Fractional Programming Problem Research Articles

A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem

A New Global Optimization Algorithm for Mixed-Integer Quadratically Constrained Quadratic Fractional Programming Problem

New Mean and Median Techniques to Solve Multiobjective Linear Fractional Programming Problem and Comparison with Other Techniques

In the field of operation research, both linear and fractional programming problems have been more encountered in recent years because they are more realistic in expressing real-life problems. Fractional programming problem is used when several rates need to be optimized simultaneously such as resource allocation planning, financial and corporate planning, healthcare, and hospital planning. There are several techniques to solve the multiobjective linear fractional programming problem. However, because of the use of scalarization, these techniques have some limitations. This paper proposed two new mean and median techniques to solve the multiobjective linear fractional programming problem by overcoming the limitations. After utilizing mean and median techniques, the problem is converted into an equivalent linear fractional programming problem; then, the linear fractional programming problem is transformed into linear programming problem and solved by the conventional simplex method or mathematical software. Some numerical examples have been illustrated to show the efficiency of the proposed techniques and algorithm. The performance of these solutions was evaluated by comparing their results with other existing methods. The numerical results have shown that the proposed techniques are better than other techniques. Furthermore, the proposed techniques solve a pure multiobjective maximization problem, which is even impossible with some existing techniques. The present investigation can be improved further, which is left for future research.

Optimality and duality results for fractional programming problems under E-univexity

Optimality and duality results for fractional programming problems under E-univexity

A fuzzy mathematical model to solve multi-objective trapezoidal fuzzy fractional programming problems

A fuzzy mathematical model to solve multi-objective trapezoidal fuzzy fractional programming problems

A study on the solution of interval linear fractional programming problem

Interval linear fractional programming problem (ILFPP) approaches uncertain-ties in real-world systems such as business, manufacturing, finance, and eco-nomics. In this study, we propose solving the interval linear fractional pro-gramming (ILFP) problem using interval arithmetic. Further, to construct the problem, a suitable variable transformation is used to form an equivalent ILP problem, and a new algorithm is depicted to obtain the optimal solution with-out converting the problem into its conventional form. This paper compares the range, solutions, and approaches of ILFP with fuzzy linear fractional pro-gramming (FLFP) in solving real-world optimization problems. The illustrated numerical examples show a better range of interval solutions on practical appli-cations of ILFPs and uncertain parameters.

On application of linear fractional programming problem using e-education system

This article focuses on an area of nonlinear programming problems known as linear fractional programming problems with multiple objectives. When tackling real-world linear fractional optimization problems, ambiguity and uncertainty in decision-making are inherent. This research aims to present a simple and computationally quick approach to solving multiple objective linear fractional programming problems with all decision variables and parameters described in terms of crisp. The proposed solution algorithm is based primarily on the fuzzy-based technique, and a membership function strategy. To resolve the multi-objective linear fractional programming problem, first consider the problem as a single objective function and along with the fuzzy programming model obtain the optimal solution using LINGO software. LINGO is a software application primarily used for solving linear, nonlinear, and integer optimization problems Moreover, an e-education setup problem demonstrates the steps of the proposed method.

A Survey on Generalized Fuzzy Parameter-Based Fractional Programming Problem

In fuzzy sets, the elements of a universal set may belong to that set completely, may not belong to that set, or may belong partially. Therefore, fuzzy sets are called generalizations of crisp sets. Due to the diverse nature of problems in real-world situations, fuzzy set theory is found to be unable to address some of the other features of ambiguity. Therefore, researchers extended fuzzy sets to picture fuzzy sets, orthopair, intuitionistic, Pythagorean, Fermatean, neutrosophic, spherical fuzzy sets, etc. Real-world problems can be solved using the method of fractional programming. Decision-makers are trying to get good results using generalized fuzzy numbers in fractional programming problems; hence, this review paper provides a specific framework for generalized fuzzy sets and generalized fuzzy fractional programming problems. Furthermore, it is a platform for researchers who want to work on generalized fuzzy parameter-based fractional programming problems. This research paper summarizes all the basic concepts and prior research on fractional programming and generalized fuzzy linear fractional programming problems.

An efficient branch and bound reduction algorithm for globally solving linear fractional programming problems

This paper investigates a class of linear fractional programs (LFP) with linear constraints, which are widely applied in transportation, economic investment and so on. We start with transforming LFP into its equivalent two-layer problem. Subsequently, we introduce a novel linear relaxation approach and integrate it within the branch and bound framework, and a new global optimization algorithm is presented in cooperation with a region deleting rule. Additionally, we discuss the convergence and complexity of this algorithm. Preliminary numerical results validate the practicality and effectiveness of our proposed method.

Optimizing generalized linear fractional program using the image space branch-reduction-bound scheme

This paper addresses solving the generalized linear fractional program problem. For this purpose, we first convert the original problem into an equivalent problem by introducing some new variables and equivalent variation. Next, by using the two-part approximation and bilinear relaxation, we construct the linear relaxation of the objective function and the constraint function, respectively. Based on the characteristics of the objective functions of the equivalence problem and the relaxation problem and the branch-and-bound structure of the algorithm, we construct some image space region reduction techniques to enhance the convergence speed of the algorithm. By combining the linear relaxation program problem and the image space region reduction techniques, we construct an image space branch-reduction-bound algorithm, prove its global convergence, and estimate its maximum number of iterations in the worst case by analysing the complexity. Finally, numerical results indicate high computational efficiency of the algorithm.

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

Development of Enhanced Chimp Optimization Algorithm (OFCOA) in Cognitive Radio Networks for Energy Management and Resource Allocation

Transmit time and power optimisation increase secondary network energy efficiency (EE). The optimum resource allocation strategy in cognitive radio networks is the enhanced chimp optimisation algorithm (OFCOA) since the EE maximising problem is a nonlinear fractional programming problem. To control resources and energy, this research offers an energy-efficient CRN opposition function-based chimpanzee optimisation algorithm (OFCOA) solution. Combining the opposition function (OF) with the chimpanzee optimisation technique is recommended. OF in COAs improves decision-making. Spectrum measurements in energy management provide energy-efficient CRN operation. The suggested technique was evaluated using channel occupancy, CRN data, and four major and secondary user scenarios. CPU power, network life, transmission rate, latency, flush, power consumption, and overhead are utilized to evaluate the proposed approach in MATLAB. The proposed method is compared to existing approaches like Particle Swarm Optimisation (PSO), Chimpanzee Optimisation Algorithm (COA), and Whale Optimisation Algorithm.

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.

The Composite Approach for Linear Fractional Programming Problem in Fuzzy Environment

The Composite Approach for Linear Fractional Programming Problem in Fuzzy Environment

Characteristics of Multi-Objective Linear Programming Problem and Multi-Objective Linear Fractional Programming Problem Taking Maximum Value of Multi-Objective Functions

Characteristics of Multi-Objective Linear Programming Problem and Multi-Objective Linear Fractional Programming Problem Taking Maximum Value of Multi-Objective Functions

Local isolated efficiency in non-smooth robust semi-infinite multi-objective fractional programming problems

Local isolated efficiency in non-smooth robust semi-infinite multi-objective fractional programming problems

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>

Sequential Henig proper optimality conditions for multiobjective fractional programming problems via sequential proper subdifferential calculus

Sequential Henig proper optimality conditions for multiobjective fractional programming problems via sequential proper subdifferential calculus

Solving neutrosophic multi-objective linear fractional programming problem using central measures

In this article, we present different kind of mean technique to solve Multi-Objective Linear Fractional Programming Problem (MOLFPP) in Neutrosophic Environment. Here in these mean techniques the MOLFPP is converted into Single Objective Linear Programming problem(SOLPP) and then we obtained the optimal solution by simplex method in Neutrosophic Environment. The proposed method is illustrated with the help of a numerical example.

A Novel Affine Relaxation-Based Algorithm for Minimax Affine Fractional Program

This paper puts forward a novel affine relaxation-based algorithm for solving the minimax affine fractional program problem (MAFPP) over a polyhedron set. First of all, some new variables are introduced for deriving the equivalence problem (EP) of the MAFPP. Then, for the EP, the affine relaxation problem (ARP) is established by using the two-stage affine relaxation method. The method provides a lower bound by solving the ARP in the branch-and-bound searching process. By subdividing the output space rectangle and solving a series of ARPs continuously, the feasible solution sequence generated by the algorithm converges to a global optimal solution of the initial problem. In addition, the algorithmic maximum iteration in the worst case is estimated by complexity analysis for the first time. Lastly, the practicability and effectiveness of the algorithm have been verified by numerical experimental results.

Distributed Multi-Agent Approach for Achieving Energy Efficiency and Computational Offloading in MECNs Using Asynchronous Advantage Actor-Critic

Mobile edge computing networks (MECNs) based on hierarchical cloud computing have the ability to provide abundant resources to support the next-generation internet of things (IoT) network, which relies on artificial intelligence (AI). To address the instantaneous service and computation demands of IoT entities, AI-based solutions, particularly the deep reinforcement learning (DRL) strategy, have been intensively studied in both the academic and industrial fields. However, there are still many open challenges, namely, the lengthening convergence phenomena of the agent, network dynamics, resource diversity, and mode selection, which need to be tackled. A mixed integer non-linear fractional programming (MINLFP) problem is formulated to maximize computing and radio resources while maintaining quality of service (QoS) for every user’s equipment. We adopt the advanced asynchronous advantage actor-critic (A3C) approach to take full advantage of distributed multi-agent-based solutions for achieving energy efficiency in MECNs. The proposed approach, which employs A3C for computing offloading and resource allocation, is shown through numerical results to significantly reduce energy consumption and improve energy efficiency. This method’s effectiveness is further shown by comparing it to other benchmarks.