Bi-level Optimization Strategy Research Articles

Low-carbon operation of smart distribution grid based on life cycle assessment and ladder-type carbon trading

A large number of EVs are commonly added to peak loads without dispatch in the smart distribution grid system, and the grid system usually suffers from excessive carbon emission problems. This paper proposes an integrated approach to control the smart distribution grid system by utilizing life cycle assessment and the market mechanism. First, the system’s carbon emissions are estimated according to life cycle assessment and carbon flow theory. Then, a bi-level optimization strategy for a smart distribution grid is presented. The upper-layer operation object is the minimum comprehensive operation cost of the smart distribution grid, which is solved using an optimization algorithm. The lower-level optimization goal is to minimize the operating cost of electric vehicles, which is solved using the CPLEX toolkit. Our simulation results demonstrate that overall operating costs have been reduced by 71.11%, while SDG’s overall carbon emissions have been reduced by 49 kg. The low-carbon growth of the smart distribution grid may be successfully promoted by appropriate trading market scheduling and efficient low-carbon dispatching.

Learning to disentangle and fuse for fine-grained multi-modality ship image retrieval

Multi-modality ship image retrieval aims to retrieve ship images from a large dataset, encompassing various modalities, when provided with a query ship image. One of the key challenges is addressing intra-modality variations and cross-modality discrepancies resulting from complex image content and different types of imaging systems. Current multi-modality retrieval methods primarily focus on extracting heterogeneous features from diverse modalities and mapping them into a shared feature space. However, these methods fail to determine the meaningfulness of the extracted features for retrieval tasks, as the features extracted across different modalities exhibit highly complex interactions. To overcome this limitation, we propose a novel framework, dubbed Disentangled Fusion Network (DFN), to decompose ship images into attribute and identity features, capturing modality-specific details and facilitating ship identification. This is achieved through an image disentanglement and fusion module, separating features across different modalities and converting the challenging multi-modality retrieval problem into a more manageable single-modality problem. To enable fine-grained retrieval, a region mining module identifies discriminative areas within ship images. The training process utilizes a bilevel optimization strategy to learn parameters, optimizing both image fusion and retrieval. Extensive experiments conducted on a publicly available multi-modality ship image dataset demonstrate the superior performance of the proposed DFN in image fusion and retrieval tasks.

Eco-environmental scheduling of multi-energy communities in local electricity and natural gas markets considering carbon taxes: A decentralized bi-level strategy

Multi-energy communities (MEC) integrated with renewable resources are known as a cost-effective and highly efficient solution to meet the diverse energy needs of subscribers. The increasing integration of MECs with electricity and natural gas networks has made it necessary to design new frameworks to optimize their energy management and then facilitate their participation in competitive energy markets. Hence, this article presents a bi-level optimization strategy for the decentralized coordination of MECs in competitive electricity and gas markets, in which the system operator adopts a robust technique to deal with operational uncertainties. The daily planning of MECs is performed in the upper level, while in the lower level, the planning of electricity and natural gas networks takes place. An adaptive alternating direction method of multipliers (ADMM) algorithm has also been introduced to settle the electricity and natural gas markets in a decentralized space while considering the CO2 footprint tax. The proposed strategy is implemented on a system containing a modified 69-bus IEEE distribution electricity network (EN) and a 65-node natural gas network (NGN). The results obtained from the case studies show that the proposed adaptive ADMM algorithm reached the optimal point in 113 iterations less than the original version, reducing the solution time by 48.01 %. The results prove that the proposed strategy has been able to coordinate the decentralized MECs with the least data sharing in the competitive electricity and gas markets. Additionally, it effectively utilizes the capabilities of renewable-based assets, storage systems, and smart EV charging to reduce the CO2 footprint, alleviate congestion, and improve the voltage and gas pressure profiles, while leading to reduced market clearing prices.

An Optimization Method of Flexible Manufacturing System Reliability Allocation Based on Two Dimension-Reduction Strategies

As increasingly extensive applications of flexible manufacturing systems (FMSs) arise, their reliability allocation has been a research hot spot. But, since FMSs are always composed of transfer and buffer devices, production machines, and complex control systems, the large number of basic elements makes the number of variables and constraints of reliability-allocation optimization increase greatly, which leads to the difficulty and inefficiency of optimization. To solve the above problem, two dimension-reduction strategies are proposed for the FMS reliability optimization with low cost and a high level of reliability as the objectives, and they are the reliability-weight double-threshold qualification strategy (RWTS) and the bi-level optimization strategy (BLOS), respectively. Based on these two strategies, an overall reliability-allocation optimization model and a bi-level reliability-allocation optimization model are established based on the FMS reliability evaluation presented in our previous work, and their algorithms based on particle swarm optimization (PSO) are presented. In terms of their contributions, for the RWTS, thresholds of reliability and the weight index of each basic element are set to dynamically reduce the number of variables in each iteration of the optimization; for the BLOS, the overall reliability-allocation optimization problem for transitioning from the FMS to basic elements can be transformed into simpler allocation optimizations from the FMS to subsystems and from subsystems to basic elements, which have fewer variables, and this can largely improve the optimization convergence performance. Through applying this to a box-parts finishing FMS, compared with the traditional optimization method, the high efficiency and the good allocation effect of the optimization based on these two strategies for improving convergence speed are verified by the simulation results. The proposed method has great significance for FMS design due to its limited cost but high-reliability requirement.

A Bi-level optimization strategy for electric vehicle retailers based on robust pricing and hybrid demand response

The high penetration of electric vehicles (EVs) poses both opportunities and challenges for power systems. EV retailers, playing a critical role in the demand response mechanism, face market risks caused by uncertainties in electricity consumption and prices. To address the operational issues of large-scale EVs and tap the potential of EV retailers, a temporal and spatial domain-based optimization strategy is proposed, which is implemented on bi-level (referring to transmission and distribution grid networks). First, a physical scheduling model of the grid is established, consisting of a novel hybrid demand response mechanism considering the incentives of EV retailers and the retail electricity price of EV users, and a new robust retail electricity pricing strategy handling the uncertainties of EV behavior and the electric market. Then, a bi-level optimization strategy is presented: at the upper level, in the transmission network, based on the robust pricing strategy, a unit commitment model that coordinates the hybrid demand response with other distributed energy resources is designed to optimize load periods of EVs in the time domain; at the lower level, in the distribution network, an optimal power flow model is proposed to spatially dispatch the location of EV loads. The impacts of retail price profile, EV penetration, hybrid demand response mechanism, and EV load location are analyzed in ten tests using the IEEE 33 distribution network. Simulation results indicate that the robust pricing strategy can effectively handle uncertainties, the integration of the hybrid demand response mechanism into scheduling can ensure the benefits of all participants, and the bi-level optimization strategy can accommodate distributed energy resources temporally and spatially.

Bi-Level Optimization Model for DERs Dispatch Based on an Improved Harmony Searching Algorithm in a Smart Grid

To satisfy the large-scale grid-connected demands of distributed energy resources (DERs), a bi-level optimization model is proposed for private DER dispatch managed by a virtual power plant (VPP) in a smart grid environment in this paper. The optimization models of the upper and lower layers serve as the planning layer and the operational layer, respectively, wherein the upper optimization model is mainly aimed at the optimization allocation of DERs under an unchanged network topology, and the lower-level optimization model is mainly responsible for the optimization of the distributed network topology from the optimization results of the upper layer. An improved harmony searching algorithm (HSA) is then applied to resolve the model through continuous iterations and communications between the upper and lower levels until an expected aim is achieved, which can satisfy the aim demand of the upper and the lower levels at the same time. Finally, six optimization scenarios are planned and selected in order to evaluate the performance of the bi-level optimization strategy in the IEEE33 bus distribution system and the 69-bus distribution system, and the optimized results show that the proposed method can effectively improve the grid-connected capacity of DERs and their system performance, and are more flexible in facing a growing ambient smart environment.

Mobile energy storage systems with spatial–temporal flexibility for post-disaster recovery of power distribution systems: A bilevel optimization approach

In recent years, the damage to power distribution systems caused by the frequent occurrence of extreme disasters in the world cannot be ignored. In the face of the customer’s demand for high power supply reliability and high power quality, it is urgent to establish a resilient distribution network that can not only resist extreme disasters and quickly recover the power distribution system loads, but also ensure a high voltage quality of the distribution system during recovery process. Therefore, mobile energy storage systems with adequate spatial–temporal flexibility are added, and work in coordination with resources in an active distribution network and repair teams to establish a bilevel optimization model. The objective of the upper-level optimization model is minimum the total load curtailment of the distribution system after the disaster. And the objective of the lower-level optimization model is minimum the voltage offset of power supply buses during the recovery stage. A modified IEEE 33-bus distribution test system is used to verify this model. The simulation results show that the bilevel optimization strategy proposed in this research can effectively reduce the voltage offset during the recovery process of distribution systems, and ensure the minimum total load curtailment simultaneously.

A triplet graph convolutional network with attention and similarity-driven dictionary learning for remote sensing image retrieval

With the explosion in the volume of collected high-resolution aerial image data, the development of effective image retrieval methods for remote sensing (RS) has become a popular area of research. The problem of content-based image retrieval (CBIR) for high-resolution remote sensing (HRRS) requires robust feature extraction and representation to extract high-level semantics followed by a similarity measurement method to compute the similarity between images based on these semantics. In this paper, we propose a novel sparse graph learning-based triplet network for deep metric learning-based HRRS CBIR. First, the graph representations of the aerial images are constructed via local feature descriptors and unsupervised segmentation that provide an efficient graph-structured representation of the images. Then, a novel attention graph convolutional network is developed to extract high-level semantics from the spatial patterns of the images’ segmented regions by aggregating region-node features. The attention mechanism and the pyramid pooling structure of the graph network help the proposed model extract powerful spatial features by preserving the structural information of the images while reducing the data’s dimensionality. Finally, a novel task-driven dictionary learning (TDDL) method based on triplet loss constructs a sparse metric space for the similarity measurement of the images in which the computed sparse codes for the images promote intra-class similarity between same-class images and inter-class dissimilarity between images of different classes. The proposed sparse features reduce the dimensionality of model parameters which mitigates overfitting and improves the generalization of the overall framework for deep metric learning. Our TDDL method adopts a bi-level optimization strategy so that the dictionary can be trained alongside the parameters of the graph representation network in an end-to-end fashion. Finally, we conduct extensive evaluations of the performance of our proposed architecture on real-world datasets compared to state-of-the-art models and obtain superior results.

Differentiable Hierarchical Optimal Transport for Robust Multi-View Learning.

Traditional multi-view learning methods often rely on two assumptions: ( i) the samples in different views are well-aligned, and ( ii) their representations obey the same distribution in a latent space. Unfortunately, these two assumptions may be questionable in practice, which limits the application of multi-view learning. In this work, we propose a differentiable hierarchical optimal transport (DHOT) method to mitigate the dependency of multi-view learning on these two assumptions. Given arbitrary two views of unaligned multi-view data, the DHOT method calculates the sliced Wasserstein distance between their latent distributions. Based on these sliced Wasserstein distances, the DHOT method further calculates the entropic optimal transport across different views and explicitly indicates the clustering structure of the views. Accordingly, the entropic optimal transport, together with the underlying sliced Wasserstein distances, leads to a hierarchical optimal transport distance defined for unaligned multi-view data, which works as the objective function of multi-view learning and leads to a bi-level optimization task. Moreover, our DHOT method treats the entropic optimal transport as a differentiable operator of model parameters. It considers the gradient of the entropic optimal transport in the backpropagation step and thus helps improve the descent direction for the model in the training phase. We demonstrate the superiority of our bi-level optimization strategy by comparing it to the traditional alternating optimization strategy. The DHOT method is applicable for both unsupervised and semi-supervised learning. Experimental results show that our DHOT method is at least comparable to state-of-the-art multi-view learning methods on both synthetic and real-world tasks, especially for challenging scenarios with unaligned multi-view data.

Multi-plant heat integration with shell-and-tube heat exchangers for multi-period operations

Multi-period heat exchanger network (HEN) can provide various system configurations for seasonal changes in demands, supplies, and different operation conditions of process streams. Current multi-period heat integration has mainly focused on the single-plant recovery, while a chemical industrial park usually consists of several plants that can be linked together through streams. In this study, multi-period HEN has been extended to a multi-plant scale to recover more waste heat. However, as the drawback of a multi-plant HEN, if an unplanned shutdown happens in one plant, other plants will be influenced due to the connected invalid heat exchangers and resort to extra utilities to reach target temperatures. To overcome this, a heat exchanger network with safety redundancy (HEN-SR) model is established for guaranteeing the continuous operation of remaining plants during an unplanned shutdown. Besides, to meet the industrial application, parameters of the real exchanger design are included, including temperature difference correction factor and the number of shell passes. The optimization results of two cases indicate that the mode switching of multi-period HEN-SR model can avoid huge economic losses caused by plant shutdowns, and the one-step synthesis method using a bi-level optimization strategy can find the HEN configuration with a lower total cost.

Not All Parameters Should Be Treated Equally: Deep Safe Semi-supervised Learning under Class Distribution Mismatch

Deep semi-supervised learning (SSL) aims to utilize a sizeable unlabeled set to train deep networks, thereby reducing the dependence on labeled instances. However, the unlabeled set often carries unseen classes that cause the deep SSL algorithm to lose generalization. Previous works focus on the data level that they attempt to remove unseen class data or assign lower weight to them but could not eliminate their adverse effects on the SSL algorithm. Rather than focusing on the data level, this paper turns attention to the model parameter level. We find that only partial parameters are essential for seen-class classification, termed safe parameters. In contrast, the other parameters tend to fit irrelevant data, termed harmful parameters. Driven by this insight, we propose Safe Parameter Learning (SPL) to discover safe parameters and make the harmful parameters inactive, such that we can mitigate the adverse effects caused by unseen-class data. Specifically, we firstly design an effective strategy to divide all parameters in the pre-trained SSL model into safe and harmful ones. Then, we introduce a bi-level optimization strategy to update the safe parameters and kill the harmful parameters. Extensive experiments show that SPL outperforms the state-of-the-art SSL methods on all the benchmarks by a large margin. Moreover, experiments demonstrate that SPL can be integrated into the most popular deep SSL networks and be easily extended to handle other cases of class distribution mismatch.

Optimization of a Hybrid Energy System with District Heating and Cooling Considering Off-Design Characteristics of Components, an Effort on Optimal Compressed Air Energy Storage Integration

In this work, the optimal design of a hybrid energy complex, including wind turbines, an internal combustion engine, and an adiabatic compressed air energy storage system is investigated. A novel bi-level optimization strategy is proposed for optimizing the capacity and operational power of each component of the system based on techno-economic considerations. The article presents information and discussions about the impacts of the partial-load operation of the energy storage system components on the optimal rated power and working strategies. The off-design characteristics are proven to have a huge negative impact on the efficiency and economy of the hybrid system. The efficiency reduction of the compressed air energy storage system is about 21% in summer and 8.9% in winter, when the system is operating in partial-load conditions. The operation cost of the system is reduced significantly when carrying out the proposed bi-level optimization strategy.

Multi-objective optimization of a renewable power supply system with underwater compressed air energy storage for seawater reverse osmosis under two different operation schemes

Water supply in rural islands or coastal areas is a basic task for people's livelihood. The all-pervading reverse osmosis (RO) technology is an energy-intensive process. To achieve sustainability goals, the development of renewable driven power supply system for RO plant is significant. Nowadays, the energy, economic and environmental indicators have rarely simultaneously investigated for the type of renewable power supply system with underwater compressed air energy storage (UW-CAES) for RO plant. In this paper, an energy-economic-environmental trade-off multi-objective optimization for such system is proposed in both grid-connected and off-grid schemes. A bi-level optimization strategy based on MOPSO algorithm and TOPSIS method is adopted to seek the optimal configuration and energy management strategy. A real-world case is implemented to demonstrate this method. The results show that the TPC/COE/EC set in optimal grid-connected scheme system is 3.716 × 106¥/0.814¥kWh−1/795.922 kg with a configuration of 511 PVs, 12 WTs and a 900 m3 bag volume in UW-CAES. Whereas, the TPC/COE/EC in optimal off-grid system is 4.076 × 106¥/2.305 kWh−1/566.254 kg with a 705/8/900 m3 configuration. In energy perspective, both schemes can match the load well. In economic perspective, the grid-connected scheme has a considerable profit, whereas the off-grid has no revenue. In environmental perspective, both schemes can reduce the carbon emission remarkably.

Bilevel energy optimization for grid-connected AC multimicrogrids

As a key component of an alternating current (AC) multimicrogrid (MMG), an energy management system must gather the necessary information and coordinate the corresponding equipment to optimize the economic benefits. To achieve this goal, this paper proposes a bilevel energy optimization model. The lower level model considers the real-time electricity price of distribution networks (DNs) to optimize the operation cost of each grid-connected submicrogrid (SMG). The upper level constructs an MMG optimization model based on graph theory, which optimizes the energy transmission path among the SMGs by considering the transmission losses. In this manner, the upper level model can further reduce the economic cost of an MMG by energy trading among the SMGs. To solve this model, a nested Jaya–Dijkstra algorithm is customized. Moreover, a Jaya algorithm with nonlinear variation capability (NVCJA) is developed to avoid the premature convergence problem and enhance the solution precision. The performance of the bilevel optimization strategy is evaluated considering a typical AC MMG system. For the proposed NVCJA, the convergence time is 24.07%, 39.47%, 37.76%, and 48.77% less, and the standard deviation is 12.97%, 28.71%, 23.89% and 35.92% lower than those for the Jaya, genetic algorithm (GA), particle swarm optimization (PSO), and artificial bee colony (ABC) algorithms, respectively. The analysis results show that the proposed optimization algorithm exhibits a high operating speed and stability. The economic cost of the proposed bilevel optimization model is 19% and 29% lower than those of the hierarchical optimization and linear relaxation optimization models, respectively. The test results show that the proposed optimization model can effectively enhance the economic benefits of an MMG.

Learning nonlocal regularization operators

<p style='text-indent:20px;'>A learning approach for determining which operator from a class of nonlocal operators is optimal for the regularization of an inverse problem is investigated. The considered class of nonlocal operators is motivated by the use of squared fractional order Sobolev seminorms as regularization operators. First fundamental results from the theory of regularization with local operators are extended to the nonlocal case. Then a framework based on a bilevel optimization strategy is developed which allows to choose nonlocal regularization operators from a given class which i) are optimal with respect to a suitable performance measure on a training set, and ii) enjoy particularly favorable properties. Results from numerical experiments are also provided.</p>

Research on Bi-Level Optimized Operation Strategy of Microgrid Cluster Based on IABC Algorithm

This paper considers the economy and reliability of the microgrid cluster system, and proposes a bi-level optimized operation strategy for the microgrid cluster, which aims to improve the economic benefits of the microgrid cluster and reduce the operating risk of microgrid. The upper layer takes the microgrid cluster as the research object, with the goal of minimizing the total operating cost of the system, and establishes the optimal model of the microgrid cluster. The lower layer takes the sub-microgrid as the research object, and establishes the microgrid optimization model with the goal of optimal operating cost and operating risk index. The method of combining mixed integer linear programming and IABC algorithm is used to solve the multi-objective bi-level optimization model, and to provide decision makers with two microgrid dispatching schemes with different focuses. Finally, an example is used to verify the effectiveness of the bi-level optimization strategy and improved algorithm proposed in this paper, as well as the practicability of the two dispatching schemes.

Time-Scale Economic Dispatch of Electricity-Heat Integrated System Based on Users’ Thermal Comfort

The electricity-heat integrated system can realize the cascade utilization of energy and the coordination and complementarity between multiple energy sources. In this paper, considering the thermal comfort of users, taking into account the difference in dynamic characteristics of electric and heating networks and the response of users’ demands, a dispatch model is constructed. In this model, taking into account the difference in the time scale of electric and thermal dispatching, optimization of the system can be improved by properly extending the thermal balance cycle of the combined heat and power (CHP) unit. Based on the time-of-use electricity prices and heat prices to obtain the optimal energy purchase cost, a user demand response strategy is adopted. Therefore, a minimum economic cost on the energy supply side and a minimum energy purchase cost on the demand side are considered as a bilevel optimization strategy for the operation of the system. Finally, using an IEEE 30 nodes power network and a 31 nodes heating network to form an electricity-heat integrated system, the simulation results show that the optimal thermal balance cycle can maximize the economic benefits on the premise of meeting the users’ thermal comfort and the demand response can effectively realize the wind curtailment and improve the system economy.

Bi-Level Optimal Strategy of Islanded Multi-Microgrid Systems Based on Optimal Power Flow and Consensus Algorithm

Aiming at problems of power allocation and economic scheduling for independent multi-microgrid systems, a bi-level optimization method based on optimal power flow and consensus algorithm is proposed. The novelty of the method is that an independent multi-microgrid system is divided into two layers: in the upper layer, with the predicted output range of the microgrids as the input data, each microgrid is considered as a virtual power supply or virtual load, and taking the minimum network loss as the goal, the energy mutual aid and power allocation among the microgrids are transformed into solving the optimal power flow; in the lower layer, taking the upper layer power distribution scheme as the constraint condition, considering load fluctuation and wind/solar generation uncertainty, the optimal dispatch model of the controllable distributed generator is established based on the distributed theory and the consensus algorithm of equal cost increment, and the "plug and play" of the distributed generator is also realized. An islanded multi-microgrid cluster is taken as an example to verify the economy, security, and reliability of the proposed scheme. The advantages of the scheme have been shown by the simulation example. Simulation results show that the upper-layer method not only realizes the optimal power allocation of microgrids, but also reduces the power loss of the energy mutual aid among the microgrids; through the optimal scheduling of controllable power supply in the microgrid, the lower-level scheme not only improves the economic benefit of the microgrid, but also well suppresses the negative effects of the uncertainties, prediction errors and power fault removal on the multi-microgrid system, which improves the robustness of the system.

A Bi-Level Optimization Approach to Charging Load Regulation of Electric Vehicle Fast Charging Stations Based on a Battery Energy Storage System

Fast charging stations enable the high-powered rapid recharging of electric vehicles. However, these stations also face challenges due to power fluctuations, high peak loads, and low load factors, affecting the reliable and economic operation of charging stations and distribution networks. This paper introduces a battery energy storage system (BESS) for charging load control, which is a more user-friendly approach and is more robust to perturbations. With the goals of peak-shaving, total electricity cost reduction, and minimization of variation in the state-of-charge (SOC) range, a BESS-based bi-level optimization strategy for the charging load regulation of fast charging stations is proposed in this paper. At the first level, a day-ahead optimization strategy generates the optimal planned load curve and the deviation band to be used as a reference for ensuring multiple control objectives through linear programming, and even for avoiding control failure caused by insufficient BESS energy. Based on this day-ahead optimal plan, at a second level, real-time rolling optimization converts the control process to a multistage decision-making problem. The predictive control-based real-time rolling optimization strategy in the proposed model was used to achieve the above control objectives and maintain battery life. Finally, through a horizontal comparison of two control approaches in each case study, and a longitudinal comparison of the control robustness against different degrees of load disturbances in three cases, the results indicated that the proposed control strategy was able to significantly improve the charging load characteristics, even with large disturbances. Meanwhile, the proposed approach ensures the least amount of variation in the range of battery SOC and reduces the total electricity cost, which will be of a considerable benefit to station operators.

Energy efficient cloud service pricing: A two-timescale optimization approach

This paper considers the scenario of a cloud service market where several Cloud Service Providers (CSP) are in operation and are competing against each other to attract and serve the demands generated by the customers. The competition arises from the fact that the customers (the individuals or organizations) who generate demand for services in the market rationally choose the CSP which offers good quality of services at a lower price. For pricing the services offered by the CSPs under this framework, we provide an analytical framework by considering the operational cost incurred by the CSP to service the given demand, the quality of service (QoS) offered and the prices other CSPs are charging. The pricing strategy we propose strikes a reasonable balance between charging too little which would result in irrationally low business profit and charging too much which would result in customer loss and thereby eventually loss of market share. In addition, the pricing strategy proposed promotes energy efficiency and renewable energy integration using a bi-level optimization strategy. The first level consisting of a Slow Timescale Optimization Procedure (STOP) addresses the economic efficiency related issues for cloud service pricing. The second level involving a Fast Timescale Optimization Procedure (FTOP) performs energy efficient job scheduling. We carry out numerical simulations to validate the proposed pricing strategy and compare it with an oracle benchmark policy, with fair profit sharing among the CSPs. We compare the proposed energy aware scheduling policy with a baseline scheduling policy. We demonstrate the efficiency and effectiveness of the proposed bi-level strategy and discuss the results.