First-stage Optimization Research Articles

Safe Maneuvering Planning for Flights in Complex Environments

Safe trajectory planning of unmanned aerial vehicles (UAVs) has drawn significant attention. For avoiding obstacles, the two prevailing methods of distance penalty and convex polyhedra confinement ignore the flight velocity, aggressive maneuvering increases the risk of collision. Other approaches ensure safety by limiting the flight speed, leading to conservative and slow trajectories. This paper presents a motion planning method that ensures flexible maneuverability and a high level of UAV safety in unknown complex environments. Firstly, an improved path planning method considering safety and search efficiency is proposed to generate discrete primitives. By representing the confident flight area with ball-shaped areas expected no obstacles included, the safe region constraint is designed and incorporated into the first-stage optimization with the low-order kinematic model. Subsequently, an agile maneuvering approach with environmental adaptability is integrated into the second-stage optimization with the high-order kinematic model. This approach can effectively adjust the agile flight according to the obstacle distribution and motion velocity. Simulations and real-world experiments are conducted to demonstrate the robustness and effectiveness of the presented approach. Moreover, benchmark comparison manifests that the proposed method outperforms the cutting-edge methods from the aspects of the perception uncertainty adaptation and flight safety.

Two-stage optimization of hydrogen and storage coordination for a multi-region flexible intermodal multi-energy port system

To address the issue of imbalanced electricity and hydrogen supply and demand in the flexible multi-energy port area system, a multi-regional operational optimization and energy storage capacity allocation strategy considering the working status of flexible multi-status switches is proposed. Firstly, based on the characteristics of the port area system, models for system operating costs, generation equipment, energy storage devices, flexible multi-status switches, and others are established. Secondly, the system is subjected to a first-stage optimization, where different regions are optimized individually. The working periods of flexible multi-status switches are determined based on the results of this first-stage optimization, targeting the minimization of the overall daily operating costs while ensuring 100% integration of renewable energy in periods with electricity supply-demand imbalances. Subsequently, additional constraints are imposed based on the results of the first-stage optimization to optimize the entire system, obtaining power allocation during system operation as well as power and capacity requirements for energy storage devices and flexible multi-status switches. Finally, the proposed approach is validated through simulation examples, demonstrating its advantages in terms of economic efficiency, reduced power and capacity requirements for energy storage devices, and carbon reduction.

A two-stage distributed optimization method for home energy management systems via multi-modal data-driven algorithm

The home energy management system (HEMS), which utilizes multi-modal data from multiple sensors to generate the knowledge about decision making, is essential to the optimization of home energy management efficiency. Load scheduling based on HEMS can improve the utilization efficiency of multi-modal data and derived knowledge, achieve power supply-demand balance, and reduce users’ electricity costs. This paper proposes a distributed load optimization scheduling method for the load scheduling problem in HEMS based on multi-modal data-driven algorithm. Additionally, a two-stage data-driven optimization method is proposed, including a first-stage optimization model based on minimizing electricity costs and a second-stage optimization model based on minimizing system load fluctuations. In the first stage, cost self-optimization is performed based on energy storage devices. In the second stage, a load optimization instruction is issued by the control center, and each user optimizes the load fluctuations based on the system load data. Compared to centralized control methods, this approach reduces the computational overhead of the control center. Finally, simulation experiments based on load scheduling in the HEMS are conducted. The results of the first optimization stage show that when the battery capacity integrated into the system increases from 3.68 kWh to 6.68 kWh, user costs can be reduced from 57.572 cents to 42.064 cents. It is not only evident that the proposed method can effectively save users on electricity costs, but the introduction of larger capacity batteries also lowers these costs. The second stage of load fluctuation optimization results show that the proposed method can effectively optimize the usage data of a group of users and decrease the absolute peak-valley difference by 8.8%.

Decentralized mixed-integer optimization for robust integrated electricity and heat scheduling

Electric power systems (EPSs) and district heating networks (DHNs) are always independently operated and dispatched but also coupled with each other at the interfaces of combined heat and power (CHP) generation, whereas the existing distributed scheduling methods for the integrated electricity and heat system (IEHS) under uncertainty are computationally expensive in practical applications. To handle this problem, this paper proposes a novel decentralized mixed-integer optimization method for robust coordination involving multiple stakeholders. Firstly, a centralized two-stage robust optimization (RO) scheduling model is installed for the IEHS considering the scheduling economy under the nominal scenario and the adjustment feasibility against uncertainty. Secondly, the Fourier-Motzkin elimination equivalently projects the second-stage feasible region of the two-stage RO scheduling model onto the first-stage optimization, thereby producing a concise centralized RO scheduling model in a mixed-integer linear programming (MILP) formulation. Finally, a dual decomposition algorithm derives the decentralized solution to the resulting MILP-type RO model with guaranteed convergence and optimality. This avoids setting up a coordination center for distributed scheduling. Case testing for two IEHSs validates that the computational efficiency of the proposed method is several tens of times speedup than the traditional distributed RO method with guaranteed solution optimality.

Fusing Conflicting Multisource Imprecise Information for Reliability Assessment of Multistate Systems: A Two-Stage Optimization Approach

Expert knowledge is an important information source for system reliability assessment, especially when historical data are limited. However, when elicited, expert knowledge is often imprecise with large uncertainty. Moreover, as experts usually own different expertise and knowledge, the elicited knowledge from different experts might be conflicting. In this article, a two-stage optimization model is put forth to fuse the imprecise and conflicting information from multiple sources to assess reliability of multistate systems. The degradation of the components in the multistate system is modeled via imprecise Markov models. Then, in the first-stage optimization, upper and lower bounds of the degradation model parameters are determined by minimizing the conflict between the prediction of the model and the multisource imprecise information elicited from experts. A particle swarm optimization algorithm is tailored to solve the computational problems brought by the presence of high-dimensional decision variables and resolve the optimization problem. The second-stage optimization is, then, conducted to identify the upper and lower bounds of the system reliability function given that the degradation model parameters are constrained in the bounds obtained from the first-stage optimization. A numerical example, along with a radar display and control system, is used to demonstrate the effectiveness and applicability of the proposed method.

Light Pareto robust optimization for IMRT treatment planning.

Robust optimization (RO) has been proposed to mitigate breathing motion uncertainty during treatment in intensity-modulated radiation therapy (IMRT) planning for breast or lung cancer. RO is a pessimistic approach that implicitly trades off average-case for worst-case treatment plan quality. Pareto robust optimization (PRO) provides a mechanism for improving nonworst-case plan outcomes, but often remains overly conservative in the averagecase. The goal of this study is to characterize the trade-off between the optimality of robust IMRT plans in the worst case and the treatment quality in nonworst-case realizations of breathing motion. We provide a light Pareto robust optimization (LPRO) method for IMRT and test its clinical viability for improving the average-case plan quality while preserving robustness, in comparison to RO and PRO plans. Five clinical left-sided breast cancer patients were included in the study, each with an associated 4D-CT dataset approximating their breathing cycle. Using simulation, 50 different breathing patterns were generated for each patient. A first-stage optimization was solved with the objective of cardiac sparing while ensuring robustness on the target dose under breathing uncertainty. Next, a second-stage objective of overdose minimization was considered to improve plan quality in a controlled LPRO framework. For the simulated breathing scenarios, the trade-off between loss of average cardiac sparing at worst-case and the overdose to the breast was quantified by calculating the accumulated dose for each plan in each breathing scenario. Finally, the RO, PRO, and LPRO plans were each evaluated using eight clinical dose-volume criteria on the target and organs atrisk. The LPRO models allowed for significantly sharper dose falloffs in the expected dose instances, relative to both RO and PRO models. Plans began looking valid for delivery with average allowances of as little as +0.1Gy additional dose to the heart, and most patients experienced diminishing returns beyond +0.2Gy. Without sacrificing robustness, the LPRO approach produces viable plans with true total-target irradiation. Furthermore, the plans produced were able to reduce the nonworst-case downside typical of RO, without the characteristic overdosing or average-case pessimism seen in prior models.

Multistage Mixed-Integer Robust Optimization for Power Grid Scheduling: An Efficient Reformulation Algorithm

The penetration of renewables into power systems is gradually increasing, but its inherent uncertainty poses tremendous challenges to the coordinated operation of power grids. To overcome the demerits of canonical two-stage mixed-integer robust optimization (RO) method that neglects the nonanticipativity requirement and the computational burden in engineering applications, this paper offers a reformulated multistage mixed-integer RO method for regional power grid scheduling. Firstly, a multistage mixed-integer RO scheduling model is established considering the scheduling requests in real-world projects. The scheduling plans under the nominal scenario are determined ahead of uncertainty in the first-stage optimization, and the multistage max-min optimization with binary recourse variables is then executed for feasibility-checking with respect to the nonanticipative realization of uncertainty. Secondly, a dedicated reformulation algorithm is proposed for this intractable multistage mixed-integer RO model. Based on the implicit affine strategy, the multistage max-min optimization is equivalently encapsulated to a single-stage max-min problem, and the dual Fourier-Motzkin elimination is put forward to eliminate both continuous and binary recourse variables in the resulting feasibility-checking optimization. Therefore, the original multistage mixed-integer RO is finally recast as a mixed-integer linear programming that can be solved directly. Numerical tests on an actual 16-bus grid, the IEEE 118-bus system and the 319-bus provincial grid verify the superiority and applicability of the proposed reformulated mixed-integer RO scheduling method, which is of great significance in guiding system operations.

Optimal design and energy management of residential prosumer community with photovoltaic power generation and storage for electric vehicles

The optimum design and management of residential photovoltaic (PV) communities are essential to the reliability to satisfy the demands of communities due to the volatility and intermittence of solar energy. The retailer for energy dispatch management is introduced to improve the economic performances of PV communities through demand-side management measures with the electric grid. This paper proposes a novel two-stage optimization model of design and electricity dispatch strategies for residential PV communities to operate electric vehicles' charges. The first-stage optimization aims to obtain the optimal capacities of PV and batteries. The second-stage optimization optimizes the retailer's hourly electricity prices and electricity dispatch strategies, in which the Stackelberg game is performed between maximizing the retailer's benefit and minimizing the electricity cost of residential basic loads and vehicle charging loads. A case study is implemented to validate the proposed model. The installation capacity of batteries is appropriately increased with the increasing active loads of electric vehicles. The optimal pricing strategies of the retailer based on the trade schemes with the electricity grid are influenced by their ratios of fixed and active loads. Compared to the community without the retailer, the annual electricity cost of users is saved by 21.2 % through the proposed management strategy.

Automated Force-Coupled Ultrasound Method for Calibration-Free Carotid Artery Blood Pressure Estimation.

We develop, automate and evaluate a calibration-free technique to estimate human carotid artery blood pressure from force-coupled ultrasound images. After acquiring images and force, we use peak detection to align the raw force signal with an optical flow signal derived from the images. A trained convolutional neural network selects a seed point within the carotid in a single image. We then employ a region-growing algorithm to segment and track the carotid in subsequent images. A finite-element deformation model is fit to the observed segmentation and force via a two-stage iterative non-linear optimization. The first-stage optimization estimates carotid artery wall stiffness parameters along with systolic and diastolic carotid pressures. The second-stage optimization takes the output parameters from the first optimization and estimates the carotid blood pressure waveform. Diastolic and systolic measurements are compared with those of an oscillometric brachial blood pressure cuff. In 20 participants, average absolute diastolic and systolic errors are 6.2 and 5.6 mm Hg, respectively, and correlation coefficients are r = 0.7 and r = 0.8, respectively. Force-coupled ultrasound imaging represents an automated, standalone ultrasound-based technique for carotid blood pressure estimation, which motivates its further development and expansion of its applications.

Optimization of roll calibrations for beam channel rolling. Part 2. Space of channel gauges

The optimization of roll pass design for rolling of channels based on the conception of two-stage optimization was realized. Roll pass design is independent functioning system and has two components of optimization: roll pass design scheme and pass schedule. Roll pass design will be considered truly optimal only if it has both an optimal scheme and an optimal pass schedule. During the first-stage optimization (search the optimal scheme of roll pass design), the most important moment is the formation of the “space of channel grooves” as the first space optimization. The above space consists of channel grooves of various types and shapes determined by known from the literature and practice roll pass designs. The “space of channel grooves” must be regularized with the use of the method of classification. As the main features of classification (groove space coordinates), the mostimp ortant geometric and technological features of the grooves were chosen: type of neck, type of actual flanges, type of false flanges, type of groove closure and quantity of rolls constituting the groove. Levels of variation for every criterion of classification have been identified and coded. Every admissible combination of variation levels specifies type and code of particular scheme of channel groove.Acknowledgements: The reported study was funded by RFBR, project number 20-38-90246.

A multi-method approach to scheduling and efficiency analysis in dual-resource constrained job shops with processing time uncertainty

In dual-resource constrained job shop scheduling, jobs have to be assigned to workers and machines. While the problem is notoriously hard in terms of computational complexity, additional practical difficulties arise from data uncertainty and worker efficiency variation. In this paper, we propose a methodological pipeline combining mathematical optimization, simulation, and data analysis to cope with these aspects over time. Accounting for uncertain worker processing times, we employ an iterative two-stage optimization-simulation approach: A first-stage optimization model determines an assignment of workers to jobs; in the second stage, the scheduling of this assignment is evaluated operationally using sampled realizations of worker processing times. Both stages are executed in an alternating fashion until no further improvement is possible in the average realized makespan. At the end of a work day, realized worker efficiencies are then measured in a slacks-based data envelopment analysis on the operations level. Workers learn about their individual efficiency and are prompted to reduce inefficiencies. The resulting overall methodology not only provides robustified schedules for dual-resource constrained job shops under uncertainty, but also reduces the impact of uncertainty over time by motivating workers to operate on the efficient frontier. Computational results are conducted in several settings with both heuristic and exact solution procedures for the second-stage dual-resource constrained job shop scheduling problem. The results demonstrate the versatility of the outline with respect to addressing uncertainty and worker inefficiency.

Two-Stage MILP Model for Optimal Skeleton-Network Reconfiguration of Power System for Grid-Resilience Enhancement

Skeleton-network reconfiguration is an important task and plays a most important role during power system restoration (PSR) after a blackout. By determining the skeleton network, the power system can be restored as soon as possible to minimize the burden of network reconfiguration. In this paper, a resilience-based skeleton-network reconfiguration (NR) strategy, i.e., a two-stage mixed-integer linear programming (MILP)–based NR strategy for grid-resilience enhancement, is proposed to minimize the impact of emergency power outages on power systems. The start-up sequence for non-black-start generators (NBSGs) and line energization sequences are determined in the first-stage optimization model. A serial restoration constraint and a transient frequency constraint are considered to achieve the serial restoration scheme of NBSGs. Except for the generator power, all the variables attained during the first stage are assumed fixed in the second stage. The second-stage optimization model determines the optimal skeleton network by determining the target transmission lines and critical load pickup during the NR phase. Furthermore, the sets of metrics (i.e., system flexibility, power loss ratio, and recovery time resilience) are presented to determine the grid operational resilience in the skeleton-network reconfiguration. Then, two stages of skeleton-NR are formulated as MILP, and the branch-and-bound method is presented to solve both models. Finally, simulation studies are performed on the two modified power system test cases and the results validate that the proposed strategy can efficiently determine the robust skeleton network for practical and detailed PSR planning.

Distributed energy storage planning method considering multi-point aggregation effect

ABSTRACT The economic performance and utilization rate have become the key factors limiting the development of energy storage systems (ESS). From the perspective of the aggregation effect manifested by multi-point ESS, an inspired concept of “aggregation configuration, decentralized location” is proposed. Based on this concept, this paper proposes a planning method using two-stage optimization including sizing, siting and operational optimization for distributed energy storage (DES). The first-stage optimization aims to maximize the net present value (NPV) of aggregate ESS, while the second stage aims to mitigate the voltage fluctuation after the integration of distributed PV generation. In addition, the operational optimization for both the aggregate ESS and individual DES units are considered to better achieve the objectives of the two-stage optimization, and the particle swarm optimization (PSO) algorithm is employed to solve the planning problem. Case studies show that the proposed method helps to ensure the global NPV over the lifespan of aggregate ESS by considering operational optimization and depth of charge (DOD). Compared with the centralized ESS solution, the proposed multi-point DES solution can improve the overall voltage fluctuation mitigation capability by more than 40%. With the PV capacity penetration rate varying from 0 ~ 210%, sensitivity analysis reveals that when the penetration rate is close to 100%, the aggregate ESS has better economic performance and voltage fluctuation mitigation capability.

Ambulance dispatching during a pandemic: Tradeoffs of categorizing patients and allocating ambulances

Amidst a pandemic, operators of emergency medical service (EMS) systems aim at upholding service at sufficiently low response times while reducing the infection probability of their personnel. Designating ambulances to serve only infected patients and suspected cases may reduce the outage probabilities of ambulances and consequently the response times of the EMS. We investigate the benefits that EMS personnel and patients can gain from such a split. As a solution method to quantify these benefits, we apply a two-stage approach. First, we run a first-stage optimization model to pre-select ambulance splits with the highest emergency call coverage. Second, we solve the approximate Hypercube Queuing Model (AHQM) to evaluate the performance of the pre-selected ambulance splits at the second stage. We contribute to the existing literature by including multiple incident categories and outages of ambulances in the AHQM and combining it with the first-stage optimization model. Further, we conduct a case study for the Coronavirus Disease 2019 (Covid-19) pandemic to draw conclusions on the benefits of splitting. We observe that an ambulance split would not reduce the average response time for the examined data set since the Covid-related call volume in Munich and the infection probability are too low. However, a sensitivity analysis shows that long isolation times and high infection probabilities make an ambulance split beneficial for patients and EMS personnel, as an ambulance split reduces the average response time without significantly increasing the mean infection probability for EMS personnel.

A two-stage optimization approach on the decisions for prosumers and consumers within a community in the Peer-to-peer energy sharing trading

In the traditional power system, the end users are independent individuals without any interaction. While the development of communication and information technology brings many possibilities for the interaction and cooperation among these individuals. This study explores the interaction and cooperative relationship among the prosumers and consumers within a community in the Peer-to-peer (P2P) energy sharing trading. In the community, a customer would like to provide some payoffs to encourage other customers to exchange certain amounts of energy to obtain more profits. We propose a two-stage optimization approach on the optimal strategies to maximize their utilities in the P2P energy sharing trading. In the first-stage optimization model, the decision on whether to participate in the P2P energy sharing trading is obtained based on the maximization of social utility function. Meanwhile, the optimal amounts of exchanged energy also can be obtained. In the second-stage optimization model, we provide an analysis of the optimal associated trading payments based on a payments bargaining model. Both of the above two optimization problems are solved based on a distributed algorithm respectively. Moreover, we demonstrate that the customers who participate in P2P energy sharing trading can improve their utilities compared with an individual optimization method based on a case study.

Two-Stage Stochastic Mixed-Integer Programming with Chance Constraints for Extended Aircraft Arrival Management

The extended aircraft arrival management problem, as an extension of the classic aircraft landing problem, seeks to preschedule aircraft on a destination airport a few hours before their planned landing times. A two-stage stochastic mixed-integer programming model enriched by chance constraints is proposed in this paper. The first-stage optimization problem determines an aircraft sequence and target times over a reference point in the terminal area, called initial approach fix (IAF), so as to minimize the landing sequence length. Actual times over the IAF are assumed to deviate randomly from target times following known probability distributions. In the second stage, actual times over the IAF are assumed to be revealed, and landing times are to be determined in view of minimizing a time-deviation impact cost function. A Benders reformulation is proposed, and acceleration techniques to Benders decomposition are sketched. Extensive results on realistic instances from Paris Charles-de-Gaulle airport show the benefit of two-stage stochastic and chance-constrained programming over a deterministic policy.

Optimal Sizing of Smart Home Renewable Energy Resources and Battery Under Prosumer-Based Energy Management

This article presents the framework of a two-stage optimization model for the optimal planning of smart home renewable energy resources (RERs) and battery integration with the association of prosumer-based energy management. The optimal sizing problem of in-house RERs and battery is addressed in the first-stage optimization with the objective function of RERs and battery's total life-cycle cost minimization. The smart home daily energy operation problem is formulated in the second stage with the help of multiobject home energy management (MOHEM). In the second-stage operation problem, the MOHEM is implemented with two different objective functions such as minimization of consumer's daily energy cost and maximization of consumer's total comfort level index. The particle swarm optimization algorithm and a mixed-integer linear programming technique are, respectively, used in this article to optimize the proposed two-stage optimization model. A typical smart home which consists of various controllable appliances is considered in this analysis to evaluate the performance of the proposed two-stage optimization model. Three different case studies are considered in the simulation to assess the effectiveness of the proposed model. Finally, an economic analysis is also done in this article to examine the smart home consumer's capital investment benefits.

Operation optimization and income distribution model of park integrated energy system with power-to-gas technology and energy storage

Power-to-gas (P2G) technology is considered as a new approach for clean energy consumption and energy conversion. However, because this technology must be combined with other energy systems to build a stable energy system, a reasonable income distribution method is necessary to guarantee this integration. Firstly, the operation optimization model of the park integrated energy system (PIES) and park independent energy system (PINES) with P2G are constructed for the first stage optimization, with the objective of maximizing net income. Secondly, the energy system performance evaluation indicators are developed to assess the system quantitatively in terms of the economic and environmental aspects. Thereafter, the income distribution models based on Shapley value and the improved Shapley value with operational risk factor are created, and the total income is optimally distributed at the second stage based on the first-stage optimization results. Finally, an industrial park in a province of China is selected for case analysis. The results show that (1) PIES can complement different systems, integrate the demands in heat, electricity, and gas, while realizing the electricity-gas-heat/electricity conversion and heat-electricity complementarity. (2) Income distribution using an improved Shapely value method is proposed, it overcomes the one-sidedness of transaction volume and lack of differences among participants, reflects the actual operational risk and the degree of contribution of participants to the whole system, and promotes the incentives of cooperation. (3) Based on the improved income distribution model, the income of the PS, P2G, and HS are redistributed. The income of P2G increased by ¥7,450, which reflects the important collaborative value of P2G. The willingness of system cooperation increased by 742.392%. Therefore, the proposed operation optimization and income distribution model can enhance the incentives of participants want to cooperate under the premise of ensuring the maximum net income of the PIES. Moreover, it can be used as reference for the formulation of an optimal operation plan and income distribution of the complex energy system and it can provide a way to promote clean energy production. • The role of P2G as a new energy conversion way is studied. • The two-stage optimization model is constructed. • The first stage is operational optimization. • The second stage is income distribution. • The improved Shapley value method is applied in park integrated energy system.

HEMS-enabled transactive flexibility in real-time operation of three-phase unbalanced distribution systems

This paper proposes a coordinated two-stage real-time market mechanism in an unbalanced distribution system which can utilize flexibility service from home energy management system (HEMS) to alleviate line congestion, voltage violation, and substation-level power imbalance. At the grid level, the distribution system operator (DSO) computes the distribution locational marginal prices (DLMP) and its energy, loss, congestion, and voltage violation components through comprehensive sensitivity analyses. By using the DLMP components in a first-stage optimization problem, the DSO generates two price signals and sends them to HEMS to seek flexibility service. In response to the request of DSO, each home-level HEMS computes a flexibility range by incorporating the prices of DSO in its own optimization problem. Due to future uncertainties, the HEMS optimization problem is modeled as an adaptive dynamic programming (ADP) to minimize the total expected cost and discomfort of the household over a forward-looking horizon. The flexibility range of each HEMS is then used by the DSO in a second-stage optimization problem to determine new optimal dispatch points which ensure the efficient, reliable, and congestion-free operation of the distribution system. Lastly, the second-stage dispatch points are used by each HEMS to constrain its maximum consumption level in a final ADP to assign consumption level of major appliances such as energy storage, heating, ventilation and air-conditioning, and water heater. The proposed method is validated on an IEEE 69-bus system with a large number of regular and HEMS-equipped homes in each phase.

Thermomechanical Coupling Analysis and Optimization of Metallic Thermal Protection System

The metallic thermal protection system (MPTS) is a key technology for reducing the cost of reusable launch vehicles, offering the combination of increased durability and competitive weights when compared with other systems. A two‐stage optimization strategy is proposed in this paper to improve thermal and mechanical performance of MTPS while minimizing its weight. Sensitivity analysis is conducted to determine the influence of various design variables, and these variables are classified into two groups according to the results. Three main parameters are optimized in the first‐stage optimization, and others are optimized in the second stage. Combining the response surface method with genetic algorithm ensures the computational efficiency of this strategy. Optimum results show that the thermal insulation capability of MTPS is improved by 20% with little mass cost, validating the feasibility of this optimization strategy.