Mixed Integer Research Articles

Distribution network topology identification method based on state estimation with mixed integer programming and structural equation model

Distribution network topology identification (DNTI) is an important prerequisite for distribution system operation. Frequent topology changes and limited measurement equipment make identifying the correct topology unavoidably challenging. To this end, this paper proposes a state estimation method for distribution network topology identification using a small amount of phasor measurement unit (PMU) measurement data. Firstly, this paper introduces the application of the structural equation model (SEM) in distribution networks and explains the relationship between branch currents and topology. Then, auxiliary variables are introduced for the feasible domain problem present in the algorithm, which improves the solvability of the algorithm. In addition, this paper reconsiders the operation mode constraints in terms of nodes from the perspective of distribution network operation mode. The Structural Equation Modeling-based Mixed Integer Programming (SEM-MIP) method proposed in this paper can be solved using existing commercial solvers, and its effectiveness has been verified by simulation in IEEE 33-node test system and IEEE 123-node test system.

Dynamic Fleet Configuration Model for Optimizing Earthmoving Operations Using Mixed Integer Linear Programming

Dynamic Fleet Configuration Model for Optimizing Earthmoving Operations Using Mixed Integer Linear Programming

Multi-Static Radar System Deployment Within a Non-Connected Region Utilising Particle Swarm Optimization

This paper is mainly devoted to studying the deployment problem of a multi-static radar system (MSRS) within a non-connected deployment region using multi-objective particle swarm optimization (MOPSO). By modeling and reformulating the problem, it can be represented as a multi-objective mixed integer programming (MOMIP), which eliminates the need for additional constraints. To enhance the algorithm performance, integer variables and continuous ones are treated separately employing multiple velocity formulas. The velocity formulas for integer variables are modified using the sigmoid function and genetic operation, leading to the proposal of two MSRS deployment algorithms, namely MOPSO-Sigmoid and MOPSO-Gene. To evaluate the performance of the proposed algorithms, they are compared with two existing MOPSO-based algorithms. The first algorithm is the MSRS deployment algorithm for the non-connected deployment region that addresses the additional constraint problem model. The second algorithm is based on an existing conventional MOPSO algorithm and addresses the equivalent MOMIP problem model. A numerical study demonstrates that MOPSO-Sigmoid and MOPSO-Gene exhibit promising efficiency and effectiveness.

Optimal management in island microgrids using D-FACTS devices with large-scale two-population algorithm

Amidst the increasing complexity of microgrid optimization, characterized by numerous decision variables and intricate non-linear relationships, there is a pressing need for highly efficient algorithms. This study introduces a tailored Mixed Integer Nonlinear Programming (MINLP) model that optimizes the charging and discharging schedules of electric vehicles (EVs) and energy storage systems (ESS) while incorporating Distributed Flexible AC Transmission System (D-FACTS) devices. To address these challenges, a novel approach based on the Large-Scale Two-Population Algorithm (LSTPA) is proposed. The model's effectiveness was evaluated using a 33-node microgrid, where the proposed method achieved a total purchased energy of 1.2 MWh, a voltage deviation of 0.0357 p.u, and a CPU time of 551 s, outperforming traditional methods like NSGA-II, PSO, and JAYA. Additionally, in a 69-node microgrid, the approach resulted in a total purchased energy of 0.3 MWh and a voltage deviation of 0.0078 p.u. These results demonstrate the superior performance of the proposed method in terms of energy efficiency, voltage stability, and computational time, advancing the efficiency of microgrid management.

The Potential for the Use of Hydrogen Storage in Energy Cooperatives

According to the European Hydrogen Strategy, hydrogen will solve many of the problems with energy storage for balancing variable renewable energy sources (RES) supply and demand. At the same time, we can see increasing popularity of the so-called energy communities (e.g., cooperatives) which (i) enable groups of entities to invest in, manage, and benefit from shared RES energy infrastructure; (ii) are expected to increase the energy independence of local communities from large energy corporations and increase the share of RES. Analyses were conducted on 2000 randomly selected energy cooperatives and four energy cooperatives formed on the basis of actual data. The hypotheses assumed in the research and positively verified in this paper are as follows: (i) there is a relationship between hydrogen storage capacity and the power of RES, which allows an energy community to build energy independence; (ii) the type of RES generating source is meaningful when optimizing hydrogen storage capacity. The paper proves it is possible to build “island energy independence” at the local level using hydrogen storage and the efficiency of the power-to-power chain. The results presented are based on simulations carried out using a dedicated optimization model implemented by mixed integer programming. The authors’ next research projects will focus on optimizing capital expenditures and operating costs using the Levelized Cost of Electricity and Levelized Cost of Hydrogen methodologies.

On Discrete Subproblems in Integer Optimal Control with Total Variation Regularization in Two Dimensions

We analyze integer linear programs that we obtain after discretizing two-dimensional subproblems arising from a trust-region algorithm for mixed integer optimal control problems with total variation regularization. We discuss NP-hardness of the discretized problems and the connection to graph-based problems. We show that the underlying polyhedron exhibits structural restrictions in its vertices with regard to which variables can attain fractional values at the same time. Based on this property, we derive cutting planes by employing a relation to shortest-path and minimum bisection problems. We propose a branching rule and a primal heuristic which improves previously found feasible points. We validate the proposed tools with a numerical benchmark in a standard integer programming solver. We observe a significant speedup for medium-sized problems. Our results give hints for scaling toward larger instances in the future. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms–Discrete. Funding: This work was supported by the Deutsche Forschungsgemeinschaft [Grant MA 10080/2-1]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2024.0680 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2024.0680 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Reallocation of chemotherapy appointments in a large health system using a mixed integer linear programming approach

ABSTRACT Outpatient chemotherapy scheduling has significant implications for both patients and health systems. Consideration of treatment location preference is important for patient satisfaction and outcomes, and it is a complex decision impacted by travel distance. In health systems with one treatment site that stands out from the rest as a destination medical center (the primary site), there are financial and resource utilization incentives to free up as much space as possible for appointments at that site. In this study, we demonstrate that leveraging the underutilized health system sites allows decompression of appointment volume at the primary site, and it takes full advantage of valuable resources such as oncology nurses and chair availability. A Mixed Integer Linear Programming approach was used to develop a model under four scenarios which reallocates appointments from the primary site to other health system sites based on patient travel distance to the sites. This approach was applied to data from the Mayo Clinic Health System Minnesota region, which demonstrated that the health system has the potential to move approximately 50% of eligible appointments out of the primary site, resulting in an overall volume change of approximately 30%. Implications for scheduling policies and infrastructure are discussed.

Integrated Scheduling of Handling Equipment in Automated Container Terminal Considering Quay Crane Faults

Quay cranes (QCs) play a vital role in automated container terminals (ACTs), and once a QC malfunctions, it will seriously affect the operation efficiency of ships being loaded and unloaded by the QC. In this study, we investigate an integrated scheduling problem of quay cranes (QCs), yard cranes (YCs), and automated guided vehicles (AGVs) under QC faults, which is aimed at minimizing the loading and unloading time by determining the range of adjacent operational QCs of the faulty QCs and reallocating unfinished container handling tasks of QCs. A mixed integer programming model is formulated to dispatch QCs, YCs, and AGVs in ACTs. To solve the model, an adaptive two-stage NSGA-II algorithm is proposed. Numerical experiments show that the proposed algorithm can significantly reduce the impact of faulty QCs on productivity while maintaining its synchronous loading and unloading efficiency. The sensitivity analysis of ship scale, location, and number of faulty QCs indicates that the number of faulty QCs has a greater influence on the loading and unloading efficiency than their locations, and the impact of faulty QCs on the efficiency of small-scale ships is greater than that of large-scale ships.

Joint optimal PMU and DULR placement in distribution network considering fault reconstruction and state estimation accuracy

Due to the rapid development of the distribution network, there is an urgent need for high-precision state estimation and safe and stable operation, this paper proposes a joint optimal placement method for Phasor Measurement Unit (PMU) and Dual Use Line Relay (DULR) in distribution networks considering fault reconstruction and state estimation accuracy. The proposed method aims to minimize the cost of PMU and DULR configuration. Based on the known pseudo-measurements and Supervisory Control and Data Acquisition (SCADA) measurements, we use the E-optimal standard design of the state estimation error covariance matrix to form the state estimation accuracy index and take the relay protection function of Feeder Terminal Unit (FTU) device and DULR device into consideration of the fault reconstruction. By solving the mixed integer semidefinite programming (MISDP) model, the optimal placement result is obtained, so that the network under normal condition and the network after multiple fault reconstruction can meet the constraints of state estimation accuracy and load loss rate respectively. The proposed method is tested on IEEE 33-node, 123-node systems as an example. The experimental results show that the proposed method is effective and practical.Note to Practitioners—This study is stimulated by the need for optimizing the placement of Micro-PMU (µPMU) in distribution network. Since the new µPMU device DULR has the same relay protection function as FTU, and distributed generation can supply power to the island after failure, this paper adds the load loss rate to the constraint conditions to study the influence of fault reconstruction on the placement scheme. A new two-step SE method considering mixed measurements was used in this paper to improve the computational efficiency of real-time SE of large-scale system while ensuring the accuracy of the calculation results. We have conducted tests in IEEE-33 and IEEE-123 systems. After preliminary verification, compared with the single fault scenario, we find that the placement scheme considering multiple fault scenarios can effectively improve the accuracy of state estimation and reduce the load loss rate of each fault scenario and only increase the cost a little. The increase in the number of DG and contact lines in the network will also effectively improve the feasibility of the placement scheme. The increase of the number of FTU configurations can effectively reduce the configuration of DULR by adding a small amount of µPMU, reduce the total cost as a result. In future studies, we will further consider the integrated configuration of µPMU, DULR and FTU, to meet more failure scenarios while reducing costs.

Asynchronous decentralized traffic signal coordinated control in urban road network

AbstractThis study introduces an asynchronous decentralized coordinated signal control (ADCSC) framework for multi‐agent traffic signal control in the urban road network. The controller at each intersection in the network optimizes its signal control decisions based on a prediction of the future traffic demand as an independent agent. The asynchronous framework decouples the entangled interdependence between decision‐making and state prediction among different agents in decentralized coordinated decision‐making problems, enabling agents to proceed with collaborative decision‐making without waiting for other agents’ decisions. Within the proposed ADCSC framework, each controller dynamically optimizes its signal timing strategy with a unique rolling horizon scheme. The scheme's individualized parameters for each controller are determined based on the vehicle travel time between the adjacent intersections, ensuring that controllers can make informed control decisions with accurate arrival flow information from upstream intersections. The signal optimization problem is formulated as a mixed integer linear program model, which adopts a flexible signal scheme without a fixed phase structure and sequence. Simulation results demonstrate that the proposed ADCSC strategy significantly outperforms the benchmark signal coordination methods in terms of average delay, travel speed, stop numbers, and energy consumption. Experimental analysis on computation time validates the applicability of the proposed optimization model for real‐time implementation. Sensitivity analysis on key parameters in the framework is conducted, offering insights for parameter selection in practice. Furthermore, the ADCSC framework is extended to a road network in Qinzhou City, China, with 45 signalized intersections, demonstrating its effectiveness and scalability in the real‐world road network.

The mixed integer trust region problem

The mixed integer trust region problem

Data-driven collaborative healthcare resource allocation in pandemics

Severe shortages of healthcare resources are major challenges in pandemics, especially in their early stages. To improve emergency management efficiency, this paper proposes a novel rolling predict-then-optimize framework that includes three interactive modules, i.e., data-driven demand prediction, healthcare resource allocation, and parameter rolling update. Such a framework uses historical data to dynamically update the control parameters of the proposed Net-SEIHRD model, which predicts the healthcare needs of each region by jointly considering government interventions and cross-regional travel behaviors. Based on the forecasted healthcare resource demand in real-time, an optimization model is then formulated to realize coordinated resource allocation across multiple regions by minimizing the total generalized cost. To facilitate model solving, the proposed mixed integer nonlinear programming model is converted into an equivalent mixed integer linear model by using some linearization techniques. Finally, the proposed method is applied to the SARS-CoV-2 emergency response and collaborative allocation of healthcare resources in Shanghai, China. The results show that the proposed prediction model can effectively predict the peak and scale of the spread of the virus. Compared with the traditional LM and SEIHR models, the prediction accuracy of the Net-SEIHRD model is improved by 10.76% and 24.11%, respectively. Moreover, coordinated relief activities across regions, such as patient transfer and drug-sharing can improve the efficiency of pandemic control and save social costs.

Operational optimization of a rural multi-energy system supported by a joint biomass-solid-waste-energy conversion system and supply chain

Biomass, as one of the most accessible renewable resources, could reduce dependency on fossil fuels and mitigate associated environmental impacts. With economic development and improved living standards, biomass in rural areas is converted into various forms of energy to meet high energy demands. However, existing studies on rural multi-energy system operations assume energy production from biomass is a given input parameter and consider it to be a fixed constant or subject to upper and lower bounds, independent of the biomass supply chain. Indeed, biomass energy production is significantly influenced by the collection, transportation, storage, and other processes within the supply chain. This work proposes a mixed integer linear program (MILP) for the joint optimization of an integrated rural multi-biomass-solid waste energy conversion system with a source-grid-demand-based biomass-solid waste supply chain (IRMBS-BSC system). The IRMBS-BSC system encompasses three sub-systems: the biomass-solid waste source sub-system, the biomass-solid waste grid sub-system, and the biomass-solid waste demand sub-system. Various biomass-solid wastes are classified, and a source model is established to evaluate their availability. Subsequently, a supply chain model is developed within the biomass-solid waste grid sub-system. Based on the available and transported quantity from the biomass-solid waste source sub-system and grid sub-system, a multi-energy system operation model, considering refined biomass conversion processes, is proposed. A case study involving a multi-energy system that integrates multiple rural community biomass-solid waste supplies is conducted. The results demonstrate that the proposed MILP, which considers the biomass-solid waste supply chain, can reduce energy imports during the load peak periods and can also decrease the overall operational costs of the multi-energy system.

A multi-level rescheduling approach for a dynamic remote operations scheduling problem

ABSTRACT In this paper, we tackle a dynamic scheduling problem faced by a large international company. The problem involves assigning installation projects arriving over time to specialised technicians who execute them remotely. Each project consists of several tasks having processing times, release dates, and execution deadlines. The company needs to assign projects to technicians and schedule tasks complying with technicians' skills, precedence constraints between tasks, and tasks requiring multiple technicians simultaneously. The problem is dynamic as new projects and tasks become available over time, requiring their allocation to technicians. We formulate the offline problem as a mixed integer linear program that minimises the makespan, and we address the dynamic version solving restricted problems within a rolling horizon framework. The approach systematically implements different levels of schedule adjustment to incorporate new information. To study scalability, we validate our algorithm by using both real-world and synthetic simulations demonstrating its efficiency and effectiveness. Additionally, we provide interesting managerial insights for the company.

Demand rerouting mechanisms with revenue management for intermodal barge transportation networks

Inland waterway transportation plays a crucial role in Europe's transportation network and economy. It is an efficient and sustainable mode of transportation, with lower emissions and energy consumption than other modes of transportation, such as road and air. However, the services provided by inland waterway transport can be significantly impacted by adverse weather conditions such as heavy rain, strong winds, and flooding. These disruptions can cause delays, cancellations, or even damage to vessels or infrastructure. To improve the system reliability, we propose a set of revenue management based (demand itinerary) rerouting mechanisms for intermodal barge transportation optimisation. Revenue Management policies including several customer categories and fare differentiation are applied. Sequential accept/reject decisions are made based on a probabilistic mixed integer programming model maximising the expected revenue of a carrier. A booking framework is defined over a rolling horizon and capacity allocation/reallocation decisions are made for a set of demands including the current and relevant past and potential future transportation requests. Several (demand) rerouting mechanisms are defined and implemented on different service network configurations. The service network status is regularly updated, in particular with respect to barge capacity variations due to changing water levels. An extensive set of experiments is performed and numerical results are analysed. The study results emphasise the added value but also the need for data availability and information sharing between the different stakeholders of Inland Waterway Transportation systems.

Part Feeding and Internal Transportation Decision Making for a Machinery Manufacturer

This research validates a mixed integer linear programming model that minimizes total feeding and acquisition costs by integrating assembly line feeding and vehicle type decisions in a machinery manufacturing company. The results show that the optimal assignment reduces costs by 56% compared with the company's current assignment.

Techno-economic optimization and feasibility of PCM-based seasonal thermal energy storage systems for district heating and cooling

Phase change materials (PCM) are an attractive seasonal thermal energy storage solution for load shifting due to relatively high energy density. Nevertheless, the choice of the right design parameters, such as storage size and phase-change temperature, is nontrivial, as these are tightly linked to the expected seasonal operation of the storage. This paper presents a combined design and operation optimization framework for sizing PCM-based seasonal thermal storage, which can capture dynamic behaviour of the storage in sensible and latent phases, and its impact on the efficiency of connected heat pumps and chillers. The proposed method, formulated as a mixed integer quadratically-constrained programming problem, was applied to a case study of heating-dominated district. It was found that the optimal PCM melting temperature equals to the heating demand supply temperature, thus removing the need of a heat pump to discharge the storage. The optimal operation of storage requires a full charging and discharging cycle of both latent and liquid phase. Higher CO2 emission price does not lead to a significant reduction of CO2 emissions, but the storage size does, leading to a higher heating coverage ratio of the storage, and consequently CO2 emissions and cost savings, which can be further enhanced with PV integration. The economic analysis indicates that, unless other benefits such as storage volume reduction are accounted for, PCM cost should drop by a factor 4 to make this solution economically viable for seasonal storage.

A two-layer strategy for sustainable energy management of microgrid clusters with embedded energy storage system and demand-side flexibility provision

The intermittent nature of renewable energy generation and the fluctuating demands pose persistent challenges in microgrid operations. In response, stakeholders and operators have turned to clustering the geographically adjacent microgrids as a solution. In this context, this paper introduces a novel two-layer energy management strategy for microgrid clusters, utilizing demand-side flexibility and the capabilities of shared battery energy storage (SBES) to minimize operational costs and emissions, while ensuring a spinning reserve within individual microgrids to prevent load-shedding. In the lower layer, the proposed approach devises optimal day-ahead operation policies, while the upper layer employs a cooperative strategy to further optimize the operational efficiency across the entire cluster. The energy management problem is accurately formulated as a mixed integer quadratic programming (MIQP) optimization, which incorporates linear terms in the problem's constraints. The formulation accounts for operational costs associated with SBES including expenses of charging/discharging and changes in operating states (CiOS). Real-world case studies with a cluster of three microgrids in Australia validate the effectiveness of this approach. Results show a reduction in operational costs for the base case scenario by 6.96 % compared to conventional microgrid management strategies. Sensitivity analyses further demonstrate the economic benefits of varying SBES capacity and flexibility pricing, with savings ranging from 6.5 % to 8.1 %. The proposed strategy also reduces CO2 emissions by up to 11.6 %, while improving system reliability. This strategy holds promise for integration into distributed energy systems with high renewable penetration and clustered local grids, offering significant advantages for utility operators and end-users through improved energy efficiency and reduced emissions.

Research on cargo volume prediction and personnel scheduling optimization of sorting center based on BP neural network and improved genetic algorithm

With the development of Internet technology, e-commerce has become the primary choice for consumers to shop, and the huge order transaction volume has generated logistics problems. As an important part of the logistics network, the sorting platform is essential to improve its management efficiency. To enhance the efficiency of the sorting center, the topological relationship diagram is used to show the logistics network, and the cargo volume of the sorting center in the next 30 days and every hour is predicted based on the BP neural network model. Based on the mixed integer linear programming model and the improved genetic algorithm SCAGA model, the total man-days are minimized to ensure that the cargo volume is processed. At the same time, to ensure that the actual hourly efficiency is as balanced as possible, the optimization problem of personnel scheduling is studied. To maintain the efficient operation of the logistics industry, the accurate prediction of the number of goods and the reasonable scheduling of personnel, to provide a set of efficient and economical personnel scheduling programs for the logistics company, thus improving the overall operational efficiency and service quality.

Scheduling Splitable Jobs on Identical Parallel Machines to Minimize Makespan using Mixed Integer Linear

The scheduling of parallel machines with and without a job-splitting property, deterministic demand,and sequence-independent setup time with the goal of minimizing makespan is examined in this work.For simultaneous processing by multiple machines, single-stage splitable jobs are broken into random(job) sections. When a job starts to be processed on a machine, an operator has to setup the machinefor an hour. By creating two Mixed Integer Linear Programming models, this work proposes amathematical programming strategy (MILP). A MILP model takes the job-splitting property intoaccount. Another model, however, does not include the job-splitting property. This study investigatesthe performance of the proposed models using Gurobi solver. These programs' numerical calculationsare based on actual problems in the Indonesian city of Bandung's plastics industry. On four identicalparallel injection molding machines, 318 jobs must be finished in 22 periods. The real schedulingmethod is contrasted with these two MILP models. The maximum workload imbalance, the maximumrelative percentage of imbalance, and the makespan of these three scheduling systems are used toevaluate their effectiveness. Without the job-splitting property, MILP can handle the real issue ofscheduling identical parallel machines on injection molding machines to reduce makespan, resultingin a 36% average decrease. The MILP model's job-splitting property can reduce makespan by anadditional 2.40%. The order of relative ranking is MILP with job-splitting property, MILP withoutjob-splitting property, and actual scheduling based on the makespan minimization, workloadimbalance, and relative percentage of imbalance.