Linear Programming Framework Research Articles

Integer estimation of inner-cell values in RxC ecological tables

The estimation of the inner entries of a set of related RxC contingency tables when only the margins are known poses one of the most difficult problems in the field of the social sciences, present in many areas from marketing to quantitative history; being particularly prevalent in political science and sociology. With dozens of methods proposed to solve this, (almost) all of them have been devised to infer conditional proportion distributions, despite interior values of contingency tables being integers. This paper develops, within the linear programming framework, a new algorithm to output integer solutions, and assesses it using real data from more than 500 elections where actual cross-distributions of votes are known. Although the new approach is proposed with the expectation that more accurate solutions would be obtained by narrowing the search space from a continuous to a discrete simplex space, the results attained suggest that the use of a pure integer approach does not lead to more accurate solutions. The recommendation is therefore to integer-adjust decimal solutions when the focus is on counts. Interested practitioners can easily use the new models as they have been programmed in the R-package lphom.

A local convergent ecological inference algorithm for RxC tables

ABSTRACT Over the years, a number of methods have been proposed to forecast the unknown inner-cell values of a set of related RxC contingency tables when only their margins are known. This is a classical problem that emerges in many areas, from economics to quantitative history, being particularly ubiquitous when dealing with electoral data in sociology and political science. However, the two current major algorithms to solve this problem, based on Bayesian statistics and iterative linear programming depend on adjustable (hyper-)parameters and do not yield a unique solution: their estimates tend to fluctuate (when convergence is reached) around a stationary distribution. Within the linear programming framework, this paper proposes a new algorithm (lclphom) that always converges to a unique solution, having no adjustable parameters. This characteristic makes it easy to use and robust to claims of hacking. Furthermore, after assessing lclphom with real and simulated data, lclphom is found to yield estimates of (almost) similar accuracy to the current major solutions, being more preferable to the other lphom-family algorithms the more heterogeneous the row-fraction distributions of the tables are. Interested practitioners can easily use this new algorithm as it has been programmed in the R-package lphom.

Advanced Applications and Methodologies in Mathematical Optimization and Operations Research: Insights into Linear Programming, Nonlinear Programming, and Decision-Making Frameworks

Mathematical optimization and operations research are pivotal disciplines in solving complex decision-making problems across industries. This research delves into advanced methodologies within these fields, with a focus on linear programming (LP), nonlinear programming (NLP), and their applications in optimizing processes and resource allocation. Linear programming, with its capacity to model and solve large-scale problems, remains a cornerstone for optimization, particularly in logistics, finance, and manufacturing. Nonlinear programming, characterized by its ability to handle complex, real-world systems with non-convex functions, expands the scope of optimization to include dynamic and intricate challenges such as energy management and machine learning. This study investigates state-of-the-art algorithms, including interior-point methods, dual simplex techniques, and gradient-based approaches, to enhance the efficiency and accuracy of solutions. By addressing theoretical advancements and practical implementations, this research bridges the gap between mathematical rigor and real-world applications. The insights gained are expected to contribute significantly to operational efficiency, strategic planning, and decision-making in diverse fields.

Robust day-ahead scheduling of cooperative energy communities considering multiple aggregators

Future cities must play a vital role in reducing energy consumption and decarbonizing the electricity sector, thus evolving from passive structures towards more efficient smart cities. This transition can be facilitated by energy communities. This emerging paradigm consists of collectivizing a set of residential installations equipped with onsite renewable generators and storage assets (i.e., prosumers), which can eventually share resources to pursue collective welfare. This paper focuses on cooperative communities, where prosumers share resources without seeking selfish monetary counterparts. Despite their apparent advantages, energy management and scheduling of energy communities suppose a challenge for conventional tools due to the high level of uncertainty (especially due to intermittent renewable generation and random demand), and privacy concerns among prosumers. This paper addresses these issues. Specifically, a novel management structure based on multiple aggregators is proposed. This paradigm preserves users' confidential features while allowing them to extract the full potential of their assets. To efficiently manage the variety of assets available under uncertainty, an adaptive robust day-ahead scheduling model is developed, which casts as a solvable and portable Mixed Integer Linear Programming framework, which eases its implementation in real-world cases. The new proposal concerns uncertain generation and demand using a polyhedral representation of the uncertainty set. A case study is conducted to validate the developed model, showing promising results. Moreover, different results are obtained and analysed. Finally, it is worth remarking on how the level of robustness impacts the collective bill, incrementing it by 75 % when risk-averse conditions are assumed. In addition, the role of storage assets under pessimistic conditions is remarked, pointing out that these assets rule the scheduling plan of the community instead of renewable generators.

Integrated risk management and maintenance planning in Oil and Gas Supply Chain operations under market uncertainty

The Oil and Gas Supply Chain (OGSC) is a multifaceted network comprising diverse activities and echelons. Instability or interruptions can cause economic fluctuations, impacting industries, markets, and consumers. Maintenance activities, which pause production but extend facilities' life, are recommended during non-peak demand periods to avoid production losses and meet customer demand. To mitigate these effects, decisions on operations planning, maintenance scheduling, and maintenance team assignments should be optimized in a risk management framework. The proposed model adopts a mixed-integer linear programming (MILP) framework and is solved via a sequential approach that incorporates the relax-and-fix (RF) heuristic in order to find a solution that is close to optimal. Subsequently, the solution serves as an initial solution for the CPLEX solver, which employs a branch-and-cut algorithm to attain the exact optimal solution. The practicality of this model has been showcased through its application to the supply chain in Saudi Arabia. The model efficiently schedules maintenance activities evenly and consistently across the OGSC plants over the planning period to reduce lost sales by keeping plants operational during high-demand periods. Furthermore, a sensitivity analysis was conducted to investigate the influence of the decision-maker's risk attitude on the outcomes that were obtained.

Optimal capacity and multi-stable flexible operation strategy of green ammonia systems: Adapting to fluctuations in renewable energy

The potential of power-to-ammonia is increasingly recognized as a large-scale renewable electrical energy storage technology in the energy-transition landscape. Unlike conventional, continuously operating Haber-Bosch production processes, power-to-ammonia processes face operational challenges stemming from fluctuations in renewable power supply. Systematic strategies that can adapt to these fluctuations are required to improve the operational flexibility and stability of power-to-ammonia processes for industrial applications. This study proposes a multi-stable flexible ammonia operation strategy, which is practical and feasible in engineering. To maximize net profit, a design scheduling coordination optimization model is established and solved using a two-stage algorithmic framework of particle swarm and mixed integer linear programming. Additionally, three flexible scenarios are designed for the simulation analysis of a grid-connected green ammonia system. Compared with the traditional constant inflexible scenario, the multi-stable flexible scenario increases annual net profit by 5.05 M$ and reduces carbon emission intensity by 1.61 kg CO2/kgNH3. Furthermore, compared with the continuous flexible scenario, the volatility of the ammonia production load is reduced by 79.89 %. The multi-stable flexible operation strategy balances the green ammonia system’s economic, safety, and low-carbon attributes. Sensitivity analysis reveals that wind and photovoltaic complementary power generation reduces green ammonia costs and carbon emissions. When the selling price of ammonia exceeds 550 $/t, ammonia production and sales should be prioritized, but at lower ammonia prices, selling electricity to the grid to optimize economic efficiency is advised. This study provides novel insights into the flexible operation of the power-to-ammonia process and is expected to offer guidance for constructing and operating green ammonia systems.

Optimizing Biomass Supply Chains to Power Plants under Ecological and Social Restrictions: Case Study from Poland

The growing demand for social and regulatory forest ecosystem services can significantly modify the availability and cost of biomass for energy purposes. This article presents a model for optimizing biomass supply chains using a linear programming framework integrated with a geographic information system (GIS). Based on a given type of biomass resource, its calorific value, price, distance from the power plant, and transportation costs, the model identifies the optimal source of biomass, allowing it to cover the demand for the required total energy value with the lowest possible costs. The case study includes the Połaniec power plant in southeastern Poland and potential sources of forest biomass and agricultural straw within 100 km of the plant. The impact of constraints on the availability and cost of biomass was analyzed in the following scenarios: (1) all forest and agriculture biomass is available, (2) forest area in Natura 2000 network is excluded, and (3) firewood and forests with dominated ecological and social function are excluded. Unit costs of biomass varied depending on biomass availability and energy demands. The lowest unit costs of biomass (3.19 EUR/MJ) were for energy demand at the level of 1 TJ yearly for all kinds of biomass and the highest (4.91 EUR/MJ) for ecological and social constraints and energy demand 4 TJ. As energy demand increased, unit costs increased, and the ability to meet this demand with just one type of biomass decreased. The energy biomass sector can utilize the model to benefit both biomass producers and their final buyers.

Balancing Possibilist-probabilistic risk assessment for smart energy hubs: Enabling secure peer-to-peer energy sharing with CCUS technology and cyber-security

This paper introduces the Possibilistic-Probabilistic Risk-based Smart Energy Hub (PPR-SEH) scheduling model, addressing cybersecurity challenges in the transition to advanced energy systems characterized by decarbonization, decentralization, and digitalization. The model integrates cutting-edge technologies like Carbon Capture Utilization and Storage (CCUS) and demand response programs. It addresses uncertainties from renewable energy sources, demand variability, fuel supply, and energy price fluctuations using a Z-number-based approach. Covering various energy types—electricity, heat, cooling, gas, and water—the PPR-SEH model offers a comprehensive energy management solution. Employing a mixed-integer linear programming (MILP) framework optimized with the CPLEX solver in GAMS software, it uses an epsilon constraint method and a fuzzy satisfying approach for solution selection. The model also evaluates the economic and environmental impacts of peer-to-peer energy-sharing markets linked with carbon emission trading, enhancing the efficiency and sustainability of energy distribution. The findings reveal that incorporating robust cybersecurity measures and integrating demand response and CCUS significantly influence operational efficiency and sustainability, evidenced by an increase in costs and pollution by approximately 11.43 % and 1.8 %, respectively, compared to deterministic approaches. This study underscores the importance of robust planning and the beneficial impact of a carbon system on load curve management and economic returns in smart energy systems.

Optimizing the Installation of a Centralized Green Hydrogen Production Facility in the Island of Crete, Greece

The European Union is committed to a 55% reduction in greenhouse gas emissions by 2030, as outlined in the Green Deal and Climate Law initiatives. In response to geopolitical events, the RePowerEU initiative aims to enhance energy self-sufficiency, reduce reliance on Russian natural gas, and promote hydrogen utilization. Hydrogen valleys, localized ecosystems integrating various hydrogen supply chain elements, play a key role in this transition, particularly benefiting isolated regions like islands. This manuscript focuses on optimizing a Centralized Green Hydrogen Production Facility (CGHPF) on the island of Crete. A mixed-integer linear programming framework is proposed to optimize the CGHPF, considering factors such as land area, wind and solar potential, costs, and efficiency. Additionally, an in-depth sensitivity analysis is conducted to explore the impact of key factors on the economic feasibility of hydrogen investments. The findings suggest that hydrogen can be sold in Crete at prices as low as 3.5 EUR/kg. Specifically, it was found in the base scenario that, selling hydrogen at 3.5 EUR/kg, the net profit of the investment could be as high as EUR 6.19 million, while the capacity of the solar and wind installation supplying the grid hydrogen facility would be 23.51 MW and 52.97 MW, respectively. It is noted that the high profitability is justified by the extraordinary renewable potential of Crete. Finally, based on our study, a policy recommendation to allow a maximum of 20% direct penetration of renewable sources of green hydrogen facilities into the grid is suggested to encourage and accelerate green hydrogen expansion.

The potential of residential load flexibility: An approach for assessing operational flexibility

This study presents a novel methodology for evaluating the flexibility of residential electricity consumers under diverse operational conditions introducing innovative flexibility indicators. The increasing demand for energy flexibility from the demand side is crucial for ensuring the power grid’s economic stability and resilience. Buildings offer a range of potential flexibility sources that can be effectively leveraged for this purpose. Accordingly, this paper formulates energy flow management in a Smart House using a Mixed-Integer Linear Programming (MILP) framework, incorporating the scheduling of shiftable appliances and an Energy Storage System (ESS). By defining different consumption strategies, the feasible region for Energy-Time Profiles (ETPs) is explored through the establishment of the corresponding optimization problems. A series of case studies are presented to evaluate the impact of operational constraints on the feasible region. Finally, by meticulously analyzing the characteristics of ETPs extracted from these case studies, the proposed flexibility indicators are introduced, quantifying the Smart House’s energy flexibility potential. Furthermore, a sensitivity analysis is conducted to scrutinize the influence of key parameters on the new flexibility indicator, encompassing ESS characteristics. The findings substantiate the efficacy of the proposed indicators in providing comprehensive insights into the potential energy flexibility under a range of operational conditions.

Optimization of hybrid renewable-diesel power plants considering operational cost, battery degradation, and emissions

Renewable energy sources have immense potential for enhancing environmental sustainability; however, addressing their intermittency and irregularity is vital for optimizing economic benefits within microgrids. Integrating renewable energy systems with energy storage presents a promising solution. This study introduces an innovative energy management system designed for hybrid renewable power stations, incorporating battery energy storage systems and diesel generators. By accounting for battery degradation costs associated with charge depth and lifespan, the study transforms long-term battery expenses into real-time operational costs. The optimization problem is formulated as a mixed integer linear programming framework with the objectives of minimizing operating costs, battery degradation costs, and pollutant gas emissions. Through diverse case studies reflecting various market profiles. The proposed approach demonstrates reductions in overall system costs.

Multiperiod Modeling and Optimization of Hydrogen-Based Dense Energy Carrier Supply Chains

The production of hydrogen-based dense energy carriers (DECs) has been proposed as a combined solution for the storage and dispatch of power generated through intermittent renewables. Frameworks that model and optimize the production, storage, and dispatch of generated energy are important for data-driven decision making in the energy systems space. The proposed multiperiod framework considers the evolution of technology costs under different levels of promotion through research and targeted policies, using the year 2021 as a baseline. Furthermore, carbon credits are included as proposed by the 45Q tax amendment for the capture, sequestration, and utilization of carbon. The implementation of the mixed-integer linear programming (MILP) framework is illustrated through computational case studies to meet set hydrogen demands. The trade-offs between different technology pathways and contributions to system expenditure are elucidated, and promising configurations and technology niches are identified. It is found that while carbon credits can subsidize carbon capture, utilization, and sequestration (CCUS) pathways, substantial reductions in the cost of novel processes are needed to compete with extant technology pathways. Further, a research and policy push can reduce the levelized cost of hydrogen (LCOH) by upwards of 2 USD/kg.

An efficient approach for identifying important biomarkers for biomedical diagnosis

In this paper, we explore the challenges associated with biomarker identification for diagnosis purpose in biomedical experiments, and propose a novel approach to handle the above challenging scenario via the generalization of the Dantzig selector. To improve the efficiency of the regularization method, we introduce a transformation from an inherent nonlinear programming due to its nonlinear link function into a linear programming framework under a reasonable assumption on the logistic probability range. We illustrate the use of our method on an experiment with binary response, showing superior performance on biomarker identification studies when compared to their conventional analysis. Our proposed method does not merely serve as a variable/biomarker selection tool, its ranking of variable importance provides valuable reference information for practitioners to reach informed decisions regarding the prioritization of factors for further investigations.

Automated Scheduling of Doppler Exoplanet Observations at Keck Observatory

Precise Doppler studies of extrasolar planets require fine-grained control of observational cadence, i.e., the timing of and spacing between observations. We present a novel framework for scheduling a set of Doppler campaigns with different cadence requirements at the W. M. Keck Observatory. For a set of observing programs and allocated nights on an instrument, our software optimizes the timing and ordering of ∼1000 observations within a given observing semester. We achieve a near-optimal solution in real-time using a hierarchical Integer Linear Programming framework. Our scheduling formulation optimizes over the roughly 103000 possible orderings. A top level optimization finds the most regular sequence of allocated nights by which to observe each host star in the request catalog based on a frequency specified in the request. A second optimization scheme minimizes the slews and downtime of the instrument. We have assessed our algorithms performance with simulated data and with the real suite of Doppler observations of the California Planet Search in 2023.

A Mixed‐Integer Linear Programming Framework for Optimization of Water Network Operations Problems

AbstractWater distribution systems (WDSs) are critical infrastructure used to convey water from sources to consumers. The mathematical framework governing the distribution of flows and heads in extended period simulations of WDSs lends itself to application in a wide range of optimization problems. Applying the classical mixed integer linear programming (MILP) approach to model WDSs hydraulics within an optimization framework can contribute to higher solution accuracy with lower computational effort. However, adapting WDSs models to conform to a MILP formulation has proven challenging because of the intrinsic non‐linearity of system hydraulics and the complexity associated with modeling hydraulic devices that influence the state of the WDS. This paper introduces MILPNet, an adjustable framework for WDSs that can be used to build and solve an extensive array of MILP optimization problems. MILPNet includes constraints that represent the mass balance and energy conservation equations, hydraulic devices, control rules, and status checks. To conform to MILP structure, MILPNet employs piece‐wise linear approximation and integer programming. MILPNet was implemented and tested using Gurobi Python API. Modeling accuracy was shown to be comparable to EPANET, a public domain software for hydraulic modeling, and sensitivity analyses were conducted to examine the impacts of the modeling assumptions on the performance of MILPNet. Additionally, application of the framework was demonstrated using pump scheduling optimization examples in single and rolling horizon scenarios. Our results show that MILPNet can facilitate the construction and solution of optimization problems for a range of applications in WDSs operations.

Optimizing spectrum efficiency in 6G multi-UAV networks through source correlation exploitation

In the context of 6G and 5G communication networks, particularly in disaster-stricken areas with a surging demand for connectivity and the rapid evolution of the internet of everything (IoE), the imperative for augmenting spectrum efficiency in unmanned aerial vehicles (UAVs) communication-enabled wireless networks becomes ever more pronounced. This work embarks on the mission of significantly enhancing spectrum efficiency by capitalizing on redundancies, such as correlations inherent in data sources like co-located video sensors. While the intuitive potential of exploiting redundancies for spectrum efficiency enhancement is apparent, our approach is systematically structured. We introduce a linear programming framework designed to meticulously allocate bandwidth to individual links based on their respective demands, while judiciously adhering to spatial spectrum reuse constraints. Subsequently, we employ this linear program to empirically quantify the improvements in spectrum efficiency engendered by source correlations. Furthermore, we elucidate various strategies for harnessing these correlations to maximize spectrum efficiency gains, while navigating the trade-off terrain between computational complexity and precision. Our findings resoundingly underscore the trans-formative power of identifying the precise set of source correlations, resulting in spectrum efficiency enhancements of up to two orders of magnitude. In terms of network performance, the judicious exploitation of source correlations grants admission to nearly 100% of delay-intolerant traffic, alongside substantial reductions in mean delay for delay-tolerant traffic.”

Support vector machines within a bivariate mixed-integer linear programming framework

Support vector machines (SVMs) are a powerful machine learning paradigm, performing supervised learning for classification and regression analysis. A number of SVM models in the literature have made use of advances in mixed-integer linear programming (MILP) techniques in order to perform this task efficiently. In this work, we present three new models for SVMs that make use of piecewise linear (PWL) functions. This allows effective separation of data points where a simple linear SVM model may not be sufficient. The models we present make use of binary variables to assign data points to SVM segments, and hence fit within a recently presented framework for machine learning MILP models. Alongside presenting an inbuilt feature selection operator, we show that the models can benefit from robust inbuilt outlier detection. Experimental results show when each of the presented models is effective, and we present guidelines on which of the models are preferable in different scenarios.

Data-driven zonotopic approximation for n-dimensional probabilistic geofencing

Advanced air mobility is a promising way of metropolitan air transportation. One critical concern that arises is how to ensure operational safety in high-dense, dynamic, and uncertain airspace environments in real time. To address this challenge, we seek a probabilistic geofence that bounds system states with high confidence. To identify the n-dimensional probabilistic geofence for arbitrary unknown uncertainties not limited to Gaussian ones, we present an online algorithm based on a data-driven approach of kernel density estimator. Considering the irregular shape of the probabilistic geofence, we formulate an optimization framework of integer linear programming whose solution determines a zonotope which provides a convex approximation for the probabilistic geofence. Leveraging this formulation, a heuristic algorithm is developed to find its solution efficiently without losing notable accuracy. This heuristic algorithm is tested on case studies that demonstrate it enjoys efficiency, accuracy, near-optimality, and robustness simultaneously.

A Resilience-Oriented Approach for Microgrid Energy Management with Hydrogen Integration during Extreme Events

This paper presents a resilience-oriented energy management approach (R-OEMA) designed to bolster the resilience of networked microgrids (NMGs) in the face of extreme events. The R-OEMA method strategically incorporates preventive scheduling techniques for hydrogen (H2) systems, renewable units, controllable distributed generators (DGs), and demand response programs (DRPs). It seeks to optimize the delicate balance between maximizing operating revenues and minimizing costs, catering to both normal and critical operational modes. The evaluation of the R-OEMA framework is conducted through numerical simulations on a test system comprising three microgrids (MGs). The simulations consider various disaster scenarios entailing the diverse durations of power outages. The results underscore the efficacy of the R-OEMA approach in augmenting NMG resilience and refining operational efficiency during extreme events. Specifically, the approach integrates hydrogen systems, demand response, and controllable DGs, orchestrating their collaborative operation with predictive insights. This ensures their preparedness for emergency operations in the event of disruptions, enabling the supply of critical loads to reach 82% in extreme disaster scenarios and 100% in milder scenarios. The proposed model is formulated as a mixed-integer linear programming (MILP) framework, seamlessly integrating predictive insights and pre-scheduling strategies. This novel approach contributes to advancing NMG resilience, as revealed by the outcomes of these simulations.

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.