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A fuzzy approach for the intuitionistic multi-objective linear fractional programming problem using a bisection method

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JOURNAL OF COMBINATORIAL OPTIMIZATION 2025年第2期49卷 1-24页

作者： Kara, Nurdan Kocken, Hale Gonce Akdemir, Hande Gunay Natl Def Univ TR-34334 Istanbul Turkiye Yildiz Tech Univ Dept Math Engn TR-34220 Istanbul Turkiye Giresun Univ Dept Math TR-28200 Giresun Turkiye

In this paper, intuitionistic fuzzy multi-objective linear fractional programming problems (IFMOLFPs) with several fractional criteria, including profit/cost, profit/time, or profitability ratio maximization, are considered. Moreover, all parameters, with the exception of the decision variables, are characterized as triangular intuitionistic fuzzy numbers. The component-wise optimization method is employed to transform IFMOLFP into an equivalent crisp multi-objective linear fractional problem. Then, we use an iterative fuzzy methodology that integrates linear programming with a bisection approach. The proposed approach addresses single-objective and real-life multi-objective organizational planning problems, which are approached using various methods in the literature. It is used for non-linear membership functions in solving these problems. Furthermore, the values obtained using the ranking function are compared. Ultimately, the decision-maker selects the most appropriate solution technique based on the weights of the objective functions.

关键词： Multi-objective linear programming fractional programming Fuzzy programming Intuitionistic fuzzy number Bisection method Membership function

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Accelerated fractional programming for Multi-User ISAC Beamforming Optimization With Per-Group Power Constraints

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IEEE WIRELESS COMMUNICATIONS LETTERS 2025年第4期14卷 1174-1178页

作者： Kim, Dogon Park, Seok-Hwan Jeonbuk Natl Univ Div Elect Engn Jeonju 54896 South Korea

This letter presents an efficient beamforming solution for a multi-user integrated sensing and communication (ISAC) system. The problem of optimizing ISAC beamforming vectors is formulated to maximize a weighted sum of communication sum-rate and radar sensing signal-to-interference-plus-noise ratio (SINR), subject to arbitrary per-group power constraints (PGPCs). To address the non-convexity, we employ fractional programming (FP) approach, transforming the original problem into a series of convex subproblems with fixed auxiliary variables. To avoid dependence on convex optimization tools, we propose an accelerated FP (A-FP) scheme that partitions the beamforming vectors into block variables, which are sequentially optimized with closed-form solutions for each block. Numerical results demonstrate that the A-FP scheme achieves almost identical performance to the FP scheme, while significantly reducing computational complexity.

关键词： Array signal processing Vectors Optimization Interference Signal to noise ratio Integrated sensing and communication Radar Antennas Computational complexity Transmitting antennas multi-user beamforming fractional programming

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Optimality conditions and DC-Dinkelbach-type algorithm for vector fractional programming problems with ratios of difference of convex functions

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OPTIMIZATION 2025年第2期74卷 427-457页

作者： Ghazi, A. Roubi, A. Hassan First Univ Fac Sci Tech Lab MISI Settat Morocco

\In this work, necessary optimality conditions of KKT type for (weak) Pareto optimality are derived and a DC-Dinkelbach-type algorithm is proposed for vector fractional mathematical programs with ratios of difference of convex (DC) functions, and DC constraints, by reducing the latter to a system of scalar parametric problems and using DC tools. The special case of vector fractional programs with ratios of convex functions is also analysed.

关键词： Vector programming fractional programming difference of convex functions optimality conditions Dinkelbach algorithm

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Optimizing water use efficiency in industrial parks under uncertainty: An inexact two-stage stochastic partial fractional programming method

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JOURNAL OF WATER PROCESS ENGINEERING 2025年 71卷

作者： Wang, Shuping Lan, Zhuoling Tan, Qian Zhang, Tianyuan Cao, Yini Jiangxi Normal Univ Key Lab Poyang Lake Wetland & Watershed Res Minist Educ Nanchang 330022 Peoples R China Guangdong Univ Technol Guangdong Basic Res Ctr Excellence Ecol Secur & Gr Sch Ecol Environm & Resources Guangdong Prov Key Lab Water Qual Improvement & Ec Guangzhou 510006 Peoples R China Jiangxi Normal Univ Sch Geog & Environm Nanchang 330022 Peoples R China Cent South Univ Forestry & Technol Coll Mat Sci & Engn Changsha 410004 Peoples R China

Optimizing water use efficiency in industrial parks under uncertainty is essential for improving economic development and alleviating water crises. However, previous industrial park water allocation models struggled to manage inflow probability uncertainties and tackle ratio objectives, hindering the improvements of water use efficiency. To address these problems, an inexact two-stage stochastic partial fractional programming (ITSPFP) method was developed for industrial park water management. This method integrates two-stage stochastic programming (TSP) and linear partial information (LPI) within a fractional programming (FP) framework. The ITSPFP method improves upon traditional inexact FP methods by effectively addressing the partial probability distribution of water inflows with the LPI method. ITSPFP also outperforms traditional industrial park water allocation models by optimizing the ratio objective related to water use efficiency and reflecting the penalties associated with water shortages using TSP. ITSPFP was utilized in a case study in Tianjin, China, to illustrate its effectiveness. By maximizing water use efficiency, ITSPFP generated multi-period water allocation plans for industrial parks under varying inflow probabilities. The results showed that higher probabilities of high inflow levels led to reduced water shortages and reclaimed water, while increasing the allocation of surface water and groundwater. Based on the benefits and penalties, prioritizing water supply for the electric power plant is recommended. Compared to the maximum-benefit models, ITSPFP can enhance water use efficiency by [4.03, 9.51]% and reduce water use by [26.80, 39.01]%. By handling uncertain probabilities, ITSPFP also exceeds previous models in avoiding missed potential solutions and enabling greater flexibility in decision making.

关键词： Two-stage stochastic programming Linear partial information Uncertainty fractional programming Industrial park water management

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A multi-stochastic fractional programming for sustainable forestry ecological restoration: Managing uncertainties in Kashgar Region, Xinjiang

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ECOLOGICAL MODELLING 2025年 506卷

作者： Bai, Yi Huang, Guohe Han, Dencheng Luo, Bin Li, Yongping Zhao, Shan Shandong Univ Sch Environm Sci & Engn Qingdao 266237 Peoples R China Univ Regina Environm Syst Engn Program Regina SK S4S 0A2 Canada Shandong Univ China Canada Ctr Energy Environm & Sustainabil Res Sch Environm Sci & Engn UR SDU Qingdao 266237 Peoples R China Beijing Normal Univ Environm & Energy Syst Engn Res Ctr Sch Environm Beijing 100875 Peoples R China

Forest ecological restoration is becoming increasingly crucial in global sustainable development plans aimed at mitigating climate change and achieving carbon neutrality. Optimal management is now a key component in this process. To address the challenges and evolving demands of stakeholders in forest ecological restoration, this study integrates interval linear programming (ILP), chance-constrained programming (CCP), mixed-integer programming (MIP), and fractional planning (FP) within an optimization framework, developing an interval linear chance-constrained mixed integer fractional programming (ICCMFP) model. The model offers several key advantages in optimizing ecological, economic, and social challenges in forestry: (1) managing compound risks from uncertainties in land resources, price fluctuations, and water availability;(2) balancing conflicting objectives while enabling broader stakeholder participation in the management process;(3) supporting multi-scenario analyses to quantitatively evaluate optimal strategies and offer valuable insights for decision-makers. Taking the Xinjiang Kashgar region as a case study, the applicability of the proposed model has been evaluated under multiple objectives and scenarios. The results indicate that the ICCMFP model provides robust strategies across various water allocation scenarios, price fluctuations, and default risks. In the CB-C model, increased carbon benefits correspond to a greater willingness to expand, resulting in the total area of expansion growing from [18,524.0, 24,953.7] ha at the Chinese carbon price to [23,503.6, 30,626.0] ha at the European Union carbon price in the S1 (pi = 0.01) scenario. Compared to the interval chance-constrained mixed integer programming (ICCMP) model, the ICCMFP model offers more flexible optimization solutions through fractional programming, demonstrating its adaptability and reliability. This model is expected to offer substantial support for decisionmaking in sustainable ecolog

关键词： fractional programming Multi-scenario Ecological values Uncertainty Land resources Water resources

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fractional programming with absolute-value functions: a fuzzy goal programming approach

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APPLIED MATHEMATICS AND COMPUTATION 2005年第1期167卷 508-515页

作者： Chang, CT Natl Changhua Univ Educ Dept Informat Management Changhua 50058 Taiwan

Fuzzy goal programming (FGP) is an important technique for solving many decision/management problems. Following the philosophy of FGP, this paper proposes a new approach to solve fractional programming with absolute-value functions (FP-A). The major contribution of this paper is that the FP-A problem can be converted to the linearized FGP problem. Then, the linearized FGP problem can be easily solved by commercialized linear programming packages. In addition, illustrative examples are included to demonstrate the correctness of the proposed method. (c) 2004 Elsevier Inc. All rights reserved.

关键词： fractional programming fuzzy goal programming absolute value

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fractional programming with convex quadratic forms and functions

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2006年第2期173卷 351-369页

作者： Benson, HP Univ Florida Dept Informat & Decis Sci Gainesville FL 32611 USA

This article is concerned with two global optimization problems (P1) and (P2). Each of these problems is a fractional programming problem involving the maximization of a ratio of a convex function to a convex function, where at least one of the convex functions is a quadratic form. First, the article presents and validates a number of theoretical properties of these problems. Included among these properties is the result that, under a mild assumption, any globally optimal solution for problem (P1) must belong to the boundary of its feasible region. Also among these properties is a result that shows that problem (P2) can be reformulated as a convex maximization problem. Second, the article presents for the first time an algorithm for globally solving problem (P2). The algorithm is a branch and bound algorithm in which the main computational effort involves solving a sequence of convex programming problems. Convergence properties of the algorithm are presented, and computational issues that arise in implementing the algorithm are discussed. Preliminary indications are that the algorithm can be expected to provide a practical approach for solving problem (P2), provided that the number of variables is not too large. (c) 2005 Elsevier B.V. All rights reserved.

关键词： global optimization fractional programming quadratic form branch and bound

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fractional-programming BY LOWER SUBDIFFERENTIABILITY TECHNIQUES

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JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS 1991年第1期68卷 95-116页

作者： BONCOMPTE, M MARTINEZLEGAZ, JE UNIV BARCELONA DEPT MATEMAT APLICADA & ANALISIS BARCELONA 7 SPAIN

The notion of lower subdifferentiability is applied to the analysis of convex fractional programming problems. In particular, duality results and optimality conditions are presented, and the applicability of a cutting-plane algorithm using lower subgradients is discussed. These methods are useful also in generalized fractional programming, where, in the linear case, the performance of the cutting-plane algorithm is compared with that of the most efficient version of the Dinkelbach method, which is based on the solution of a parametric linear programming problem.

关键词： fractional programming LOWER SUBDIFFERENTIABLE FUNCTIONS DUALITY OPTIMALITY CONDITIONS CUTTING PLANES

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fractional programming with absolute-value functions

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2002年第1期141卷 233-238页

作者： Chadha, SS Univ Wisconsin Dept Math Eau Claire WI 54702 USA

This paper considers a fractional functionals programming problem of the type: maximize z = Sigma(1)(n)C(j)\x(j)\ + alpha/Sigma(1)(n)d(j)\x(j)\ = beta subject to Ax = b. x is unrestricted. In general, adjacent extreme point (simplex-type) methods [Naval Res. Logist. Quart. II (1964) 135] cannot be used to solve this class of problems. However, this work presents the conditions under which simplex-type algorithms can be used to arrive at an optimal solution for a fractional programming problem with an absolute value objective function. (C) 2002 Elsevier Science B.V. All rights reserved.

关键词： absolute value fractional programming

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fractional programming-Based Uplink Transmission Power Allocation for User-Centric Cell-Free Massive MIMO Systems

IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING

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IEEE TRANSACTIONS ON GREEN COMMUNICATIONS AND NETWORKING 2024年第1期8卷 50-63页

作者： Sarker, Manobendu Fapojuwo, Abraham O. Univ Calgary Dept Elect & Software Engn Calgary AB T2N 1N4 Canada

In this paper, two centralized power allocation schemes are proposed for data transmission during the uplink phase in the user-centric cell-free (CF) massive multiple-input multiple-output (mMIMO) systems. The proposed schemes solve two non-convex power allocation problems of maximizing the summation of spectral efficiency (SE) (max-sum-SE) and that of maximizing the minimum SE (max-min-SE) to improve the overall SE and fairness performance while simultaneously reducing the per-user equipment (UE) transmission power. To solve the max-sum-SE problem, we utilize the fractional programming (FP) method to transform the non-convex problem into a series of convex problems. Furthermore, the max-min-SE problem is solved after reformulating it with the help of the FP method along with the alternating direction method of multipliers (ADMM) technique. The proposed schemes are computationally efficient as they solve the aforementioned problems iteratively by using only closed-form updates for the decision variables, which is one of their strongest features, and suitable for allocating power in large-scale CF mMIMO systems. Numerical results demonstrate that, compared to the no power control scheme, the proposed schemes improve the average SE performance by up to 47% while reducing the average transmission power by up to 95%.

关键词： Resource management Minimax techniques Optimization programming Computational efficiency Performance evaluation Interference Massive MIMO cell-free massive MIMO centralized control data power allocation max-min fairness fractional programming ADMM max-sum-SE B5G

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