Linear Programming Problem Research Articles

Fuzzy Mathematical Approach for Solving Multi-Objective Fuzzy Linear Fractional Programming Problem with Trapezoidal Fuzzy Numbers

Fuzzy Mathematical Approach for Solving Multi-Objective Fuzzy Linear Fractional Programming Problem with Trapezoidal Fuzzy Numbers

Multi-beam line observation optimization strategy based on random variable unitary iterative model

Multibeam system has many advantages such as large measurement range, fast speed, high accuracy, etc., which can be applied in many fields such as marine topographic survey. In this paper, the relationship between coverage width and other variables is obtained by analyzing the geometric relationship between each parameter, and a multibeam sounding model based on geometric relationship is established. And based on the intelligent optimization algorithm, an iterative optimization model with random variable singularization is designed independently. And the actual terrain data were visualized and simplified into various parameters in line with the model. With the help of the definition of the coverage rate, the relationship between the coverage width and other variables, and the one-to-one correspondence between the translation distance of the slope and the coverage rate, the complex measurement problem can be transformed into a simple linear programming problem, and the relationship model between the coverage rate and other variables is established. In the end, the model can be used to derive the optimal wiring scheme to realize high-precision and full-coverage sweeping of the seabed terrain in the given sea area without omission, provided that the ship speed, beam opening angle and other factors are reasonable.

Computing Parameter Estimates of a Homogeneous Nested Piecewise Linear Regression

Objective. The aim of the study is to develop an algorithm for identifying the parameters of a homogeneous nested piecewise linear regression model of the first type by the method of least modules. Method. Estimation of its unknown parameters is carried out with the help of reduction to the problem of linear Boolean programming. Its solution should not cause computational difficulties due to a significant number of effective software tools - for example, the well-established and freely available program LPsolve on the Internet. Result. The generated linear programming problem has an acceptable dimension for solving practical modeling problems. Conclusion. The results of solving a numerical example indicate the effectiveness of the method proposed in the work for calculating parameter estimates for a homogeneous nested piecewise linear regression model of the first type by the method of least modules.

Multi-source multicast service chaining model guaranteeing reliability of network services

Service chaining provides network services to users by processing packets with a series of virtualized network functions (VNFs). Multicast communication can suppress the network load compared to unicast communication when the same service is provided to multiple users simultaneously. Network providers need to ensure that services are provided to users under reliability requirements. Existing service chaining models can cause failure-intolerant or cost-inefficient resource allocation for multicast services. This paper proposes a multi-source multicast service chaining model that guarantees the reliability of network services with flexible routing and VNF placement. The proposed model determines the routing and VNF placement for each service chain request with redundancy so as to minimize the total resource utilization cost while satisfying the reliability requirement. In order to obtain cost-efficient feasible solutions, we introduce two heuristic algorithms. One is an algorithm that iteratively solves an integer linear programming problem until the reliability requirements are satisfied for all requests. The other is an algorithm that determines the VNF placement by using a metric based on the betweenness centrality and server failure rate. Numerical results show that the proposed model allocates the network and computation resources for services with lower total cost compared to the existing model. We also show illustrative examples of the resource allocation to compare the characteristics of two heuristic algorithms.

Mobility-aware task offloading in MEC with task migration and result caching

Numerous computation-intensive applications have emerged, demanding lower delay and energy consumption. Multi-access Edge Computing (MEC) provides task offloading services for mobile users (MUs) through proximate MUs, effectively minimizing service delay and energy consumption. However, the challenges of supporting MUs’ mobility persist, and ensuring uninterrupted task offloading services from MEC servers still needs to be solved. Additionally, applications like autonomous driving generate repetitive tasks, introducing unnecessary computational overhead. This paper adopts a task migration strategy to tackle these issues, specifically addressing task offloading failure due to MU mobility. Simultaneously, a computation-result cache-assisted technique is leveraged to alleviate the burden of repetitive computation. The objective is to minimize the system cost, which consists of the processing delay and energy consumption of tasks for all MUs. The problem is modeled as an integer linear programming problem, and the optimal solution is meticulously derived. In response to the high computational complexity inherent in obtaining the optimal solution, a low-complexity heuristic algorithm (CMHA) is introduced. Simulation results demonstrate that optimal and heuristic schemes significantly reduce the overall system delay and energy consumption.

Transformations of mixed solution types of interval linear equations system with boundaries on its left-hand side to linear inequalities with binary variables

To determine the solution set of an interval linear equations system Ax=b, it is necessary to know the semantics of the system. In addition to strong and weak semantics, there are four other important semantics: tolerance, control, left-localized, and right-localized. A solution x with one of these semantics provides that particular behavior in every equation of the system. It could happen that there is a solution x with one semantic in some equations and another semantic in the remaining equations of the system. This solution generates another solution type. We provide fifteen combinations of solution types generated by tolerance, control, left-localized, and right-localized semantics and prove that the solution set containing all four semantics is the weak (united) solution set. We show that each of these fifteen nonnegative solution types with some given boundaries on Ax can be transformed to be the solution set of linear inequalities with binary variables. The transformed system is deterministic and can be used in a linear programming problem with interval linear equation constraints to find an optimistic solution satisfying the semantics of the interval linear equations. Task management and course assignment examples are provided to show the necessity of these solution types.

An approximation algorithm for bus evacuation problem

In large-scale disasters, evacuation using public transport, such as buses, is always essential, especially with limitations on the time window and resources available. Unfortunately, a Bus Evacuation Problem (BEP) is NP-hard in nature. This means it is impossible to find an optimal evacuation plan within a reasonable time window. Therefore, it is efficacious and requisite to use an approximation algorithm such that a sub-optimal plan can be derived quickly in large-scale disasters. In the literature, an approximation algorithm for BEP has been presented. However, there is not only a lack of rigorous proof of the approximation ratio, but also the computation time of the approximation algorithm is influenced by the number of evacuees. In this work, firstly the approximation ratio is derived as 2nb+7, where nb is the number of buses, which is fundamentally more precise than the existing work. Further, the approximation ratio can be reduced to nb+6 through a new proof provided in this work. More importantly, a new approximation algorithm is proposed in this work, with an aggregated network flow model that can be quickly solved as a linear programming problem in polynomial time. The approximation ratio of the new algorithm is proven to be nb+1 when there is a pile of buses, and the computation time is insensitive to the number of evacuees. Finally, 10 sets of random cases and a real-life disaster, the flooding in Xingguo, China in 2019 are studied to illustrate the efficiency and practical applicability of the proposed approximation algorithm.

Process design methodology for rankine cycle based on heat matching

The Rankine cycle serves as a crucial technical tool for waste-heat recovery. Matching heat sources and working fluids presents a challenging problem among the extensive research on the process design and selection of working fluids for the Rankine cycle. This study introduces a process design methodology for the Rankine cycle based on heat matching. It can optimize the performance between heat sources and working fluids without the need to preset the configuration for the cycle. The objective is to ultimately derive the most efficient configuration and operating conditions for the Rankine cycle. This method relies on establishing a matching relationship between temperature and heat diagram curves of both heat sources and working fluids. The relationship can be described by a simple linear programming problem, serving as the fundamental model for the proposed method. Demonstration of the feasibility and accuracy of this method involved computing the performance of a subcritical Rankine cycle for waste heat recovery in an ammonia-diesel dual-fuel engine. Three different working fluids were considered: ammonia, R123, and R245fa. Ammonia exhibited superior performance with an overall system efficiency improvement of 5.18 %, surpassing R123 (5.01 %) and R245fa (5.00 %). The competitiveness of the ammonia Rankine cycle has been established, resulting in a nearly zero-carbon-emission power system potentially achieving an overall efficiency of 53.23 %. The process design method based on heat matching notably reduces the modeling efforts required for the Rankine cycle. This reduction provides substantial support for engineering design and facilitates wider applications of the Rankine cycle.

Enhancing target benefits of power system stakeholders: A columns and constraint generation-based power-to-gas linked economic dispatch

Economic dispatch (ED) plays a crucial role in optimizing power plant output to minimize the cost of electricity production and ensure economic efficiency in complex power systems. However, with the growing emphasis on carbon neutrality policies and the increased use of renewable energy sources (RES), traditional ED models may lead to economic losses for independent power producers (IPP) and renewable energy providers (REP). To address this challenge, a new ED model is proposed in this study, which integrates power-to-gas (P2G) technology and takes into account the perspectives of all stakeholders, including independent system operator (ISO) IPP, and REP. The proposed approach is tested in the context of the cost based pool (CBP) market structure in S. Korea, where a mixed integer linear programming (MILP) problem is solved for each target benefit using columns and constraint generations (C&CG). By ensuring the target benefits of each stakeholder group, this improved ED model aims to encourage their participation in the power system and support economic efficiency. The simulation results of the P2G-linked ED proposed in this paper verify that as the capacity of the integrated P2G increases, there is an increase in the improvement rate of each target benefit for ISO, IPP, and REP.

Joint optimization of UPF placement and traffic routing for 5G core network user plane

This paper investigates the dynamic deployment of the 5G core network user plane functions (UPFs) in the edge network under time-varying traffic conditions. The objective is to minimize the total cost, including energy consumption, user plane latency, and UPF deployment costs by jointly optimizing UPF placement and traffic routing over the entire planning horizon. We formulate the optimization problem as a mixed-integer linear programming (MILP) problem, which is proven to be NP-hard. To obtain the optimal solution for the problem, we propose a Benders decomposition-based algorithm. However, the high computational complexity of this algorithm limits its practical applicability for large-scale networks. Therefore, we propose a low-complexity algorithm based on nested Benders decomposition that can solve the problem suboptimally. The simulation results demonstrate the convergence and computational efficiency of the proposed algorithm and show that it outperforms two existing algorithms. Moreover, we demonstrate that cost-saving can be achieved by using more power-efficient servers or deploying more servers. Additionally, we show that adjusting the cost parameters can achieve a good tradeoff between energy consumption and user plane latency.

DESAIN MODEL PEMBELAJARAN DENGAN MODEL KOOPERATIF TIPE THINK PAIR SHARE DAN PENDEKATAN ILMIAH TERHADAP KEMAMPUAN SISWA DALAM PEMAHAMAN KONSEP DAN PEMECAHAN MASALAH PADA MATERI PROGRAM LINEAR DI KELAS XI SMA NEGERI 1 SUNGGAL

This research uses quasi-experimental research. The population in this study were students of Class XI MIPA at SMA Negeri 1 Sunggal T.P. 2019/2020. This research aims to make it easier for students to achieve learning goals in understanding concepts and solving linear programming problems using a Think Pair Share (TPS) type cooperative model and a scientific approach. The research results show that the learning model that has been designed is good for use. The tcount value for the problem solving test is 5.0350 while ttable = 1.667, which means tcount > ttable, meaning it is accepted or rejected, so it is concluded that learning using the think pair share type cooperative model is better than the scientific approach to linear programming problem solving in Class XI Sunggal 1 Public High School T.P. 2019/2020. Keywords: Cooperative Think Pair Share Type, Scientific Approach, Concept Understanding

Analisis Optimalisasi Produksi Dengan Linear Programming Melalui Metode Simpleks (Studi Kasus UMKM Aqisa Rumah Rosella Surabaya)

The simplex method is a method used to solve linear programming problems with repeated (repeated) calculations done many times to reach an optimal solution. To solve linear programming problems, it is necessary to determine the constraints and inequalities contained in the linear program. The simplex method can solve linear programming problems involving many inequalities and many variables. This study aims to optimize the production of rosella flower tea drinks and rosella flower syrup at UMKM Aqisa Rumah Rosella Surabaya. This study is a literature study, namely a literature study by examining books, journals and reports that are relevant to the field under study. The steps for optimizing production results include: (1) observation, (2) data collection, (3) mathematical modeling, (4) optimizing production results using the simplex method, (5) optimizing production results using POM-QM. The results of simplex linear program calculations using the POM-QM application, in order to get maximum profit, UMKM Aqisa Rumah Rosella needs to increase production of rosella tea drinks to 35 bottles per day and for rosella syrup it is necessary to reduce production to 5 bottles per day. With a total profit of IDR 142,500. Profits earned increased by 5%

Solution of Z-number-based multi-objective linear programming models with different membership functions

In a universe full of fuzziness and uncertainty, it is an absolute blessing if some information is reliable to some degree. Considering the amount of uncertainty, Zadeh proposed the idea of Z-number, which carries both uncertainty and the reliability of the information. Uncertain information can be reliably conveyed using Z-numbers. On the other hand, one of the important and widely used decision-making techniques is linear programming. Currently, linear programming has been extensively explored using fuzzy information. Decisions made using linear programming with uncertain data are highly uncertain due to the lack of reliability of the information. An effective decision-making method is multi-objective linear programming (MOLP), in which the decision-maker attempts to draw conclusions from information containing conflicting attributes. In the MOLP problem, there may be different solution vectors corresponding to each objective function. One needs to find a compromise solution vector that satisfies each objective function to a certain extent based on the decision maker's suggested preferences. In this study, we use Z-number and MOLP to model the Z-number MOLP problem (ZMOLPP). Furthermore, we propose a strategy for solving ZMOLPP by transforming it into a crisp MOLP problem, and finally converting this crisp MOLP problem into a single-objective linear programming problem (LPP) using different shape functions. Additionally, we compare the results with existing MOLP problems in fuzzy settings to validate the proposed strategy.

An outer approximation algorithm for generating the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems

In this paper, we present an outer approximation algorithm for computing the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems (MOMILPs). It produces the extreme points (i.e., the vertices) as well as the facets of the Edgeworth–Pareto hull. We note that these extreme points are the extreme supported non-dominated points of a MOMILP. We also show how to extend the concept of geometric duality for multi-objective linear programming problems to the Edgeworth–Pareto hull of MOMILPs and use this extension to develop the algorithm. The algorithm relies on a novel oracle that solves single-objective weighted-sum problems and we show that the required number of oracle calls is polynomial in the number of facets of the convex hull of the extreme supported non-dominated points in the case of MOMILPs. Thus, for MOMILPs for which the weighted-sum problem is solvable in polynomial time, the facets can be computed with incremental-polynomial delay—a result that was formerly only known for the computation of extreme supported non-dominated points. Our algorithm can be an attractive option to compute lower bound sets within multi-objective branch-and-bound algorithms for solving MOMILPs. This is for several reasons as (i) the algorithm starts from a trivial valid lower bound set then iteratively improves it, thus at any iteration of the algorithm a lower bound set is available; (ii) the algorithm also produces efficient solutions (i.e., solutions in the decision space); (iii) in any iteration of the algorithm, a relaxation of the MOMILP can be solved, and the obtained points and facets still provide a valid lower bound set. Moreover, for the special case of multi-objective linear programming problems, the algorithm solves the problem to global optimality. A computational study on a set of benchmark instances from the literature is provided.

Leveraging Deep Q-Learning to maximize consumer quality of experience in smart grid

The smart grid system has addressed the problems of traditional power grid by not only meeting energy demand in real-time but also limiting its wastage. The two key objectives of a smart grid system are to ensure a higher Quality of Experience (QoE) for consumers and to reduce consumer costs using dynamically varying pricing concepts. However, these two objective parameters oppose each other as maximizing the consumer QoE requires the availability of sufficient electric power at any given time, which in turn increases power purchase cost. In this paper, we introduce an efficient power management system architecture of a smart grid and develop an Optimal Energy Allocation and Prediction system based on Deep Q-Leaning, namely OEAP-DQL, that brings a trade-off between the two. The developed OEAP-DQL system is a multi-objective linear programming (MOLP) problem that predicts consumer electricity demand by exploiting four different weighted and regressive moving average forecasting methods in the action space to accurately capture dynamically varying customer demand behaviors. Furthermore, iterative exploitation of multiple learning methods decreases forecasting error and intelligent stored power management helps the OEAP-DQL smart grid operator (SGO) to enhance its profit. The results of our simulation experiments show that the OEAP-DQL system outperforms the state-of-the-art works in terms of QoE and cost.

An iterative approach for the solution of fully fuzzy linear fractional programming problems via fuzzy multi-objective optimization

<abstract><p>The primary goal of optimization theory is to formulate solutions for real-life challenges that play a fundamental role in our daily lives. One of the most significant issues within this framework is the Linear Fractional Programming Problem (LFrPP). In practical situations, such as production planning and financial decision-making, it is often feasible to express objectives as a ratio of two distinct objectives. To enhance the efficacy of these problems in representing real-world scenarios, it is reasonable to utilize fuzzy sets for expressing variables and parameters. In this research, we have worked on the Fully Fuzzy Linear Fractional Linear Programming Problem (FFLFrLPP). In our approach to problem-solving, we simplified the intricate structure of the FFLFrLPP into a crisp Linear Programming Problem (LPP) while accommodating the inherent fuzziness. Notably, unlike literature, our proposed technique avoided variable transformation, which is highly competitive in addressing fuzzy-based problems. Our methodology also distinguishes itself from the literature in preserving fuzziness throughout the process, from problem formulation to solution. In this study, we conducted a rigorous evaluation of our proposed methodology by applying it to a selection of numerical examples and production problems sourced from the existing literature. Our findings revealed significant improvements in performance when compared to established solution approaches. Additionally, we presented comprehensive statistical analyses showcasing the robustness and effectiveness of our algorithms when addressing large-scale problem instances. This research underscores the innovative contributions of our methods to the field, further advancing the state-of-the-art in problem-solving techniques.</p></abstract>

Utilization of neutrosophic Kuhn-Tucker’s optimality conditions for Solving Pythagorean fuzzy Two-Level Linear Programming Problems

This article considers a bi-level linear programming with single valued trapezoidal fuzzy neutrosophic cost coefficient matrix and Pythagorean fuzzy parameters in the set of constraints both in the right and left sides. Based on the score functions of the neutrosophic numbers and Pythagorean fuzzy numbers, the model is changed to the corresponding crisp bi-level linear programming (BLP) problem. This problem is designated as a Pythagorean fuzzy bi-level linear programming (PFBLP) problem under neutrosophic environment. Kuhn-Tucker's conditions for optimality are necessary and sufficient for the existence of the optimal solution to a BLP problem. Using the suggested methodology, the problem is formulated as a single-objective non-linear programming problem with several variables and constraints. Two typical numerical examples are examined to illustrate the proposed approach.

Minimum cost flow problems in generalized fuzzy environments. Credibilistic CVaR minimization approach

The paper focuses on the problems of linear programming (LP) with generalized fuzzy numbers (GFNs) as coefficients of the objective function. It is necessary to characterize consistent arithmetic operations to lower the error and information loss compared to the minimum operator usage and normalization in cases where experts are not completely certain of their subjective opinions. The uncertainty is eliminated using the total cost as a loss function and credibilistic conditional value at risk (CVaR) minimization. To crispify and generate a GFN, we utilize a ranking function that allows us to consider risky realizations. By solving many deterministic problems with LP solvers, projections of the error in the objective function can be presented. To describe and implement our methodology, we mainly focus on network optimization problems, especially generalized fuzzy transportation, assignment, and shortest path problems.

Towards neutrosophic Circumstances goal programming approach for solving multi-objective linear fractional programming problems

Indeterminacy is common in practical decision-making circumstances. So the mathematical models of decision making represent the situations in a better way if the parameters are considered as neutrosophic. This article studies a general framework of multi-objective neutrosophic linear fractional programming problem (MONLFPP) and proposes unique approach. The issue's parameters are thought of as triangular neutrosophic numbers. The problem is converted into an equal crisp multi-objective linear programming problem (MOLPP) with the help of variable transformation technique and a ranking function. Fuzzy goal programming is used to solve the MOLPP that has been obtained. Finally, the usefulness of the proposed technique is established using two mathematical models.

Enhancing neutrosophic fuzzy compromise approach for solving stochastic bi- level linear programming problems with right- hand sides of constraints follow normal distribution

In this paper, a bi-level chance constrained programming problem is considered when the coefficients of the objective function is presented as neutrosophic numbers and the right- hand side of the constraints is normal variables and the constraints have a joint probability distribution. While the probability problem and applying the score and accurate functions the problem is converted into an equivalent deterministic non- linear programming problem, a fuzzy programming approach is applied by defining membership function. A linear membership function is used for obtaining optimal compromise solution. A numerical example is given to illustrate the proposed methodology.