Mixed Integer Linear Programming Problem Research Articles

A three-level robust scenario-based model for resilience-oriented placement of remote-controlled switches in distribution networks

This paper introduces an innovative strategy to improve the resilience of Distribution Networks (DN) following natural disasters. The approach involves a multi-stage model for the strategic placement of Remote-Controlled Switches (RCS) to expedite fault isolation and service restoration. The model integrates various resilience enhancement techniques, such as network reconfiguration and microgrid formation, throughout the pre-disaster, disaster progression, and post-disaster phases. To mitigate uncertainties related to line failures and ensure planning robustness, a novel three-level Robust Scenario-based Model (RSM) is introduced. The RSM optimizes the strategic RCS placement to enhance System Performance Criteria (SPC) in response to anticipated line failure scenarios, considering individual line vulnerabilities and disaster severity. Subsequently, the model identifies the most critical failures from each predicted scenario based on RCS placements and then recalibrates the placements to enhance DN resilience against both anticipated and critical failures. The RSM is formulated as a mixed-integer linear programming problem to maximize SPC by allocating resources optimally to serve maximum weighted loads while adhering to structural and operational constraints. The effectiveness and validity of the proposed model are demonstrated through case studies conducted on a modified IEEE 33-bus test system and a modified real DN.

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.

Automated hybrid distillation sequence synthesis framework of mixed azeotropes and nonazeotropes

Distillation technology is a crucial, energy-intensive component of energy-supply systems, thereby motivating the improved design of distillation systems. This study investigated an automated framework for synthesizing hybrid distillation sequences, providing a systematic approach for the design and optimization of distillation sequences involving azeotropes. The proposed method separated mixed azeotropes and nonazeotropes by replacing the simple columns in the superstructure of a conventional distillation sequence with extractive distillation columns. The automated calculation of the superstructures was implemented by calling the external interface of the process simulator. The results of these calculations were used to formulate a mixed-integer linear programming problem that was optimized with the objective function of the total annualized cost (TAC). Finally, the optimal solution and all feasible alternatives were obtained. Moreover, the reliability and efficiency of the proposed framework were demonstrated through two case studies. The results show that the separation position of the azeotrope in the sequence and the presence or absence of heat integration significantly impact the TAC of the system. However, using an existing component versus an external component as an entrainer makes very little difference in the TAC for the optimal sequences.

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.

An improved ALNS for hybrid pickup and drones delivery system in disaster by penalizing deprivation time

Humanitarian logistics aims to reduce the time relief goods and services take to reach affected areas; deprivation time is one of the most significant factors in such conditions. Thus, utilizing a suitable transport fleet, including modern vehicles like drones, is essential. This paper introduces a new hybrid vehicle routing problem with pickup and delivery services, minimizing deprivation costs with multiple trucks and drones in a disaster. The model is presented as a mixed-integer linear programming problem focusing on minimizing deprivation cost in post-disaster situations through proper routing and inventory decisions made by heterogeneous vehicles. The deprivation time is divided into three main categories based on the arrival time of relief goods to affected areas and will be served by multiple relief goods. Due to the complexity of the problem, an improved adaptive large neighborhood search (ALNS) metaheuristic has been developed. This algorithm employs a heuristic algorithm to generate high-quality initial solutions and improve solutions with 17 destroy and repair operators. The algorithm was tested on a large-scale dataset based on real-world data from a crisis such as the Tehran earthquake, and the results demonstrate its superiority in providing better-quality solutions and lower solution time.

Accurate and robust linear representation for containership stability conditions with ballast water

Stowage planning involves optimizing the placement of cargo on a ship while ensuring the ship's stability conditions are met. This optimization problem is typically formulated as a mixed-integer linear programming problem. However, a challenge arises in representing stability conditions as linear constraints since these conditions have non-linear relationships to the decision variables. Although there are methods for linearizing these stability conditions, they lack a systematic modeling approach and numerical verification of accuracy and reliability. In particular, the complex and diverse nature of ballast water contributes to significant non-linearity, posing a considerable challenge in developing an accurate linear approximation. This study proposes linear prediction methods that incorporate ballast water to address major stability conditions such as trim, drafts, shear force, bending moment, torsion, and transverse metacentric height. We introduce a comprehensive training and testing methodology for prediction, and validate the proposed method by comparing it with true values on two ships of different capacities, demonstrating its accuracy and scalability.

Peer-to-peer multi-period energy market with flexible scheduling on a scalable and cost-effective blockchain

Peer-to-Peer (P2P) electricity trading is an emerging means for allowing communities to share local energy production and demand response through direct trading. It is projected to play an important role in the future energy market by increasing the incentive to own and operate distributed energy resources (DERs) and participate in demand response (DR). A common approach to implementing P2P trading is with blockchain, however, existing solutions feature limitations. Typically, concerns involve either scalability and high transaction costs or projects implementing a permissioned blockchain that does not provide the trust and decentralization desired. In addition, the majority of market designs are simplified and do not capture the distinct complexity of electricity markets. They do not consider the inter-temporal constraints of appliances and DERs that need to run for multiple periods. Complex market designs that address these issues have not been implemented in blockchain based systems due to the computational limitations of such systems. To improve these two aspects, this paper proposes a market formulation that supports products running multiple periods with flexible scheduling, modeled as a mixed integer linear programming problem that optimizes social welfare. The trading platform is then implemented as a side chain of Polkadot, a network of blockchains designed to be secure, scalable, and economically feasible to foster an ecosystem of application-specific sidechains. This design is demonstrated to improve social welfare and achieve scalability by benchmarking the number of transactions that can be included per second, based upon typical assumptions of the market size. The result is a decentralized and performant system that allows for complex market designs to be implemented in a blockchain environment. This approach simplifies the process for participants, allowing them to bid DER or DR devices, directly and easily, even when this requires constraints across periods.

Designing function-specific minimal microbiomes from large microbial communities

Microorganisms exist in large communities of diverse species, exhibiting various functionalities. The mammalian gut microbiome, for instance, has the functionality of digesting dietary fibre and producing different short-chain fatty acids. Not all microbes present in a community contribute to a given functionality; it is possible to find a minimal microbiome, which is a subset of the large microbiome, that is capable of performing the functionality while maintaining other community properties such as growth rate and metabolite production. Such a minimal microbiome will also contain keystone species for SCFA production in that community. In this work, we present a systematic constraint-based approach to identify a minimal microbiome from a large community for a user-proposed function. We employ a top-down approach with sequential deletion followed by solving a mixed-integer linear programming problem with the objective of minimising the L1-norm of the membership vector. Notably, we consider quantitative measures of community growth rate and metabolite production rates. We demonstrate the utility of our algorithm by identifying the minimal microbiomes corresponding to three model communities of the gut, and discuss their validity based on the presence of the keystone species in the community. Our approach is generic, flexible and finds application in studying a variety of microbial communities. The algorithm is available from https://github.com/RamanLab/minMicrobiome.

Optimization method for renewable energy investment planning in the electricity carbon coupling market environment considering economy

China is developing rapidly in renewable energy development, electricity market reform, and carbon market construction, using market mechanisms for efficient planning and investment. The electricity and carbon markets are interrelated for market entities. This context has led to a dual-level optimization model for renewable energy investment planning, considering cost recovery and new power system goals. The model includes deriving electricity carbon coupling quotations for conventional units based on dynamic carbon emission characteristics and proposing an electricity spot market mechanism influenced by carbon quota trading. The model’s upper level maximizes renewable energy investment capacity, determining its size and location, while the lower level simulates electricity spot and voluntary emission reduction market trading to guide investment decisions. The model transformed into a mixed integer linear programming problem for optimal solutions was validated numerically, examining various factors affecting optimal renewable energy investment capacity.

Novel process optimization based on machine learning: A study on biohydrogen production from waste resources

The biomass poultry litter and sewage sludge co-gasification is a good thermochemical method to produce hydrogen energy meanwhile to mitigate the consumption of fossil fuels. However, the operation optimization in the complex process system is important while computationally difficult because of high nonlinearity and many first-principle constraints. To address the optimization of this biohydrogen production process, a methodology framework for achieving the optimal operations is thus presented. The complete process system is first simulated and decomposed into upstream gasification process and downstream hydrogen purification for reducing computational complexity through the thermodynamic equilibrium-based simulation. Totally 1400 data points by pairing total 15 operating conditions with a composite sustainability index objective are generated through the random sampling and data classification strategies, which are then used for the construction of the artificial neural network (ANN)-based prediction models. ANN models of two subprocesses demonstrate the satisfactory prediction accuracy with R2 value of 0.98 and 0.99, respectively, which are then integrated with mixed-integer linear programming (MILP) for the optimization of upstream process and downstream process step-by-step. The MILP problems based on the ANN models are solved with lower optimization time of 45∼100 s compared to the heuristic algorithm optimization (3–6 h) based on the thermodynamic equilibrium-based simulation. The optimal sustainability index values of two processes are 0.80 and 0.91 which are both improved compared to the existing optimization results (0.79 and 0.84). This study emphasizes the optimization potential of the integration approach of machine learning-based modelling and mathematical programming for developing the optimal waste-to-energy processes.

Intersection control based on Fine-grained Phases for connected and automated vehicles

Traditional traffic signal control is one of the most widely used urban traffic control methods, due to its high efficiency, robustness, and simplicity. However, in the era of connected and automated vehicles (CAVs), it is prospective to enhance traffic control precision and achieve vehicle coordination in a more efficient manner. Focusing on an isolated intersection, this study proposes an innovative concept of Fine-grained Phase (FP) for CAV-enabled traffic control, which realizes more refined right-of-way allocation than traditional signal phases while preserving the simplicity and scalability. The development of FP jointly optimizes traffic control strategy and intersection layout design to fully utilize time-space resources, and multiple forms of FP could be generated in response to various traffic demands; meanwhile, vehicle coordination is achieved in an offline–online manner to balance solution quality and efficiency. Under the FP-based control, each lane is assigned with periodical entry time points using FP design results, then vehicles are supposed to catch up with the appropriate time points to fulfill their trips. Theoretical analyses are conducted under stationary vehicle arrival patterns, where the average delay and the intersection capacity associated with different forms of FP can be analytically acquired. For the implementation of FP-based control, we construct a general offline–online framework, consisting of an offline model that optimizes the geometry of the conflict zone at intersections and the control strategy of vehicles simultaneously, which is formulated as a mixed-integer linear programming problem, and an online FP adoption mechanism that can adapt to varying demand patterns. Under the framework, limited online computation is required, facilitating its practical real-time implementation. Simulation studies under a variety of demand settings show that FP-based control is advantageous over benchmark methods in reducing vehicle delay and also improving intersection capacity in most cases; even for cases with extremely imbalanced demands, FP-based control can admit comparable throughput, while the average delay is much smaller. In addition, results of computation time reveal that FP-based control could realize real-time implementation with negligible computation burden.

Resilience-Oriented Planning of Urban Distribution System Source–Network–Load–Storage in the Context of High-Penetrated Building-Integrated Resources

Building-integrated flexible resources can offer economical availability to accommodate high-penetrated renewable energy sources (RESs), which can be potentially coordinated to achieve cost-effective supply. This paper proposes a resilience-oriented planning model of urban distribution system source–network–load–storage in the context of high-penetrated building-integrated resources. In this model, source–network–load–storage resources are cost-optimally planned, including the lines, soft open point (SOP), building-integrated photovoltaics (BIPVs), building-integrated wind turbine (BIWT), building-integrated energy storage system (ESS), etc. To enhance fault recovery capability during extreme faults, fault scenarios are incorporated into the distribution system operation via coupled multiple recovery stages. The resilience-oriented planning is a thorny problem due to its source–network–load–storage couplings, normal-fault couplings, etc. The original resilience-oriented planning is reformulated as a mixed-integer linear programming (MILP) problem, which can then be solved with a two-stage method and evaluated via a multi-dimensional evaluation metrics. The proposed planning methodology is benchmarked over a Portugal 54-node urban distribution system to verify the superiority and effectiveness on the system economy and resilience levels. Case studies show that the proposed methodology can exploit the optimal synergies of different source–network–load–storage components and enhance system dispatchability.

A hybrid multi-objective solution approach for a reliable truck-drone routing problem integrated with pickup and delivery services

ABSTRACT Humanitarian logistics aims to reduce the arrival time of relief goods and optimize services in disaster-affected regions. This paper introduces a multi-objective hybrid truck-drone routing problem with pickup and delivery services, considering reliability (MHTDRP-PD-R) to enhance relief operations within humanitarian logistics. The model is formulated as a mixed-integer linear programming problem with the simultaneous goals of minimizing transportation time and maximizing reliability through routing and inventory decisions made by multiple trucks and drones. An adaptive large neighborhood search (ALNS) algorithm, coupled with heuristic technique, is developed to tackle the problem. The ALNS algorithm refines initial solutions through destroy and repair operators, integrated with multi-objective optimization methods to create a unified objective function. Small and large-scale test problems are then employed to evaluate solution quality using multi-objective optimization. The calculation results show the superiority of the developed ALNS integrated with the ε-constraint method regarding the objective value and solution time.

Interdependent Expansion Planning for Resilient Electricity and Natural Gas Networks

This study explores enhancing the resilience of electric and natural gas networks against extreme events like windstorms and wildfires by integrating parts of the electric power transmissions into the natural gas pipeline network, which is less vulnerable. We propose a novel integrated energy system planning strategy that can enhance the systems’ ability to respond to such events. Our strategy unfolds in two stages. Initially, we devise expansion strategies for the interdependent networks through a detailed tri-level planning model, including transmission, generation, and market dynamics within a deregulated electricity market setting, formulated as a mixed-integer linear programming (MILP) problem. Subsequently, we assess the impact of extreme events through worst-case scenarios, applying previously determined network configurations. Finally, the integrated expansion planning strategies are evaluated using real-world test systems.

Techno-economic evaluation of developing a zero-carbon highway service area energy system

ABSTRACT To further reduce CO2 emissions from highway service areas, this study proposes a novel zero-carbon highway service area energy system (S3). This system not only addresses energy supply challenges in remote locations but also expedites the reduction of CO2 emissions. A mixed-integer linear programming problem is formulated to optimize the configuration and operation of the proposed system. The system is compared with the conventional (S1) and low-carbon (S2) highway service area systems. Focused on northwest China, the results indicate that S3 can achieve zero CO2 emissions. However, the energy efficiency ratio (EER) of S1 is the highest at 84%, surpassing S3 by 2.4% (82%). In terms of economic analysis, the total cost and levelized cost of electricity (LCOE) of S1 are the highest at 1.62 MUSD and 0.14 USD/kWh, respectively. These values are 100% and 180% higher than those of S3, which are 0.81 MUSD and 0.05 USD/kWh.

Incorporating local uncertainty management into distribution system planning: An adaptive robust optimization approach

As the penetration of renewable energy sources (RES) significantly increases, their inherent uncertainty has brought about a paradigm shift in distribution system planning and operation. The existing planning methodologies usually consider the uncertainty during the investment and day-ahead stages while neglecting the interactive power fluctuations during the intraday stage, resulting in planning schemes with a risk of inadequate regional stability. In light of this, this paper proposes a novel adaptive robust distribution system planning approach that integrates local uncertainty management (LUM) to provide a comprehensive and refined consideration of uncertainty. First, we introduce the concept of LUM that can effectively address the deviations between predicted and actual power of RES and load. Second, we propose the adaptive robust planning model for the distribution system, in which the investment and day-ahead operation are considered in the first stage, while LUM is considered in the second stage to maintain the local stability of interactive power. The proposed model can actively manage uncertainties of RES and load demand, reaching the optimal balance between the investment cost, operational cost, and LUM cost. Finally, by employing the column-and-constraint generation (C&CG), the adaptive robust planning model is decoupled into a master min problem and a slaver max-min problem, after which the max-min problem is converted into a single mixed-integer linear programming (MILP) problem through the strong duality theory and big-M method. The effectiveness of the proposed model is demonstrated using a real-world distribution system located in Fujian Province, China. The simulation results indicate that the proposed model achieves a quantitative decrease of approximately 10% in total cost compared to deterministic planning. Sensitivity analysis is also conducted to reveal the trade-off between economic cost and robustness level.

Integrating Compressed CO2 Energy Storage in an Integrated Energy System

The integration of an energy storage system into an integrated energy system (IES) enhances renewable energy penetration while catering to diverse energy loads. In previous studies, the adoption of a battery energy storage (BES) system posed challenges related to installation capacity and capacity loss, impacting the technical and economic performance of the IES. To overcome these challenges, this study introduces a novel design incorporating a compressed CO2 energy storage (CCES) system into an IES. This integration mitigates the capacity loss issues associated with BES systems and offers advantages for configuring large-scale IESs. A mixed integer linear programming problem was formulated to optimize the configuration and operation of the IES. With an energy storage capacity of 267 MWh, the IES integrated with a CCES (IES–CCES) system incurred an investment cost of MUSD 161.9, slightly higher by MUSD 0.5 compared to the IES integrated with a BES (IES–BES) system. When not considering the capacity loss of the BES system, the annual operation cost of the IES–BES system was 0.5 MUSD lower than that of the IES–CCES system, amounting to MUSD 766.6. However, considering the capacity loss of the BES system, this study reveals that the operation cost of the IES–BES system surpassed that of the IES–CCES system beyond the sixth year. Over the 30-year lifespan of the IES, the total cost of the IES–CCES system was MUSD 4.4 lower than the minimum total cost of the IES–BES system.

Micro-grid tri-level EPEC based model for finding equilibria in the day-ahead and balancing markets

This paper presents a model that explores the strategic bidding equilibrium within a microgrid and its interactions with other strategic and non-strategic rivals in a joint energy and balancing market. The model utilizes a tri-level mathematical program with equilibrium constraints (MPEC) to represent the behavior of each strategic producer. Upper level maximizes the profit of each strategic producer, including microgrid and another strategic rival. The first lower-level problem involves maximizing social welfare through the day-ahead market clearing process, while the second lower-level problem deals with the balancing market clearing process. These objectives form the core of the proposed model. To simplify the tri-level problem, duality theory and the Karush-Kuhn-Tucker (KKT) optimally conditions are employed to transform it into a mixed integer linear programming (MILP) problem. By simultaneously solving all MPECs, an equilibrium problem with equilibrium constraints (EPEC) is formulated. The resulting EPEC is then addressed using a diagonalization algorithm and game theory to obtain a market Nash equilibrium, which constitutes the secondary objective of this paper. The effectiveness of the model is evaluated using the 6-bus test system as a case study. The results indicate that, at the equilibrium point, both the microgrid and rivals experience reduced profits compared to the initial state.