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SOLVING A fractional programming problem IN A COMMERCIAL BANK

JOURNAL OF INDUSTRIAL AND MANAGEMENT OPTIMIZATION 2022年第6期18卷 4183-4190页

作者： Chuluunbaatar, Ankhbayar Rentsen, Enkhbat Natl Univ Mongolia Sch Business Ulaanbaatar 14200 PC Mongolia Mongolian Acad Sci Inst Math & Digital Technol Ulaanbaatar 13330 PC Mongolia

We formulate a new optimization problem which arises in the Bank Asset and Liability Management (ALM). The problem is a fractional programming which belongs to a class of global optimization. Most of optimization problems in the Bank Asset and Liability Management are return maximization or risk minimization problems. For solving the fractional programming problem, we propose curvilinear multi-start algorithm which finds the best local solutions to the problem. Numerical results are given based on the balance sheets of 5 commercial banks of Mongolia.

关键词： fractional programming problem curvilinear multi-start algorithm Asset and liability management

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Multi-Objective Probabilistic fractional programming problem Involving Two Parameters Cauchy Distribution

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MATHEMATICAL MODELLING AND ANALYSIS 2019年第3期24卷 385-403页

作者： Acharya, Srikumar Belay, Berhanu Mishra, Rajashree KIIT Deemed Be Univ Sch Appl Sci Dept Math Bhubaneswar 751024 India

The paper presents the solution methodology of a multi-objective probabilistic fractional programming problem, where the parameters of the right hand side constraints follow Cauchy distribution. The proposed mathematical model can not be solved directly. The solution procedure is completed in three steps. In first step, multi-objective probabilistic fractional programming problem is converted to deterministic multi-objective fractional mathematical programming problem. In the second step, it is converted to its equivalent multi-objective mathematical programming problem. Finally, epsilon-constraint method is applied to find the best compromise solution. A numerical example and application are presented to demonstrate the procedure of proposed mathematical model.

关键词： multi-objective programming problem probabilistic programming problem fractional programming problem epsilon-constraint method

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Solution of fuzzy linear fractional programming problem

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OPSEARCH 2011年第2期48卷 129-135页

作者： Jain, Sanjay Mangal, Adarsh Parihar, P. Govt Coll Dept Math Sci Ajmer 305001 India Govt Engn Coll Dept Math Ajmer 305025 India Govt Coll Dept Math Dungarpur 314001 India

In this paper a method is proposed to solve fractional programming problem in which the functional relationship between the decision variables and the objective function is not completely known. Here we established the crisp functional relationship between the objective function and the decision variables and solve the resulting programming problem to find a fair optimal solution to the original problem. An example is given in the last to illustrate the result.

关键词： fractional programming problem Optimal solution Decision variables Crisp value

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Duality for a Nondifferentiable Multiobjective Second-Order fractional programming problem Involving (F, α, ρ, d)-V-type-I Functions

Duality for a Nondifferentiable Multiobjective Second-Order ...

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International Conference on Recent Trends in Mathematical Analysis and its Applications (ICRTMAA)

作者： Dubey, Ramu Gupta, S. K. Indian Inst Technol Roorkee Dept Math Roorkee 247667 Uttar Pradesh India

ISBN: (纸本)9788132224853;9788132224846

In this paper, a nondifferentiable multiobjective fractional programming problem in which a support function appears in the numerator and denominator of each objective function as well as in each constraint function. We propose Schaible type dual for a nondifferentiable second-order fractional programming problem. Next, we prove appropriate duality results using second-order (F, alpha, rho, d)-V-type-I convexity assumptions.

关键词： fractional programming problem Support function Duality results (F, alpha, rho, d)-V-type-I functions

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Analyzing the performance measures of Multi-Objective Water Cycle Algorithm for Multi-Objective Linear fractional programming problem 2

Analyzing the performance measures of Multi-Objective Water ...

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2nd International Conference on Intelligent Computing and Control Systems (ICICCS)

作者： Veeramani, C. Sharanya, S. PSG Coll Technol Dept Math Coimbatore 641004 Tamil Nadu India PSG Coll Technol Coimbatore 641004 Tamil Nadu India

ISBN: (纸本)9781538628423

This paper proposes a metaheuristic approach called as Multi Objective Water Cycle Algorithm (MOWCA) for Fuzzy Multi Objective Non-Linear programming problem (FMONLPP). The suggested approach initially defines a fuzzy goal for each objective function with hyperbolic membership function. Further, the converted Fuzzy Multi-Objective Linear fractional programming problem (FMOLFPP) is changed into Fuzzy Multi Objective Non-Linear programming problem (MONLPP) and to find pareto solutions by the proposed metaheuristic approach. Generally, the efficiency of the metaheuristic algorithm is evaluated through various performance measures. In the present study, the following performance measures Generational Distance (GD), Reversed Generational Distance (RGD), Maximum spread (MS), Metric of spacing (S) and Delta Metric (Delta) are used to show the efficiency of the proposed algorithm. Finally, the comparative study is carried out with other existing metaheuristic approaches.

关键词： Multi-objective optimization Water cycle algorithm fractional programming problem

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Optimization of fuzzy K-objective fractional assignment problem using fuzzy programming model

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JOURNAL OF INTELLIGENT & FUZZY SYSTEMS 2023年第4期44卷 6425-6433页

作者： Gomathi, S., V Jayalakshmi, M. Vellore Inst Technol Sch SAS Dept Math Vellore Tamil Nadu India

The assignment problem is one of the core combinatorial optimization problems in the optimization branch, and the theory and applications of fractional programming have made great strides in recent years. Usually, the possible coefficient values of linear fractional programming and real-world problems are frequently only known to the decision in vague or uncertain terms. Hence, it would be more acceptable to interpret the coefficients for as fuzzy numerical information. In this paper, a fuzzy bi-objective fractional assignment (FBOFAP) has been formulated. A problem has been defined. Here, triangular shapes are used to indicate the parameters. The fuzzy problem is turned into a typical crisp problem through alpha-cut using a fuzzy number and then the compromise solution is generated by fuzzy programming.

关键词： Assignment problem fractional programming problem hyperbolic membership function fuzzy numbers fuzzy programming

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Avoid Maximum Cost Method for Solving Linear fractional Transshipment problem

INTERNATIONAL JOURNAL OF MATHEMATICAL ENGINEERING AND MANAGE...

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INTERNATIONAL JOURNAL OF MATHEMATICAL ENGINEERING AND MANAGEMENT SCIENCES 2025年第3期10卷 654-675页

作者： Pradhan, Avik Karan, Ashis Das, Satyajit Biswal, M. P. Adamas Univ Sch Basic & Appl Sci Kolkata W Bengal India Indian Inst Technol Kharagpur Dept Math Kharagpur W Bengal India

This study contributes valuable insights into linear fractional transshipment problem which is a special class of mathematical programming problem. We present the mathematical model for the linear fractional transshipment problem and develop an efficient algorithm based on the 'Avoid Maximum Cost Method (AMCM)' for finding an initial basic feasible solution (IBFS) of the given model. AMCM is based on the concept of making the maximum possible allocation to either a column or a row of the transportation cost matrix in such a way that the allocation to the corresponding cell that has the highest cost will be avoided in the further steps. The methodology is composed of the following two steps: firstly, we formulated an equivalent transportation model of the problem by considering the cost-profit ratio matrix. Secondly, we apply AMCM to find an IBFS of the problem. In a nutshell, this article finds the solution to a linear fractional transshipment model by applying AMCM to the cost-profit ratio matrix. The applicability of the proposed approach is illustrated with some suitable numerical examples. The contribution ends by introducing a comparative analysis to show the efficiency of the proposed algorithm.

关键词： Transshipment problem fractional programming problem Avoid maximum cost method

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Some dual characterizations of Farkas-type results for fractional programming problems

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OPTIMIZATION LETTERS 2018年第6期12卷 1403-1420页

作者： Sun, Xiangkai Tang, Liping Long, Xian-Jun Li, Minghua Chongqing Technol & Business Univ Coll Math & Stat Chongqing 400067 Peoples R China Chongqing Univ Arts & Sci Sch Math & Finance Chongqing 402160 Peoples R China

In this paper, we present some Farkas-type results for a fractional programming problem. To this end, by using the properties of dualizing parametrization functions, Lagrangian functions and the epigraph of the conjugate functions, we introduce some new notions of regularity conditions and then obtain some dual forms of Farkas-type results for this fractional programming problem. We also obtain sufficient conditions for alternative type theorems. As an application of these results, we obtain the corresponding results for a convex optimization problem.

关键词： Duality Farkas-type results Alternative type theorems fractional programming problem

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Multi-objective interval fractional programming problems : An approach for obtaining efficient solutions

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OPSEARCH 2015年第1期52卷 156-167页

作者： Bhurjee, Ajay Panda, Geetanjali Indian Inst Technol Kharagpur Kharagpur 721302 WB India Indian Inst Technol Kharagpur Fac Math Dept Math Kharagpur 721302 WB India

This paper addresses a general multi-objective fractional programming problem whose parameters in the objective functions and constraints are intervals. Existence of the efficient solution of this model is studied. A methodology is developed to determine its efficient solutions. This methodology is illustrated through a numerical example.

关键词： Interval optimization Multi-objective optimization problem Efficient solution fractional programming problem

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Energy efficiency optimisation of large-scale multiple-input-multiple-output system with transmit antenna selection

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IET COMMUNICATIONS 2017年第8期11卷 1224-1229页

作者： Hei, Yongqiang Liu, Yongli Li, Wentao Liu, Jiao Li, Xiaohui Xidian Univ State Key Lab ISN Xian Peoples R China

The rapid development of wireless communication comes at the cost of dramatically increasing energy consumption, which makes the optimisation of energy efficiency (EE) extremely important. In this study, the authors focus on maximising EE of large-scale multiple-input-multiple-output system by optimising the transmit power and the number of selected base station antennas. First, the EE optimisation problem, i.e. finding the optimal EE-based values of each parameter, when the other one is fixed, is investigated. Then, the optimisation problem jointly considering these two parameters to maximise EE is studied. Moreover, the EE optimisation problem is extended to multi-user (MU) system. Owing to the formulation of EE, the EE optimisation problem is reformulated as the fractional programming problem, and the Dinkelbach method is proposed to deal with this problem instead of the binary search algorithm (BSA) by switching the objective function to a weighted sum of rate and power. Simulation results show that the EE can be improved with the proposed Dinkelbach method, and it has a faster convergence speed than the BSA without any performance loss for both single-user system and MU system.

关键词： MIMO communication antenna arrays energy conservation mathematical programming energy efficiency optimisation large-scale multiple-input-multiple-output system transmit antenna selection wireless communication fractional programming problem Dinkelbach method binary search algorithm

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