users (UEs), the dual-hop MIMO relay channel possesses the two-timescale characteristics, i.e., the UEs-RS channel varies in a short-timescale manner whereas the RS-BS channel varies in a long-timescale manner. In order to acquire the knowledge of all individual channels at the BS directly, we propose two-timescale channel estimation algorithms with one-stage training (OST) scheme based on the above time-varying channel characteristics. Specifically, the two-timescale channel estimation problem is firstly formulated as an approximate maximum likelihood (AML) problem. Then, we design batch algorithm to solve the resultant optimization problem. Moreover, to overcome the drawbacks of batch algorithm, a low-complexity online algorithm is also proposed based on the two-stage stochastic optimization framework. Finally, simulation results are provided to verify the effectiveness of the proposed two-timescale channel estimation algorithms.

Designing on Optical Wireless Communication for 5G Mobile Applications

The emphasis of this paper is on designing 5G networks infrastructure, offering a better wireless and optical network segment transport scheme with domains for applications for mobile phones. Identify the appropriate set of power grid wireless (optical/optical) technologies) and processing modules needed to facilitate 5G mobile services in an energy-efficient a two-stage optimization framework and the premium way is suspected. A multi-objective method in the first iteration is for optimization, where reflects on the element of the transport network strives to jointly reduce the expenditures on investment of the 5G mobile network. This is done to determine the minimum mobile technologies for wireless and optical power grids. The second stage focuses on the branch of the web server and aims to define effective modules of processing to which 5G operational systems need to be distributed. The performances of the proposal are investigated using separate clustering algorithms, reasonable traffic statistics choices such as mm-wave and optical passive networks (PONs) for optical grid transport, fixed, and elastic networks in Bristol, UK, via a city-wide topology. To give more advantages to 5G applications, our paper proposed a 5G communication using optical wireless technology.

Two-Stage Bayesian Optimization for Scalable Inference in State-Space Models.

State-space models (SSMs) are a rich class of dynamical models with a wide range of applications in economics, healthcare, computational biology, robotics, and more. Proper analysis, control, learning, and decision-making in dynamical systems modeled by SSMs depend on the accuracy of the inferred/learned model. Most of the existing inference techniques for SSMs are capable of dealing with very small systems, unable to be applied to most of the large-scale practical problems. Toward this, this article introduces a two-stage Bayesian optimization (BO) framework for scalable and efficient inference in SSMs. The proposed framework maps the original large parameter space to a reduced space, containing a small linear combination of the original space. This reduced space, which captures the most variability in the inference function (e.g., log likelihood or log a posteriori), is obtained by eigenvalue decomposition of the covariance of gradients of the inference function approximated by a particle filtering scheme. Then, an exponential reduction in the search space of parameters during the inference process is achieved through the proposed two-stage BO policy, where the solution of the first-stage BO policy in the reduced space specifies the search space of the second-stage BO in the original space. The proposed framework's accuracy and speed are demonstrated through several experiments, including real metagenomics data from a gut microbial community.

A two-stage robust optimization framework for land-water-environment nexus management

On the premise of rational utilization of soil and water resources, systematic engineering method is widely considered to balance agriculture and ecology. Regular planning is carried out by the authority based on historical data and future expectation, however, uncertain environment cannot be ignored. Hence, we propose an adjusted dynamic two-stage robust optimization framework to explore comprehensive managerial insights of irrigative areas and forest expansion. Dynamic planning is adopted to reflect the long-period planning, and two-stage is to differ “wait-and-see” decision from “right-and-now” decision. Considering the whole system’ benefit, economic and ecological benefits are maximized and water scarcity, water/soil erosion penalties are minimized. To solve the proposed two-stage robust model, we propose two structural properties to obtain the global solution. After transformation, a C&CG algorithm is designed to calculate the proposed model.

DRNet: A Depth-Based Regression Network for 6D Object Pose Estimation.

This paper focuses on 6Dof object pose estimation from a single RGB image. We tackle this challenging problem with a two-stage optimization framework. More specifically, we first introduce a translation estimation module to provide an initial translation based on an estimated depth map. Then, a pose regression module combines the ROI (Region of Interest) and the original image to predict the rotation and refine the translation. Compared with previous end-to-end methods that directly predict rotations and translations, our method can utilize depth information as weak guidance and significantly reduce the searching space for the subsequent module. Furthermore, we design a new loss function function for symmetric objects, an approach that has handled such exceptionally difficult cases in prior works. Experiments show that our model achieves state-of-the-art object pose estimation for the YCB- video dataset (Yale-CMU-Berkeley).

A two-stage optimization framework for scheduling of responsive loads in smart distribution system

The implementation of demand response (DR) in distribution system extends several benefits to customers and distribution system operator (DSO) by altering the consumption pattern of responsive loads. However, the acceptability of any DR program is possible only if it can benefit both the stakeholders. Therefore, an appropriate strategy for scheduling of responsive loads is required to address the interest of both customers and DSO. In this regard, this study proposes a two-stage optimization method for scheduling of responsive loads in distribution system. In the first stage, scheduling of responsive loads is performed to minimize electricity cost of customers present in the distribution system. In the second stage, a multi-objective optimization is implemented to improve network’s reliability and economic benefit of DSO. The second stage objectives are to simultaneously minimize energy not supplied (ENS) and maximize profit of DSO. The second stage is implemented with constraint of customer cost obtained from first stage. The constraint imply that the customer bill should not exceed the payments obtained from stage one. The ∊-constraint method is adopted to solve the multi-objective problem of second stage and trade-off solution is obtained utilizing fuzzy satisfying technique. The proposed two-stage mechanism is implemented on 33-bus distribution system and a comparative analysis for different scenarios is presented to highlight the efficacy of proposed methodology. Results highlight that the proposed approach reduces customer’s electricity bill by 5.52%, ENS by 8.81% and increases profit of DSO by 9.89% respectively as compared to the scenario when DR is not considered.

Robust facility location under demand uncertainty and facility disruptions

Facility location decision is strategic: the construction of a new facility is typically costly and the impact of the decision is long-lasting. Environmental changes, such as population shift and natural disasters, may cause today’s optimal location decision to perform poorly in the future. Thus, it is important to consider potential uncertainties in the design phase, while explicitly taking into account the possible customer reassignments as recourse decisions in the execution phase. This paper studies a robust fixed-charge location problem under uncertain demand and facility disruptions. To model this problem, we adopt a two-stage robust optimization framework, where the first-stage location decision is made here-and-now and the second-stage allocation decision can be deferred until the uncertainty information is revealed. We develop a column-and-constraint generation (C&CG) algorithm to solve the models exactly and benchmark it with the other C&CG algorithm in the literature. We further extend our modeling and solution schemes to facility fortification problems under uncertainties, where investment decisions are made for already existing supply chain systems to protect facilities from disruptions and against uncertain demand. We conduct extensive numerical tests to study the differences in solutions produced by the three robust models and the impacts of uncertainties on solution configuration. Results show that our C&CG algorithm can solve more instances to optimality and consume less computing time on average, compared to the benchmark algorithm. Several managerial insights are also drawn from our numerical experiments.

Retail supply chain network design with concurrent resilience capabilities

In this paper, we address the problem of designing/redesigning a resilient retail supply chain network under uncertainty. Considering pre- and post-disruption scenarios, this study proposes a two-stage stochastic optimization framework with multiple resilience strategies for designing a resilient retail supply chain. We consider facility fortification, inventory prepositioning, direct-to-store delivery, reserved capacity, inventory sharing and multiple set covering as our resilience strategies, covering all the three dimensions of resilience capabilities, namely, proactive, reactive, and network design quality. Taking into account the prominent role of retail outlets during Covid-19 epidemic outbreaks, through a real case study, we evaluate the impact of random and targeted disruptions on the performance of the retail supply chain network and provide managerial insights regarding the right balance between cost efficiency and resilience. Furthermore, we evaluate the effectiveness of these resilience capabilities in a number of simulated scenarios to show their applicability and importance under different disruptive situations. We show that when implemented concurrently, these resilience capabilities have a synergistic effect where the whole becomes larger than the sum of its parts. Subject to extensive stress testing, our results show that using any mixture of these resilience capabilities increases the retail network's resilience while considerably decreasing post-disruption costs.

A Decision Model for an Electricity Retailer With Energy Storage and Virtual Bidding Under Daily and Hourly CVaR Assessment

This paper presents a short-term decision-making model for an electricity retailer with battery energy storage system (BESS) and virtual bidding through a two-stage stochastic optimization framework. In the first stage, the retailer determines the amount of power to be purchased in the day-ahead wholesale market and the optimal incremental and decremental virtual bidding strategies. In the second stage, the optimal energy storage decisions and the retailer's involvement in the real-time market are determined. The proposed model minimizes the retailer's expected procurement cost and generates the optimal power and virtual bidding curves in the day-ahead market. Two types of Conditional Value at Risk (CVaR) are integrated in the proposed model to manage the retailer's hourly and daily risks, respectively. Case studies with real-world data are performed to verify the retailer's cost reduction obtained with the integration of BESS and virtual bidding and to study how the hourly and daily risk-management strategies affect the retailer's procurement cost distribution for different risk-aversion levels.

A two-stage optimal sensor placement method for multi-type structural response reconstruction

Optimal multi-type sensor placement has gained considerable attention in the structural health monitoring field during the past few years. Although a structural response reconstruction-oriented optimization method for a multi-type sensor has been developed, the challenge of information redundancy in the collected signal deserves further investigation. To tackle this challenge, this paper presents a two-stage optimization framework for response reconstruction with the capability to reduce the multi-type sensor information redundancy. In the first stage, the optimization of multi-type sensor placement for response reconstruction is performed to initially determine the optimal sensor deployment scheme. After the optimal sensor locations are selected, the second-stage optimization introduces a metric, called the distance coefficient, to evaluate the information independence level between sensor locations with the goal of reducing the sensor information redundancy. A numerical study on a bridge model is first performed to evaluate the feasibility of the proposed framework, after which a lab-scale physical bridge model is tested to validate its effectiveness. Both the numerical and experimental results demonstrate that the proposed two-stage optimization framework can reduce the sensor information redundancy and, at the same time, produce a satisfying result in the response reconstruction of key locations.

Adaptive kriging-assisted optimization of low-thrust many-revolution transfers to geostationary Earth orbit

ABSTRACT To effectively optimize low-thrust many-revolution transfer trajectories to geostationary Earth orbit (GEO), this article proposes a novel metamodel-based low-thrust GEO transfer optimization scheme. A simplified control law is used to convert the optimal low-thrust transfer problem into a parameter optimization problem, where the gains of control law are optimized to determine the time-minimum trajectories. An adaptive kriging-assisted two-stage optimization framework is developed to solve the optimization problem. In the first stage, the kriging metamodels are constructed to replace the expensive transfer model for optimization. The kriging metamodels are gradually refined via a probability of constrained improvement-based infill sampling process to efficiently determine an initial guess of the gains. In the second stage, a sequential quadratic programming-based local search is conducted to precisely compute the gains. Finally, two engineering examples are investigated to demonstrate the effectiveness of the proposed optimization scheme for solving real-world low-thrust GEO transfer optimization problems.

Optimal Allocation and Economic Analysis of Battery Energy Storage Systems: Self-Consumption Rate and Hosting Capacity Enhancement for Microgrids with High Renewable Penetration

Recent advances in using renewable energy resources make them more accessible and prevalent in microgrids (MGs) and nano grids (NGs) applications. Accordingly, much attention has been paid during the past few years to design and operate MGs with high renewable energy sources (RESs) penetration. Energy storage (ES) is the crucial enabler for reliable MG operation to help MGs become more resistant to disruptions, particularly with the increased penetration of RESs. In this regard, this paper formulates a two-stage optimization framework to improve a grid-connected MG performance. Firstly, the optimal allocation decisions of the battery ES systems (BESSs) are provided to enhance the self-consumption rate of the RESs and the hosting capacity (HC) of the MG. Secondly, an operation strategy with the results (number, location, and capacity) of the BESSs obtained from the first stage is handled as an objective function to minimize the MG’s total operation cost. The IEEE 33-bus radial system is modified to act as the MG with high RESs penetration. The problem is solved using a recent swarm intelligence optimization algorithm called the Harris hawks optimization (HHO) algorithm. The proposed optimal operation strategy considers numerous constraints, such as the charge-discharge balance, number and capacity limitations of the BESSs, and the different technical performance constraints of the MG. The results obtained verify the proposed optimization framework’s effectiveness for grid-connected MGs and validate the benefits gained from the appropriate allocation of BESSs. The results also indicate that oversized storage or using many unneeded storage units may adversely influence the MG’s total power losses.

Assessing the performance of uncertainty-aware transactive controls for building thermal energy storage systems

Energy storage systems provide a wide range of technological approaches to manage the balance between energy supply and demand in the electric grid. With the increasing uncertainty and variability that comes with wide-spread adoption of grid-scale and behind-the-meter renewable energy, it is imperative to develop stochastic operational planning and control approaches that can account for uncertainty in future conditions. Although, coordination of multiple thermal energy storage resources can support the transition to low carbon energy by enabling valuable system flexibility, few stochastic planning and control approaches have been developed for coordinating building-level thermal energy storage resources. In addition, there is also a need to analyze the potential benefits of an aggregator-level stochastic control framework versus applying stochastic planning and controls at each building individually. This work addresses these needs by developing an uncertainty-aware transactive control (UA-Tx) framework for an aggregator to coordinate the thermal energy storage (TES) assets of multiple buildings. A two-stage stochastic optimization framework is formulated for day-ahead energy procurement that considers uncertainty in building occupancy patterns, weather conditions, and real-time energy prices of the following day. In the second stage, possible recourse decisions through modifying TES operation are also considered. The dispatch of TES operational strategies is implemented through transactive controls, which use market mechanisms and customer preferences to achieve changes in building demand. During real-time operation, a local demand response aggregator determines the transactive clearing prices to dispatch the flexibility enabled by TES. Simulation case studies were conducted to demonstrate the capabilities of the uncertainty-aware aggregator control framework compared to the performance of applying intelligent controllers at each individual building. Up to 3.7% energy cost savings were observed for buildings under the UA-Tx aggregator control framework. Other potential benefits of the control approach are also discussed, along with anticipated future extensions.

Distributionally Robust Two-Stage Energy Management for Hybrid Energy Powered Cellular Networks

Energy harvesting has been recognized as a good paradigm to decrease traditional grid energy expenditure, which caters for 5G visions on the green evolution of cellular networks. However, the harvested energy at each base station is random and intermittent, which imposes a great challenge to reliably satisfy the time-varying users’ wireless traffic requirements. What's worse, the perfect probability distributions of harvested energy and wireless traffic are hard to obtain in practical systems, making it difficult to apply the conventional optimization approach to cope with the uncertainties in the energy management problems. Inspired by this fact, we propose a distributionally robust two-stage stochastic optimization framework to minimize the expected total energy cost of mobile network operators (MNOs) in the finite time horizon. To circumvent the computational difficulty of this stochastic optimization problem, we define a novel ambiguity set to capture the uncertainties of the harvested energy and wireless traffic based on their first- and second-order statistics information. By employing the distributionally robust optimization (DRO) methodology, we equivalently transform the original two-stage stochastic programming problem into a computationally tractable second-order cone programming problem. Then, a distributionally robust two-stage energy management algorithm (DRTEMA) is proposed, which has good performance of low complexity and only requires partial information of the stochastic parameters. Rigorous computational complexity analysis and extensive numerical simulations are conducted to show the advantages of the proposed algorithm.

Optimal design of flexible heat-integrated crude oil distillation units using surrogate models

The design of distillation columns often considers a given fixed feedstock and nominal operating conditions. Here we present an optimization-based approach for the optimal design of these units considering a flexible operation under a range of potential feedstocks. Our method combines an artificial neural network with a support vector machine to model the crude oil distillation unit. The artificial neural network model predicts the performance of the distillation unit for a given crude oil feedstock whilst the support vector machine classifier filters out infeasible design alternatives from the solution space (i.e., designs that are unlikely to converge when simulated using a rigorous model). The inputs to the artificial neural network include the column structural variables and operating conditions, whilst the outputs are process variables linked to the column performance. The artificial neural network models and support vector machines constructed for different crude oil feedstocks are integrated into a two-stage optimization framework in order to optimize the column structural variables and operating conditions, where the minimum utility demand is estimated using the pinch analysis. An effective solution strategy that combines stochastic and deterministic optimization algorithms is applied to search for economically viable and flexible design alternatives that can operate over a given range of crude oil feedstocks while satisfying the product quality specifications. The capabilities of the proposed approach are illustrated using an industrially-relevant case study, where we clearly show that the proposed approach can identify design alternatives capable of handling various feedstocks effectively.

Multi-objective electricity-gas flow with stochastic dispersion control for air pollutants using two-stage Pareto optimization

In consideration of the deteriorating global warming and air pollution, a multi-objective electricity-gas flow (MOEGF) is proposed in this paper. Different from the existing emission control modes, a novel stochastic dispersion (SD) control for air pollutants is formulated in the MOEGF. The SD control considering district-varying environmental tolerance introduces the Gauss puff dispersion model to precisely describe the emission dispersion, and further reduces the influence on air pollutant concentration. In addition, a scenario-based strategy is developed to enhance the robustness of SD control in the atmospheric condition uncertainty. To solve the MOEGF involving complex constraints and multiple conflictive objectives, a two-stage Pareto optimization framework is proposed. In the first stage, the nonconvex natural gas flow is linearized, and then an improved homogenized adjacent points method (I-HAPM) is developed to calculate a high-quality Pareto solution set of the simplified MOEGF, to provide diversified trade-off between objectives. Owing to the cooperation of the linearized gas flow and the Pareto optimizer I-HAPM, the computational quality and efficiency of the Pareto solution set is improved. In the second stage, a tailored compromise solution for operation is determined from the Pareto solution set according to real dispatch requirements, which is convexified with the penalty convex–concave procedure to guarantee the operation security. Case studies demonstrate that the MOEGF effectively reduces carbon emissions and influence on air pollution of the combined system, with a low-level cost sacrifice. Besides, the effectiveness of the two-stage Pareto optimization is validated.

A Robust Mixed-Integer Linear Programming Model for Mitigating Rail Transit Disruptions Under Uncertainty

In this paper, we propose a two-stage robust optimization framework to evaluate widely controllable commuter flow strategies that can help mitigate uncertain disruption impacts on rail transit commuter flows. In the operation-as-usual stage, preemptive control strategies including timetable adjustment, commuter path choice diversion, and commuter trip starting time diversion are planned within budget and other requirement constraints. In the disruption stage, optimal contingency routing is derived to minimize disruption impacts. To this end, a linear programming model that simulates the commuter movement logic under train service and platform disruption events is developed, which is then integrated in a mixed-integer max-min optimization model to evaluate the worst-case impacts on commuter flows arising from a set of uncertain disruption scenarios. We show that the two-stage robust optimization framework can be solved by a cutting plane algorithm efficiently using high performance and parallel computing platforms. Finally, we demonstrate the application of the model in mitigating disruption impacts through computational studies based on an actual rail transit network.