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Design and mixed integer linear programming optimization of a solar/battery based Conex for remote areas and various climate zones

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SUSTAINABLE ENERGY TECHNOLOGIES AND ASSESSMENTS 2021年 45卷 101104-101104页

作者： Taslimi, Melika Ahmadi, Pouria Ashjaee, Mehdi Rosen, Marc A. Univ Tehran Sch Mech Engn Coll Engn Tehran Iran Univ Ontario Inst Technol Fac Engn & Appl Sci Oshawa ON L1G 0C5 Canada

In this research paper, a multi-objective optimization for sizing a stand-alone photovoltaic system for a Conex in remote areas is developed based on a mixed integer linear programming (MILP) technique. The stand-alone system is composed of a photovoltaic array, a cooling/heating system, battery banks, an inverter, and a charge controller. The MILP model is employed to obtain the optimal size and specifications of system components, including model and number of photovoltaic panels, the coefficient of performance of cooling/heating system, and the battery size, with respect to two conflicting objective functions, total cost and loss of power supply probability. The weighted factor method is employed in the model, and the final optimal solutions are achieved by MATLAB software. The suggested model is optimized for four cities in Iran, representing different climate types, but it can be utilized for any site with known climate data. In order to observe the conflict between the two objective functions, the Pareto frontiers are shown. The average cost of supplied electrical power is found to be 160,000, 250,000, 150,000, and 60,000 Iranian Rials per kWh, (180,000 Iranian Rials is equal to 1 US dollar in April 2020), for Tehran, Tabriz, Kerman, and Bandar Abbas, respectively. Based on the optimization results, the system is cost-efficient and suitable for remote applications, especially in desert and semiarid regions. Hence, the proposed system can provide the required electricity of the Conex for approximate initial costs of 440 and 290 million Rials for Kerman and Bandar Abbas, respectively. Finally, the optimum solutions through various weighted factors are shown, considering operator purpose and budget preferences, which permit advantageous utilization of solar energy.

关键词： Stand-alone photovoltaic system Optimal sizing Multi-objective optimization mixed-integer linear programming Remote areas

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Conjugate active and reactive power management in a smart distribution network through electric vehicles: A mixed integer -linear programming model

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SUSTAINABLE ENERGY GRIDS & NETWORKS 2020年 22卷

作者： Pirouzi, Sasan Latify, Mohammad Amin Yousefi, G. Reza Isfahan Univ Technol Dept Elect & Comp Engn Esfahan *** Iran

Electrical Vehicles (EVs) have a growing penetration rate in many countries aimed at the reduction of fossil fuel consumption and declining environmental issues. The high penetration rate of EVs, as new electrical energy demands, can cause operational problems for distribution networks. Therefore, designing and implementation of monitoring and management mechanisms for EVs charging is a necessity. EVs are equipped with power electronic-based chargers, bringing them a high degree of flexibility in conjugate active and reactive power control. This capability can be employed not only to reduce the adverse impacts of the high penetration rate of EVs on distribution networks operation but also to support the active and reactive management in distribution networks. In this paper, to employ EVs conjugate active and reactive power control capability, a model for central active and reactive power management in a smart distribution network is proposed. The proposed model is an optimization problem in which the objective function consists of two terms, namely, "minimizing the cost of energy" and "improving the voltage profile", over the operation planning horizon. The constraints of the optimization problem include distribution network operation constraints and charging and discharging constraints related to the EVs batteries and chargers. This problem is modelled as a mixed integer linear programming (MILP) problem and is implemented on the 33-bus, 69-bus, and 133-bus distribution networks. The results show that the proposed model can obtain the lowest energy cost and energy loss and the best operational voltage profile in a completely acceptable calculation time. Moreover, by using the proposed model, supplying the required energy for EVs during their plugin time interval is guaranteed and, increasing the penetration rate of EVs into the network is facilitated. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： Conjugate active and reactive power management Electric vehicles mixed-integer linear programming Smart distribution network operation

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PAAMP: Polytopic Action-Set And Motion Planning for Long Horizon Dynamic Motion Planning via mixed integer linear programming

arXiv

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arXiv 2024年

作者： Jaitly, Akshay Farzan, Siavash Robotics Engineering Department Worcester Polytechnic Institute WorcesterMA01609 United States Electrical Engineering Department California Polytechnic State University San Luis ObispoCA93407 United States

— Optimization methods for long-horizon, dynamically feasible motion planning in robotics tackle challenging non-convex and discontinuous optimization problems. Traditional methods often falter due to the nonlinear characteristics of these problems. We introduce a technique that utilizes learned representations of the system, known as Polytopic Action Sets, to efficiently compute long-horizon trajectories. By employing a suitable sequence of Polytopic Action Sets, we transform the long-horizon dynamically feasible motion planning problem into a linear Program. This reformulation enables us to address motion planning as a mixed integer linear Program (MILP). We demonstrate the effectiveness of a Polytopic Action-Set and Motion Planning (PAAMP) approach by identifying swing-up motions for a torque-constrained pendulum as fast as 0.75 milliseconds. This approach is well-suited for solving complex motion planning and long-horizon Constraint Satisfaction Problems (CSPs) in dynamic and underactuated systems such as legged and aerial robots. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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TOWARDS FOUNDATION MODELS FOR mixed integer linear programming

arXiv

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arXiv 2024年

作者： Li, Sirui Kulkarni, Janardhan Menache, Ishai Wu, Cathy Li, Beibin MIT United States Microsoft Research

mixed integer linear programming (MILP) is essential for modeling complex decision-making problems but faces challenges in computational tractability and interpretability. Current deep learning approaches for MILP focus on specific problem classes and do not generalize to unseen classes. To address this shortcoming, we take a foundation model training approach, where we train a single deep learning model on a diverse set of MILP problems to generalize across problem classes. As existing datasets for MILP lack diversity and volume, we introduce MILP-Evolve, a novel LLM-based evolutionary framework that can generate a large set of diverse MILP classes with an unlimited number of instances. We study our methodology on three key learning tasks that capture diverse aspects of MILP: (1) integrality gap prediction, (2) learning to branch, and (3) a new task of aligning MILP instances with natural language descriptions. Our empirical results show that models trained on the data generated by MILP-Evolve achieve significant improvements on unseen problems, including MIPLIB benchmarks. Our work highlights the potential of moving towards a foundation model approach for MILP that can generalize to a broad range of MILP problem classes. Our code and data are publicly available at https://***/microsoft/OptiGuide. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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Learning to Select Cutting Planes in mixed integer linear programming Solving

arXiv

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arXiv 2024年

作者： Zhang, Xuefeng Chen, Liangyu Yang, Zhengfeng Zeng, Zhenbing Software Engineering Institute East China Normal University China College of Sciences Shanghai University China

Cutting planes (cuts) are crucial for solving mixed integer linear programming (MILP) problems. Advanced MILP solvers typically rely on manually designed heuristic algorithms for cut selection, which require much expert experience and cannot be generalized for different scales of MILP problems. Therefore, learning-based methods for cut selection are considered a promising direction. State-of-the-art learning-based methods formulate cut selection as a sequence-to-sequence problem, easily handled by sequence models. However, the existing sequence models need help with the following issues: (1) the model only captures cut information while neglecting the linear programming (LP) relaxation;(2) the sequence model utilizes positional information of the input sequence, which may influence cut selection. To address these challenges, we design a novel learning model HGTSM for better select cuts. We encode MILP problem state as a heterogeneous tripartite graph, utilizing heterogeneous graph networks to fully capture the underlying structure of MILP problems. Simultaneously, we propose a novel sequence model whose architecture is tailored to handle inputs in different orders. Experimental results demonstrate that our model outperforms heuristic methods and learning-based baselines on multiple challenging MILP datasets. Additionally, the model exhibits stability and the ability to generalize to different types of problems. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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A multi-objective mixed integer linear programming model for supply chain planning of 3D printing

arXiv

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arXiv 2024年

作者： Talebi, Amirreza Department of Integrated Systems Engineering The Ohio State University ColumbusOH United States

3D printing is considered the future of production systems and one of the physical elements of the Fourth Industrial Revolution. 3D printing will significantly impact the product lifecycle, considering cost, energy consumption, and carbon dioxide emissions, leading to the creation of sustainable production systems. Given the importance of these production systems and their effects on the quality of life for future generations, it is expected that 3D printing will soon become one of the global industry's fundamental needs. Although three decades have passed since the emergence of 3D printers, there has not yet been much research on production planning and mass production using these devices. Therefore, we aimed to identify the existing gaps in the planning of 3D printers and to propose a model for planning and scheduling these devices. In this research, several parts with different heights, areas, and volumes have been considered for allocation on identical 3D printers for various tasks. To solve this problem, a multi-objective mixed integer linear programming model has been proposed to minimize the earliness and tardiness of parts production, considering their order delivery times, and maximizing machine utilization. Additionally, a method has been proposed for the placement of parts in 3D printers, leading to the selection of the best edge as the height. Using a numerical example, we have plotted the Pareto curve obtained from solving the model using the epsilon constraint method for several parts and analyzed the impact of the method for selecting the best edge as the height, with and without considering it. Additionally, a comprehensive sensitivity and scenario analysis has been conducted to validate the results. Copyright © 2024, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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ON THE TIGHTNESS OF linear RELAXATIONS OF ALTERNATIVE mixed integer programming FORMULATIONS FOR THE GENERATOR MAINTENANCE SCHEDULING PROBLEM

arXiv

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arXiv 2025年

作者： Andrade, Tiago PSR Rio de Janeiro Brazil

This paper presents a comprehensive theoretical analysis of six distinct mixed-integer programming (MIP) formulations for preventive Generator Maintenance Scheduling (GMS), a critical problem for ensuring the reliability and efficiency of power systems. By comparing the tightness of their linear relaxations, we identify which formulations offer superior dual bound and, thus, better computational performance. Our analysis includes establishing relationships between the formulations through definitions, lemmas, and propositions, demonstrating that some formulations provide tighter relaxations that lead to more efficient optimization outcomes. These findings offer valuable insights for practitioners and researchers in selecting the most effective models to enhance the scheduling process of preventive generator maintenance. Copyright © 2025, The Authors. All rights reserved.

关键词： mixed-integer linear programming

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Supervised Learning for Real-time Model Predictive Control Leveraging Multi-parametric mixed integer Quadratic programming

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Journal of Institute of Control, Robotics and Systems 2025年第2期31卷 98-105页

作者： Yoo, Seungjun Gwon, Minwoo Kim, Kwang-Ki Department of Electrical and Computer Engineering Inha University Korea Republic of

This paper presents a novel supervised learning framework for real-time optimization of multi-parametric mixed-integer quadratic programming (mp-MIQP) problems. The framework utilizes a multi-layer perceptron (MLP) model to efficiently predict both continuous and binary control inputs while classifying the feasibility of the optimization problem. To address the computational burden of branch-and-bound methods and the memory limitations of explicit model predictive control (MPC), this framework learns optimal control inputs across diverse system states and prediction horizons through offline training. Comparative evaluations reveal that the proposed method significantly outperforms traditional approaches in computational speed and memory efficiency while maintaining high accuracy in approximating optimal solutions. These advancements position the framework as a transformative solution for real-time control applications, offering a robust and efficient alternative for online optimization in mp-MIQP problems. © ICROS 2025.

关键词： mixed-integer linear programming

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Solving a Global-mixed integer Signomial Geometric Fractional programming Problem

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Neutrosophic Sets and Systems 2025年 81卷 655-666页

作者： Nejad, J. Shirin Saraj, M. Department of Mathematics Research Institute of Education and training Khuzestan Ahvaz Iran Department of Mathematics Faculty of Mathematical Sciences and Computer Shahid Chamran University of Ahvaz Ahvaz Iran

This article addresses mixed integer fractional signomial geometric programming (MIFSGP) problems, which have been widely used in industrial design. In this paper, first, we convert fractional signomial programming into a nonfractional problem so that it maintains its geometric structure. Then, convex relaxation is used to reach a mixed integer global solution. Although, in many cases, we obtain a better objective function value with this process, designers may still be dissatisfied with the rupture between the original objective function value and the relaxed value. Therefore, we apply a spatial branch and bound algorithm to decrease that distance to an acceptable extent and maintain the global solution. Finally, a real design problem is considered to evaluate the efficiency and accuracy of the proposed technique. © 2025, University of New Mexico. All rights reserved.

关键词： mixed-integer linear programming

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Constrained dynamic programming of mixed-integer linear problems by multi-parametric programming

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COMPUTERS & CHEMICAL ENGINEERING 2014年第0期70卷 172-179页

作者： Rivotti, Pedro Pistikopoulos, Efstratios N. Univ London Imperial Coll Sci Technol & Med Dept Chem Engn Ctr Proc Syst Engn London SW7 2AZ England

This work addresses the topic of constrained dynamic programming for problems involving multi-stage mixed-integer linear formulations with a linear objective function. It is shown that such problems may be decomposed into a series of multi-parametric mixed-integer linear problems, of lower dimensionality, that are sequentially solved to obtain the globally optimal solution of the original problem. At each stage, the dynamic programming recursion is reformulated as a convex multi-parametric programming problem, therefore avoiding the need for global optimisation that usually arises in hard constrained problems. The proposed methodology is applied to a problem of mixed-integer linear nature that arises in the context of inventory scheduling. The example also highlights how the complexity of the original problem is reduced by using dynamic programming and multi-parametric programming. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Dynamic programming Multi-parametric programming mixed-integer linear programming

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