Integer Linear Programming Problem Research Articles

Robust Optimization Models for Planning Drone Swarm Missions

This article presents methods of planning unmanned aerial vehicle (UAV) missions in which individual platforms work together during the reconnaissance of objects located within a terrain. The planning problem concerns determining the flight routes of a swarm, where each UAV has the ability to recognize an object using a specific type of sensor. The experiments described in this article were carried out for drone formation; one drone works as a swarm information hub and exchanges information with the ground control station (GCS). Numerical models for mission planning are presented, which take into account the important constraints, simplifying the description of the mission without too much risk of losing the platforms. Several types of objective functions were used to optimize swarm flight paths. The mission models are presented in the form of mixed integer linear programming problems (MILPs). The experiments were carried out on a terrain model built on the basis of graph and network theory. The method of building a network on which the route plan of a drone swarm is determined is precisely presented. Particular attention was paid to the description of ways to minimize the size of the network on which the swarm mission is planned. The presented methods for building a terrain model allow for solving the optimization problem using integer programming tasks.

An optimal scheduling method for heavy haul trains with virtual coupling technology

ABSTRACT Heavy haul transportation enjoys the benefits of cost-efficiency by using long trains, but suffers from high cost in combination process and low efficiency in bottleneck areas. Virtual coupling technology (VCT) is helpful in resolving the dilemma. In this paper, we propose an optimal method for scheduling the route, timetable, and combination scheme of heavy haul trains with VCT in an integrated way. Specifically, six groups of constraints are first established, in which the sequence and train length problems incorporated by virtual coupling are properly handled. Then, a combined objective function comprised makespan and total flowtime indicators is proposed to optimize the throughput and turnover rate and further speeds up the optimization convergence. Finally, the optimization problem equipped with the proposed constraints and the combined objective function is transformed into an integer linear programming problem and solved by GUROBI. Simulation results demonstrate the effectiveness and advantages of the proposed method in leveraging VCT, and the benefits of virtual coupling over traditional physical coupling for heavy haul transportation.

Efficient predictive control method for ORC waste heat recovery system based on recurrent neural network

The model predictive control performs well in regulating operating parameters and ensuring system safety when the organic Rankine cycles are operating with variable heat sources. However, traditional nonlinear predictive control based on the organic Rankine cycle mechanism model involves significant computational complexity, making it challenging to quickly find a control solution. This limitation hinders its application in the organic Rankine cycle for rapid response control. To address this issue, a fast model predictive control method is proposed in this work. A recurrent neural network model is well-trained using the input–output data of the organic Rankine cycle process, and it is used as a surrogate model in the design of the model predictive controller for the control of organic Rankine cycle operating parameters. The formulated optimal control problem is then transformed into a mixed integer linear programming problem, which can obtain high-quality and fast solutions during the control process. Through comparison with recurrent neural network-based nonlinear predictive control and pseudo-sequential method-based fast nonlinear predictive control, the results show that the designed controller can effectively accomplish the control of organic Rankine cycle operating parameters with smaller overshoot. Moreover, its average control solution time is shorter by 89.59% and 93.27% respectively while the total net output power of the system during the control process is 0.54% and 1.3% higher than that of the other two controllers. It exhibits superior control performance, even under variable waste heat conditions.

Task and motion planning using mixed integer linear programming for solving fetch-and-carry tasks by a mobile manipulator

This manuscript describes a TAsk and Motion Planning (TAMP) method for mobile manipulators. We focus on fetch-and-carry tasks, and we aim to simultaneously generate both a sequence of actions and a motion sequence for each action. The number of factors to be considered in solving such a problem, and the interactions among them are complex due to the multifaceted characteristics of mobile manipulation. As a result, straightforwardly performing simultaneous TAMP may require a significant amount of processing time. Therefore, we reduce the complexity of the problem by formulating fetch-and-carry planning for a Mixed Integer Linear Programming (MILP) problem. The proposed method can obtain the sequence of actions and the movement of the mobile manipulator in less than one second in many cases. The effectiveness of the proposed method is verified in environments in which delivery objects and obstacles are placed in various patterns, using a robot with an omnidirectional mobile platform and a serial link manipulator.

A novel and cost-effective model for cloud energy storage based on a dual storage setup in active distribution grid with resilience consideration

The rising occurrences of natural disasters, terrorist actions, and cyber-attacks that result in extensive, long-lasting, and expensive disruptions have necessitated a shift in focus towards the resilience of electrical grids for network operators. However, the task of designing a resilient network remains complex and costly. One potential solution to bolster resilience is the deployment of battery energy storage devices on the consumer side, known as distributed energy systems (DES). Despite its effectiveness, the high construction costs and lengthy payback period associated with investing in energy storage devices have led consumers to exhibit reluctance in adopting them. Cloud energy storage (CES) is an innovative and cost-effective solution to address those challenges. In the CES platform, investors install storage facilities in the network which can be rented by consumers to fulfill their needs and they become holders of the virtual batteries. By adopting this approach, consumers are relieved from the burden of maintenance, repair, and installation. While a single CES facility offers reduced costs and increased comfort for consumers, it compromises the resilience of the grid when compared to the Distributed Energy Storage (DES) mechanism. In order to bridge this gap, this paper proposes a dual CES model which serves as an intermediate solution between DES and single CES. The dual CES model strikes a balance between the resilience of the grid and cost-effectiveness. It provides a higher level of resilience compared to a single CES and a lower level compared to DES. Additionally, the costs associated with the dual CES model fall between that of a single CES and DES. This model not only increases the profit margin for investors but also enhances the overall comfort and well-being of consumers compared to the single CES. To validate the proposed model, a Mixed Integer Linear Programming (MILP) problem is formulated and simulated on the IEEE 33 bus network. Three cases are considered: DES, single CES, and dual CES. The results indicate that the dual CES reduces consumers' costs by 28 %, losses by 27 %, unsupplied load costs by 45 %, and return on investment by 33 %. Moreover, it increases the stability margin time by 2 intervals and improves robustness by 47 %.

Short-term load distribution model for giant cascade serial diversion-type hydropower stations

With the development of complex cascade serial diversion-type hydropower plants (CSDHP) in Southwest China, it has become imperative to study short-term scheduling challenges that are distinctive to this type of hydropower facility. Unlike conventional cascade hydropower stations, which have large reservoirs to regulate the outflow between stations, the CSDHP system consists of several diversion-type hydropower plants connected in series, requiring strict matching of turbine discharge between upstream and downstream facilities. In addition, these plants impose complex operation constraints, such as multiple units sharing one tunnel, which greatly increases the difficulty of short-term scheduling. This paper proposes a short-term optimal scheduling model for CSDHP systems aimed at achieving efficient load distribution among units while minimizing water consumption. The model takes into account the strict matching of turbine discharge and the complex constraints of multiple units sharing one tunnel. Subsequently, the model is transformed into a mixed integer linear programming problem using specified linearization techniques, with complexity further addressed via an iterative resolution method. A case study of a cascade illustrates the model’s efficacy in facilitating effective unit load distribution under complex hydraulic and electrical constraints, which substantially reduces the system’s water consumption by up to 6.1% during the dry season and 1.8% during the flood season, and reducing the number of crossing forbidden zones by 50.0% and 52.0%, respectively. The result shows the models’ potential to enhance day-ahead scheduling for the CSDHP system.

Two stage beamforming and combining scheme for FDD massive MIMO systems with multi‐antenna users

AbstractThis paper proposes a two‐stage beamforming and combining scheme in frequency division duplex (FDD) massive multiple‐input multiple‐output (MIMO) systems with multi‐antenna users. Specifically, the proposed scheme is a two‐stage scheme, where the pre‐beamforming matrix and pre‐combining matrix are designed using the channel covariance matrix (CCM) in the first stage. The problem of the pre‐beamforming matrix and pre‐combining matrix design are formulated as an 0–1 quadratic integer programming problem. To solve this problem, it is further transformed into an 0–1 mixed linear integer programming problem. In the second stage, the sparse code multiple access and multi‐user precoding and combining are adopted to mitigate the inter‐user interference. Different from the previous transmission scheme using CCM, the proposed scheme consider the multi‐antenna user system, and uses the CCM to design both the pre‐beamforming and pre‐combining matrices to sparsify the effective channel matrix, such that the overhead of pilot and feedback can be reduced. Moreover, the sparse code multiple access can help to better reduce the inter‐user interference. Simulation results validate the good performance of the proposed scheme.

Planning a Hybrid Battery Energy Storage System for Supplying Electric Vehicle Charging Station Microgrids

This paper presents a capacity planning framework for a microgrid based on renewable energy sources and supported by a hybrid battery energy storage system which is composed of three different battery types, including lithium-ion (Li-ion), lead acid (LA), and second-life Li-ion batteries for supplying electric vehicle (EV) charging stations. The objective of this framework is to determine the optimal size for the wind generation systems, PV generation systems, and hybrid battery energy storage systems (HBESS) with the least cost. The framework is formulated as a mixed integer linear programming (MILP) problem, which incorporates constraints for battery ageing and the amount of unmet load for each year. The system uncertainties are managed by conducting the studies for various scenarios, generated and reduced by generative adversarial networks (GAN) and the k-means clustering algorithm for wind speed, global horizontal irradiation, and EV charging load. The studies are conducted for three levels of unmet load, and the outputs are compared for these reliability levels. The results indicate that the cost of hybrid energy storage is lower than individual battery technologies (21% compared to Li-ion, 4.6% compared to LA, and 6% compared to second-life Li-ion batteries). Additionally, by using HBESS, the capacity fade of LA batteries is decreased (for the unmet load levels of 0, 1%, 5%, 4.2%, 6.1%, and 9.7%, respectively), and the replacement of the system is deferred proportional to the degradation reduction.

The United Kingdom electricity market mechanism: A tool for a battery energy storage system optimal dispatching

In this paper, the role of a Battery Energy Storage System (BESS) in the United Kingdom (UK) electricity market is investigated. Such device is selected since research works related to the topic demonstrate that BESSs help facing challenges caused by renewable energy sources increasing penetration in the power systems’ field. Indeed, in the next future, BESSs will assume a relevant role thanks to their fast response time. In the present paper, an optimization model is implemented to encode the UK market rules and output the optimal set of offers on day-ahead and intraday markets, dynamic frequency response services and imbalance settlement. The market rules are formalised in a mathematical model considering market temporal sequencing and BESS technical limitations. The tool also models the state of energy management, necessary since BESSs are energy limited assets. Objective function and constraints are linearized to define a Mixed Integer Linear Programming problem to reduce the computational burden and to integrate the model in the Energy Management System previously developed at University of Genoa. Specific tests are performed including and excluding ancillary services to evaluate the related advantages. The obtained outcomes reveal that ancillary services are the most convenient options within all the implemented scenarios.

Measure this, not that: Optimizing the cost and model-based information content of measurements

Model-based design of experiments (MBDoE) is a powerful framework for selecting and calibrating science-based mathematical models from data. This work extends popular MBDoE workflows by proposing a convex mixed integer (non)linear programming (MINLP) problem to optimize the selection of measurements. The solver MindtPy is modified to support calculating the D-optimality objective and its gradient via an external package, SciPy, using the grey-box module in Pyomo. The new approach is demonstrated in two case studies: estimating highly correlated kinetics from a batch reactor and estimating transport parameters in a large-scale rotary packed bed for CO2 capture. Both case studies show how examining the Pareto-optimal trade-offs between information content measured by A- and D-optimality versus measurement budget offers practical guidance for selecting measurements for scientific experiments.

Wasserstein generative adversarial networks-based photovoltaic uncertainty in a smart home energy management system including battery storage devices

Rooftop photovoltaic (PV) power generation uncertainty is one of the prominent challenges in smart homes. Home Energy Management (HEM) systems are essential for appliance and Energy Storage System (ESS) scheduling in these homes, enabling efficient usage of the installed PV panels' power. In this context, effective solar power scenario generation is crucial for HEM load and ESS scheduling with the objective of electricity bill cost reduction. This paper proposes a two-step approach, where a machine learning technique, Wasserstein Generative Adversarial Networks (WGANs), is used for PV scenario generation. Then, the generated scenarios are used as input for the HEM system scheduler to achieve the goal of cost minimization. The generated solar energy scenarios are considered in a single household case study to test the presented method's effectiveness. The WGAN scenarios are evaluated using different metrics and are compared with the scenarios generated by Monte Carlo simulation. The results prove that WGANs generate realistic solar scenarios, which are then used as input to a Mixed Integer Linear Programming (MILP) problem aiming for electricity bill minimization. A 41.5% bill reduction is achieved in the presented case study after scheduling both the load and ESS, with PV fluctuations taken into account, compared to the case where no scheduling, PV, or ESS are considered.

Optimizing the number, locations, and chlorine dosages of booster chlorination stations in water distribution networks

ABSTRACT Safe and reliable drinking water is essential for sustaining life. Chlorination is widely used for disinfection in water distribution networks (WDNs). A higher dose of chlorine is required in an overhead service reservoir to maintain minimum residual chlorine at the farthest end in WDNs. However, delivering high dosages of chlorine from storage tanks can pose public health issues, especially for the residents living near overhead service reservoirs due to the formation of trihalomethanes, haloacetic acids, and chlorophenols. In addition, a higher dosage will lead to increased chlorine consumption and will accelerate pipe corrosion. Booster chlorination (BC) stations with smaller dosages are a solution to this problem. However, identifying the optimal number, locations, and dosage of each BC station in a cost-effective manner is challenging. This study proposes a methodology for determining the optimal number, locations, and chlorine dosages of BC stations in WDNs using a mixed integer linear programming problem. The methodology is illustrated through a simplified WDN in Holeta town, Ethiopia. The results indicate that if one adds two BC stations beyond the three dosage stations at the source, it will lead to a 49% reduction in chlorine use and a 27% decrease in the life cycle cost.

Integrated real-time signal control and routing optimization: A two-stage rolling horizon framework with decentralized solution

This paper presents an integrated framework for optimizing signal control and vehicle routing. An important feature of the proposed framework is the ability to simultaneously determine signal states and individual vehicle routes in real time. The general objective is to minimize the network travel time, which can be represented as a trade-off between the total route length of all vehicles and traffic conditions at signalized intersections. A two-stage rolling horizon framework is proposed to explicitly describe the relationship between individual vehicle routes and predicted traffic flow dynamics at signalized intersections. The first stage involves a signal optimization problem, while the second stage optimizes a joint signal control and vehicle routing problem. Both stages are formulated as mixed integer linear programming problems. The optimization procedure is decentralized, and the effects of vehicle routing on control performance is considered by incorporating the route length cost into the objective function. Simulation experiments validate the advantages of the proposed framework over advanced signal control strategies and dynamic user-optimal routing strategies in various scenarios. The effectiveness in improving network capacity, alleviating spillback, and decreasing congestion dissipation time under over-saturation conditions is discussed. The results of vehicle routing suggest that the total travel time can be reduced at a low rerouting cost. Sensitivity analyses demonstrate the network control performance under different compliance rates and model coefficients. Moreover, the computational feasibility of the framework is verified.

Air cargo transportation, loading, and phase-based maintenance service scheduling in demand channel routes

The article proposes an approach for modeling and solving the air cargo transportation, loading, and phase-based maintenance scheduling problems within demand channels. Demand channel transportation presents unique challenges to meeting the earliest pickup and delivery requirements during emergencies. The complexities in transportation involve issues with airport-aircraft compatibility, fleet selection, task assignments, route construction, and effective loading–unloading procedures. The challenges include coping with flight connections due to airport-aircraft compatibility, dealing with limited refueling and maintenance facilities, and swiftly adapting to unforeseen maintenance events by identifying and utilizing available fleets. In this context, the article delineates a demand channel route planning strategy that considers airport-aircraft compatibility, task integrity, priority, partial refueling strategy, and maintenance schedules spanning short to long-haul phases. Formulated as a Mixed Integer Linear Programming (MILP) problem, the solution employs a novel acyclic route construction procedure within a fuel-conscious network. We propose an insertion heuristic with multi-faceted algorithmic interconnections for producing a near-optimal solution suitable for real-world applications. Our insertion procedure has been shown to have very high computational performance, with an average 1.32 percent optimality gap. It can be scaled up to the most critical cargo mission, with up to 190 ports, 95 aircraft, and 380 tasks.

The one-station bike repositioning problem

In bike sharing systems the quality of the service to the users strongly depends on the strategy adopted to reposition the bikes. The bike repositioning problem is in general very complex as it involves different interrelated decisions: the routing of the repositioning vehicles, the scheduling of their visits to the stations, the number of bikes to load or unload for each station and for each vehicle that visits the station. In this paper we study the problem of optimally loading/unloading vehicles that visit the same station at given time instants of a finite time horizon. The goal is to minimize the total lost demand of bikes and free stands in the station. We model the problem as a mixed integer linear programming problem and present an optimal algorithm that runs in linear time in the size of the time horizon.

Game-Theory-Based Design and Analysis of a Peer-to-Peer Energy Exchange System between Multi-Solar-Hydrogen-Battery Storage Electric Vehicle Charging Stations

As subsidies for renewable energy are progressively reduced worldwide, electric vehicle charging stations (EVCSs) powered by renewable energy must adopt market-driven approaches to stay competitive. The unpredictable nature of renewable energy production poses major challenges for strategic planning. To tackle the uncertainties stemming from forecast inaccuracies of renewable energy, this study introduces a peer-to-peer (P2P) energy trading strategy based on game theory for solar-hydrogen-battery storage electric vehicle charging stations (SHS-EVCSs). Firstly, the incorporation of prediction errors in renewable energy forecasts within four SHS-EVCSs enhances the resilience and efficiency of energy management. Secondly, employing game theory’s optimization principles, this work presents a day-ahead P2P interactive energy trading model specifically designed for mitigating the variability issues associated with renewable energy sources. Thirdly, the model is converted into a mixed integer linear programming (MILP) problem through dual theory, allowing for resolution via CPLEX optimization techniques. Case study results demonstrate that the method not only increases SHS-EVCS revenue by up to 24.6% through P2P transactions but also helps manage operational and maintenance expenses, contributing to the growth of the renewable energy sector.

Demand Response Power-Gas Interconnection Energy System and Power Metering Based on SOGA

Under the double background of global energy crisis and environmental pollution, China vigorously develops renewable energy while accelerating the construction of energy Internet. Taking demand response into account, this paper proposes the optimal design of power-gas interconnection energy system and power metering, and establishes the optimization research model of IEGES (integrated electricity-gas energy system) with demand response. Firstly, the structure model of the electric-gas interconnection energy system with CHP (Cogeneration, combined heat and power) as the core is constructed, and the energy conversion relationship and different energy flow directions of the coupling equipment are expounded from three aspects. The natural gas source point, pipeline equation, power side branch equation, voltage and current equation are modeled and sorted out, and the square term in the equation is linearized by second-order cone programming method, and the mixed integer nonlinear programming problem is transformed into mixed integer linear programming problem. A single objective genetic algorithm with “elite strategy” was selected to solve the equipment capacity optimization problem of IEGES system with system economy as the optimization objective. After a long time of parameter combination attempts, the current population size is 30, the number of iterations is 600, the crossover rate is 0.8, and the heritability is 0.3. The above parameters can obtain better convergence results on the basis of considering the operation time. Finally, a stochastic optimization method of energy Internet considering integrated demand response and uncertainty of wind power is proposed, which aims to meet the energy demand of end users while minimizing the operating cost of the system. The comprehensive demand response strategy including internal and external demand response is considered in the model. Internal demand response is realized by adjusting the internal operation mode of EH, while external demand response is implemented by the end user’s active response, and the load is time-shifted or interrupted under the guidance of external signals.

Модель оптимізації портфеля купівлі-продажу електричної енергії компанією-постачальником

The study examined the market dynamics of an electricity supply company and proposed an optimization model aimed at enhancing its profitability in the wholesale market. This model is formulated as a mixed integer linear programming problem. By solving this optimization problem, the most advantageous contractual terms for purchasing and selling electricity from those available on the market are determined. This allows the company to efficiently manage its electricity portfolio and meet its consumption schedule as per existing supply contracts with consumers. The IBM ILOG CPLEX Optimization Studio software was employed to develop and solve the optimization problems related to the company's portfolio. The computational experiments conducted provide insights into the effectiveness of the proposed model and its practical applicability. These results demonstrate the model's adequacy and its potential for real-world implementation.

Integrated optimization of charging infrastructure, fleet size and vehicle operation in shared autonomous electric vehicle system considering vehicle-to-grid

Shared autonomous electric vehicles (SAEVs) are predicted to become a significant solution to reduce global emissions and energy consumption resulting from urban transportation. The centralized operation of SAEVs not only allows large-scale travel demand response but also can provide essential ancillary services to the smart grid through the concept of vehicle-to-grid (V2G). With V2G technology, unused electric vehicles can work as a distributed energy storage facility for the electricity grid to smoothen the intermittent demand. Designing and operating a V2G-enabled SAEV system is challenging. This problem involves complicated planning and operational decisions, as well as time-varying electric tariffs. In this work, a flow-based Integer Linear Programming (ILP) model is formulated for determining the optimal configurations (charging infrastructure and fleet size) and daily operation strategies (serving passengers, relocation, charging/discharging). The developed mathematical model allows for maximizing the total profit, comprising investment cost, revenue from serving passengers, and V2G profit through charging/discharging schedules. A two-stage Benders decomposition-based algorithm is proposed to address the sophisticated ILP problem. Via testing instances in the Manhattan network based on real-world and synthetic data, we have demonstrated the feasibility of our approaches and studied the benefits of integrating V2G in the SAEV system.

A Set Covering Approach to Design Maximally Permissive Supervisors for Flexible Manufacturing Systems

The supervisory control of Petri nets aims to enforce the undesired behavior as unreachable by designing a set of control places. This work presents a set cover approach to design maximally permissive supervisors. For each first-met bad marking, an integer linear programming problem is developed to obtain a control place to prohibit it. An objective function is formulated to make the maximal number of first-met bad markings forbidden. Then, we develop a set covering approach to minimize the number of selected control places. The proposed approach can guarantee the maximal permissiveness of the obtained supervisor and provide a trade-off between structural complexity and computational cost. Several examples are considered to validate the proposed method.