Integer Linear Programming Method Research Articles

Optimal PMU placement in the Southern Cameroon interconnected grid considering the effect of a group of ZIBs for complete observability and dynamic stability

In this paper, a solution for optimal PMU placement in the southern Cameroon interconnected grid (SIG) is proposed to the issue of dynamic stability within the network. The power system under consideration relies on SCADA parameter monitoring, which offers unsynchronized measurements and inconsistent state estimation of the grid. Moreover, SCADA system's data scan rate hinders its efficiency in capturing the dynamic and transient behaviours in the power grid. The Approach in this research is based on the integer linear programming (ILP) considering the effect of a group of zero-injection buses (ZIBs). Subsequently, a comparative analysis is conducted to evaluate the performance of the ILP method in terms of the number of PMUs, the number of buses observable from one or more nodes, and the sum of redundancy index (SORI) in comparison to other optimization algorithms. The results obtained using MATLAB 2020a demonstrate that the ILP method, considering the effect of a group of ZIBs and the SORI, provides the most optimal solution. Furthermore, a PMU-based dynamic stability assessment is performed, validating the improvement of the visibility of voltage signals.

The Chinese Postman Problem and Simulated Annealing applied to urban forest inventory

Routing is the process of defining paths between geographically distinct points, and it has been applied in decision-making processes for services that include displacement, with potential application in the planning of urban forest inventories. Linear Programming is an operations research technique often applied to solve complex problems, such as those related to routing. Thus, the objective of this study was to verify whether the application of a routing model via Integer Linear Programming (ILP) increases the efficiency of an urban forest inventory using real data. First, we compared the empirical division used in the inventory with the application of the ILP method for routing. We also tested an approximate method (Simulated Annealing, SA) to solve the routing problem and reduce the processing time. Finally, we simulated the consequences of applying ILP in different scenarios. The results showed that the ILP improved the inventory efficiency by 6.36%, and the use of SA reduced the processing time by 43,200 times for the most complex scenario, resulting in a solution that was 1.87% of the ILP response value. Our findings show the potential application of ILP in the planning of urban forest inventories, with gains directly proportional to the number of lots in the inventory.

Neuron grouping and mapping methods for 2D-mesh NoC-based DNN accelerators

Deep Neural Networks (DNNs) have gained widespread adoption in various fields; however, their computational cost is often prohibitively high due to the large number of layers and neurons communicating with each other. Furthermore, DNNs can consume a significant amount of energy due to the large volume of data movement and computation they require. To address these challenges, there is a need for new architectures to accelerate DNNs. In this paper, we propose novel neuron grouping and mapping methods for 2D-mesh Network-on-Chip (NoC)-based DNN accelerators considering both fully connected and partially connected DNN models. We present Integer Linear Programming (ILP) and simulated annealing (SA)-based neuron grouping solutions with the objective of minimizing the total volume of data communication among the neuron groups. After determining a suitable graph representation of the DNN, we also apply ILP and SA methods to map the neurons onto a 2D-mesh NoC fabric with the objective of minimizing the total communication cost of the system. We conducted several experiments on various benchmarks and DNN models with different pruning ratios and achieved an average of 40-50% improvement in communication cost.

A novel dynamic batching energy management strategy for multi-microgrid networks with enhanced privacy

This article presents a novel energy management approach termed Dynamic Batching EMS (DBEMS) designed specifically for day-ahead scheduling within multi-microgrid (MMG) networks. The prime aim of this strategy is to curtail operational costs within the MMG network, fortify the privacy of individual microgrids, and optimize the utilization of available resources, surpassing existing methodologies like centralized, decentralized, and nested management strategies. The emphasis is chiefly on orchestrating cost-effective operations while bolstering data privacy for each microgrid within the complex MMG framework. The efficacy of the proposed strategy is evaluated across both grid-connected and islanded modes, focusing on a network comprising four microgrids. The model formulation is executed utilizing the Mixed Integer Linear Programming method. In the islanded mode, optimization is conducted for scenarios both inclusive and exclusive of Battery Energy Storage Systems (BESS). Comparative assessments are made against centralized and nested strategies, considering parameters including operational costs, privacy enhancements, load-shedding, computation time, and computational burden.

Optimizing spot intensity with lower bound constraints for IMPT: Exposing shortcomings and introducing an enhanced strategy.

Intensity Modulated Proton Therapy (IMPT) is a sophisticated radiation treatment allowing for precise dose distributions. However, conventional spot selection strategies in IMPT face challenges, particularly with minimum monitor unit (MU) constraints, affecting planning quality and efficiency. This study introduces an innovative Two-Stage Mixed Integer Linear Programming (MILP) method to optimize spot intensity in IMPT with Lower Bound (LB) constraints. This method seeks to improve treatment planning efficiency and precision, overcoming limitations of existing strategies. Our approach evaluates prevalent IMPT spot selection strategies, identifying their limitations, especially concerning MU constraints. We integrated LB constraints into a MILP framework, using a novel three-phase strategy for spot pool selection, to enhance performance over traditional heuristic methods and L1+L∞ strategies. The method's efficacy was tested in eight study cases, using Dose-Volume Histograms (DVHs), spot selection efficiency, and computation time analysis for benchmarking against established methods. The proposed method showed superior performance in DVH quality, adhering to LB constraints while maintaining high-quality treatment plans. It outperformed existing techniques in spot selection, reducing unnecessary spots and balancing precision with efficiency. Cases studies confirmed the method's effectiveness in producing clinically feasible plans with enhanced dose distributions and reduced hotspots, especially in cases with elevated LB constraints. Our Two-Stage MILP strategy signifies a significant advancement in IMPT treatment planning. By incorporating LB constraints directly into the optimization process, it achieves superior plan quality and deliverability compared to current methods. This approach is particularly advantageous in clinical settings requiring minimum spot number and high MU LB constraints, offering the potential for improved patient outcomes through more precise and efficient radiation therapy plans.

Dinamic Economic Dispatch (DED) Berbasis Mixed Integer Linear Programming (MILP) Dengan Mempertimbangkan Pembangkit EBT Pada Kelistrikan Pulau Sumbawa

In the Dynamic Economic Dispatch (DED) based on Mixed Integer Linear Programming (MILP) for the electricity of Sumbawa Island by considering RE (Renewable Energy) power plants, several aspects need to be considered, namely Variable Addition and Limitations: In the MILP model, the new variable must include the allocation of power from RE sources, such as solar power plants or geothermal power plants. Relevant technical and operational constraints should also be applied, such as capacity limits, characteristic curves and sustainability limits for renewable energy sources. The Sumbawa Island electricity system must consider the technical limitations related to RE Power plants. This includes capacity limitations, sustainability limitations (such as solar radiation levels or water discharge during the dry season), as well as the system's ability to handle variations in power generated by RE Power plants that depend on natural energy sources. One of the challenges in integrating RE Power plants is its variability. Renewable energy sources such as solar and hydropower tend to fluctuate in their power output depending on weather conditions. Therefore, the DED model must consider predictions or estimates of the power generated by RE Power plants to optimize accurate power allocation and minimize operational costs. The simulation results show that the Mixed Integer Linear Programming (MILP) method is able to provide a simple and economical solution to the DED problem. The change in operation using gas fuel and cofiring by 5% is a factor in the existence of minimal fixed power in the system. This thesis is a DED solution using Mixed Integer Linear Programming (MILP) by considering fuel changes as the main consideration in mathematical calculations to determine plant operation. With the change in PLTMG fuel type from B35 to gas, total generation costs decreased by 10.89%. With the change in PLTMG fuel type from B35 to gas and PLTU cofiring by 5%, total generation costs decreased by 10.94%.

The establishment of a performance evaluation model using education informatization to evaluate teacher morality construction in colleges and universities

Abstract To improve the effectiveness of the construction of teacher morality in colleges and universities, this article employs the performance evaluation model of education informatization to construct an evaluation system for the construction of teacher morality in colleges and universities. The evaluation of the construction effect of teacher morality is carried out through intelligent data analysis, and the significant error is used as the parameter of the teacher’s morality to make estimations. Moreover, a binary variable is introduced to judge whether the data have a significant error. Mixed integer linear and nonlinear programming methods are employed to detect significant errors. In addition, the idea of synchronizing teachers’ moral data is added. The effectiveness of the proposed method is verified by a simulation study using MATLAB 2017. The results show that it is necessary to establish and improve the talent flow mechanism that conforms to the requirements to promote the rational flow of teachers.

Optimization of Algorithms and Models in Two Scenarios for Picking up-Dropping off Disaster Victims in Islands Cities

Earthquakes in the past have caused significant damage, injuries, and deaths. The remaining resources do not equal the amount needed. For this reason, effective and efficient disaster management methods are needed. Learning from recent research that describes how they optimize the coordination function of hospital systems to overcome the imbalance between need and care capacity, we add the bed occupancy ratio (BOR) of healthcare facilities to the modeling. This paper aims to provide information about the distribution mechanism for injured victims by minimizing the total time to arrive at the healthcare facility. This victim evacuation modeling uses the integer linear programming method with two scenarios. Simulations were carried out on 164 injured victims, estimated by residents who live in areas that cross the Great Sumatran fault. The results show that the second scenario, which involves distributing it to the nearest healthcare facility, is 3.6 hours shorter compared to taking it to the general hospital in the first scenario.

Economic, energy and environmental analysis and evaluation of hybrid CCHP system considering different buildings: A two-level optimization model

Combined cooling, heating and power (CCHP) integrated energy systems can realize the gradient utilization of energy and the coordination and complementarity of multiple energy sources, which is the primary choice for solving the energy crisis and alleviating the environmental pressure. However, most current design and operational optimizations for CCHP are performed under rule-based operational strategies. This paper constructs a two-level alternating optimization framework for the planning-operation of the CCHP system with an embedded scheduling strategy. The upper-level solves for the optimal capacity configuration of the system to optimize energy, economic and environmental performance, and the lower-level solves for the operating capacity of the equipment system to optimize the operation and maintenance cost. In order to obtain the optimal configuration scheme and scheduling strategy for the system, a novel multi-objective weIghted meaN oF vectOrs (MOINFO)-mixed integer linear programming (MILP) method is proposed. The optimization results suggest that the hybrid CCHP for three buildings (market, office, and restaurant) under the two-level optimization model can achieve better economic, energy, and environmental performance than the rule-based single-level optimization model. Generally, for the market, office and restaurant, the two-Level model achieves maximum economic, energy and environmental performance improvements of 29.12%, 29.88%, and 42.13%; 38.32%, 19.56%, and 34.68%; and 47.37%, 30.93%, and 45.47%, respectively.

Optimization of production planning using integer linear programming method (case study of bakpia menik)

Bakpia Menik is a Small and Medium Enterprise (UKM) which operates in the field of bakpia production. Bakpia is one of the local cakes which is the main souvenir from Yogyakarta, so there is a big potential for increasing production. However, SMEs still lack production management planning to optimize resource use. So it is difficult to capture this big opportunity to maximize profits for SMEs. Seeing these problems, this research designed an integer linear programming mathematical model to optimize profits by using existing resources. Integer Linear Programming (ILP) is a mathematical model for maximizing profit and minimizing cost based on a mathematical model involving integer variables represented in a linear relationship. This research produces an integer linear programming model that presents the variables, resources, and constraints of Bakpia Menik. The model output shows that the optimal production amount by maximizing resource use is 31232 units and the maximum profit is IDR 33,431,750. From the model output, it can also show the advantages and disadvantages of Bakpia resources, so that resource availability planning can be carried out which can minimize holding costs.

A novel multi document summarization with document-elements augmentation for learning materials using concept based ILP and clustering methods

Multi Document Summarization (MDS) is a technique for extracting succinct summaries from groups of related documents. The usage of MDS in the e-learning context is more appealing for providing summaries for learning materials, which helps students and teachers to focus on key concepts of the learning materials. In a learning material, availability of non-textual document-elements such as figures/diagrams, plots, graphs, tables and algorithms can be seen widely, but keeping such document-elements in the summary is not possible as they are non-textual. This proposed work incorporates the text summarization approach with document-elements augmentation to the summary to provide a detailed coverage of information without exceeding the summary length constraint. The key information in the source text is identified by important phrase features and sentence features, and the summaries are generated by selecting important sentences using the Integer Linear Programming (ILP) framework while reducing the redundancy using pre-trained sentence vectors. The relationships between the summary and document-elements are identified through document-element snippet extraction and a Hierarchical Agglomerative Clustering approach. Experimental results of the proposed summary extraction and augmentation on educational dataset (EduSumm) show better performance compared to the state-of-the-art approaches.

Coco: conservation design for optimal ecological connectivity

Despite global conservation efforts, biodiversity continues to decline, causing many species to face extinction. These efforts include designing protected areas to function as ecologically connected networks for habitat and movement pathway conservation. Ecological connectivity is defined as the connectivity of landscapes and seascapes that allows species to move and ecological processes to function unimpeded. It facilitates long-term species persistence and resilience, mitigates the impact of habitat fragmentation due to climate change and land-use change, and addresses ecological processes that support ecosystems. Thus, ecological connectivity is key in the design of habitat conservation networks. To incorporate many complicating factors in this process, it relies on decision-support frameworks to decide which areas to include to protect biodiversity while minimizing cost. Various approaches emerged to deal with the computational complexity involved in habitat conservation design. However, despite the importance of designing ecologically connected conservation networks, these widely used decision-support frameworks do not offer functionality to optimize ecological connectivity directly during conservation design. Here, we present a fast, exact method to use connectivity metrics during the biodiversity conservation design process. Our method is exact in the sense that it always returns optimal solutions in our model. We extend an existing Reserve Selection problem (RSP) formulation with vertex-weighted connectivity constraints to include edge-weighted connectivity constraints. Further, we describe two novel variations of the RSP to directly optimize over connectivity metrics, one with cost minimization and one with a fixed cost. We introduce Coco, an open-source decision-support system to design ecologically connected conservations. Coco provides an integer linear programming (ILP) method to include connectivity in conservation design. To this end, we formulate our novel RSP variations as an ILP. We test Coco on simulated data and two real datasets, one dataset of the Great Barrier Reef and a large-scale dataset of the marine area in British Columbia. We compare the performance of Coco to Marxan Connect and show that Coco outperforms Marxan Connect both in runtime and solution quality. Further, we compare the results of our proposed methods to the existing RSP formulation and show that our novel methods significantly increase connectivity at a lower cost.

Optimal scheduling of a dairy industry based on energy hub considering renewable energy and ice storage

The use of energy in industrial processes is a vital aspect of their proper functioning and productivity. However, with the increasing demand for energy and the need for more sustainable energy sources, managing energy efficiently has become crucial for industries. In this context, energy management systems (EMS) have emerged as a solution to integrate different energy sources and optimize their use. This work proposes a model for the optimal scheduling of a dairy industry based on an energy hub, considering the integration of renewable energy sources and Ice Storage. The proposed model aims to minimize daily operating costs by satisfying the electrical and thermal demands of the industrial process while considering the availability and costs of different energy sources. The model takes into account the use of microturbines (MT), photovoltaic (PV) sources, wind generation (WT), electrical storage systems (ESS), and energy from the electrical grid for the generation of electrical energy, and a boiler and an Ice Storage for thermal energy. A case study is conducted in this paper at the dairy farm belonging to UDLA in Nono, Ecuador, where the advantages of the proposed energy hub model for the dairy industry are analyzed. The suggested scheduling optimization model is solved using Pyomo library with a mixed integer linear programming method showing the benefits of including Ice Storage Systems and renewable energy.

Carbon trading-based layered operation optimization of the electric–thermal multi-energy-flow coupling system with photothermal power stations

With the increasing development of low-carbon economy, the coupling degree of electric thermal gas system is deepening day by day. The operation mode of traditional energy supply system using electric heating separation mode and hierarchical dispatching of transmission and distribution network has been difficult to mine the whole network resources and realize the global optimal operation strategy. In order to increase the consumption of new energy and solve the multi-energy current coupling system, this paper puts forward a layered optimization operation strategy for the electric-thermal multi-energy current coupling system with Concentrated solar power (CSP) plant and carbon trading mechanism. The upper layer is the solution layer of multi-energy coupled flow system. In order to solve the matrix values of complex multi-energy coupled flow system, Newton's method, improved Newton’s method and improved second-order cone collaborative solution methods are proposed. The lower layer is the multi-energy flow optimization layer. According to the system solution values obtained from the upper layer, the lower layer optimization aims at economic minimization of the total user cost. The carbon trading mechanism model is introduced to optimize the time sequence output of the electric thermal unit under different scenarios, and the mixed integer linear programming method is adopted. Finally, the validity is verified by a simulation example. The results show that this method can optimize the operation of the system, improve the accuracy and rapidity of the system, and “carbon trading and CSP power station” method can better constrain the carbon emission of the multi-energy flow coupling system, reduce the energy pressure of the device, and improve the economy of the total cost of the user.If this method is adopted, it can be used for reference in the future energy management and system decision of multi-energy flow coupling system.

Optimal Configuration of Power/Thermal Energy Storage for a Park-Integrated Energy System Considering Flexible Load

The park-integrated energy system can achieve the optimal allocation, dispatch, and management of energy by integrating various energy resources and intelligent control and monitoring. Flexible load participation in scheduling can reduce peak and valley load, optimize load curves, further improve energy utilization efficiency, and reduce system costs. Based on this, firstly, a flexible power-load model is established considering the translatable load, transferable load, and reducible load; and a thermal flexible load model is established based on the fuzziness of user perception of temperature in this study; then, the mixed integer linear programming method is adopted, and the sum of the carbon transaction cost, operation and maintenance cost, compensation cost, power purchase cost, gas purchase cost, wind and light abandonment penalty cost and investment cost of the system is minimized as the objective function, and the configuration of the integrated energy system is optimized, and the optimal capacity of each equipment and the output of each period are obtained. Finally, taking an industrial park in Liaoning Province of China as an example, the analysis is carried out. The example results show that by scheduling the flexible electrical load and flexibly adjusting the indoor temperature, renewable energy consumption can be promoted, and electricity load and heat-load curves can be optimized to increase the installed capacity of wind turbines, reduce the capacity of gas turbines, batteries, and heat-storage tanks, improve system economy, and improve the penetration rate of renewable energy.

Analysis and forecast of the substitution potential of China's wind power-hydrogen production for fossil fuel hydrogen production

The predominant utilization of fossil fuels for hydrogen production in China leads to substantial carbon emissions, posing a challenge to China's objective of achieving carbon neutrality. With the rapid development of wind power in China, hydrogen can be produced through water electrolysis powered by wind-generated electricity. This process offers the potential to gradually replace the hydrogen production from fossil fuel (grey hydrogen), thus promoting the low-carbon transformation of China's hydrogen energy industry. However, further investigation is required to determine the potential displacement of grey hydrogen through the production of hydrogen from wind power in China in the future. To address this issue, this study first obtained wind speed data for the entire China region from the MERRA-2 database. Subsequently, based on the wind speed data for each specific area, the wind turbine model with the lowest power generation cost was selected from the eight available wind turbine models. On this basis, the mixed integer linear programming method is used to construct the cost analysis model of wind power-hydrogen production (WPHP). Based on the local wind power generation data, calculations are performed to determine the optimal installed capacity of the wind turbine, electrolyzer, and hydrogen storage tank within the WPHP system. Additionally, the optimal scheduling of the WPHP system is determined. These optimizations collectively result in the best WPHP cost. Based on this research, the optimal cost of WPHP for each geographical grid in China can be calculated and compared with the local grey hydrogen cost. The analysis reveals that in some areas of Xinjiang, Gansu, and Guizhou, exhibit low costs of wind power. This suggests that the substitution of grey hydrogen with WPHP can be achieved in these areas. Based on technological progress and changes in carbon trading prices, this paper predicts that WPHP in China could potentially replace 16.35–28.69 million tons of grey hydrogen by 2040. Moreover, by 2060, WPHP in China is projected to replace 76.72–92.01 million tons of grey hydrogen. According to the sensitivity analysis conducted, it has been determined that the efficiency of the electrolyzer and the price of the wind power equipment exert the greatest impact on the cost of hydrogen production.

A computationally inexpensive method to outsource facility maintenance services through the internet in real-time

The paper introduces a real-time framework for selecting maintenance contractors to address building facility breakdowns promptly and cost-effectively. A faster and resource-efficient approach utilizing a Mixed Integer Linear Programming (MILP) method is proposed to achieve this. The method optimizes contractor selection by leveraging structured linked data and integrating maintenance into the Internet of Things (IoT) framework, reducing processing time. Implemented initially for elevator systems, this framework can be extended to other mechanical and electrical systems in buildings. It consists of three modules: the building's integrated data module, the application module, and the maintenance provider module. The first module integrates building databases through structured linked data, establishing a centralized information source. The second module employs mixed integer linear programming to select contractors based on cost, time, previous services quality score, and maintenance urgency. The third module facilitates communication between contractors and the building facility manager, enabling maintenance requests and offers. The MILP model considers budget and time constraints, as well as maintenance urgency to prioritize immediate maintenances. A case study demonstrates that this model offers a fast and effective information processing solution. The results indicate that the proposed framework significantly reduces decision-making time for facility managers, streamlining contractor selection. Furthermore, compared to conventional methods, this framework provides a more efficient and effective automated maintenance decision-making solution, thus making a valuable contribution to the field of building maintenance management.

A constraint programming approach to a real-world workforce scheduling problem for multi-manned assembly lines with sequence-dependent setup times

For over five decades, researchers have presented various assembly line problems. Recently, assembly lines with multiple workers at each workstation have become very common in the literature. These lines are often found in the manufacturing of large vehicles, where workers at a workstation may perform their assigned tasks at the same time. Most research on multi-manned assembly lines focuses on balancing tasks and workers among workstations and scheduling tasks for workers. This study, however, concentrates on assigning tasks to workers already assigned to a specific workstation, rather than balancing the entire line. The problem was identified through an industrial case study at a large vehicle manufacturing company. The study presents two methods, one using mixed integer linear programming and the other using constraint programming, to minimise the number of workers required on a multi-manned assembly line with sequence-dependent setup times. The results of the computational experiments indicate that the constraint programming method performs better than the mixed integer linear programming method on several modified benchmark instances from the literature. The constraint programming model is also tested on the real-world scenario of our industrial case study and leads to significant improvements in the productivity of the workstations.

Integrated simulation and optimization framework for quantitative analysis of near-face stockpile mining

A new conceptual mining method called the near-face stockpile (NFS), which combines the in-pit crushing and conveying IPCC system with a pre-crusher stockpile, has recently been proposed for large open pits with sufficient pit bottom width. In the past, stockpiles mainly act as a "buffer" to improve the stability of the production system. However, in NFS ore will be dumped into the pre-crusher stockpile located at the bottom of the current pit and be fed into the crusher after blending to the desired head grade, instead of being dumped directly into the crusher. Theoretically, this design not only retains the high efficiency and high output of IPCC, but also endows the mining system with better quantity and quality stability. Verifying these advantages and objectively evaluating the NFS method has become a problem worth studying. Since the NFS method exhibits distinctive layout and feeding mechanisms, which distinguish it from other mining methods, a novel simulation model is required for the accurate modeling of the NFS method and quantitatively evaluating the performance of NFS methods. In addition, this paper also proposes an optimization model for short-term production scheduling for NFS method based on the mixed integer linear programming (MILP) method. An oil sands mine case study is implemented to verify the proposed simulation model. One year simulation results reveal that compared to the traditional mining method, the overall production increased by 5.06%, the transporting distance of minerals by trucks was reduced by 17.87%, and the shovels’ and crusher's utilization increased by 4.96% and 4.85%, respectively, when using NFS method.

An energy-aware combinatorial auction-based virtual machine scheduling model and heuristics for green cloud computing

Considering the increasing demand for cloud computing, and the financial and environmental impact of the increasing energy consumption trend of data centers, improving energy efficiency is vital for cloud service providers. In this study, an energy-aware virtual machine scheduling model is proposed which is based on the multi-unit nondiscriminatory combinatorial auction. The model includes a powerful bidding language that allows users to declare their complicated virtual machine requests using logical AND and OR relations along with the time constraints. The study also presents the formal definition of the model and the associated optimization problem for determining the optimum schedule and energy-efficient placement of VMs on physical servers. The optimization problem is formulated using integer linear programming and several heuristic solution methods including the Genetic Algorithm are proposed for this problem. The performances of the model and the proposed heuristics are assessed on a comprehensive test suite. The proposed model is estimated to provide approximately a 37% improvement in revenues, and the solution methods are estimated to provide high-quality solutions within only 5% of the optimum which enable the model to be deployed in large-scale clouds.