Two-stage Optimization Strategy Research Articles

Optimizing energy efficiency in multi-chiller systems: A comprehensive Modelica-based approach

To achieve sustainable development of buildings, this paper investigates the energy-saving potential of multi-chiller systems by examining the interactions between sequencing optimization, load optimization, and parameter optimization in systems with varying capacities. A Modelica-based simulation platform, adaptable to various programming languages optimization engines, was developed for this purpose. The study introduces a sequencing optimization threshold function that considers both wet-bulb temperature and cooling load. Additionally, a two-stage optimization strategy that prioritizes parameter adjustments before sequencing is proposed. Case studies demonstrate that this threshold function and reversed optimization order can further enhance overall energy savings. Focusing on a system with three large chillers and one small chiller, the study reveals the energy benefits of activating the small chiller under specific conditions, improving overall system efficiency. The proposed optimization achieved a cumulative energy saving of 650,463 kWh over the summer, with sequencing contributing 5.64 %. Frequency conversion control of the water pump is identified as a significant energy-saving factor. This research provides a comprehensive approach to optimizing diverse chiller systems, highlighting substantial potential for energy conservation.

Demand response of an Electric Vehicle charging station using a robust-explicit model predictive control considering uncertainties to minimize carbon intensity

This paper presents a novel approach to address uncertainties and enable demand response in Electric Vehicle (EV) charging station optimization. A two-stage optimization strategy is proposed, integrating Robust Optimization and explicit Model Predictive Control (eMPC). The first stage involves day-ahead planning using Robust Optimization technique to limit the hourly power consumption of EVs, considering worst-case scenarios caused by uncertainties in EV consumption and CO2 emissions. The objective is to minimize environmental impact by reducing CO2 emissions. An Explicit Model Predictive Control strategy is developed in the second stage for real-time operation. The explicit solution, calculated offline, models uncertainties such as the initial state of charge of the battery energy storage, photovoltaic power production, and EV power consumption. During real-time operation, the explicit solution is accessed using measured data from the charging station, refining the schedule derived from the first stage. The proposed solution is implemented and evaluated at an EV charging station in Trieste, Italy. The results demonstrate a significant 69% reduction in CO2 emissions compared to a deterministic approach while maintaining a real-time computation time of less than 0.1 s.

Optimization Strategies for Electric Vehicle Charging and Routing: A Comprehensive Review

Based on information from recent research, by 2045, Electric Vehicles (EV) will dominate the roads with presence of more than 80% of its kind. Hence, these vehicles' grid level penetration will increase proportionally, which challenges the existing grid infrastructure in terms of its reliability and energy management capabilities. New techniques to store and consume massive quantities of energy from the power grid, as well as infusing the captive energy within the EV in response to grid demands, are emerging with the advent of electric vehicles. Everything could be handled smoothly only if we schedule the EV operation (charging/discharging) more optimally and efficiently using scheduling algorithms. Despite the existence of many routings and charging schedule computations, nature-inspired optimization approaches might play a critical role in responding to such routing challenges. Researchers have created several optimum scheduling approaches, such as Dynamic Programming, Differential Evolutionary Optimization Techniques, Collaborative Optimization Scheduling, Two-stage optimal scheduling strategy, and so on. The optimum schedule review examines the operation of an EV fleet while considering uncertainty sources and varied EV operating circumstances by integrating heuristic and meta-heuristic techniques. This paper exhibits a deep review on the various EV optimal scheduling techniques and adopted algorithms which are the emerging best practices like predictive analytics, dynamic routing, user centric planning, multi-objective optimization, etc. that reflect the industry's focus on leveraging advanced technologies, data-driven decision-making, and collaborative approaches to enhance the efficiency and sustainability of electric vehicle routing and charging scheduling.

Delving into Multimodal Prompting for Fine-Grained Visual Classification

Fine-grained visual classification (FGVC) involves categorizing fine subdivisions within a broader category, which poses challenges due to subtle inter-class discrepancies and large intra-class variations. However, prevailing approaches primarily focus on uni-modal visual concepts. Recent advancements in pre-trained vision-language models have demonstrated remarkable performance in various high-level vision tasks, yet the applicability of such models to FGVC tasks remains uncertain. In this paper, we aim to fully exploit the capabilities of cross-modal description to tackle FGVC tasks and propose a novel multimodal prompting solution, denoted as MP-FGVC, based on the contrastive language-image pertaining (CLIP) model. Our MP-FGVC comprises a multimodal prompts scheme and a multimodal adaptation scheme. The former includes Subcategory-specific Vision Prompt (SsVP) and Discrepancy-aware Text Prompt (DaTP), which explicitly highlights the subcategory-specific discrepancies from the perspectives of both vision and language. The latter aligns the vision and text prompting elements in a common semantic space, facilitating cross-modal collaborative reasoning through a Vision-Language Fusion Module (VLFM) for further improvement on FGVC. Moreover, we tailor a two-stage optimization strategy for MP-FGVC to fully leverage the pre-trained CLIP model and expedite efficient adaptation for FGVC. Extensive experiments conducted on four FGVC datasets demonstrate the effectiveness of our MP-FGVC.

Optimized shared energy storage in a peer-to-peer energy trading market: Two-stage strategic model regards bargaining and evolutionary game theory

With the increasing demand of users for distributed energy storage (ES) resources and the emerging development of peer to peer (P2P) transaction technology, shared energy storage (SES) has great potential to contribute into new business models of demand-side ES. In order to compromise essential elements like safety, stability and efficiency of P2P trading, as well as to improve the utilization rate of demand-side ES, this paper devotes to construct a P2P transaction framework based on a partially decentralized topology and proposes a two-stage trading optimization strategy of SES in a P2P market, considering the equilibrium state of supply and demand flow. In the first stage, this paper simultaneously balances the interests of buyers and sellers and brings the carbon trading mechanism into the transaction process. The interaction of interests of bilateral parties with consideration of carbon trading mechanism has been investigated, and a SES capacity sharing model is, then, established based on the bargaining game theory. In the second stage, a unique pricing mechanism for SES leasing fee is designed based on a multi-strategy evolutionary game model, considering bounded rational decision-making for SES operators and communities. Finally, numerical simulation verified the feasibility and superiority of the proposed P2P trading strategy of SES.

Multi-objective two-stage optimization scheduling algorithm for virtual power plants considering low carbon

Abstract With the continuous growth of energy demand, the importance of developing and utilizing low-carbon energy is becoming increasingly prominent. In this context, virtual power plant technology has been proposed. It is a technology for integrating, coordinating and optimizing distributed energy resources, which has significant effects in improving energy utilization efficiency and reducing carbon emissions. This article proposed a virtual power plant scheduling method based on multi-objective two-stage optimization scheduling algorithm considering low carbon. This method first determines the production and consumption of various energy resources in the virtual power plant, including wind power, thermal power and hydropower. Then, with the goal of minimizing costs and reducing carbon emissions, multi-objective optimization algorithms are used to allocate and schedule energy resources in the virtual power plant. On this basis, a two-stage optimization strategy was introduced, combining long-term optimization and short-term scheduling to adapt to energy allocation and scheduling needs at different time scales. The experimental results indicate that this method can effectively improve the energy utilization efficiency and economy of virtual power plants, and reduce carbon emissions.

A New Gradient-Accelerated Two-Stage Multiobjective Optimization Method for CO2-Alternating-Water Injection in an Oil Reservoir

Summary CO2-water-alternating-gas (CO2-WAG) is a reservoir development method that can simultaneously enhance oil recovery and achieve CO2 storage. However, improperly designed parameters for CO2 injection and oil production may significantly reduce the oil displacement efficiency and CO2 storage. Furthermore, optimizing the injection parameters is computationally expensive due to the high computational cost of the compositional simulation. This work aims to propose an efficient optimization method to obtain a series of well-control schemes that balance maximizing net present value (NPV) and CO2 storage for decision-makers. Given the number of CO2-WAG cycles and the duration of each cycle, we optimize the water injection rate, gas injection rate, and half-cycle for the injection well and the bottomhole pressure (BHP) for the production well. In this paper, a two-stage optimization strategy is proposed to enhance the optimization efficiency. The first stage performs the surrogate-assisted single-objective optimizations of each considered objective. It is designed to find the endpoints of the Pareto front that connect all solutions of the multiobjective optimization; this stage not only provides important search directions for the subsequent multiobjective optimization but also improves the accuracy of the surrogate model near the Pareto front. The second stage is the surrogate-assisted multiobjective optimization, which aims to find all the solutions along the Pareto front based on the Pareto endpoints obtained from the first stage. In addition, this study successfully combines the gradient of the objective functions with the meta-heuristic algorithm during the multiobjective optimization, which ensures a faster convergence to the global optimum. The proposed multiobjective optimization algorithm shows faster convergence than the conventional optimization methods when applied to the three multiobjective optimization test functions. Finally, a comparison with the conventional multiobjective optimization is conducted based on one test function and two benchmark reservoir simulation models to verify the correctness and efficiency of the proposed method. It is confirmed that the proposed method outperforms the conventional ones for the optimization of CO2-WAG injection.

A two-stage optimal scheduling strategy of hybrid energy system integrated day-ahead electricity market

A two-stage optimal scheduling strategy of hybrid energy system integrated day-ahead electricity market

Optimal Placement of PV Smart Inverters With Volt-VAr Control in Electric Distribution Systems

The high R/X ratio of typical distribution systems makes the system voltage vulnerable to the active power injection from distributed energy resources (DERs). Moreover, the intermittent and uncertain nature of the DER generation brings new challenges to the voltage control. This article proposes a two-stage stochastic optimization strategy to optimally place the photovoltaic (PV) smart inverters with Volt-VAr capability for distribution systems with high PV penetration to mitigate voltage violation issues. The proposed optimization strategy enables a planning-stage guide for upgrading the existing PV inverters while considering the operation-stage characteristics of the Volt-VAr control. One advantage of this planning strategy is that it utilizes the local control capability of the smart inverter that requires no communication, thus avoiding issues related to communication delays and failures. Another advantage is that the Volt-VAr control characteristic is internally integrated into the optimization model as a set of constraints, making placement decisions more accurate. The objective of the optimization is to minimize the upgrading cost and the number of the smart inverters required while maintaining the voltage profile within the acceptable range. Case studies on an actual 12.47 kV, 9-km-long Arizona utility feeder have been conducted using OpenDSS to validate the effectiveness of the proposed placement strategy in both static and dynamic simulations.

Two-stage robust optimization strategy for spatially-temporally correlated data centers with data-driven uncertainty sets

Data center buildings (DCBs) in data center parks consume significant and ever-growing amounts of electric power for processing tremendous data workloads in a modern city. The workloads are divided into two types: interactive workloads (IWs) with spatially transferrable characteristics and batch workloads (BWs) with temporally shiftable characteristics. The unique spatially-temporally workloads show great demand response capability, enabling reducing the electricity cost of DCBs. However, the source-load uncertainties such as the number of arriving workloads, and photovoltaic output affect the cost-efficient operation of DCBs in the electricity market. Inadequate server numbers during worst-case scenarios may result in the inability to fulfill user contracts. This paper presents a model for DCBs that incorporates battery energy storage systems, photovoltaic generation, and electrical loads for processing spatially-temporally correlated workloads. Considering multiple uncertainties, a two-stage robust optimization strategy is proposed to coordinate workload and power for DCBs. To accurately determine the boundaries of the uncertainty sets, a data-driven method using the 1-Wasserstein metric is adopted. This method is reformulated into a distributionally robust chance-constrained programming model. The nested column-and-constraint generation (C&CG) method is used to resolve the established two-stage robust optimization problem with mixed-integer recourse. Finally, case studies verify the effectiveness of the proposed method.

Charging and discharging optimization strategy for electric vehicles considering elasticity demand response

The electrification of urban transportation systems is a critical step toward achieving low-carbon transportation and meeting climate commitments. With the support of the Chinese government for the electric vehicle industry, the penetration rate of electric vehicles has continued to increase. In the context of large-scale electric vehicles connected to the grid, a coordinated charging-discharging system is particularly vital studied to avoid grid overload caused by customers' random charging. In this paper, a two-stage optimization strategy for electric vehicle charging and discharging that considers elasticity demand response based on particle swarm optimization was proposed, allowing the user to respond autonomously according to the reference value of the charge and discharge demand response and select the optimization weight independently to meet their travel and charging needs. To facilitate the user to balance the charging cost and the charging energy, we have introduced the virtual SOC to calculate the optimization result in advance. The results show that the optimized scheme can reduce the charging cost by 40%∼110%, and the load variance of the distribution network can be reduced by 19%∼100%, realizing the "win-win" benefit of the grid side and the user side. In addition, our research found that under the proposed strategy, the cost of battery loss caused by cyclic charging and discharging is negligible compared to the discharge benefit.

Large-scale mobile users deployment optimization based on a two-stage hybrid global HS-DE algorithm in multi-UAV-enabled mobile edge computing

Multi-UAV (unmanned aerial vehicle)-supported mobile edge computing system deploys multiple UAVs as flight edge clouds for large-scale users. In this system, how to optimize the deployment of UAVs is important for providing good service for all mobile users. Specifically, for each mobile user, we need to determine whether the task can be performed locally or on the drone (i.e., the unload decision) and how much resources should be allocated. In this paper, a new two-level optimization method is proposed for UAV deployment and task scheduling problem to minimize the system energy consumption. The proposed algorithm is named TSHGHSDE algorithm, in which a few features are designed to enhance the algorithm performance. Firstly, a two-stage optimization strategy is proposed based on HS-DE algorithm. In the early stage, HS algorithm is used for the local search in a limited space, and the DE algorithm is employed for the global search in the late stage. Secondly, we design an effective control parameter to adjust the search process, which aims to effectively combine the local search ability of HS algorithm and the global search ability of DE algorithm. Thirdly, a novel encoding mechanism is proposed in the process of the UAV deployment optimization. A global search strategy is designed to enhance the performance of the proposed algorithm. To assess the performance of the proposed algorithm, some well-known algorithms are used for comparison in experiments. The results demonstrate that the proposed algorithm performs better in terms of the search efficiency, search accuracy and stability.

A Practical Approach to Select Representative Deterministic Models Using Multiobjective Optimization from an Integrated Uncertainty Quantification Workflow

Summary Selecting a set of deterministic (e.g., P10, P50, and P90) models is an important and difficult step in any uncertainty quantification workflow. In this paper, we propose to use multiobjective optimization to find a reasonable balance between the often conflicting features that must be captured by these models. We embed this approach into a streamlined uncertainty quantification workflow that seamlessly integrates multirealization history matching, production forecasting with uncertainty ranges, and representative deterministic model selection. Some uncertain parameters strongly impact simulated responses representing historic (production) data and are selected as active parameters for history matching, whereas others are important only for forecasting. An ensemble of conditional realizations of active history-matching parameters is generated in the multirealization history-matching stage using a distributed optimizer that is integrated with either a randomized maximum likelihood (RML) or a Gaussian mixture model (GMM). This ensemble is extended with unconditional realizations of forecast parameters generated by sampling from their prior distribution. Next, the petroleum engineer must select primary and secondary key performance indicators and identify models from this ensemble that optimally generate P10, P50, and P90 values for these indicators. In addition to matching target values of these key performance indicators (e.g., cumulative oil/gas/water production and recovery factor), selected representative models (RMs) typically must satisfy regulatory or management-imposed requirements or constraints (e.g., the value of some key parameters must be within a user-specified tight range). It can be quite difficult to find a set of RMs that satisfy all requirements. Even more challenging, some requirements may conflict with others, such that no single model can satisfy all requirements. To overcome these technical difficulties, we propose in this paper to formulate different requirements and constraints as objectives and develop a novel two-stage multiobjective optimization strategy to find a set of Pareto optimal solutions based on the concept of dominance. In the first stage, we propose selecting P10, P50, and P90 candidates by minimizing the indicator mismatch function and constraints violation function. In the second stage, we propose selecting combinations of P10, P50, and P90 candidates from the previously generated posterior ensemble, obtained in the first stage by optimizing other objectives. One or more sets of RMs can then be selected from the set of optimal solutions according to case-dependent preferences or requirements. Because the number of P10, P50, and P90 candidates selected in the first stage is much smaller than the number of all samples, the proposed two-stage approach performs much more efficiently than directly applying the traditional multiobjective optimization approach or clustering-based approaches. The proposed method is tested and validated against a realistic example. Our results confirm that the proposed method is robust and efficient and finds acceptable solutions with no or minimal violations of constraints. These results suggest that our advanced multiobjective optimization technique can select high-quality RMs by striking a balance between conflicting constraints. Thus, a better decision can be made while running much fewer simulations than would be required with traditional methods.

Electric Vehicle Routing Problem With Variable Vehicle Speed and Soft Time Windows for Perishable Product Delivery

This work studies perishable products’ distribution using electric commercial vehicles (ECVs). Extra energy is consumed for refrigeration to keep such products from deteriorating, which shortens the limited driving range of ECVs. Besides charging at public recharging stations, their travel speed can be adjusted to improve their driving range and decrease distribution cost. We propose an Electric Vehicle Routing problem with variable vehicle speed and soft time windows for perishable products (EVRP-VS). An energy consumption rate function of refrigerated ECVs during driving is introduced into the problem. The function considers refrigeration and has a nonlinear relationship with ECV speed and weight. As long as the carriage is not empty, the vehicle needs refrigeration during driving and during its stay at customers and stations. A mathematical programming model is developed for EVRP-VS, to minimize total distribution cost, including vehicle cost, power cost, refrigeration cost, and penalty cost due to delayed delivery. An adaptive hybrid ant colony optimization (AHACO) with a two-stage speed optimization strategy is proposed to solve EVRP-VS. In the first stage, local speed optimization is used to optimize the speed of each ant (ECV) in each transfer step. In the second one, global speed optimization further optimizes the speed for each fixed route constructed by ants. AHACO is applied to many problem instances. Experimental results show that it can effectively solve EVRP-VS in comparison with CPLEX and other meta-heuristics.

A two-stage optimal strategy for flexible interconnection distribution network considering the loss characteristic of key equipment

The flexible interconnection distribution networks (FIDN) based on soft open points (SOP) provides an opportunity to improve the economy and reliability of distribution networks. However, the existing optimal strategies have mainly focused on line power loss reduction, and the loss characteristic of SOPs and distribution transformers is ignored. Therefore, the capability of reducing total power loss for the existing optimization strategy needs further improvement. Thus, based on SOP's locating, sizing and optimal operation, a two-stage optimal strategy for FIND is proposed considering the loss characteristic of key equipment including SOPs and distribution transformers. Firstly, considering the transformer equivalent loss model and different load states, an improved loss sensitivity model is proposed to determine the optimal access location of SOP. Further, the SOP’s capacity is designed by the total cost optimization model. Secondly, based on the loss characteristic of key equipment, the optimal operation strategy is proposed to reduce the total power loss of FIND while realizing optimal economic area operation of transformers. Finally, the case studies were performed on a FIND test system with 22-bus and 15-bus to validate the proposed two-stage optimal strategy, and the results of the case studies show that the economy of FIND is greatly improved.

Deployment and Robust Hybrid Beamforming for UAV MmWave Communications

We deploy an unmanned aerial vehicle (UAV) equipped with a large-scale uniform planar array (UPA) to serve multiple ground users in millimeter-wave band. Particularly, the practical UAV jitter is carefully considered, which may affect the beam gains and impact the communication quality. To provide a stable service, we first model the attitude change of the UPA caused by UAV jitter. Then, an optimization problem is formulated to maximize the minimum achievable rate of the users by optimizing the position and robust hybrid beamforming of the UAV. To solve the non-convex problem with highly coupled variables, a two-stage optimization strategy is developed. The first stage aims to decouple the beamforming from the original problem and design the UAV deployment under the assumption of an ideal beam pattern. The second stage aims to design robust hybrid beamforming with the obtained UAV position. Specifically, we first design analog beamforming for wide beams to cover the potential jitter angle range for each user via a chirp sequence-inspired method. Then, with equivalent channel estimation, we design digital beamforming by combining zero-forcing and water-filling power allocation algorithms. Extensive simulation results show the performance superiority of the proposed solution compared to the benchmark algorithms.

Integrated carbon footprint with cutting parameters for production scheduling

A large part of the global carbon footprint comes from manufacturing. Apart from material distribution during product assembly, rational optimization of cutting parameters and production scheduling during processing are the main ways to realize low-carbon manufacturing. The existing researches mainly focus on cutting parameters or production scheduling when reducing manufacturing carbon emissions, but seldom considers the coupling relationship between the two. This limits the reduction of emissions to some extent. On this basis, a collaborative low-carbon optimization system suitable for the actual use of enterprises was developed. The optimization of production scheduling is a discrete problem, while cutting parameters are continuous and processing time brought by different cutting parameters will cause different effects on the scheduling scheme. Therefore, a two-stage optimization strategy is adopted to achieve collaborative optimization of cutting parameters and production scheduling. To achieve multi-objective optimization of the model and speed up convergence, the Crowding Niche mechanism and elite retention strategy are introduced into the selection operator to improve the genetic algorithm based on Pareto Optimality. In addition, different from the traditional that need to manually determine the machine tool and cutting tool according to the demand, a knowledge base module is integrated into the system. The knowledge base module is qualified for the knowledge acquisition and instance matching of the model in order to meet the processing capacity and constraints and enhance the ability of intelligent decision-making during production. Finally, the interactive application interface of the collaborative low-carbon optimization system has been implemented and the effectiveness of the system is verified by taking the manufacturing case of electromechanical enterprises as an example.

Two-stage optimization strategy of multi-objective Volt/Var coordination in electric distribution network considering renewable uncertainties

Renewable energy is connected to the distribution network in the form of distributed generation, and its output is random and fluctuating. The high penetration of renewable energy will weaken the security and economy of the electric distribution network. In view of the uncertainty of renewable power output, Monte Carlo simulation method and simultaneous backward reduction method are used to scenario generation and reduction of wind power and photovoltaic, so as to represent their randomness. On this basis, a two-stage optimization strategy for Volt/Var coordination in distribution network is proposed. In the first stage, a network reconfiguration model with the goal of minimizing the power loss of the system is established, and the particle swarm optimization algorithm is used to solve it. In the second stage, a Volt/Var optimization model with the goal of minimizing the node voltage offset and the system power loss is established, and the multi-objective model is solved by combining the network topology obtained in the first stage with the reactive power adjustment device and voltage regulating equipment such as switching capacitor, static var compensator and on-line tap changer. The distribution network’s Volt/Var is optimized using the non-dominated sorted genetic algorithm-II. The optimization results of the first stage are regarded as the conditions of the second stage. Lastly, the IEEE 33-node extension system is used to validate the effectiveness of the suggested strategy.

Two-stage real-time optimal electricity dispatch strategy for urban residential quarter with electric vehicles’ charging load

Two-stage real-time optimal electricity dispatch strategy for urban residential quarter with electric vehicles’ charging load

A Two-Stage Optimization Approach for Healthcare Facility Location- Allocation Problems With Service Delivering Based on Genetic Algorithm.

Objective: This study assesses a multi-period capacitated maximal-covering location-allocation model for healthcare services, taking interservice referral as well as equity access into account. Methods: A two-stage optimization strategy is used to formulate the model. In the first stage, facilities are located to maximize covered demand, and in the second stage, patients are allocated to capacitated facilities based on their radius of coverage over multiple time periods. The problem, which belongs to the NP-hard class of optimization problems, is solved using a linear mixed-integer programming (MILP) model. Results: A numerical example is presented to evaluate the efficiency of the proposed model. In addition, to identify near-optimal solutions for large instances, a hybrid genetic-sequential quadratic programming approach (GA-SQP) is developed. To examine the performance and efficiency of the GA-SQP, we employed several randomly generated test instances of various sizes and compared them to those obtained using the exact method. Conclusion: The proposed model has demonstrated an excellent ability in locating healthcare facilities and allocating health services while taking shortage and equity into account during each time period.