Fractional Programming Problem Research Articles

The Different Approach of Solution for Multi-objective Fractional Programming Problems Under Fuzzy Environment

The Different Approach of Solution for Multi-objective Fractional Programming Problems Under Fuzzy Environment

Robust α-exponential estimate for polytopic uncertain positive discrete-time systems with bounded time-varying delay

In this paper, the problem of finding a robust α-exponential estimate for a class of perturbed positive discrete-time time-delay systems with polytopic uncertainties will be addressed. By proposing a linear parameter-dependent Lyapunov function, a condition for the existence of robust α-exponential estimates will be introduced. Some optimisation techniques are also incorporated to obtain a more accurate estimate. In particular, a procedure to reformulate a class of fractional programming problems into a linear programming problem which can be solved efficiently. A numerical example is presented to demonstrate the effectiveness of the proposed method.

Optimality results for nondifferentiable multiobjective fractional programming problems under E-B-invexity

In this article, we study nonconvex multiobjective fractional programming problems involving E-differentiable functions (MFPE). We establish the E-Karush–Kuhn–Tucker (E-KKT) sufficient E-optimality conditions for nonsmooth vector optimization problems under the assumption of E-B-invexity. To demonstrate the validity of the derived results, we provide an example where the involved functions exhibit E-B-invexity.

Modified Double Inertial Extragradient-like Approaches for Convex Bilevel Optimization Problems with VIP and CFPP Constraints

Convex bilevel optimization problems (CBOPs) exhibit a vital impact on the decision-making process under the hierarchical setting when image restoration plays a key role in signal processing and computer vision. In this paper, a modified double inertial extragradient-like approach with a line search procedure is introduced to tackle the CBOP with constraints of the CFPP and VIP, where the CFPP and VIP represent a common fixed point problem and a variational inequality problem, respectively. The strong convergence analysis of the proposed algorithm is discussed under certain mild assumptions, where it constitutes both sections that possess a mutual symmetry structure to a certain extent. As an application, our proposed algorithm is exploited for treating the image restoration problem, i.e., the LASSO problem with the constraints of fractional programming and fixed-point problems. The illustrative instance highlights the specific advantages and potential infect of the our proposed algorithm over the existing algorithms in the literature, particularly in the domain of image restoration.

Investigation of Markovian Process in Server Break-down

In day to day life goods produced at a number of places are consumed at different locations and then the problem faced by producer or dealer is to transfer goods from numerous places of origin to various places of consumption such that cost of transportation, time required, damages to the product etc. are optimum. This is called classical transportation problem. In this study we have studied transportation problem solve by Markov Decision Process. Introduction to the operations research is made along with over view of optimization techniques of single objective transportation problem. For literature review in the subject of multi objective fractional as well as linear multi objective transportation problems. In basic concepts of Markov Decision Process are given for further usage in the thesis work. We have stated algorithms for solving different types of multi objective programming problems. In entire work we have used basically linear membership functions, hyperbolic membership function and exponential membership function. These membership functions are Markov Decision Process. In case of linear membership function weighted arithmetic mean, weighted quadratic mean, geometric mean is used to find compromise solution. Almost everywhere we have found that the compromise solutions are fairly close to optimal solution when the problem is solved as single objective function. We have solution procedure for multi objective linear transportation is given using Markov Decision Process. Introduction to fractional programming is made and solutions of multi objective linear fractional programming problems are discussed. We have solutions of multi objective linear fractional transportation problem. In this topic fractional objective functions are approximated as linear functions using Taylor’s theorem and then applied method to solve the multi objective linear transportation problem discussed earlier. We focus on solution to fractional transportation problem with Markov Process coefficients. To multi objective fractional transportation problem with goal programming approach. We deal with general integer programming problem along with fractional transportation problems. The main result of this thesis is a characterization of increasing Marko processes satisfying certain conditions. At the end bibliography and research papers published by authors are given. Keywords: Markov Process, Transportation, Queen analyses Server system.

(G, V)-invexity nondifferentiable generalized minimax fractional programming

In this paper, we study the nondifferentiable generalized minimax fractional programming problem under (G, V )-invexity. G-sufficient optimality conditions for the considered nondifferentiable generalized minimax fractional programming problem are established under the concept of (G, V )-invexity. Further, two types of dual models are formulated and G-duality theorems relating to the primal minimax fractional programming problem and dual problems are established. These results extend several known results to a wider class of programs.

On the new solution to interval linear fractional programming problems

On the new solution to interval linear fractional programming problems

An efficient image space branch-reduction-bound algorithm to globally solve generalized fractional programming problems for large-scale real applications

This study focuses on finding a global optimal solution to a generalized fractional programming problem (GFP) in the perspective of large-scale applications. However, few algorithms exist to solve the GFP due to its nonconvexity and NP-hard. Therefore, it is significant to propose an efficient algorithm for the GFP. For this purpose, first of all, using logarithmic and exponential properties, we transform the GFP into an equivalent problem (EP) by introducing some image space variables. Next, the relaxation problem (RP) is constructed using a two-phase relaxation method and bilinear relaxation technique based on the structure of the EP. Furthermore, through the comprehensive utilization of the unique structures of EP and RP, along with the attributes of branch and bound algorithms, some novel region-reduction techniques have been introduced to eliminate regions devoid of the global optimal solution. Subsequently, the integration of the two-phase relaxation method and region-reduction techniques within the branch-and-bound framework has led to the design of the image space branch-reduction-bound algorithm (ISBRBA). Moreover, the convergence and computational complexity of the ISBRBA are analyzed by considering the infinite approximation property between the objective functions of the EP and RP. Finally, the effectiveness and robustness of the ISBRBA are demonstrated through numerous numerical experiments.

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.

Problem fazi linearnog frakcionog programiranja pomoću leksikografskog metoda

Introduction/purpose: In solving real-life fractional programming problems, uncertainty and hesitation are often encountered due to various uncontrollable factors. To overcome these limitations, the fuzzy logic approach is applied to these problems. Methods: The discussion focused on solving the fuzzy linear fractional programming problem (FLFPP). First, the FLFP problem was converted into a lexicographic optimization problem, which was then solved to obtain the solution. Results: A numerical example was presented to simplify the explanation of the algorithm. While most researchers solve FLFPPs using the ranking function method, this approach reduces the efficiency of the fuzzy problem. Conclusion: This research contributes a comprehensive methodology for addressing fuzzy linear fractional programming problems using the lexicography method. The findings offer valuable insights for researchers, practitioners, and decision-makers grappling with optimization challenges in settings where imprecise information significantly influences the decision landscape.