Lower-level Problem Research Articles

Resiliency Improvement of Distribution Network Considering the Charge/Discharge Management of Electric Vehicles in Parking Lots through a Bilevel Optimization Approach

Due to the growing use of Plug-in Electric vehicles (PEVs) in transportation networks, the charge/discharge scheduling of PEVs in Electric Vehicles Parking Lots (EVPLs) can be effective on the distribution network’s (DN) resiliency. This paper presents a bilevel optimization model to improve the resiliency of the DN taking into account the interaction between the DN islanding problem and the charge/discharge scheduling of PEVs in the energized EVPLs. In the Upper-Level (UL) problem, regarding the electrical loads and managing the charge/discharge of PEVs, the islands’ boundaries are determined with the aim of maximizing the amount of restored load. Knowing the islands’ boundaries and the energized EVPLs from the UL problem, the changes in travels characteristic including destination EVPLs are determined in the Lower-Level (LL) problem to identify the nearest energized EVPL to the out-of-service destination EVPL. The number of PEV drivers that change their deenergized destination depends on the distance between the nearest energized EVPL to the destination. A combination of mathematical programming and evolutionary algorithm is applied to reach the final solution. The proposed model is implemented by applying several concurrent faults to the 118-bus active DN, which is coupled with a 25-node traffic network. The results confirm the efficiency of the proposed model for improving the resiliency of DNs with managing the charge/discharge of PEVs in the restored EVPLs.

A multi-criteria approach to designing and managing a renewable energy community

The energy communities based on the integration of microgrids make it possible to gain economic, environmental, technical, and social benefits. The paper aims to propose a unified multi-criteria approach covering both the planning stage and the stage of managing the energy community, in the context of various interests of its participants. Planning stage should take into account the long-term goals of the community and possible changes in external conditions. Therefore, we suggest an approach relying on the multi-attribute value theory considering the uncertainty of decision makers' preferences. Interval estimators used to express preferences enable a choice of community configuration with robust performance under changing conditions within some limits. In the operation stage, the new multi-criteria model of an intelligent "energy community operator" is proposed. It is based on bi-level programming and reinforcement learning, implementing the structure of a fair local market for sustainable development of the community. To optimize the operation of individual microgrids within the community, the multi-objective Monte-Carlo Tree Search (MCTS) algorithm is used, which helps to improve the convergence in the Stackelberg game. The multi-criteria version of the MCTS algorithm allows implementing an adaptive local automation model to solve a multi-objective lower-level problem: minimize operating costs, risk of power shortage, and CO2 emissions; smooth load peaks, and optimize power exchange between microgrids. At the top level, a management strategy that will be beneficial to all members of the community is chosen to guarantee their long-term aggregation. The effectiveness of the proposed approach is demonstrated by the example of an energy community created for three remote villages located on the coast of the Sea of Japan. The natural and climatic conditions of the area allow the efficient use of wind, solar, and biomass resources. Building the community involves the consideration of three scenarios, in which priority is given to economic efficiency, environmental efficiency, or balanced development.

A Partnership of Virtual Power Plant in Day-Ahead Energy and Reserve Markets Based on Linearized AC Network-Constrained Unit Commitment Model

This paper presents coordinated energy management as a virtual power plant (VPP) framework with a wind farm, a storage system, and a demand response program in the transmission network according to the cooperation of VPPs in day-ahead energy and reserve markets. This strategy is based on a bilevel method, where it maximizes the expected VPP revenue in the proposed markets subject to constraints of renewable and flexible sources and the VPP reserve model in the upper-level problem. Also, a market-clearing model based on network-constrained unit commitment (NCUC) is explained in the lower-level problem so that it minimizes the expected operating cost of generation units constrained to a linearized AC-NCUC model. The scenario-based stochastic programming (SBSP) models the uncertainties of loads and WF power generation. Then, the master/slave decomposition method solves the bilevel problem to achieve an optimal solution at a low computational time. Also, since the lower-level problem is mixed-integer linear programming, the Benders decomposition algorithm is adopted to solve this problem. Finally, the suggested approach is implemented on IEEE test networks in GAMS software, and numerical results confirm the efficiency of the coordinated VPP management in DA energy and reserve markets and its capabilities in improving network operation.

Optimal Planning and Bidding Strategy for Wind Farms in Joint Balancing and Day‐Ahead Energy Markets

Due to the fact that wind farms have a meagre operating cost, it is expected that their optimum utilization in the transmission network would improve the economic and technical condition of the network. Henceforth, this work aims to allocate wind farms' locations in the transmission network while persuading the farm owners to participate in the balancing and day-ahead energy markets. The proposed scheme is formulated in the form of a bi-level optimization model. The upper-level problem aims to maximize wind farms' profit in joint day-ahead and balancing markets bounded by the location and operational constraints. On the other hand, the lower-level problem provides the operating model of the transmission network. Herein, the network operator is in authority to minimize the operational cost of non-renewable resources, considering the linearized AC power flow and technical constraints of resources. Then, the Karush—Kuhn–Tucker is adopted to extract the proposed scheme single-level model. One of the eminent novelties of this work is to propose a linear model for wind farms and to introduce an incentive plan for farm owners in the energy market by considering bidding errors. In the end, by implementing this scheme on IEEE 6-bus and 24-bus transmission networks, the numerical outcomes indicate the proposed scheme's potential to improve the economic and operational status of wind farms and the transmission network. With linear programming based on optimum utilization of wind farms, the utilization of traditional units, energy prices, energy plans, and the maximum voltage drop are reduced by 35%, 15%, 20%, and 21%, respectively, compared to the cases without wind farms penetrations.

A novel algorithm for optimal equipment scheduling and dispatch of chilled water systems with ice thermal storage

Using thermal energy storage in chilled water systems can reduce electricity bill charges and required chiller cooling capacity through load shifting and peak demand shavings. As opposed to simple heuristic strategies, optimal storage dispatch maximizes savings by considering the time of use tariffs and system efficiency. In this paper, we propose a solution to the optimal equipment scheduling and storage dispatch problem of multi-chiller chilled water systems with ice thermal storage. We model the system in a bi-level optimization formulation that is solved using the genetic algorithm. The upper level minimizes daily operation costs and decides the storage dispatch amount over the next 24 h. The decided upon dispatch amount is fed to the lower-level optimizer to solve the equipment scheduling problem sequentially and return the corresponding system power consumption over the next 24 h. Flowrate and energy balancing constraints are handled using the penalty function method. Tuning of the penalty factors and genetic algorithm parameters significantly diminished and eliminated the problem of premature convergence. While the genetic algorithm is computationally taxing, we reduced the run time to 1–2 min by pre-solving the lower-level problem under various input conditions and tri-linearly interpolating between them. We compared the developed optimal control strategy to two commonly used heuristic storage dispatch strategies: chiller priority control and storage priority control in three scenarios of cooling demand under a time of use electricity pricing. Our model suggests optimal control reduces cost and energy by 11–14% and 10–12%, respectively, relative to storage priority control, and 16–33% and 1–9%, respectively, relative to chiller priority control. In a scenario with a demand charge, optimized control reduces demand charges by 17% relative to storage priority and 26% relative to chiller priority control. The gains from the proposed approach are augmented when a more sophisticated tariff structure is present.

Bilevel hyperparameter optimization for support vector classification: theoretical analysis and a solution method

Support vector classification (SVC) is a classical and well-performed learning method for classification problems. A regularization parameter, which significantly affects the classification performance, has to be chosen and this is usually done by the cross-validation procedure. In this paper, we reformulate the hyperparameter selection problem for support vector classification as a bilevel optimization problem in which the upper-level problem minimizes the average number of misclassified data points over all the cross-validation folds, and the lower-level problems are the l_1-loss SVC problems, with each one for each fold in T-fold cross-validation. The resulting bilevel optimization model is then converted to a mathematical program with equilibrium constraints (MPEC). To solve this MPEC, we propose a global relaxation cross-validation algorithm (GR–CV) based on the well-know Sholtes-type global relaxation method (GRM). It is proven to converge to a C-stationary point. Moreover, we prove that the MPEC-tailored version of the Mangasarian–Fromovitz constraint qualification (MFCQ), which is a key property to guarantee the convergence of the GRM, automatically holds at each feasible point of this MPEC. Extensive numerical results verify the efficiency of the proposed approach. In particular, compared with other methods, our algorithm enjoys superior generalization performance over almost all the data sets used in this paper.

Saving a Path and Maximizing Dynamic Contra ow: A Bilevel Programming Approach

An important aspect of evacuation planning is to save human population by sending the people in dangerous areas (sources) to the safe places (sinks). Optimization models for evacuation planning focus on regulating the tra_c ow in urban road networks so as to maximize the number of evacuees reaching the safe places or to minimize the evacuation time of evacuees. Recent studies show that reversing the direction of the usual tra_c ow in necessary road segments increases the tra_c ow and decreases the evacuation time signi_cantly. However, this may block the ow of some necessary support towards the source. Based on network ow models, we consider the problem of saving a path from a given node to the source, in a single-source-single-sink network, as a bilevel program. With an objective to minimize a function depending on ow rate and the path chosen, the upper level selects a path from a given node to the source, and the lower level maximizes the dynamic ow allowing arc reversals in the resulting network within a given time horizon. We discuss a solution strategy based on replacing the lower level problem by the corresponding KKT conditions. GANIT J. Bangladesh Math. Soc. 42.1 (2022) 010- 024

Market-based hosting capacity maximization of renewable generation in power grids with energy storage integration

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.

A 5G Hubs Location Hierarchized Problem that Balances the Connection of the Users

In this paper, a telecommunication network situation is studied. Particularly, the problem considers an upper-level decision maker that enables different types of hubs in the network and another one that connects the users to the enabled hubs. The objective of the upper-level decision maker is to balance the number of users connected to the enabled hubs. However, the connection of users is performed by another decision maker with lower hierarchy, the one associated to the lower-level problem. Hence, decisions at the upper level are given as parameters to the lower level. So that, the lower level is solved to obtain feasible bi-level solutions. In this case, the rational reaction of the decision-maker assigned to the lower level is obtained. Due to the complexity of this problem, an evolutionary algorithm is proposed to obtain a good approximation. Numerical experimentation shows the efficiency and robustness of the proposed solution scheme. Based on the results, it can be concluded that the proposed algorithm provides good alternatives for the bi-level decision-making process. Also, some managerial insights are given regarding the different types of enabled hubs and the connection of the users.

Heterogeneous Cluster Application Communication Optimization and Computer Big Data Management

In order to adapt to the constantly updated heterogeneous hardware and super-large-scale parallel computing environment and solve the problems of low programming level and difficult development, modification, and debugging of commonly used solutions, the author proposes a method for application communication optimization and computer big data management based on heterogeneous clusters. A new language mechanism is introduced to describe the multidimensional rule structure, arrangement, and communication mode of data and threads; and a software migration and optimization method between different types of heterogeneous systems based on the new language mechanism is proposed. And take direct method turbulence simulation as an example. Experimental results show that based on the Parray mechanism, it took only one week to complete the rapid migration of turbulence simulation applications on the Tianhe 1A system, and it was successfully run on a scale of 8192 cubic meters. Conclusion. The method realizes communication optimization and fast porting in different heterogeneous systems.

Time-Optimal Coordination for Connected and Automated Vehicles at Adjacent Intersections

In this paper, we provide a hierarchical coordination framework for connected and automated vehicles (CAVs) at two adjacent intersections. This framework consists of an upper-level scheduling problem and a low-level optimal control problem. By partitioning the area around two adjacent intersections into different zones, we formulate a scheduling problem for each individual CAV aimed at minimizing its total travel time. For each CAV, the solution of the upper-level problem designates the arrival times at each zones on its path which becomes the inputs of the low-level problem. The solution of the low-level problem yields the optimal control input (acceleration/deceleration) of each CAV to exit the intersections at the time specified in the upper-level scheduling problem. We validate the performance of our proposed hierarchical framework through extensive numerical simulations and comparison with signalized intersections, centralized scheduling, and FIFO queuing policy.

Bi-level scheduling in high-end equipment R&D: when more algorithm strategies may not be better

Motivated by the practical research and development (R&D) process in high-end equipment manufacturing, this study investigates a bi-level scheduling problem in a complex R&D project network, where each project contains multiple modules with a complete task network. In the bi-level scheduling problem, the upper-level problem is that the R&D project leader makes the decision on allocating all R&D project modules to limited R&D researchers and the objective is to minimise the total penalty cost of all projects, and the lower-level problem is that the researchers schedule and sort the assigned tasks to minimise their minimum makespan. The different capacity of researchers is considered, and some structural properties are derived based on the capacity analytics. To tackle this complex scheduling problem, an effective Variable Neighborhood Search algorithm based on the ‘less is more' concept is proposed, where a Multi-Greedy Heuristic is incorporated. Interestingly, we observe that simpler algorithmic strategies may lead to better algorithmic performance. Computational experiments are carried out to demonstrate that the performance of the proposed algorithm is efficient and stable.

E-Commerce across Boarder Logistics Risk Evaluation Model Based on Improved Neural Network

BP neural network is a typical algorithm in artificial intelligence network. It has strong nonlinear mapping ability and is the most prominent part to solve some nonlinear problems. In the traditional BP algorithm, the coincidence initialization of weights and thresholds is random, which reduces the efficiency of the algorithm on the one hand and affects the accuracy of the algorithm results on the other hand. In order to solve these problems, this paper studies an e-commerce cross-border logistics risk assessment model based on improved neural network. This model can help merchants engaged in cross-border e-commerce to select appropriate third-party settlement platforms, so as to reduce the cost of merchants in the process of capital settlement. The key information in BP neural network algorithm is stored in weights and thresholds, which is enough to prove the importance of weights and thresholds for the effective operation of the whole network. The e-commerce cross-border logistics risk assessment model based on improved neural network aims to solve the problem of low level of risk assessment and the bottleneck of logistics risk assessment. The improved e-commerce cross-border logistics risk assessment model based on neural network can be used for risk rating before business development, so as to adopt different risk management methods for different risk levels.

Modeling the Truck Appointment System as a Multi-Player Game

Background: Random truck arrivals at maritime container terminals are one of the primary reasons for gate congestion. Gate congestion negatively affects the terminal’s and drayage firms’ productivity and the surrounding communities in terms of air pollution and noise. To alleviate gate congestion, more and more terminals in the USA are utilizing a truck appointment system (TAS). Methods: This paper proposes a novel approach to modeling the truck appointment system problem. Unlike previous studies which largely treated this problem as a single-player game, this study explicitly models the interplay between the terminal and drayage firms with regard to appointments. A multi-player bi-level programming model is proposed, where the terminal functions as the leader at the upper-level and the drayage firms function as followers at the lower-level. The objective of the leader (the terminal) is to minimize the gate waiting cost of trucks by spreading out the truck arrivals, and the objective of the followers (drayage firms) is to minimize their own drayage cost. To make the model tractable, the bi-level model is transformed to a single-level problem by replacing the lower-level problem with its equivalent Karush–Kuhn–Tucker (KKT) conditions and the model is solved by finding the Stackelberg equilibrium in one-shot simultaneous-moves among players. For comparison purposes, a single-player version of the TAS model is also developed. Results: Experimental results indicate that the proposed multi-player model yields a lower gate-waiting cost compared to the single-player model, and that it yields higher cost savings for the drayage firms as the number of appointments per truck increases. Moreover, the solution of the multi-player model is not dependent on the objective function coefficients, unlike the single player model. Conclusions: This study demonstrates that a TAS is more effective if it considers how the assigned appointment slot affects a truck’s drayage cost. It is recommended that terminal operators and port authorities initiate conversations with their TAS providers about incorporating this element into their TAS.

Variable heat pricing to steer the flexibility of heat demand response in district heating systems

Flexibility from low-temperature district heating (LTDH) systems favors the integration of renewable energy in power systems. Flexibility from LTDH systems may be revealed and steered through dynamic pricing for heat. For the purpose of optimal heat pricing, the heat market with variable heat pricing is modeled as a Stackelberg game (i.e., with a bi-level structure). The upper-level problem of the heat provider is to maximize net profit by issuing hourly heat prices day-ahead, while the lower-level problem of heat consumers is to minimize costs by adjusting heat demand based on the dynamic price. The proposed model is tested on a groundwater-based LTDH system with one provider and three consumers. It is evaluated based on the operational cost of the heat provider and the average heat unit price for the consumers, compared to flat heat pricing.

A Socio-Economic Formation: Problems of Efficiency and Low Level of Anti-Corruption Security

The paper examines the influence of socio-economic formation on crime. The author comes to the conclusion that the determinism of the existing economic, social and regulatory causes of corruption is based on an inefficient socio-economic formation. The author notes that an inefficient form of public administration, as well as a type of socio-economic formation, are not able to eliminate the causes of corruption, since this formation does not at all imply elimination of these causes, but, on the contrary, contributes to their existence and development. This takes place due to the fact that the form of public administration limits the possibility of applying and implementing a different, more effective form of public administration and socio-economic formation. Corruption as a phenomenon exists in a socio-economic formation in which socially useful principles, guidelines and attitudes are poorly organized or absent. The use of effective measures to combat corruption is not possible in the socio-economic formation where the main vices of society still exist or are idealized: selfishness, greed, thirst for power, excessive exploitation of an individual, etc. A corrupt behavior model becomes the norm in a situation when the state power and the state economy are dependent on private capital and investors. The author comes to the conclusion that the use of combined forms of public administration is effective and expedient. An effective use of combined forms of public administration can eliminate the main set of causes, circumstances and conditions that contribute to the emergence, growth and development of both corruption and crime in the country as a whole. A combined form of public administration presupposes the uniform participation of society, business entities and authorities in the implementation of socio-economic policy, which has common socially useful goals based on socially useful attitudes and guidelines.

Distributionally robust heat-and-electricity pricing for energy hub with uncertain demands

In this work, we investigate the energy market pricing problem of an energy hub (EH) under endogenous uncertain demands. While traditional pricing problems consider exogenous energy demands, in multi-energy scenarios, the difference between power and heat prices could affect the compliance of residents to use certain energy, and therefore affect the realization of stochastic demand. Moreover, the probability distribution of such endogenous uncertainty and how it is influenced by energy prices may not be known exactly. This article proposes a bilevel optimization framework based on the game theory containing an upper-level EH dispatch with energy pricing and a series of lower-level household energy management problems. This framework seeks for optimal heat-and-electricity market prices for both EH and users to minimize their expected costs. To address uncertain probability distributions in decision-making processes, a modified distributionally robust chance-constrained programming approach is employed. The results demonstrate that the proposed framework could provide an effective pricing scheme for EH.

Expansion planning of a price-maker virtual power plant in energy and reserve markets

This paper addresses the expansion planning problem of a virtual power plant considering the possibility of building new assets such as conventional, renewable, and energy storage units. The VPP is modeled as a price-maker player that strategically participates in energy and reserve markets by altering the prices of these markets to its own benefit. The VPP includes flexible demands, conventional and renewable generating units, and energy storage units. Variabilities in renewable production levels are modeled using a modified clustering K-medoids method, while the uncertain reserve request coefficients are represented using a set of scenarios. The present problem is formulated as a two-stage stochastic bi-level model, where the upper-level problem represents the expected profit of the VPP to be maximized by building new assets, while the lower-level problems model the clearing of the energy and reserve electricity markets for different market conditions, which aim to maximize the social welfare and reduce the cost of the ancillary systems, respectively, and determine the market prices of both markets. The stochastic bi-level model is converted to a single-level mixed-integer linear programming problem by replacing the lower-level problems by their Karush–Kuhn–Tucker optimality conditions and by applying exact linearization techniques. Numerical results show that considering the VPP as a price-maker player influences its expansion decisions and allows the VPP to increase its profit up to 108.8% in comparison with a price-taker behavior. Also, the numerical results indicate that the participation in the reserve market increases a 26.76% the expected profit achieved by the VPP.

Routing and Charging Facility Location for EVs Under Nodal Pricing of Electricity: A Bilevel Model Solved Using Special Ordered Set

We consider the problem of identifying optimal location of electric vehicle (EV) charging stations, while accounting for (i) route optimization and (ii) charging cost optimization by the EV fleets, where the electricity price is obtained endogenously by an optimal power flow (OPF) model. We solve the problem using a bi-objective bilevel programming framework with the objectives being one of minimising travel time and the other of minimising EV charging cost. The upper level problem consists of the facility location and the transportation model and the lower level problem consists of the OPF model. After reformulating this computational hard problem as a mathematical program with equilibrium constraints (MPEC), we solve the problem using a special ordered sets-type 1 (SOS1)-based approach. We record the significant improvement in speed by our method, as opposed to the standard Big-M approach. Finally, we apply the technique to the Sioux Falls transportation network with the IEEE 14-bus electricity network embedded on it. We observe that solutions through our models results in as much 37% lower operating costs for the EVs.

Trajectory Optimization with Optimization-Based Dynamics

We present a framework for bi-level trajectory optimization in which a system’s dynamics are encoded as the solution to a constrained optimization problem and smooth gradients of this lower-level problem are passed to an upper-level trajectory optimizer. This optimization-based dynamics representation enables constraint handling, additional variables, and non-smooth behavior to be abstracted away from the upper-level optimizer, and allows classical unconstrained optimizers to synthesize trajectories for more complex systems. We provide a path-following method for efficient evaluation of constrained dynamics and utilize the implicit-function theorem to compute smooth gradients of this representation. We demonstrate the framework by modeling systems from locomotion, aerospace, and manipulation domains including: acrobot with joint limits, cart-pole subject to Coulomb friction, Raibert hopper, rocket landing with thrust limits, and planar-push task with optimization-based dynamics and then optimize trajectories using iterative LQR.