Linear Programming Algorithm Research Articles

Design and economic analysis of energy storage optimization allocation for campus microgrid

In the twenty-first century, the "double carbon" plan is advancing steadily. Energy saving and emission reduction is one of the key points of the plan. A power grid independent park, if energy storage equipment can be configured, it can greatly improve the park microgrid power utilization, in order to achieve the purpose of energy saving. Therefore, research on the optimization of the proportion of power grid and microgrid in the park and the optimization of the configuration of energy storage devices can greatly improve the energy utilization rate, so as to achieve the significance of environmental protection. After collecting and sorting the daily load, daily wind power generation and 12-month daily wind power generation data of the three parks A, B and C, and processing the data, a linear function model is established. After using linear programming, operations research and genetic algorithm, the research results are obtained when the three parks are combined and equipped with 50kW/100kWh energy storage devices.

A subspace‐adaptive weights cubature method with application to the local hyperreduction of parameterized finite element models

AbstractThis article is concerned with quadrature/cubature rules able to deal with multiple subspaces of functions, in such a way that the integration points are common for all the subspaces, yet the (nonnegative) weights are tailored to each specific subspace. These subspace‐adaptive weights cubature rules can be used to accelerate computational mechanics applications requiring efficiently evaluating spatial integrals whose integrand function dynamically switches between multiple pre‐computed subspaces. One of such applications is local hyperreduced‐order modeling (HROM), in which the solution manifold is approximately represented as a collection of basis matrices, each basis matrix corresponding to a different region in parameter space. The proposed optimization framework is discrete in terms of the location of the integration points, in the sense that such points are selected among the Gauss points of a given finite element mesh, and the target subspaces of functions are represented by orthogonal basis matrices constructed from the values of the functions at such Gauss points, using the singular value decomposition (SVD). This discrete framework allows us to treat also problems in which the integrals are approximated as a weighted sum of the contribution of each finite element, as in the energy‐conserving sampling and weighting method of C. Farhat and co‐workers. Two distinct solution strategies are examined. The first one is a greedy strategy based on an enhanced version of the empirical cubature method (ECM) developed by the authors elsewhere (we call it the subspace‐adaptive weights ECM, SAW‐ECM for short), while the second method is based on a convexification of the cubature problem so that it can be addressed by linear programming algorithms. We show in a toy problem involving integration of polynomial functions that the SAW‐ECM clearly outperforms the other method both in terms of computational cost and optimality. On the other hand, we illustrate the performance of the SAW‐ECM in the construction of a local HROMs in a highly nonlinear equilibrium problem (large strains regime). We demonstrate that, provided that the subspace‐transition errors are negligible, the error associated to hyperreduction using adaptive weights can be controlled by the truncation tolerances of the SVDs used for determining the basis matrices. We also show that the number of integration points decreases notably as the number of subspaces increases, and that, in the limiting case of using as many subspaces as snapshots, the SAW‐ECM delivers rules with a number of integration points only dependent on the intrinsic dimensionality of the solution manifold and the degree of overlapping required to avoid subspace‐transition errors. The Python source codes of the proposed SAW‐ECM are openly accessible in the public repository https://github.com/Rbravo555/localECM.

A fast strategy-solving method for adversarial team games utilizing warm starting

Adversarial team games (ATGs) have garnered significant attention in recent years, leading to the emergence of various solutions such as linear programming algorithms, multi-agent reinforcement learning, and game tree transformation. The ATGs involve large-scale game trees, resulting in higher time costs for computation. In this paper, we focus on expediting the solution of team-maxmin equilibrium with correlation (TMECor), which can be considered the equilibrium that maximizes the team’s payoff. To address this, we propose a transformation with seed strategies (TSS). TSS leverages reinforcement learning to calculate player strategies. We initialize the strategies of all players, referred to as seed strategies, and incorporate them into the multi-agent game tree during the transformation process. These seed strategies serve as the starting strategies for counterfactual regret minimization (CFR). CFR initializes the strategies and cumulative regret of all players based on the seed strategy. By warm starting the whole process, our method accelerates the solving of TMECor. We conducted nine experiments using Kuhn poker and Leduc Hold’em poker. The results demonstrated that TSS improved the solving speed of TMECor.

Multi-objective application placement in fog computing using graph neural network-based reinforcement learning

We propose a framework designed to tackle a multi-objective optimization challenge related to the placement of applications in fog computing, employing a deep reinforcement learning (DRL) approach. Unlike other optimization techniques, such as integer linear programming or genetic algorithms, DRL models are applied in real time to solve similar problem situations after training. Our model comprises a learning process featuring a graph neural network and two actor-critics, providing a holistic perspective on the priorities concerning interconnected services that constitute an application. The learning model incorporates the relationships between services as a crucial factor in placement decisions: Services with higher dependencies take precedence in location selection. Our experimental investigation involves illustrative cases where we compare our results with baseline strategies and genetic algorithms. We observed a comparable Pareto set with negligible execution times, measured in the order of milliseconds, in contrast to the hours required by alternative approaches.

Robust baseline correction for Raman spectra by constrained Gaussian radial basis function fitting

Accurate baseline correction is a fundamental requirement for extracting meaningful spectral information and enabling precise quantitative analysis using Raman spectroscopy. Although numerous baseline correction techniques have been developed, they often require meticulous parameter adjustments and yield inconsistent results. To address these challenges, we have introduced a novel approach, namely constrained Gaussian radial basis function fitting (CGF). Our method involves solving a curve-fitting problem using Gaussian radial basis functions under specific constraints. To ensure stability and efficiency, we developed a linear programming algorithm for the proposed approach. We evaluated the performance of CGF using simulated Raman spectra and demonstrated its robustness across various scenarios, including changes in data length and noise levels. In contrast to standard methods, which frequently require complicated parameter adjustments and may exhibit varying errors, our approach provides a simple parameter search and consistently achieves low errors. We further assessed CGF using real Raman spectra, leading to enhanced accuracy in the quantitative analysis of the Raman spectra of chemical warfare agents. Our results emphasize the potential of CGF as a valuable tool for Raman spectroscopy data analysis, significantly advancing sophisticated analytical techniques.

Creating a renewable energy-powered energy system: Extreme scenarios and novel solutions for large-scale renewable power integration

The large-scale integration of renewable power sources, such as wind and solar, is pivotal in achieving climate change mitigation goals and reducing dependency on fossil fuels within energy systems. This manuscript explores the integration of substantial wind and solar power capacities into Luxembourg's energy framework, addressing challenges like variability, intermittency, and curtailment. It delves into scenarios that include power-to-heat (P2H) and vertical farming (VF) technologies to improve system flexibility and promote the incorporation of renewable energy. Utilising a mixed-integer linear programming (MILP) algorithm, an energy balance model with hourly resolution optimises the system. This algorithm guides the operation of individual plants, ensuring optimal performance based on a variety of criteria. Notable findings underscore the significant influence of an appropriate mix of renewable power resources, indicating a potential increase in renewable power consumption by up to 50% within the system. Furthermore, curtailment management solutions are shown to enhance renewable power integration by as much as 30%, highlighting the importance of strategic, system-wide approaches. Additionally, vertical farming emerges as a promising avenue for significantly augmenting the utilisation of surplus solar power, potentially by up to 100%. While the integration of large-scale renewable power is demonstrably viable, it necessitates a meticulously crafted strategy that considers technological innovations and strategic planning.

Industry Class Clustering of Software Expertise Competency at SMKN 2 Kraksaan Using Constrained K-Means Clustering Algorithm

Addressing the gap between school education and industry needs is a recurring concern, as many graduates struggle to enter the workforce due to lacking practical skills. Industry Classes aim to bridge this gap by preparing students with relevant skills and knowledge aligned with real-world industry demands. This study focuses on the application of Constrained K-Means Clustering to categorize students in the software engineering competency classes at SMKN 2 Kraksaan. This algorithm modifies traditional K-Means by utilizing Linear Programming Algorithm (LPA), ensuring each cluster meets predefined subject requirements. The research involves analyzing academic proficiency test data (TKDA) from 96 X-grade students, evaluating their abilities in analogy, series, figural, mathematical, and recall skills. Using a 3-cluster approach, each with 32 to 60 student capacity constraints, the study aims to optimize student distribution for effective learning outcomes. Evaluation through silhouette method yielded a score of 0.3199, indicating satisfactory separation between clusters with overlap to address. Cluster analysis revealed Cluster 2 as the most proficient, showcasing strengths in recall and series attributes critical for software engineering. These findings suggest that Constrained K-Means Clustering is effective in classifying students, highlighting Cluster 2 as optimal for software engineering competencies at SMKN 2 Kraksaan. Future research should focus on enhancing data quality, expanding sample size, and refining algorithms for improved clustering accuracy and effectiveness.

Sustainable food choices require product-specific environmental footprints: The case of packaged food in Australia

The current food system is a major driver of global environmental change. Despite significant research interest in the environmental impacts of alternative diets, most studies estimate the effects of dietary shifts based on assumed changes in the consumption of raw agricultural commodities instead of simulating changes in the actual food and beverages consumed. In response to increasing consumer demand for product-specific health and sustainability labelling on packaged food products, it is necessary to develop robust environmental footprinting approaches to estimate the environmental impacts of foods and beverages available through retail outlets. This study quantifies the environmental impacts of 63,926 packaged food products in Australian supermarkets across five indicators including greenhouse gas emissions, land use, water use, acidification, and eutrophication potential. We integrated cradle-to-retail environmental estimates from life cycle assessment databases with ingredient proportions derived through a linear programming algorithm to measure product-specific impacts. Meat products consistently showed the highest impacts across all environmental indicators, while fruits, vegetables, plant-based meat alternatives, and non-alcoholic beverages had the lowest impacts. This study also shows that the dietary environmental footprints of Australian consumers can be significantly reduced by switching from high-impact to low-impact products within the same food category (e.g., meat products). Transitioning from high-impact to low-impact products across all food categories could reduce greenhouse gas emissions by up to 96 %, with synergies across all other environmental indicators. The comprehensive results of this study can empower consumers, producers, and governments to identify context-specific opportunities for improving food system sustainability in Australia.

Research on optimization algorithms for localization and capacity determination of chargers considering the spatiotemporal distribution of electric vehicles

The optimized layout of electric vehicle (EV) chargers is not only crucial for users' convenience but also a key element in urban sustainable development, energy transition, and the promotion of new energy vehicles. In order to provide a basis for the problem of localization and capacity determination of chargers and compare the merits of several mainstream algorithms, this paper first establishes an optimization model with the objective of minimizing the total investment cost of all the chargers and the constraint of meeting the charging demands of all electric vehicles. Optimizations were performed using genetic algorithm (GA), surrogate optimization algorithm (SOA), and mixed integer linear programming (MILP) algorithm, respectively. In the case of using MILP, the original nonlinear optimization problem was transformed into a linear problem. In the planning of city-level EV chargers, MILP took 14182.57 s to calculate the minimum cost of 34.62 million yuan. After retaining only 10% of the original data amount, SOA took 87651.34 s to calculate the minimum cost of 3.01 million yuan. The results indicate that GA is prone to falling into local optima and is not suitable for large-scale optimization problems. SOA, on the other hand, requires significant memory consumption, so the issue of memory usage needs to be carefully considered when using it directly. Although MILP is only applicable to linear programming problems, it has the advantages of lower memory usage and higher reliability if the problem can be transformed into a linear one.

An Optimization Tool to Formulate Diets within a Supplementary Nutrition Program for Children

BackgroundIn large supplementary feeding programs for children, it is challenging to create and sustain contextual, acceptable, nutritionally complete, and diverse supplemental foods. For example, the Indian Supplementary Nutrition Program (SNP) supplements the dietary intake of children, pregnant and lactating women, and severely acutely malnourished (SAM) children by offering dry take home rations (THRs) or hot cooked meals (HCMs) across India, but an optimization tool is necessary to create local contextual recipes for acceptable and nutritionally adequate products. ObjectivesThis study aimed to create a linear programming (LP) model to optimize diverse food provisions for a SNP to meet its program guidelines, using locally available foods, within budgetary allocations. MethodsA LP algorithm with appropriate constraints was used to generate an optimal THR based on raw foods, or an optimal weekly HCM menu comprised of a lunch meal with mid-morning snacks, based on user choices of foods and recipes. The database of foods used was created by a prospective survey conducted across all states of India for this purpose, such that the recipe and food optimization was diverse and specific to the guidelines for each beneficiary group. ResultsAn interactive web-based app, which can optimize feeding programs at any population level, was developed for use by program implementers and is hosted at https://www.datatools.sjri.res.in/SNP/. In the Indian example analyzed here, the recommended optimized diets met the guidelines for diversified and nutritionally complete SNP provision but at a cost that was almost 25% higher than the present Indian budget allocation. ConclusionsThe optimization model developed demonstrates that contextual SNP diets can be created to meet macronutrient and most essential micronutrient needs of large-scale feeding programs, but appropriate diversification entails additional costs.

OPTIMIZATION OF CYBER-PHYSICAL SYSTEM PARAMETERS BASED ON INTELLIGENT IOT SENSORS DATA

The optimization of cyber-physical systems (CPS) parameters is researched with focusing on the integration of computation, networking, and physical processes with the Internet of Things (IoT). The use of intelligent IoT sensors is crucial for collecting real-time data, which is necessary for enhancing the efficiency, reliability, and performance of CPS. Various methods of CPS parameters optimization are analyzed and categorized into model-based approaches, data-driven approaches, and hybrid approaches. The model-based approaches rely on mathematical models to describe CPS behavior and use optimization algorithms like linear programming and evolutionary algorithms to predict system responses and optimize parameters. But, the limitations of model-based approaches are related to complex systems with uncertain or dynamic behavior. The data-driven approaches are more suitable for complex cyber-physical systems. These approaches utilize machine learning and data analytics techniques to extract patterns from sensor data, which are then used to adjust system parameters. The hybrid approaches combine elements of both model-based and data-driven methods. The method of cyber-physical system parameters optimization based on intelligent IoT sensors data processing is developed with using of distributed neural network. The optimization problem is formulated with constraints for the system parameters. The neural network mathematical model and learning algorithm are proposed. The performed research shows the importance of developing optimization methods for CPS parameters based on intelligent IoT sensor data, considering the evolving nature of IoT technology. The integrating intelligent sensors into CPS offers new opportunities for optimizing system performance but also presents challenges in data management and security that should be addressed in future.

<span>System for university and college admission projects: Design and Implementation based on Linear Programming</span>

The rapid development of information technology and network infrastructure has brought about numerous opportunities and breakthrough applications in management and operations across all sectors of modern life, with education holding a significant position. Currently, the Ministry of Education and Training has implemented transactional portals to support universities and colleges in constructing admission plans. However, these transactional portals only provide basic support such as uploading data on lecturers, floor area, student scale, and some forms and reports. Despite some improvements, these systems are still incomplete and not consistently updated with admission plan data over the years. Additionally, there is no automated mechanism to propose an optimal solution for balancing the faculty size, student scale, and floor area to estimate admission targets for specific fields and disciplines. Therefore, we propose a new solution: building a web-based system integrated with linear programming algorithms. The goal is to optimize the admission process, balance the faculty, minimize errors, and enhance efficiency, thereby fixing the limitations of the current Ministry's system.

Research on Personnel Scheduling Optimization in Logistics Sorting Centers Based on Linear Programming and Heuristic Algorithms

Research on Personnel Scheduling Optimization in Logistics Sorting Centers Based on Linear Programming and Heuristic Algorithms

Multi-Objective Optimization of an Energy Community Powered by a Distributed Polygeneration System

This paper presents a multi-objective optimization model for the integration of polygeneration systems into energy communities (ECs), by analyzing a case study. The concept of ECs is increasingly seen as beneficial for reducing global energy consumption and greenhouse gas emissions. Polygeneration systems have the potential to play a crucial role in this context, since they are known for producing multiple energy services from a single energy resource, besides the possibility of being fed also by renewable energy sources. However, optimizing the configuration and operation of these systems within ECs presents complex challenges due to the variety of technologies involved, their interactions, and the dynamic behavior of buildings. Therefore, the aim of this work is developing a mathematical model using a mixed integer linear programming (MILP) algorithm to optimally design and operate polygeneration systems integrated into ECs. The model is applied to a case study of an EC comprising nine buildings in a small city in the northeast of Italy. The work rests on the single- and multi-objective optimization of the polygeneration systems taking into account the sharing of electricity among the buildings (both self-produced and/or the purchased from the grid), as well as the sharing of heating and cooling between the buildings through a district heating and cooling network (DHCN). The main results from the EC case study show the possibility of reducing the total annual CO2 emissions by around 24.3% (about 1.72 kt CO2/year) while increasing the total annual costs by 1.9% (about 0.09 M€/year) or reducing the total annual costs by 31.9% (about 1.47 M€/year) while increasing the total annual CO2 emissions by 2.2% (about 0.16 kt CO2/year). The work developed within this research can be adapted to different case studies, such as in the residential–commercial buildings and industrial sectors. Therefore, the model resulting from this work constitutes an effective tool to optimally design and operate polygeneration systems integrated into ECs.

Introducing storage operators for coordinating residential batteries in distribution networks under time-of-use tariffs and adaptive power limits

The transition towards Time of Use (ToU) tariffs has become a promising solution for addressing power system challenges resulting from increased installations of renewable energy systems. ToU tariffs encourage residential Battery Energy Storage System (BESS) adoption to reduce customers' bills through maximizing energy storage during low-price intervals (e.g., middle of the day). However, simultaneous BESS charging affects diversity of load, which may lead to the violation of distribution networks constraints. Traditional network management with conservative fixed and static power limits leads to inefficient network capacity use since they do not consider changes in network operating conditions and status of BESS facilities. Specially, these approaches do not allow higher import limits when proportion of BESS facilities are in idling state. To better allocate the capacity of distribution networks to active BESS facilities (charging/discharging), this work introduces an independent storage operator to coordinate BESS control actions by employing time-varying and adaptive power limits. For this purpose, a Mixed Integer Linear Programming (MILP) algorithm is proposed for storage operator to manage BESS facilities while respecting network constraints and customers' desired bills. At each time step, the algorithm decides power limits for active BESS facilities based on predefined linear functions. These functions are generated offline by using Optimal Power Flow (OPF) to establish relationships between power limits and number of active BESS. The application of the algorithm using a real Jordanian distribution network demonstrates its effectiveness to allow a larger number of customers achieving their desired bills compared to using fixed power limits.

Multi-response optimization of charcoal briquettes process for green economy using a novel TOPSIS linear programming and genetic algorithms based on response surface methodology

The production of charcoal briquettes was based on the concept of utilizing waste for sustainable and eco-friendly solutions within the green economy. This study introduces a new approach for optimizing important properties of charcoal briquettes. The approach aims to determine the appropriate operating conditions using a hybrid method. It integrates a novel TOPSIS linear programming with genetic algorithms based on response surface methodology. The experiment used an optimal mixture ratio of 25:10:6, including coconut shell, bagasse ash, and corncob. The results of the responses showed increased heating value and burning time by 5.13 % and 5.71 %, respectively, and moisture content decreased by 15.12 %. Furthermore, confirmation experiments within a 95 % confidence interval verified that the three responses obtained at the optimal operating conditions of process factors. The total cost of charcoal briquettes is 0.903 USD/kg and a payback period of 4.85 years. This illustrates that process improvement also aligns with the broader goals of promoting green and a circular economy.

Isogeometric topology optimization of structures using the overweight approach

In this paper, a 2D isogeometric formulation of the material distribution for structural topology optimization considering minimum weight and local stress constraints using the overweight approach is proposed. The aim of this isogeometric formulation is to provide solutions with high spatial definition using a lower number of design variables in comparison with the formulations previously developed to define the material layout. Despite of this, an important number of local stress constraints has to be considered in the solution of the problem. For this purpose, an Overweight Constraint is used to consider all of them. The structural analysis is performed by means of the Isogeometric Analysis (IGA) and the distribution of material is modeled by means of quadratic B-splines. Moreover, the optimization is addressed by means of the Sequential Linear Programming algorithm (SLP) that is driven by the information provided by a full first-order sensitivity analysis extension of the IGA formulation. Finally, the proposed formulation is tested by means of some benchmark problems, and the results show that the isogeometric formulation provides solutions with high spatial definition. A comparison with a Finite Element Method (FEM) topology optimization formulation is included.

A simplex approach for binary linear programming

This article is a research, design, and development effort, on an algorithm for Binary Linear Programming (BLP). The idea of the algorithm is based on the concepts borrowed from the Simplex method of Linear Programming (LP). The Simplex method has both column selection and row selection logics for generating a pivot. In this article we select both logics of LP to use as only the column selection logic for the BLP. The article provides the complete implementable C-language source code of this version of the BLP algorithm to show all the details of the logics. In addition, it provides a simple software requirement for embedded engineering products based on the laws of nature. It helps to design, modify, and maintain a simpler code for the algorithms. Therefore, the article uses a multidisciplinary approach. It integrates optimization theory, matrix algebra, computer programming, software engineering design requirements, social science, laws of nature, etc. This BLP algorithm will shed some light on the P-NP problem and its solution.

APPLICATION OF TRANSPORTATION MODEL TO SOLVE TANKERS’ – ROUTING PROBLEM

The problem of selecting minimum cost routes for tankers in distributing petroleum products and satisfying customers’ requirement without scarcity in Nigeria remains a huge challenge to major marketers in the oil industries. The cost of transporting petroleum products from sources to destinations matters a lot to oil marketers because of the direct impact it has on their profits. The means of distributing petroleum products from refineries to depots or filling stations are tankers’ routing and pipelines. In this research, we extended some existing tankers’-routing models in literature which use a discrete integer programming approach to determine efficient and effective distribution of petroleum products. Consequently, we developed a new transportation linear programming algorithm to determine minimum cost routes in the delivery of petroleum product from their supply centers (refinery) to demand centers (filling stations). The significance of the application we adopted in this research lies in the modified distribution approach to tackle the complexity involved when transportation problems are formulated as linear programming problem having several variables and constraints. In this research, we formulate a new version of transportation model of tankers’ routing with the aim of reducing the cost of petroleum products delivery. The proposed transportation linear programming model was applied to a numerical example alongside other existing transportation algorithms. It is observed that, the new algorithm produced approximately the same total cost obtained by using other existing algorithms

Optimizing code allocation for hybrid on-chip memory in IoT systems

With the increasing application of IoT devices, the memory subsystem, as the performance and energy bottleneck of IoT systems, has received a lot of attention. One of the keys is on-chip memory which can bridge the performance gap between the CPU and main memory. While many off-the-shelf embedded processors utilize the hybrid on-chip memory architecture containing scratchpad memories (SPMs) and caches, most existing literature ignores the collaboration between caches and SPMs. This paper proposes static SPM allocation strategies for the architecture mentioned above in IoT systems, which try to minimize the overall instruction memory subsystem latency and/or energy consumption. We capture the intra- and inter-task cache conflict misses via a fine-grained temporal cache behavior model. Based on this cache conflict information, we propose an integer linear programming (ILP) algorithm to generate an optimal static function level SPM allocation for system performance. Furthermore, to improve the scalability of the proposed allocation scheme for an enormous task set, we offer the interference factor to calculate the interference impact quantitatively. Then, based on the interference factor, we present two approximate knapsack based heuristic algorithms to provide near optimal static allocation schemes at both function- and basic block-level granularities, which favors fast design space exploration. The experiment results demonstrate that the proposed solution achieves a 30.85% improvement in memory performance, and up to 31.39% reduction in energy consumption, compared to the existing SPM allocation scheme at the function level. In addition, the proposed basic block level allocation algorithm shows better performance than our function level allocation algorithm and other basic block level allocation algorithm.