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The configuration of user-side energy storage can effectively alleviate the timing mismatch between distributed photovoltaic output and load power demand, and use the industrial user electricity price mechanism to earn revenue from peak shaving and valley filling. The configuration of photovoltaic & energy storage capacity and the charging and discharging strategy of energy storage can affect the economic benefits of users. This paper considers the annual comprehensive cost of the user to install the photovoltaic energy storage system and the user’s daily electricity bill to establish a bi-level optimization model. The outer model optimizes the photovoltaic & energy storage capacity, and the inner model optimizes the operation strategy of the energy storage. And calculate the actual life of the energy storage through the rain flow counting method. Use the fmincon function in the optimization toolbox to solve the problem on the matlab platform. The result of the calculation example verifies the improvement effect of the bi-level optimization model proposed in this paper on user economy.

In recent years, microgrid (MG) deployment has significantly increased, utilizing various technologies. MGs are essential for integrating distributed generation into electric power systems. These systems’ economic dispatch (ED) aims to minimize generation costs within a specific time interval while meeting power generation constraints. By employing ED in electric MGs, the utilization of distributed energy resources becomes more flexible, enhancing energy system efficiency. Additionally, it enables the anticipation and proper utilization of operational limitations and encourages the active involvement of prosumers in the electricity market. However, implementing controllers and algorithms for optimizing ED requires the independent handling of constraints. Numerous algorithms and solutions have been proposed for the ED of MGs. These contributions suggest utilizing techniques such as particle swarm optimization (PSO), mixed-integer linear programming (MILP), CPLEX, and MATLAB. This paper presents an investigation of the use of model predictive control (MPC) as an optimal management tool for MGs. MPC has proven effective in ED by allowing the prediction of environmental or dynamic models within the system. This study aims to review MGs’ management strategies, specifically focusing on MPC techniques. It analyzes how MPC has been applied to optimize ED while considering MGs’ unique characteristics and requirements. This review aims to enhance the understanding of MPC’s role in efficient MG management, guiding future research and applications in this field.

This paper addresses a supply chain situation, in which a company distributes commodities over a selected subset of customers while a manufacturer produces the commodities demanded by the customers. The distributor company has two objectives: the maximization of the profit gained by the distribution process and the minimization of CO 2 emissions. The latter is important due to the regulations imposed by the government. A compromise between both objectives exists, since profit maximization only will attempt to include as many customers as possible. But, longer routes will be needed, causing more CO 2 emissions. The manufacturer aims to minimize its manufacturing and shipping costs. Since a predefined hierarchy between both companies exists in the supply chain, a bi-level programming approach is employed. This problem is modelled as a bi-level programming problem with two objectives in the upper level and a single objective in the lower level. The upper level is associated with the distributor, while the lower level is associated with the manufacturer. Due to the inherent complexity to optimally solve this problem, a heuristic scheme is proposed. A nested bi-objective tabu search algorithm is designed to obtain non-dominated bi-level feasible solutions regarding the upper level. Considering simultaneously both objectives of the distributor allow us to focus on the minimization of CO 2 emissions caused by the supply chain, but bearing in mind the distributor's profit. Numerical experimentation shows that the Pareto frontiers obtained by the proposed algorithm provide good alternatives for the decision-making process and also, some managerial insights are given. [ABSTRACT FROM AUTHOR]

The regulation of the grid voltage within operational limits becomes increasingly challenging as residential photovoltaic (PV) adoption rises. Therefore, this study proposes a method for the efficient planning of multiple community battery energy storage systems (BESS) in low voltage distribution systems embedded with high residential rooftop PV units. A bi-level optimization method based on a Neural Network Optimization Algorithm is developed to regulate the voltage in grid-connected solar PV. Since BESS characteristics are crucial for the reliable operation of the distribution networks, the objective of the bi-level optimization problem is to optimally place and operate BESS collectively at a distributed system level. The charging/discharging protocol of the batteries management system is obtained utilizing linear programming that minimizes the daily voltage signal. Simulations were carried out on a modified IEEE low voltage test feeder to examine the impact of PV integration and BESS installation on the voltage profile. Experimental results show the efficacy of the proposed method in enabling the utility to determine the optimal location, capacity, and number of BESS in the distribution system to keep the network voltage magnitude within acceptable bounds. In addition, results demonstrate that the network topology, load profiles, and amount of PV power highly influence the BESS characteristics. [ABSTRACT FROM AUTHOR]

Optimal Volt/VAR control (VVC) in distribution networks relies on an effective coordination between the conventional utility-owned mechanical devices and the smart residential photovoltaic (PV) inverters. Typically, a central controller carries out a periodic optimization and sends setpoints to the local controller of each device. However, instead of tracking centrally dispatched setpoints, smart PV inverters can cooperate on a much faster timescale to reach optimality within a PV inverter group. To accommodate such PV inverter groups in the VVC architecture, this paper proposes a bi-level optimization framework. The upper-level determines the setpoints of the mechanical devices to minimize the network active power losses, while the lower-level represents the coordinated actions that the inverters take for their own objectives. The interactions between these two levels are captured in the bi-level optimization, which is solved using the Karush-Kuhn-Tucker (KKT) conditions. This framework fully exploits the capabilities of the different types of voltage regulation devices and enables them to cooperatively optimize their goals. Case studies on typical distribution networks with field-recorded data demonstrate the effectiveness and advantages of the proposed approach. [ABSTRACT FROM AUTHOR]

Over the last decade, deep neural networks have shown great success in the fields of machine learning and computer vision. Currently, the CNN (convolutional neural network) is one of the most successful networks, having been applied in a wide variety of application domains, including pattern recognition, medical diagnosis and signal processing. Despite CNNs' impressive performance, their architectural design remains a significant challenge for researchers and practitioners. The problem of selecting hyperparameters is extremely important for these networks. The reason for this is that the search space grows exponentially in size as the number of layers increases. In fact, all existing classical and evolutionary pruning methods take as input an already pre-trained or designed architecture. None of them take pruning into account during the design process. However, to evaluate the quality and possible compactness of any generated architecture, filter pruning should be applied before the communication with the data set to compute the classification error. For instance, a medium-quality architecture in terms of classification could become a very light and accurate architecture after pruning, and vice versa. Many cases are possible, and the number of possibilities is huge. This motivated us to frame the whole process as a bi-level optimization problem where: (1) architecture generation is done at the upper level (with minimum NB and NNB) while (2) its filter pruning optimization is done at the lower level. Motivated by evolutionary algorithms' (EAs) success in bi-level optimization, we use the newly suggested co-evolutionary migration-based algorithm (CEMBA) as a search engine in this research to address our bi-level architectural optimization problem. The performance of our suggested technique, called Bi-CNN-D-C (Bi-level convolution neural network design and compression), is evaluated using the widely used benchmark data sets for image classification, called CIFAR-10, CIFAR-100 and ImageNet. Our proposed approach is validated by means of a set of comparative experiments with respect to relevant state-of-the-art architectures. [ABSTRACT FROM AUTHOR]

Currently, most Graph Structure Learning (GSL) methods, as a means of learning graph structure, improve the robustness of GNN merely from a local view by considering the local information related to each edge and indiscriminately applying the mechanism across edges, which may suffer from the local structure heterogeneity of the graph (i.e., the uneven distribution of inter-class connections over nodes). To overcome the drawbacks, we extract the graph structure as a learnable parameter and jointly learn the structure and common parameters of GNN from the global view. Excitingly, the common parameters contain the global information for nodes features mapping, which is also crucial for structure optimization (i.e., optimizing the structure relies on global mapping information). Mathematically, we apply a generic structure extractor to abstract the graph structure and transform GNNs in the form of learning structure and common parameters. Then, we model the learning process as a novel bi-level optimization, i.e., Generic Structure Extraction with Bi-level Optimization for Graph Structure Learning (GSEBO), which optimizes GNN parameters in the upper level to obtain the global mapping information and graph structure is optimized in the lower level with the global information learned from the upper level. We instantiate the proposed GSEBO on classical GNNs and compare it with the state-of-the-art GSL methods. Extensive experiments validate the effectiveness of the proposed GSEBO on four real-world datasets. [ABSTRACT FROM AUTHOR]

The existing electricity market mechanisms designed to promote the consumption of renewable energy generation complicate network participation in market transactions owing to an unfair market competition environment, where the low cost renewable energy generation is not reflected in the high bidding price of high cost conventional energy generation. This study addresses this issue by proposing a bi-level optimization based two-stage market clearing model that considers the bidding strategies of market players, and guarantees the accommodation of renewable energy generation. The first stage implements a dual-market clearing mechanism that includes a unified market for trading the power generations of both renewable energy and conventional energy units, and a subsidy market reserved exclusively for conventional generation units. A re-adjustment clearing mechanism is then proposed in the second stage to accommodate the power generation of remaining renewable energy units after first stage energy allocations. Each stage of the proposed model is further described as a bi-level market equilibrium problem and is solved using a co-evolutionary algorithm. Finally, numerical results involving an improved IEEE 39-bus system demonstrate that the proposed two-stage model meets the basic requirements of incentive compatibility and individual rationality. It can facilitate the rational allocation of resources, promote the economical operation of electric power grids, and enhance social welfare. [ABSTRACT FROM AUTHOR]

Semi-infinite programming can be used to model a large variety of complex optimization problems. The simple description of such problems comes at a price: semi-infinite problems are often harder to solve than finite nonlinear problems. In this paper, we combine a classical adaptive discretization method developed by Blankenship and Falk [Infinitely constrained optimization problems. J Opt Theory Appl. 1976;19(2):261–281. https://doi.org/10.1007/BF00934096] and techniques regarding a semi-infinite optimization problem as a bi-level optimization problem. We develop a new adaptive discretization method which combines the advantages of both techniques and exhibits a quadratic rate of convergence. We further show that a limit of the iterates is a stationary point, if the iterates are stationary points of the approximate problems. [ABSTRACT FROM AUTHOR]

Ensemble learning encompasses methods that generate many well-diversified predictors and aggregates their results to perform a better prediction. These predictors are usually weak and low-cost for obtaining when they are alone. However, they reveal excellent performance when they are skillfully used together in the form of a learning architecture. Metaheuristic methods have been used to form such architecture optimally during recent years. Along this stream, in this paper, a bi-level optimization based on discrete-continuous genetic algorithm is utilized to enhance the performance of an ensemble learning metaalgorithm which benefits decision tree classification. Feature selection and tree model constructing for any ensemble member are done by the metaheuristic method. It allows us to have advantages of tree-based prediction models, ensemble learning, and solution optimality simultaneously. The proposed system is compared to some well-known ensemble learning methods. Results show significant superiority of the proposed system in terms of prediction accuracy. [ABSTRACT FROM AUTHOR]

As the increasing penetration of sustainable energy brings risks and opportunities for energy system reliability, at the same time, considering the multi-dimensional differentiation of users' reliability demands can further explore the potential value of reliability resources in Integrated Energy Microgrid (IEM). To activate the reliability resources in a market-oriented perspective and flexibly optimize the operational reservation in dispatch, an optimal dispatching model in IEM considering reliability principal–agent contracts is proposed. We establish the reliability principal–agent mechanism and propose a cooperative gaming model of Integrated Energy Operator (IEO) and Integrated Energy User (IEU) based on the optimal dispatching model. At the upper level, the economic dispatching model of IEO is established to optimize the operation reservation, and the reliability principal–agent contract from users in the lower level would influence reliability improvement. Each IEU in the lower level maximizes its energy utilization and gives the corresponding reliability principal–agent incentives according to the reliability improvement degree and its actual demand. The bi-level model is solved by the KKT condition and strong duality theorem. A case study verifies the effectiveness of the proposed model in reducing the energy dispatch cost, improving the economic benefits of each participant, realizing the optimal allocation of reliability resources and optimizing the IEM energy structure, and the sensitivity analysis of dispatch cost with the user's energy-using benefits is discussed. [ABSTRACT FROM AUTHOR]

Extensive studies have revealed that smart grid is vulnerable to cyber-physical attacks. However, these strategies only focus on the cascading initiation phase to induce single-stage failures with multiple branch tripping, lacking of exploring the attack effectiveness in the propagation phase so that the deeply-hidden cascading failures are underestimated. In this paper, we propose a novel false load injection attack strategy that can intentionally penetrate into the cascading propagation phase to drive multi-stage dynamical failures with a cascading process. Specifically, we formulate a bi-level optimization problem to model the adversarial game between operator and attacker. The former is in charge of security-constrained economic dispatching to minimize the generation cost, and the latter aims to maximize the cumulative number of tripped branches. Further, we reformulate this NP-hard bi-level problem as a mixed integer linear program for tractable computation. Finally, we perform numerical simulations on different-scale IEEE test systems to validate our strategy in driving the dynamical failures. [ABSTRACT FROM AUTHOR]

Due to the significant motion of wind turbines (WTs) during operation, the coupling of wake effect in floating offshore wind farm (FOWF) is intensified, making the optimization problem combining layout and operation challenging. To address this issue, a bi-level multi-objective intelligent optimization framework for FOWF is proposed. Based on the interaction among operation control, force-induced motion and wake effect, an efficient repositioning model that considers the aerodynamic effect on moveable WT is established. On this basis, a generalized wake control method called "Wake Escape" is defined, taking into account the relationship between optimization variables and objectives in layout design and operation control. To solve the bi-level multi-objective optimization problem of FOWF, FOWFBi-Mopt platform is constructed, on which multi-objective particle swarm optimization and equilibrium optimizer are developed. Additionally, the key parameters and dimensional characteristics are integrated between the layout and operation, facilitating the coordination process of optimization objectives by associating the inner and outer-level algorithms. The simulation results demonstrate that the proposed bi-level optimization framework effectively mitigates the adverse effect of moveable WTs from both layout and operation. Diverse solutions are obtained from Pareto front, achieving comprehensive optimization of FOWF, with the maximum reduction of 1.183 % in the levelized production cost. • Focusing on the FOWF with moveable wind turbines from both control and layout • A generalized wake control method named "Wake Escape" based on mobility • The bi-level multi-objective optimization definition and framework for FOWF • Platform FOWFBi-Mopt that achieves wake escape by coordinated optimization. • Exploring and mitigating the adverse wake effect of mobility in FOWF. [ABSTRACT FROM AUTHOR]

To improve the utilization of flexible resources in microgrids and meet the energy storage requirements of the microgrids in different scenarios, a centralized shared energy storage capacity optimization configuration model for microgrids based on bi-level optimization is proposed. First, the response characteristics of the shared energy storage and controllable load in the resilience microgrid are analyzed, and the centralized shared energy storage operation mode meeting the regulatory demand of multi-scenarios is designed. Then, a bi-level optimal allocation model is constructed, which takes the maximum net income of centralized shared energy storage as the upper layer and the minimum payment cost of load in the microgrid as the lower layer. Furthermore, the multi-objective whale optimization algorithm is used to solve the bi-level optimization model. The results show that the shared energy storage can jointly meet the regulation demand of multi-scenarios by coordinating the transferable load and cuttable load in the microgrid and improving the utilization rate of shared energy storage.

In an attempt to achieve net zero, the operation and planning of the energy system face techno-economic challenges brought by integrating large-scale distributed energy resources (DERs) with low carbon footprints. Previous work has analyzed the technical challenges including hosting capacity (HC) for DERs. In light of the deregulation of the power industry and the transition to power system with renewables at its center, this article takes the lead to maximizing renewable integration in power grids from a market viewpoint. It solves a significant problem brought forth by the fall in electricity prices, resulting from increasing renewable penetration that jeopardizes investment cost recovery and prevents sustainable grid integration of renewables. To this end, a novel bi-level optimization model is formulated, where the upper-level problem aims to maximize the HC of renewables ensuring the recovery of investment, and the lower-level problem describes the market clearing process considering network constraints. The optimal solution of devised bi-level problem can be found after reformulating it to a single-level mixed-integer linear problem (MILP) using the strong duality theorem and a special ordered set-type 1 (SOS1) founded linearization approach. Case studies confirm the significance of the devised model and quantitatively analyze the impact of different network capacities, renewable subsidies, and energy storage, respectively, on the market-based HC obeying its profitability constraint.

In response to increasing environmental deterioration, the vigorous development of the integrated energy system is an important measure to achieve the goal of carbon neutrality. In order to ensure that the system takes into account the economic operation under the premise of low carbon and environmental protection, this paper proposes a bi-level optimal low-carbon economic operation model for the regional integrated energy system (RIES). At the upper level, the objective of the RIES is economic optimization, which contains the carbon emission cost so that the system would change its preference for high-carbon energy to limit the carbon emission of the system. At the lower level, an electricity and natural gas pricing model is established, and a carbon emission flow (CEF) model is used to calculate the price of carbon emissions. This proposed bi-level optimization model is converted to a single-level mathematical problem with KKT (Karush–Kuhn–Tucker) conditions for efficient calculation. The proposed optimal model is tested on the five-bus power system and seven-node natural gas system, and numerical results indicate the optimal operating model with this proposed carbon pricing method can effectively reduce carbon emissions and minimize the total operating cost of RIES.

Hub-and-spoke (HS) networks are cost-effective because they allow the realization of economies of density. However, the cost of point-to-point (PP) networks may be lower than that of HS networks when certain conditions, such as cargo demand, bunker price, vessel size, and the shippers’ value of time change. This study explores the factors that influence the cost-effectiveness of HS and PP networks. We developed a mixed-integer programming model that allows for bi-level optimization between shipping lines and shippers. As a case study, we applied it to Chinese and Japanese ports, with both HS and PP networks. We found that high cargo demand increases the use of PP networks while enlarging vessel size increases the use of HS networks. These findings enable us to predict the occurrence of hubbing—shifting from a PP to an HS network—and de-hubbing—shifting from an HS to a PP network.

The energy crisis and environmental concerns have accelerated the development of the active distribution network (ADN) with a high proportion of renewable energy, which poses a challenge to the operation of the power system. Moreover, using active management means to promote the consumption of renewable energy is an important task of ADN. Therefore, as an important operation means, the network reconfiguration is used to enhance the adjustable capacity of the power system at the planning stage. Firstly, a “wind–light–load” uncertain scenario set is constructed to address the uncertainty of wind speed, lighting, and load. On this basis, a robust optimization model for distributed power generation taking into account network reconstruction and in ADN is proposed. In addition, the distributed generator (DG) permeability indicator is introduced in the planning model to improve the ADN ability of absorbing renewable energy. A linearized AC power flow model is utilized to calculate the power flow. Finally, via simulation in an IEEE 33-bus system and IEEE 69-bus system, the influence of network reconfiguration and robustness on distributed generator planning, economy and reliability of ADN is analyzed, and the validity of the model is verified.

Investing in wind energy is a tool to reduce greenhouse gas emissions without negatively impacting the environment to accelerate progress towards global net zero. The objective of this study is to present a methodology for efficiently solving the wind energy investment problem, which aims to identify an optimal wind farm placement and capacity based on fractional programming (FP). This study adopts a bi-level approach whereby a private price-taker investor seeks to maximize its profit at the upper level. Given the optimal placement and capacity of the wind farm, the lower level aims to optimize a fractional objective function defined as the ratio of total generation cost to total wind power output. To solve this problem, the Charnes-Cooper transformation is applied to reformulate the initial bi-level problem with a fractional objective function in the lower-level problem as a bi-level problem with a fractional objective function in the upper-level problem. Afterward, using the primal-dual formulation, a single-level linear FP model is created, which can be solved via a sequence of mixed-integer linear programming (MILP). The presented technique is implemented on the IEEE 118-bus power system, where the results show the model can achieve the best performance in terms of wind power output.

State Estimation (SE) plays a critical role in various applications of power systems including the electricity market. False Data Injection Attacks (FDIAs) are capable of manipulating the power system SE process aiming to gain financial profits by the players. In this paper, the potential economic influences of FDIA on SE and consequently the Real-Time (RT) electricity market are examined. Therefore, a new bi-level optimization framework is proposed to realistically model the FDIAs from the attacker perspective. At the upper-level, the attacker intends to intelligently choose the most critical congested transmission lines and manipulate their associated meter readings to maximize the expected financial profitability. At the lower-level, the RT market-clearing model is formulated under the influence of FDIA. Considering the incomplete attacker's prior knowledge of the network topology i.e., connection/disconnection of transmission lines, the angles of the phase-shifting transformers, and the real-time load uncertainty, the proposed formulation is extended to a new bi-level scenario-driven stochastic model. The developed attack model, which must remain undetectable by the system operator in all scenarios, is solved using the Karush–Kuhn–Tucker (KKT) approach. The correctness and effectiveness of the proposed optimization scheme have been validated in GAMS software using CONOPT and OQNLP solvers based on the IEEE 14-bus test system and also comparative results are presented to demonstrate the merits of the proposed formulation. [ABSTRACT FROM AUTHOR]

Optimal energy management in multi-area smart grids could increase social welfare and reduce economic costs and environmental pollution. This study presents a mixed-integer quadratic programming model for optimal energy management in multi-area microgrids to reduce economic and environmental costs and increase social welfare considering energy storage systems, Demand-Side Management (DSM), and renewable resources. Due to damage of peak load and consumption to power grids, a codified and long-term program should be designed to divide the peak load during the hours of the day and reduce its impacts on power grids. This study presents a bi-level approach to solving the proposed model. Thus, minimizing economic costs and pollution is formulated as a high-level problem, and maximizing social welfare is formulated as a low-level problem. Participation of responsive loads could reduce this connection and improve voltage profile and losses. Given that participation in responsive loads is accompanied by financial incentives, they should be proportional to the improvement of the defined indicators. In this paper, the cost of participating in the project is considered in modeling. After defining the proposed model, the problem space is searched using the Modified Gray Wolf Optimization (MGWO) algorithm and, finally, the optimal solution is obtained. Simulation is performed by Gurobi solver in MATLAB environment. The proposed bi-level optimization method outperforms alternative approaches by achieving a reduction of approximately 10% in operation time, completing the task in just 21 seconds compared to 95 seconds and 250 seconds for Pareto optimization and weighting factor methods, respectively. Additionally, the final objective function value of $164,252 demonstrates a decrease of 23% compared to the values obtained through other algorithms, indicating significant cost savings and efficiency gains. [Display omitted] [ABSTRACT FROM AUTHOR]

Hybrid renewable energy systems (HRES) comprise a group of different energy sources and storage units that feed a specific load, efficiently. This research paper aims to develop a new methodology that provides the optimal size of the proposed HRES and runs it efficiently. Bi-level mixed-integer nonlinear programming (BMINLP) optimization approach is used to combine the sizing task and the energy management strategy (EMS) established utilizing the economic model predictive control (EMPC) method. The sizing task (upper layer) is formulated as mixed integer nonlinear programming (MINLP) optimization that has been implemented by the solver: multi-objective genetic algorithm (MOGA). EMS task (lower layer) is represented as a constraint embedded within the upper layer and executed as mixed integer linear programming (MILP) per each applied solution of the sizing task. The principal findings indicate that the total cost of the system is about 114,224 $. In detail, the annual fixed operation and maintenance, investment, and operating costs are 15,090 $, 28,351 $, and 70,783 $, correspondingly. Furthermore, around 90 % of the overall produced power is imported from the grid, while the load power represents about 95 % of the total demanded power. [Display omitted] • HRES with PV-Wind and different types of energy storage systems. • Optimal size and efficient performance of HRES. • Bi-level mixed-integer nonlinear programming optimization technique. • Real application of a grid-connected HRES in a real case study in Irbid, Jordan. [ABSTRACT FROM AUTHOR]

This paper provides insights for cyber defenders of power systems with high penetration of electric vehicles (EVs) by proposing a novel consecutive attack model based on load redistribution for price control in both transmission networks (TNs) and distribution networks (DNs). The target of the attack is to induce massive EV users in DNs to charge simultaneously and cause a spike of loads in the TN at peak hours. The problem is formulated as a multi-slot bi-level optimization problem, where the upper level describes the hacker behavior and attacking constraints. The lower level explains the TN operator and DN operators' behaviors and the relationship between the local marginal price and retail charging price. The bi-level problem is converted into an equivalent single-level mix-integer linear problem and is solved based on greedy algorithm. Simulations on IEEE 30-bus system prove the effectiveness of the attack strategy. • The local marginal price and electric vehicle charging price are introduced into the load redistribution model. • Hackers trigger a load spike of EVs in peak hours by load redistribution attacks. • The multi-slot bi-level optimization problem is reduced to a mix-integer linear problem. • The instant attack and consecutive attack are carried out in the IEEE 30-bus test system. [ABSTRACT FROM AUTHOR]

This paper aims to address the bidding strategy optimization in the real-time multi-participant electricity market with short-term load dynamics. In order to avoid the sub-optimal solution and the dependence on the complete information in traditional mathematical programming methods, an electricity market bidding strategy optimization algorithm based on deep reinforcement learning (DRL) is developed. While conventional reinforcement learning algorithms (e.g., Q-learning and deep Q-learning) are only capable of handling simple problems in discrete state spaces, the proximal policy optimization (PPO) algorithm is implemented in the bidding strategy optimization since it can optimize the bidding strategy in the continuous action and state spaces. In order to substantiate the aforementioned perspective, this paper conducts a two-part experimental study. First, experiments which consider the fixed demand load of market participants show that the developed method can reach the Nash equilibrium just like the bi-level optimization, and higher profits can be achieved by adjusting hyperparameters. Then, complex experiments which consider the time-varying demand load verify the DRL-based electricity market bidding strategy performs better than bi-level optimization-based methods and increases the profits of generators. • A PPO-EMBSA is proposed to overcome the limitations of the MPEC-based in two distinct aspects. First, PPOEMBSA does not need to transform the lower-level problem of the bi-level programming to the corresponding KKT condition. Second, agents select appropriate strategies by PPO-EMBSA in an environment with incomplete information and optimizes the present strategy for future rewards. • The PPO-EMBSA improves the accuracy and the stability of RL-based-electricity market bidding strategy. • Experiment results show that the PPO-EMBSA derives appropriate bidding strategies in situations of both fixed demand load and time-varying load, and the proposed method is more competitive than bidding algorithms based on Q-learning, DQN and A3C. In particular, additional ablation studies discuss the sensitivity of PPO-EMBSA to some hyper-parameters. [ABSTRACT FROM AUTHOR]

This study addresses the bi-level multi-objective optimization problems (MOP) that raise in robust design and optimization of engineering systems through establishing a state-of-the-art game theoretic scenario. A novel leader-follower decentralized decision-making scenario is proposed, leveraging the synergy of game theory, Robust Design Optimization (RDO), Monte Carlo Simulation (MCS), and Artificial Intelligence (AI). The proposed algorithm can be employed for optimum robust Pareto design of a wide range of dynamical systems. In order to achieve a robust design, both the mean and variance of each objective function are considered as players in a multi-agent game setting. In this approach, both Stackelberg and cooperative games are utilized to model the behaviors of the players. Genetic Programming (GP) meta-models are employed to capture the Stackelberg protocol between two levels specifically for constructing the follower's rational reaction set (RRS). Additionally, the Nash bargaining function is -utilize to model the cooperative behaviors among players in each level. The proposed approach is applied and demonstrated through a case study involving multi-objective robust design of planar four-bar linkages. In this manner, four objective functions are assigned to four players within the system. Each player is responsible for optimizing a specific objective criterion, namely the mean of tracking error (TE), variance of tracking error, mean of transmission angle and variance of transmission angle (TA) of the linkage. As a result, the four-objective optimization problem of mechanism is transformed into a single-objective robust synthesis problem. The comparisons of the results show a significant enhancement in the robust behavior of the linkage, while ensuring that deterministic criteria such as quality of motion and precision are preserved. [ABSTRACT FROM AUTHOR]

A co-evolutionary traffic signal control using reinforcement learning approach (CORLA) is proposed for time-varying road networks under stochastic capacity. Classic reinforcement learning based traffic signal control cannot effectively reduce traffic congestion for large-scale road networks while standard evolutionary metaheuristics often suffer from significantly high computational cost. A co-evolutionary decomposition algorithm (CODA) is proposed to improve traffic mobility for urban road networks with time-varying traffic flow. To capture time-varying spatial evolution of traffic flow inside road links, a stochastic traffic model is presented. To fully consider road users' response, a stochastic bi-level optimization problem (SBOP) is given where road users' route choice can be fully taken into account. To efficiently implement CORLA in a large-scale road network against high-consequence realization for stochastic capacity, a coordinated co-evolutionary two phase control (CCTPC) is proposed. Numerical experiments are performed at a real-data city road network and various sizable traffic grids. As compared to state-of-the-art traffic signal control for various traffic conditions, obtained results showed that CCTPC exhibits sufficient gain of achieving road network performance and suffers from the least computational cost in all cases. • A co-evolutionary reinforcement learning-based traffic signal control (CORLA) is presented. • A novel Q-learning based Performance Index (QPI) is presented. • A stochastic bilevel optimization problem (SBOP) is proposed to minimize total travel cost. • A scalable coordinated co-evolutionary two phase control (CCTPC) is presented to reduce computational complexity. [ABSTRACT FROM AUTHOR]

• A bi-level market-clearing mechanism to minimize the WPS is proposed. • Considering the impact of uncertainty in WPG and load demand. • Determining the optimal participation of DR in overall objectives. • The upper level is to minimize the WPS, LS, PLs, and CO 2 emissions. • The lower level is to maximize social welfare. • Studying the impact of the integration between the DR and the DTLR. Spilling has already occurred as a result of rising the penetration of intermittent renewable generation, and it is anticipated that the level of renewable energy curtailment will continue to soar. This leads to an increase in operating costs, CO 2 emissions, and not good utilization of renewable energy resources. A bi-level multi-objective optimization model is proposed in this paper to reduce wind power spillage (WPS) based on demand response (DR) and dynamic thermal line rating (DTLR). In the upper level, multiple objectives will be satisfied based on the optimal allocation and time of DR programs considering DTLR obtained in the lower level. The minimization of WPS, load shedding, power losses, and CO 2 emissions are the objectives of this level. While the lower-level aims to maximize social welfare under different scenarios and overall system constraints. Under the uncertainty of the wind power and load demand, a collection of lower-level problems that represent the market clearing conditions is used to constrain the upper-level. The effectiveness of the proposed algorithm is examined on a modified two-area IEEE 24-bus test system. Results depict that the suggested bi-level model enables considerable reductions in the WPS by up to 32.7 %. Also, there is an enhancement in load shedding, power losses, and CO 2 emissions by 28.93 %, 23.07 %, and 13.9 % respectively. Finally, the social welfare increased by up to 36.6 %. [ABSTRACT FROM AUTHOR]

Buildings are typically integrated with multiple distributed energy resources (DERs), enabling them to act as building prosumers engaged in both energy production and consumption. Peer-to-peer (P2P) energy trading among building prosumers is crucial to improve their benefits. However, further exploration is required to balance the benefits between building prosumers and the system operator (e.g., the integrated community energy system (ICES) operator) since they are different entities. In this context, this paper proposes a comprehensive network charge and energy sale pricing scheme for the ICES operator on heterogeneous building prosumers with P2P multi-energy trading. The interaction between the ICES operator and building prosumers is modelled as a bi-level optimization problem that belongs to the hierarchical structure, while considering the heterogeneity of thermal insulation performance of buildings. At the upper level, the ICES operator optimizes the electricity/heat network charge prices and electricity/heat sale prices to maximize its revenue. At the lower level, building prosumers with a parallel structure optimize the schedules including P2P multi-energy trading and buildings' heating loads to minimize their costs. Furthermore, to address the bi-level optimization problem with parallel and hierarchical coupling structures, an accelerated asynchronous distributed algorithm based on alternating direction method of multipliers (ADMM) is developed, integrating a warm start strategy and a dual update accelerated iteration strategy for further improving computational efficiency. Finally, case studies demonstrate that the proposed scheme can effectively benefit both the ICES operator and building prosumers in P2P multi-energy trading at the same time. Meanwhile, the feasibility and effectiveness of the proposed algorithm are validated. • An optimal pricing scheme for ICES operator on building prosumers is proposed. • A bi-level optimization is proposed for ICES operator and prosumers with P2P. • An accelerated asynchronous distributed algorithm based on ADMM is developed. • Benefits of ICES operator and prosumers through several scenarios are analyzed. [ABSTRACT FROM AUTHOR]

In the power sector, competitive strategic bidding optimization has become a major challenge. Digital plate-form provides a superior technical base as well as backing for the optimization's execution. The state-of-the-art frameworks used for simulating strategic bidding decisions in deregulated electricity markets (EM's) in this article are bi-level optimization and neural networks. In this research, we provide HHO-NN (Harris Hawk Optimization-Neural network), a novel algorithm based on Harris Hawk Optimization (HHO) that is capable of fast convergence when compared to previous evolutionary algorithms for automatically searching for meaningful multilayered perceptron neural networks (MPNNs) topologies for optimal bidding. This technique usually demands a considerable amount of time and computer resources. This method sets up the problem in multi-dimensional continuous state-action spaces, allowing market players to get precise information on the effect of their bidding judgments on the market clearing results, as well as implement more valuable bidding decisions by utilizing a whole action domain and accounting for non-convex operating principles. Due to the use of the MPNN, case studies show that the suggested methodology delivers a much larger profit than other state-of-the-art methods and has a better computational performance than the benchmark HHO technique. [ABSTRACT FROM AUTHOR]

With the rapid development of social economy, energy consumption has continued to grow, and the problem of pollutant emissions in various energy sources has gradually become the focus of social attention. Cities account for two-thirds of global primary energy demand that make urban energy systems a center of sustainable transitions. This paper builds a bi-level planning model for steady-state optimal configuration to realize the reasonable planning of the urban energy structure. The first level mainly analyzes the steady-state relationship between energy systems, the second level is based on the steady-state relationship of multiple energy sources to minimize the construction and operating costs of urban energy systems and pollutant emissions. Nonlinear system dynamics and the Improved Moth Flame Optimization Algorithm (IMFO) algorithm are implemented to solve the model. In addition, this paper uses instances to verify the application of a planning model in a certain city energy system in China. Under the premise of ensuring the stability of the urban energy system, two energy planning programs are proposed: mainly coal or mainly high-quality energy. The coal planning volumes are used as the basis for sub-scenario planning and discussion. Lastly, this paper proposes a series of development suggestions for different planning schemes. [ABSTRACT FROM AUTHOR]

A bi-level model for traffic signal optimization is developed. The model predictive framework is applied for traffic control in an urban traffic network. The potential of the bi-level formalization is used to increase the space of control influences with simultaneous evaluation of the green light and cycle durations. Thus, the increased control space allows more traffic parameters to be considered, such as vehicles queues and traffic flows. A particular modification of the bi-level control is applied for the synchronization of the traffic lights in the network. The model predictive approach is used for the real-time management of the traffic in the network. The control implementations are constrained by the shortest evaluated cycle. Thus, a synchronization of the traffic lights is applied for the minimization of the queues and maximization of the outgoing flows from the network. The bi-level model has been numerically tested on a set of intensive crossroads in Sofia. The numerical simulations prove the superiority of the developed bi-level control in comparison with the classical optimization of queue lengths. [ABSTRACT FROM AUTHOR]

In Wireless Rechargeable Sensor Networks (WRSNs), charging scheme optimization is one of the most critical issues, which plays an essential role in deciding the sensors' lifetime. An effective charging scheme should simultaneously consider both the charging path and the charging time. Existing works, however, mainly focus on determining the optimal charging path and adopt the full charging strategy. The full charging approach may increase the sensors' charging delay and eventually lead to sensor energy depletion. This paper studies how to optimize the charging path and the charging time at the same time to avoid energy depletion in WRSNs. We first formulate the investigated problem with a Mixed-Integer Linear Programming model. We then leverage the bi-level optimization approach and represent the targeted problem with two levels: the charging path optimization at the upper level and the charging time optimization at the lower level. A combination of Genetic Algorithm and Greedy method is proposed to determine the optimal charging path. Besides, to reduce the computational complexity of charging time identification level, we propose a Particle Swarm Optimization (PSO) algorithm to optimize the charging time of the best charging path in each evolutionary generation. The experimental validation on various network scenarios demonstrates our proposed charging scheme's superiority over the existing algorithms. [ABSTRACT FROM AUTHOR]

This research aims to design a bi-level optimization model for a supply chain that integrates decentralized quantitative and qualitative decisions at strategic and tactical levels. The manufacturer, as upperlevel decision-maker, offers quantity discounts to encourage customers to order more quantity. At the lower level, customers tend to obtain economies of scale by aggregating their orders through cooperative purchasing. This is one of the first studies that investigate the model of customer expectations with the optimization model of manufacturers at the same time with real data from the supply chain in order to find the optimal solutions to the problem of the medical equipment supply chain in Iran. In addition, there have been no studies to date that consider quantitative discount strategies for the seller and customer behavior in a bi-level planning model simultaneously. The results and analyses reveal that the designed bi-level model compared to the one-level model for the customer and the manufacturer is more suited to the real world and will lead to a long-term relationship between the parties through customer participation. Research suggestions and directions for future research are also provided. [ABSTRACT FROM AUTHOR]

Abstract As a key component of an integrated energy system (IES), energy storage can effectively alleviate the problem of the times between energy production and consumption. Exploiting the benefits of energy storage can improve the competitiveness of multi-energy systems. This paper proposes a method for day-ahead operation optimization of a building-level integrated energy system (BIES) considering additional potential benefits of energy storage. Based on the characteristics of peak-shaving and valley-filling of energy storage, and further consideration of the changes in the system’s load and real-time electricity price, a model of additional potential benefits of energy storage is developed. Aiming at the lowest total operating cost, a bi-level optimal operational model for day-ahead operation of BIES is developed. A case analysis of different dispatch strategies verifies that the addition of the proposed battery scheduling strategy improves economic operation. The results demonstrate that the model can exploit energy storage’s potential, further optimize the power output of BIES and reduce the economic cost.

Virtual bidding provides a mechanism for financial players to participate in wholesale day-ahead (DA) electricity markets. The price difference between DA and real-time (RT) markets creates financial arbitrage opportunities for financial players. Physical market participants (MP), referred to as participants with physical assets in this paper, can also take advantage of virtual bidding but in a different way, which is to further amplify the value of their physical assets. Therefore, this work proposes a model for such physical MPs to maximize the profits. This model employs a bi-level optimization approach, where the upper-level subproblem maximizes the total profit from both physical generations and virtual transactions while the lower-level model mimics the multi-period network-constrained DA market clearing process. In this model, uncertainties associated with other MPs as well as RT market prices are considered. Moreover, the conditional value-at-risk (CVaR) metric is utilized to measure the risk of diverse strategies. The optimal strategy of the strategic physical MP is derived by solving this bi-level optimization model. The proposed bi-level model is transformed to a single level mixed integer linear programming (MILP) model using Karush–Kuhn–Tucker (KKT) optimality conditions and the duality theory. Case studies show the effectiveness of the proposed method and reveal physical MPs may choose to deploy virtual transactions in a very different way than pure financial MPs.

Nowadays, developing an integrated energy system (IES) is considered as an effective pattern to improve energy efficiency and reduce energy supply costs. This study proposes a new index—convertibility index (CI)—to quantitatively assess the flexibility of the IES regarding the energy conversion processes between different energy flow types. Based on the CI constraint, a planning problem is modeled as a bi-level optimization problem. To solve the proposed bi-level problem, a hybrid genetic algorithm (GA)—MILP algorithm—is developed. A case study is carried out to verify the effectiveness of the proposed method. The results show that the total cost of the IES will increase with the CI constraint. For a given case study, the total cost increases by 26.2% when the CI decreases to 0.7 and increases by 3.7% when the CI increases to 1.6. Sensitivity analysis shows that the total numbers and capacities of conversion devices show an overall increasing trend with the increase in the CIs. Meanwhile, the total cost decreases quickly at first and then slightly increases, which, in a whole, shows a “Nike” shape. With different CI constraints, the IES MW per CI ranges from 31.8 to 37.5 MW, and the average cost increase is 2.229 million yuan (2.1%/0.1 CI).

Considering the economy, reliability, and output characteristics of multiple power sources (MPS) and energy storage (ES) comprehensively, a multi-source system integrated with offshore wind farms (OWFs) and its construction cost, and operating and maintenance cost model are established. The system is mainly composed of OWFs, thermal power plants, gas turbine power plants, and pumped hydro storage plants. Given the economy of the power system and offshore wind power accommodation, a bi-level optimal capacity configuration and operation scheduling method is proposed for the multi-source system integrated with OWF clusters with the objective function of optimal total cost. Then, a robust bi-level planning method for the multi-source system integrated with OWFs considering the dual uncertainty of load and offshore wind power prediction is proposed, in which the upper and lower models are solved by an improved particle swarm optimization (PSO) algorithm and CPLEX solver, respectively. Based on the method, the cost-optimal capacity configuration and operation scheduling scheme of an MPS and ES can be obtained. Finally, an OWF group in Shandong Province is taken as an example to check the validity and feasibility of the proposed method.

With the power of social media being harnessed to coordinate events and revolutions across the globe, it is important to identify the key sets of individuals that have the power to mobilize crowds. These key sets have higher resources at their disposal and can regulate the flow of information in social networks. They can maximize information spread and influence/manipulate crowds when they are coordinating. But due to the inherent drawbacks in node-based and network-based community detection algorithms, neither of these types of algorithms can be used to detect/identify these key sets. In this study, we present a bi-level max-max optimization approach to identify these key sets, where the degree centrality is used to identify individuals' influence at the commenter-level, while the network-level is designed to evaluate the spectral modularity values. We also present a set of evaluation metrics that can be used to rank these key sets for an in-depth investigation. We demonstrated the efficacy of the proposed model by identifying key sets hidden in a YouTube network spreading fake news about the conflict in South China Sea. The network consisted of 47,265 comments, 8477 commenters, and 5095 videos. A co-commenter network was constructed, where two commenters were linked together if they comment on same video. The proposed model efficiently identified key sets of commenters spread information to the whole network to manipulate YouTube's recommendation and search algorithm to increase the information dissemination. Moreover, the projected approach could identify sets of commenters that were key connectors to multiple groups, high influence across the network, higher interactions, and reachability than other regular communities. Besides, the Girvan–Newman modularity method, the depth-first search method, and text analysis was applied to validate the outcomes, categorize the identified key sets, and monitor the commenters' behaviors and information spread strategies in the network. In addition, the model considered a multi-criteria problem to rank these key sets of commenters based on the small real-world networks' features. [ABSTRACT FROM AUTHOR]

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