Linear Programming Method Research Articles

Optimal Scheduling of Battery Energy Storage Systems Using a Reinforcement Learning-based Approach

This article proposes a novel energy management algorithm that controls the battery energy storage system (BESS) and on-grid supply. It employs the deep-Q-network agent with prioritized experience replay, and its efficacy is validated and verified by comparison to a benchmark method for mixed integer linear programming. The grid and energy storage systems are governed by switching operations initiated by BESS controllers via the automatic transfer switch. The primary objective is to accomplish optimal scheduling of batteries one day in advance to reduce electricity costs while maintaining battery health and primary power supply reliability. The methods proposed in this work provide practicable grid and battery operation patterns that test all conceivable planning scenarios for energy storage operation. Finally, a comparative analysis is performed to evaluate the efficacy of the proposed BESS operation scheduling methods.

Methods for optimal placement of PMU devices to assess the stability of the Azerbaijan power system

This article discusses the method of integer linear programming, a method based on estimating the rate of change in operating conditions when conditions become more complex or disturbances occur. In the first method, the criterion for placing PMUs in the energy system of Azerbaijan is to ensure full observability; the second method examines the rate of change in the relative angles of synchronous generators under large disturbances. Based on the obtained parameters, weak nodes are identified where it is necessary to install PMU devices.

Experimental research of transition processes of asynchronous motors of belt conveyors on mathematical modeling

The purpose of the study. increasing the performance of belt conveyors and reducing transportation costs based on the developed mathematical modeling of transient processes of asynchronous motors of open-pit conveyor transport. The object of the research is the operating modes of asynchronous motors of belt conveyors of mining enterprises. The subject of research is the starting and braking modes of operation of asynchronous motors of belt conveyors of mining enterprises. Research methods are based on the modern theory of electrical machines, methods of linear and nonlinear mathematical programming, mathematical statistics, as well as methods of system analysis. The practical results of the study are as follows: the actual coefficient of resistance to the rotation of the conveyor rollers and the coefficient of resistance to the movement of the belt, leading to a decrease in the tractive effort, were determined; a method was developed for determining the additional power consumption of electric motors of belt conveyors, taking into account the overall volume, weight and speed of transported lumpy cargo; a mathematical model of braking and starting modes of induction motors of belt conveyors of mining enterprises was developed, taking into account the resistance coefficient of the belt and rollers.

A new method for calculating volumetric structural elements in the general case of their stress-strain state

The parametric equations of the strength surface in the space of internal force factors (IFF) are given for 9 forces and 9 moments in homogeneous anisotropic bodies. As special cases, similar equations are given for isotropic bodies that resist tension and compression differently (and equally). A variant of the kinematic method of the theory of limit equilibrium is proposed. A rigid-plastic model of a deformable solid body is used. It is assumed that massive structural elements are destroyed by dividing into parts that deform relatively little (“absolutely rigid finite elements”, ARFE) and have 6 degrees of freedom in three-dimensional space. The process of destruction of the material goes along infinitely thin generalized destruction surfaces (GDS), on which the work of all active IFFs is taken into account. To determine the minimum kinematically possible load, the simplex linear programming (LP) method was used.

Production business operation planning of a wood processing plant

A generalised production model of a wood processing plant has been modelled. The model which has allowed to connect dynamic and statistical characteristics of the enterprise is developed. The bases of the material-production system of the technological process are given. The goal criteria of enterprise activity are investigated: profit/cost, strictly on time, minimisation of stocks; algorithms of control of the choice of optimum resource distribution are developed. Software has been developed that implements linear and dynamic programming methods. Simulation of software on the example of furniture production with a feasibility study of the optimal production of products. The models and algorithms developed will allow to provide planning of business process of wood processing enterprise.

Математическая модель оптимизации комплекса инструментов «зелёной» логистики

«Green» supply chain management involves development and implementation of environmental solutions. The objective of their substantiation and evaluation under conditions of limited resources for their implementation is of particular importance. In order to highlight a whole complex of environmental solutions, the generalized concept of «green» logistics tools» is used in this research paper. The selection of optimal «green» logistics tools for implementation of material, financial, information resources and services in the elements of a logistics system is described. A technique for combining linear programming and multicriteria decision-making methods (MCDM) is presented. A system of «green» logistics tools has been formed for the six standard elements of a logistics system. The calculation results of the values of weight coefficients for tools and logistics elements are provided. The calculations of the weight coefficients were made using the developed CDM model constructed by combining DEMATEL and MARCOS multicriteria methods. The dependencies of the efficiency of «green» logistics tools on changes in available logistics resources are obtained. It is illustrated that the redistribution of logistics resources for implementation of various «green» logistics tools in the range of 7,5-15 % allows achieving the maximum effect from implementation of these tools in a logistics system or supply chain. A calculated example of a choice of 105 «green» logistics tools for six logistics elements is given in the article.

Data-Driven Control Design With LMIs and Dynamic Programming

The goal of this paper is to study model-free data-driven control evaluation and design strategies for discrete-time linear time-invariant systems, where the system model is unknown. In particular, our main contribution is twofold: 1) new state-input exploration and data collection schemes from experiences; 2) new data-driven linear matrix inequalities and dynamic programming methods for stabilization and optimal control problems. The proposed exploration and data collection schemes theoretically guarantee to acquire sufficient information from the system’s state-input trajectories that can solve the underlying control design problems. We prove that under mild assumptions, as more and more data is accumulated, the collected data can solve the problems with higher probability along with the proposed algorithms.

A Hybrid Linear Programming-Reinforcement Learning Method for Optimal Energy Hub Management

Reinforcement learning (RL) is a subset of artificial intelligence in which a decision-making agent tries to act optimally in an environment by controlling different parameters. There is no need to identify and mathematically formulate the environmental constraints in such a method. Moreover, the RL agent does not need prior information about future outcomes to act optimally in the current situation. However, its performance is adversely affected by the environmental complexity, which increases the agent’s effort to choose the optimal action in a particular condition. Integrating RL and linear programming (LP) methods is beneficial to tackle this problem as it reduces the state-action space that the agent should learn. In this regard, the optimization variables are divided into two categories. First, experience-dependent variables which have an inter-time dependency, and their values depend on the agent’s decision. Second, experience-independent variables whose values depend on the LP model and have no inter-time connection. The numerical results of integrating mentioned methods have demonstrated the hybrid model’s effectiveness in converging to the global optimum with more than 95% accuracy.

An adaptive method to solve multilevel multiobjective linear programming problems

This paper is a follow-up to a previous work where we defined and generated the set of all possible compromises of multilevel multiobjective linear programming problems (ML-MOLPP). We introduce a new algorithm to solve ML-MOLPP in which the adaptive method of linear programming is nested. First, we start by generating the set of all possible compromises (set of all non-dominated solutions). After that, an algorithm based on the adaptive method of linear programming is developed to select the best compromise among all the possible settlements achieved. This method will allow us to transform the initial multilevel problem into an ML-MOLPP with bonded variables. Then, apply the adaptive method which is the most efficient to solve all the multiobjective linear programming problems involved in the resolution process instead of the simplex method. Finally, all the construction stages are carefully checked and illustrated with a numerical example.

Optimization of transport network using mathematical methods

The aim of this paper is to outline the possibilities of implementing mathematical methods in optimization of the costs in the transport network. Transport accounts for between 50% and 60% of distribution costs and is an element of the supply chain that is most often the subject of outsourcing. Transport problems, like most logistics problems, can be reduced to optimization problems that are efficiently solved using mathematical methods. This paper presents mathematical methods of linear programming that are used to reduce transport costs on the real case study in the Adria region.

ВЕРИФИКАЦИЯ ОПТИМИЗАЦИОННОЙ МОДЕЛИ ПЕРЕРАБОТКИ ВАГОНОПОТОКОВ НА СОРТИРОВОЧНОЙ СТАНЦИИ МЕТОДОМ ИМИТАЦИОННОГО МОДЕЛИРОВАНИЯ

As a rule, current planning of operation of marshalling station is carried out with the use of heuristic algorithms and simulation modeling. It is possible to improve the quality of planning on the basis of strict optimization models. With the use of the mixed integer linear programming method the authors have created a mathematical and a computer model of car traffic processing at a marshalling station. The paper considers questions of verification of the optimization model with the use of simulation modeling.

FCSN 3-D PU: Fully Connected Spatiotemporal Network Based 3-D Phase Unwrapping

Phase Unwrapping (PU) based on spatial networks is a key procedure in time series synthetic aperture radar interferometry (TS-InSAR). Although the state-of-the-art techniques have shown good success in common cases, their performance remained uncertain in some challenging cases where the reliability of spatial network is difficult, e.g., reservoir areas with sparse points. In this context, this letter presents a new 3D PU method based on the fully connected spatiotemporal network (FCSN) to improve both accuracy and robustness of PU. The rationale behind is that we first implement a spatiotemporal network refinement including temporal interferogram pair selection and spatial network optimization. Based on the generated spatiotemporal network, we then establish a 3D PU mathematical framework by elaborating the 2D edgelist PU theory into the 3D domain. In this framework, all interferograms are unwrapped using integer linear programming method under the minimum <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">L</i> <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup> -Norm criterion. The new feature of the proposed method is that after a single solution search, all interferograms are unwrapped with a relatively high accuracy. The experimental results on two real datasets confirm its effectiveness.

Optimization of multi-period investment planning in street lighting systems by mixed-integer linear programming

This article proposed the use of multi-period mixed-integer linear programming method for investment planning to support decision-making processes in upgrading and managing street lighting systems. The technique incorporates a multi-variate model that maximizes energy-saving by considering budget constraints, the state of the lighting system, and the available technology in the market to replace the existing streetlights. This topic is novel because the complexity of the problem relies on the existence of several potentially large investments. As explained in this paper, the proposed method optimally considers the investments and returns as a combination that maximizes energy savings. The method was tested using actual data from an undisclosed public lighting system in Colombia. The results obtained revealed that multi-period investment optimization based on mixed-integer linear programming is an ideal investment plan, particularly in streetlight systems. Therefore, it forms an invaluable tool for street lighting systems' administrators and decision-makers in optimizing and facilitating the critical decision-making process in their work environment.

Mathematical Method to Construct Linear Programming Scheme of Football Training

Abstract Linear programming is a widely applicable mathematical operation method. In this paper, two solutions of linear programming and state parameter extraction can be used to simplify the inequality group and transfer the high-dimensional state utility function in football. This can speed up the generation of joint strategies for football teams in the game. This paper uses the free-kick technical football cooperation as an example to conduct an empirical study on the linear programming method of state parameters. In this paper, combined with the traditional motion information modeling method, a free ball path planning based on the linear programming gradient method is established. At the same time, this paper adopts an asymptotic method based on linear programming to solve the trajectory of any football. Finally, an experimental study on the linear programming gradient method for state feature vectorization is carried out. Experiments verify the effectiveness of this method. The mathematical model accurately predicts the linear programming of football training.

Safe Ship Control using Linear Programming

The presented work is part of the project to implement a simulator for determining the ship's trajectory in collision situations. The aim of this article is to model an optimal ship control system in collision situations taking into account the International Regulations for the Prevention of Collisions at Sea. The main task was to design and realize a trajectory visualization in the form of a simulation. An analysis of the simulation results was also carried out and used to formulate conclusions. In this paper, an algorithm based on the static linear programming method for determining a multistage ship trajectory was developed and presented. The block diagram of the algorithm and the basics of linear programming are described. A series of simulations in various navigational situations involving a foreign ship sailing on a course of 0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315° was carried out and the influence of the various parameters on the course of the simulation itself was examined. Based on the data obtained, graphs were drawn up to enable an easier analysis of the simulation results. It was also found that, depending on the complexity of the navigational situation, the results are more or less predictable and that, in order to obtain the optimal outcome of the situation, all the simulation parameters must be chosen accordingly.

Optimized Operation Plan for Hydrogen Refueling Station with On-Site Electrolytic Production

The cost reduction of hydrogen refueling stations (HRSs) is very important for the popularization of hydrogen vehicles. This paper proposes an optimized operation algorithm based on hydrogen energy demand estimation for on-site hydrogen refueling stations. Firstly, the user’s hydrogen demand was estimated based on the simulation of their hydrogenation behavior. Secondly, mixed integer linear programming method was used to optimize the operation of the hydrogen refueling station to minimize the unit hydrogen energy cost by using the peak–valley difference of the electricity price. We then used three typical scenario cases to evaluate the optimized operation method. The results show that the optimized operation method proposed in this paper can effectively reduce the rated configuration of electrolyzer and storage tank for HRS and can significantly reduce the unit hydrogen energy cost considering the construction cost compared with the traditional method. Therefore, the optimization operation method of a local hydrogen production and hydrogen refueling station proposed in this paper can reduce the cost of a hydrogen refueling station and accelerate the popularization of hydrogen energy vehicles. Finally, the scope of application of the proposed optimization method and the influence of the variation of the electricity price curve and the unit cost of the electrolyzer are discussed.

Multi-Objective Operation Strategy for a Community with RESs, Fuel Cell EVs and Hydrogen Energy System Considering Demand Response

Nowadays, it can be said that loads in the residential and transportation sector constitute an important part of global energy consumption. In this respect, due to environmental problems and in terms of ensuring energy reliability, it is seen that the energy demand is moving towards supplying it from on-site, renewable energy sources (RESs) and in a small-scale region, namely community. In this context, in this study, a multi-objective stochastic optimum energy management model for a renewable-supported hydrogen-based community is proposed with mixed-integer linear programming method. In the structure, the hydrogen energy system (HES) consisting of an electrolyzer, hydrogen tank, and fuel cell provides energy to the community and fuel support for hydrogen fuel cell electric vehicles (HFCEVs). In addition, a demand response (DR) program is implemented, where the room temperatures of the houses are remotely controlled. While electricity can be purchased from the power grid, hydrogen can be traded with the main hydrogen gas network. Besides, renewable spillage and carbon emission costs are considered. Various case studies are conducted using real data from Spain to demonstrate the effectiveness of the presented model. According to the results obtained, the proposed method can reduce the cost of the community by 58.67%.

Proses Manufaktur Pada Mesin Primer dan Sekunder PT XYZ Menggunakan Metode Linear Programming

The purpose of this study was to determine the manufacturing process on PT XYZ's primary and secondary machines using the Linear Programming method. This causes that in each period, the company experiences excess and decrease in production so that the company's profit is not optimal and results in large holding costs. This situation occurs because the company has been implementing production planning based on core. The method used as a solution is Linear Programming. The research method used is qualitative and descriptive methods and data collection techniques for library studies through various literature such as journals, books, magazines, articles obtained through Google Scholar with the keywords used namely manufacturing keywords, primary and secondary machines, and linear programming methods. so as to obtain accurate and in-depth data regarding the manufacturing process with the linear programming method. The results showed that the manufacturing process on PT XYZ's primary and secondary machines using the linear programming method could be more efficient in the use of existing resources and the policies implemented. So that feelings related to product combinations and changes related to profit per product with the loss of resources.

Proses Manufaktur Pada Mesin Primer dan Sekunder PT XYZ Menggunakan Metode Linear Programming

The purpose of this study was to determine the manufacturing process on PT XYZ's primary and secondary machines using the Linear Programming method. This causes that in each period, the company experiences excess and decrease in production so that the company's profit is not optimal and results in large holding costs. This situation occurs because the company has been implementing production planning based on core. The method used as a solution is Linear Programming. The research method used is qualitative and descriptive methods and data collection techniques for library studies through various literature such as journals, books, magazines, articles obtained through Google Scholar with the keywords used namely manufacturing keywords, primary and secondary machines, and linear programming methods. so as to obtain accurate and in-depth data regarding the manufacturing process with the linear programming method. The results showed that the manufacturing process on PT XYZ's primary and secondary machines using the linear programming method could be more efficient in the use of existing resources and the policies implemented. So that feelings related to product combinations and changes related to profit per product with the loss of resources.

FORMALISING A RAIL PLANNING TASK FOR A MINING COMPANY

The formalisation of the task of railway planning, namely, the formation of freight trains and their routes along the railway network of the mining company is considered. The statement of the problem including parameters of the problem, variables, system of constraints and target function is presented. An integer formulation of the problem, taking into account the constraints of a particular mining company, is proposed. The problem of railroad planning is relevant despite the various approaches and solutions available, since each case encounters different constraints. This formalisation differs from the others because there are different types of locomotives, and hence different capacities, and there are different types of materials to be transported. Four different categories of restrictions are presented. In addition, the existence of an extensive network of stations, a huge number of non-stationary constraints and other factors significantly increase the dimensionality of such problems, which increases the interest of researchers to them and contributes to the emergence of new and the development of existing methods and approaches to their solution. In the introduction, a description and features of the considered railway network of a mining company are presented. It then presents the formulation of the problem to be formalised, including parameters, variables, constraint system and target function. Then a numerical example with a solution is given. The integer linear programming method is used as a method for solving this problem. An example of scheduling freight trains for a network including four stations connected by double-track runs and having a star form is considered. The task of constructing routes is not considered in this example, as it is a separate complex task and is not required for this example, as there is a direct path from each departure station to each destination station.