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A multi-objective solid transportation problem that includes source, destination, and mode of transport parameters may have fractional objective functions in real-life applications to maximize the profitability ratio, which could be the profit/cost or profit/time. We refer to such transportation problems as multi-objective fractional solid transportation problems. In addition, although most of the studies in the literature deal with the standard equality-constrained form of the multi-objective fractional solid transportation problem, the mixed-constrained type is addressed in this paper. With these mixed constraints, the multi-objective fractional solid transportation problem offers more flexible modeling of real-world problems that exist in many application areas, but mixed constraints also make the optimization process more challenging. This article presents an iterative fuzzy approach that combines the use of linear programming and the bisection algorithm using linear membership functions to obtain a strongly efficient solution. The algorithm's ability to convert a nonlinear problem into a set of linear problems is one of its main advantages, and it also decreases the amount of time needed to solve large-scale problems. A numerical example from the literature is adopted to illustrate the solution procedure. Moreover, large-scale instances are generated to further test the presented algorithm, and a comparison between the traditional fuzzy approach and the proposed method is presented. [ABSTRACT FROM AUTHOR]

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We present a proximal point type algorithm tailored for tackling pseudomonotone equilibrium problems in a Hilbert space which are not necessarily convex in the second argument of the involved bifunction. Motivated by the extragradient algorithm, we propose a two-step method and we prove that the generated sequence converges strongly to a solution of the nonconvex equilibrium problem under mild assumptions and, also, we establish a linear convergent rate for the iterates. Furthermore, we identify a new class of functions that meet our assumptions, and we provide sufficient conditions for quadratic fractional functions to exhibit strong quasiconvexity. Finally, we perform numerical experiments comparing our algorithm against two alternative methods for classes of nonconvex mixed variational inequalities. [ABSTRACT FROM AUTHOR]

The employment of Intelligent Reflecting Surface (IRS) in MIMO systems has been extensively studied as a feasible alternative to relays. IRS can operate either actively or passively. In the case of a passive IRS configuration, no signal processor or amplifier is required, allowing for signal reflection in the desired phase shift with lower power consumption and cost. However, the passive IRS gain is significantly decreased due to the path loss in the IRS channel. In the active IRS structure, each reflective element is fitted with a power amplifier that enables it to reflect the signal to the intended destination at an appropriate power level. This confers a greater benefit to the system than a passive structure. Consequently, a hybrid active–passive IRS is recommended as it results in a higher sum rate, more energy gain, and a balance between the higher rate and lower energy consumption. In this paper, we examine a practical Rician channel hybrid IRS-assisted multiuser MIMO system with the goal of maximizing the sum rate. To accomplish this, we simplified the objective function of the main problem using the Fractional Programming (FP) method and modified the formulations in order to divide the main problem into a series of sub-problems. Then, using the Block Coordinate Descent (BCD) method and placing sub-problems into consecutive blocks, we solve each sub-problem to obtain the optimal solution for each block and, ultimately, the answer to the main problem. Finally, simulations were conducted for the proposed scenario, indicating that the sum rate of the hybrid IRS structure varied between the active and inactive IRS structure, depending on transmission power. However, adjusting the number of elements in the active and passive structures can achieve higher overall rates than traditional structures at low power levels. [ABSTRACT FROM AUTHOR]

To enhance the performance of non-orthogonal multiple access (NOMA)-assisted integrated sensing and communication (ISAC) systems in multi-user distributed scenarios, an improved Gaussian Mixture Model (GMM)-based user clustering algorithm is proposed. This algorithm is tailored for ISAC systems, significantly improving bandwidth reuse gains and reducing serial interference. First, using the Sum of Squared Errors (SSE), the algorithm reduces sensitivity to the initial cluster center locations, improving clustering accuracy. Then, direction weight factors are introduced based on the base station position and a penalty function involving users' Euclidean distances and sensing power. Modifications to the EM algorithm in calculating posterior probabilities and updating the covariance matrix help align user clusters with the characteristics of NOMAISAC systems. This improves users' interference resistance, lowers decoding difficulty, and optimizes the system's sensing capabilities. Finally, a fractional programming (FP) approach addresses the non-convex joint beamforming design problem, enhancing power and channel gains and achieving co-optimizing sensing and communication signals. The simulation results show that, under the improved GMM user clustering algorithm and FP optimization, the NOMA-ISAC system improves user spectral efficiency by 4.3% and base station beam intensity by 5.4% compared to traditional ISAC systems. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Cell-free millimeter wave (mmWave) multiple-input multiple-output (MIMO) can effectively overcome the shadow fading effect and provide macro gain to boost the throughput of communication networks. Nevertheless, the majority of the existing studies have overlooked the user-centric characteristics and practical fronthaul capacity limitations. To solve these practical problems, we introduce a resource allocation scheme using statistical channel state information (CSI) for uplink user-centric cell-free mmWave MIMO system. The hybrid beamforming (HBF) architecture is deployed at each access point (AP), while the central processing unit (CPU) only combines the received signals by the large-scale fading decoding (LSFD) method. We further frame the issue of maximizing sum-rate subject to the fronthaul capacity constraint and minimum rate constraint. Based on the alternating optimization (AO) and fractional programming method, we present an algorithm aimed at optimizing the users' transmit power for the power allocation (PA) subproblem. Then, an algorithm relying on the majorization–minimization (MM) method is given for the HBF subproblem, which jointly optimizes the HBF and the LSFD coefficients. [ABSTRACT FROM AUTHOR]

This paper considers a non-smooth semi-infinite multi-objective fractional programming problem under uncertain data constraints. The non-smooth robust necessary optimality conditions for a local isolated efficient solution of the considered problem and its non-smooth parametric problem, formulated in the generalized Dinkelbach approach, is investigated under an extended form of a robust type constraint qualification. Finally, with the assumption of generalized convexity, the non-smooth robust sufficient optimality conditions are established. [ABSTRACT FROM AUTHOR]

In this article, we build a pair non-differentiable second-order symmetric multiobjective fractional variational programming models with cone constraints, where each objective function component has a support function for a compact convex set. The (C, ρ, θ)-convexity/(C, ρ, θ)-pseudo-convexity/(C, ρ, θ)-quasiconvexity functions are defined and also, constructed concrete numerical examples for existing such type of functions. The duality results are established by using these aforesaid assumptions. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Waveform diversity (WD) represents a dynamic and transformative technology widely used in radar systems to enhance sensitivity and discrimination capabilities. Recently, WD techniques have been extensively explored for their potential ambiguity suppression within synthetic aperture radar (SAR) systems. Among these, the alternate transmitting mode combined with orthogonal waveforms emerges as a particularly promising solution. This study focuses on optimizing the power spectrum density (PSD) of signals to design and generate an orthogonal waveform pair that achieves both a low cross-correlation-to-autocorrelation ratio (CAR) and satisfactory imaging performance. Initially, we construct a fractional programming model with convex constraints to minimize the CAR. To address this challenge, we introduce an iterative optimization procedure for the PSD variable, which sequentially reduces the CAR. Each optimization step can be efficiently solved using a quadratically constrained quadratic program, ensuring that the resulting computational complexity remains low. Building on the optimized PSD, we established a parametric piecewise linear model to generate an orthogonal waveform pair. This model not only maintains a low CAR but achieves satisfactory imaging performance in real-time applications. Consequently, this orthogonal waveform pair effectively suppresses range ambiguity in SAR systems. Finally, we demonstrated the practicability and effectiveness of the proposed orthogonal waveforms through detailed simulation experiments, specifically targeting ambiguity suppression in conventional quad-polarization SAR systems. [ABSTRACT FROM AUTHOR]

Motivation and Justification: Regular humanitarian logistics (R-HL) plays an increasingly important role in alleviating suffering of beneficiaries struck by catastrophes and war. A key challenge that humanitarian organizations face is the lack of guidance on decision-making tools when conducting R-HL. Aim of the study: A core tenet of this article is to incorporate cost performance in R-HL models to ensure delivery strategies that lead to the greatest good for the greatest number of people with lowest cost. Methodology: Our study introduces cost performance, quantifying the alleviation of human suffering per unit economic cost. We formulate a mixed integer fractional programming model for the location-routing and delivery frequency problem with the objective of maximizing the cost performance. The neighborhood search-assisted genetic algorithm is designed to solve the intractable problem. Additionally, using real data from typhoon-prone Shenzhen and flood-affected Hefei in China, we validate our model and demonstrate its effectiveness. Findings: Several numerical experiments have revealed that cost performance can provide moderate transportation and delivery strategies in both decreasing suffering of beneficiaries and lowering the cost according to comparisons with other objectives such as social costs minimization. Significance and originality: Our study proposes a new objective function for efficiency and effectiveness trade-offs and suggests the use of cost performance as the preferred objective function for R-HL models. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surface (RIS) is a groundbreaking technology that has a significant potential for sixth generation (6G) networks. Its unique capability to control wireless environments makes it an attractive option. However, the spatial diversity increased by assisting users with all deployed RISs, this investigation has two drawbacks the high complexity design, and the received signals by the far RISs are severely attenuated. Therefore, we propose a RIS selection strategy to select the proper RISs as a pre-stage before the joint beamforming between the base station (BS) and RISs to reduce the high complexity of joint beamforming optimization. Furthermore, the joint active and passive beamforming problem based on the selection is formulated. Hence, achieving spatial diversity by examining cooperation between passive beamforming of multi-hop RIS, leads to a challenging problem. To tackle this issue, we design an algorithm for the RIS selection scheme. Also, to relax the non-convexity of the proposed problem, we decouple the problem into solvable subproblems by utilizing the fractional programming (FP) and quadratic transform (QT) optimization methods. Simulation results have demonstrated through different user locations the effectiveness of the selection strategy in performance enhancement by 30% in the sum rate, besides an obvious reduction in the complexity cost than other techniques. [ABSTRACT FROM AUTHOR]

In this paper, by making use of some advanced tools from variational analysis and generalized differentiation, we establish necessary optimality conditions for a class of robust fractional minimax programming problems. Sufficient optimality conditions for the considered problem are also obtained by means of generalized convex functions. Additionally, we formulate a dual problem to the primal one and examine duality relations between them. In our results, by using the obtained results, we obtain necessary and sufficient optimality conditions for a class of robust fractional multi-objective optimization problems. [ABSTRACT FROM AUTHOR]

Since non-orthogonal multiple access (NOMA) has become a promising technology to enhance network energy efficiency (EE) thanks to its low latency,high reliability and massive connectivity, the optimization of EE in NOMA-based uplink heterogeneous networks (HetNets) is considered in this paper. The optimization problem for EE maximization is formulated as a combination of user association (base station selection, sub-channel allocation) and power control, which is hardly tractable. To address it, a user association algorithm satisfied the many-to-one relationship between mobile users, base stations and sub-channels is firstly proposed based on matching theory. Then, an iterative power control algorithm evolved from fractional programming and difference of convex programming is presented by proving the concavity of the sum-rate of sub-channels. Finally, simulation results are shown that NOMA-based HetNets equipped with our designed algorithms yield much higher EE than that with the compared schemes. [ABSTRACT FROM AUTHOR]

Let K/\mathbb {Q}_p be a finite unramified extension, \overline {\rho }:\mathrm {Gal}(\overline {\mathbb {Q}}_p/K)\rightarrow \mathrm {GL}_n(\overline {\mathbb {F}}_p) a continuous representation, and \tau a tame inertial type of dimension n. We explicitly determine, under mild regularity conditions on \tau, the potentially crystalline deformation ring R^{\eta,\tau }_{\overline {\rho }} in parallel Hodge–Tate weights \eta =(n-1,\cdots,1,0) and inertial type \tau when the shape of \overline {\rho } with respect to \tau has colength at most one. This has application to the modularity of a class of shadow weights in the weight part of Serre's conjecture. Along the way we make unconditional the local-global compatibility results of Park and Qian [Mém. Soc. Math. Fr. (N.S.) 173 (2022), pp. vi+150]. [ABSTRACT FROM AUTHOR]

This article examines a conical tank nonlinear system’s level control. A crucial component of facilities like milk processing plants and sugarcane mills is the conical tank. The fluid drains entirely due to the conical shape of the tank. The conical form of the system causes nonlinear dynamics. The conical tank nonlinear system transfer mechanism is not easily accessible, and different operating heights require different transfer mechanisms, making controller design difficult. Developing the Fractional-Order Integral Terminal Sliding-Mode (FO-ITSM) Controller system for Advanced Golden Jackal Optimisation (GJO) based conical tank systems is the main objective of this paper. This is utilised to deliver real-time liquid level management in non-linear conical systems. The dynamics of these models make it possible to identify the conical tank system that produces control signals from liquid samples taken at reference levels with greater accuracy. This system, which is employed on multiple platforms, maintains and controls the liquid level while meeting all design specifications, including time constant, no overshoot, less settling, and rise time. For research simulation work, MATLAB software’s FOMCON toolbox is utilised. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

We give a priori error estimates of second order in time fully explicit Runge–Kutta discontinuous Galerkin schemes using upwind fluxes to smooth solutions of scalar fractional conservation laws in one space dimension. Under the time step restrictions τ ≤ ch for piecewise linear and τ ≲ h4/3 for higher order finite elements, we prove a convergence rate for the energy norm ‖⋅‖Lt∞Lx2+|⋅|Lx2Hxλ/2 that is optimal for solutions and flux functions that are smooth enough. Our proof relies on a novel upwind projection of the exact solution. [ABSTRACT FROM AUTHOR]

The majorization approximation procedure consists in replacing the resolution of a non-linear optimization problem by solving a sequence of simpler ones, whose objective and constraint functions upper estimate those of the original problem. For generalized fractional programming, i.e., constrained minimization programs whose objective functions are maximums of finite ratios of functions, we propose an adapted scheme that simultaneously upper approximates parametric functions formed by the objective and constraint functions. For directionally convex functions, that is, functions whose directional derivatives are convex with respect to directions, we will establish that every cluster point of the generated sequence satisfies Karush–Kuhn–Tucker type conditions expressed in terms of directional derivatives. The proposed procedure unifies several existing methods and gives rise to new ones. Numerical problems are solved to test the efficiency of our methods, and comparisons with different approaches are given. [ABSTRACT FROM AUTHOR]

Predicting the exact outcome of a real-life problem, which may occur in various fields like the industrial or healthcare sector, is challenging. Due to high information uncertainty and complicated factors influencing the industrial sector, traditional data-driven prediction approaches can hardly reflect real changes in practical situations. Fuzzy programming is a powerful prediction reasoning and risk assessment model for uncertain environments. This article mainly explores and applies a modified form of fuzzy programming, namely the Fuzzy Linear Fractional Programming Problem (FLFPP), having the coefficients of the objectives and constraints as Triangular Fuzzy Numbers (TFNs). The FLFPP is converted into an equivalent crisp Multi-Objective Linear Fractional Programming Problem (MOLFPP) and solved individually to associate an aspiration level. Then, by applying the Fuzzy Goal Programming (FGP) technique, the maximum degree of each membership goal is obtained by minimizing the negative deviational variables. We carry out two industrial application simulations in a hypothetical industrial scenario. Our study shows that the proposed model is practical and applicable to the uncertain practical environment to realize the prediction, and the results obtained are compared with those of the existing methods. [ABSTRACT FROM AUTHOR]

Due to the possibility of blockage during communication, the communication quality may be poor. Therefore, Reconfigurable Intelligent Surface (RIS) technology can effectively solve this problem. In order to increase the capacity of RIS-assisted wireless communication systems, joint optimization of beamforming design is crucial. However, the complexity of the optimization algorithm increases with the increase in the number of base station antennas and RIS elements deployed. Therefore, we propose a joint low-complexity optimization beamforming design based on fractional programming (FP) to address this issue. Specifically, we first use perfect channel state information to maximize the system's sum rate, as this problem is non-convex, we decompose the original problem into three sub-problems, and then introduce appropriate auxiliary variables. We derive optimal closed-form solutions for active and passive beamforming types, respectively. As the optimal solution obtained leads to higher computational complexity with an increase in the number of base station antennas and RIS elements, we reduce the computational complexity of obtaining the optimal solution based on the Woodbury transformation and scalar transformation. The proposed algorithm is also extended to the case where there is channel state information error. Finally, simulation results show that the proposed algorithm has certain advantages over other algorithms. [ABSTRACT FROM AUTHOR]

Over the last decade, dual active bridge (DAB) converters have become critical components in high-frequency power conversion systems. Recently, intensive efforts have been directed at optimizing DAB converter design and control. In particular, several strategies have been proposed to improve the performance of DAB control systems. For example, fractional-order (FO) control methods have proven potential in several applications since they offer improved controllability, flexibility, and robustness. However, the FO controller design process is critical for industrializing their use. Conventional FO control design methods use frequency domain-based design schemes, which result in complex and impractical designs. In addition, several nonlinear equations need to be solved to determine the optimum parameters. Currently, metaheuristic algorithms are used to design FO controllers due to their effectiveness in improving system performance and their ability to simultaneously tune possible design parameters. Moreover, metaheuristic algorithms do not require precise and detailed knowledge of the controlled system model. In this paper, a hybrid algorithm based on the chaotic artificial ecosystem-based optimization (AEO) and manta-ray foraging optimization (MRFO) algorithms is proposed with the aim of combining the best features of each. Unlike the conventional MRFO method, the newly proposed hybrid AEO-CMRFO algorithm enables the use of chaotic maps and weighting factors. Moreover, the AEO and CMRFO hybridization process enables better convergence performance and the avoidance of local optima. Therefore, superior FO controller performance was achieved compared to traditional control design methods and other studied metaheuristic algorithms. An exhaustive study is provided, and the proposed control method was compared with traditional control methods to verify its advantages and superiority. [ABSTRACT FROM AUTHOR]

The complexity of historical data in financial markets and the uncertainty of the future, as well as the idea that investors always expect the least risk and the greatest return. This study presents a multi-period fractional portfolio model in a fuzzy environment, taking into account the limitations of asset quantity, asset position, transaction cost, and inter-period investment. This is a mixed integer programming NP-hard problem. To overcome the problem, an improved genetic algorithm (IGA) is presented. The IGA contribution mostly involves the following three points: (i) A cardinal constraint processing approach is presented for the cardinal constraint conditions in the model; (ii) Logistic chaotic mapping was implemented to boost the initial population diversity; (iii) An adaptive golden section variation probability formula is developed to strike the right balance between exploration and development. To test the model's logic and the performance of the proposed algorithm, this study picks stock data from the Shanghai Stock Exchange 50 for simulated investing and examines portfolio strategies under various limitations. In addition, the numerical results of simulated investment are compared and analyzed, and the results show that the established models are in line with the actual market situation and the designed algorithm is effective, and the probability of obtaining the optimal value is more than 37.5% higher than other optimization algorithms. [ABSTRACT FROM AUTHOR]

Decision making problems with ambiguous data often arise in numerous practical fields which can be formulated as optimization models in fuzzy environment. This paper develops a new mathematical model using a proposed methodology to efficiently solve a multi-objective linear fuzzy fractional programming problem in trapezoidal fuzzy environment and generate a set of nondominated solutions. The concept of fuzzy cuts with different degrees of satisfaction is implemented which transforms the fuzzy optimization into an equivalent interval valued optimization. Subsequently, interval valued linear functions approximate the fuzzy valued fractional functions based on Taylor's series expansion. Finally, a proposed concept using weighting sum approach with varying weight vectors is utilized to design a mathematical model which generates the set of nondominated solutions. Two numerical examples including an existing problem and an additional practical problem in the field of production, are solved for the illustration of the proposed model. The results of the numerical problems are comparatively discussed with graphical analysis to justify the feasibility and applicability of the proposed model. [ABSTRACT FROM AUTHOR]

One of the problematic research areas in optimization is determining a global optimum for non-convex quadratic fractional optimization problems as a hard problem. This study seeks the quadratic fractional optimization problem in the complex field with two second-order cone constraints. An equivalent quadratic reformulation of the problem is given using the well-known Dinkelbach method, which can obtain its global optimum by applying the semidefinite relaxation approach and rank-one decomposition algorithm at each iteration of some classical methods. Finally, the results show the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

This research paper develops an algorithm to solve a neutrosophic linear fractional optimization problem, where the cost of the objective functions, the technology coefficients, and the resources are neutrosophic numbers (triangular and trapezoidal numbers). Two defuzzification methods are used here to convert the neutrosophic linear fractional optimization problem into a multi-objective linear fractional optimization problem (MOLFOP). The fractional objective function is defuzzified using the component-wise optimization method, and the linear constraints are defuzzified using the aggregation ranking function strategy. Hence, the MOLFOP is then solved using the fuzzy goal programming method. In order to further explain our suggested algorithm, two numerical examples are solved at the end, and the outcomes obtained by our method are compared with the outcomes obtained using the other algorithm. [ABSTRACT FROM AUTHOR]

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 realworld 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-theart in problem-solving techniques. [ABSTRACT FROM AUTHOR]

The uncertainty of socioeconomic development and climate change poses challenges to the sustainable management of water resources in Taiyuan, China. The study proposes a type-2 fuzzy chance-constrained ordered multi-objective fractional programming (T2FCC-ORMOFP) model to address the allocation of water under uncertainties. The model incorporates type-2 fuzzy programming and chance-constrained programming into an overall framework to handle multiple uncertainties under multi-level and multi-objective conflicts, while using fractional programming to reflect the marginal benefits of the system. It prioritizes the principles of optimal, fair, and stable distribution by the upper-level governing authorities, while considering the social and economic environmental benefits of lower-level decision-making. The optimal water allocation scenarios were obtained under different hydrological guarantee rates, violation levels of water supply constraints, and net economic benefits of type-2 fuzzy numbers for 2030. Additionally, groundwater is replaced by reclaimed water in varying proportions for flexible water supply. The results show that the water demand in Taiyuan cannot be ignored, and the risk of water shortage is more sensitive for the agricultural and industrial sectors. The recycled water substitution strategy can optimize the water supply structure and improve social and economic benefits (9–12%). Also T2FCC-ORMOFP can improve overall efficiency (20%) compared with a single-level model. HIGHLIGHTS The model takes into account the upper-level criteria of optimality, equity, and stability, along with the lower-level considerations of social and economic environmental benefits.; It tackles the intricacies stemming from the design of type-2 fuzzy- chance-constrained ordered multi-objective fractional programming.; Utilizing reclaimed water as an alternative can effectively mitigate the overexploitation of groundwater resources in Taiyuan.;

The ongoing water crisis poses significant threats to the socioeconomic sustainability and ecological security of arid and semi-arid river basins. Achieving Sustainable Development Goals (SDGs) within a complex socio-ecological nexus requires effective and balanced resource management. However, due to the intricate interactions between human societies and environmental systems, the tradeoffs and synergies of different SDGs remain unclear, posing a substantial challenge for collaborative management of natural resources. Here we introduce a gray fractional multi-objective optimization (GFMOP) model to balance multi-dimensional SDGs through a novel water–energy–economy–carbon–ecology nexus perspective. The model was applied to a typical arid river basin in Northwest China, where thirty-two scenarios were explored, considering factors such as shared socioeconomic pathways, carbon removal rates, water conveyance efficiencies, and ecological requirements. The results reveal a strong tradeoff between marginal benefit and carbon emission intensity, indicating that improving the economic efficiency of water use can simultaneously reduce emissions and protect the environment. Given the immense power generation potential, wind power development should be prioritized in the future, with its share in the energy structure projected to increase to 23.3% by 2060. Furthermore, promoting carbon capture technologies and expanding grassland coverage are recommended to achieve regional carbon neutrality, contributing 39.5% and 49.1% to carbon absorption during 2021–2060, respectively. Compared with traditional single-objective models, GFMOP demonstrates a superiority in uncovering interrelationships among multiple SDGs and identifying compromised alternatives within the compound socio-ecological nexus. The model also provides detailed strategies for resource allocation and pollutant control, offering valuable guidance to policymakers and stakeholders in pursuing sustainable and harmonious watershed management.

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. [ABSTRACT FROM AUTHOR]

This paper addresses the numerical computation of critical angles between two convex cones in Euclidean spaces. We present a novel approach to computing these critical angles by reducing the problem to finding stationary points of a fractional programming problem. To efficiently compute these stationary points, we introduce a partial linearization-like algorithm that offers significant computational advantages. Solving a sequence of strictly convex subproblems with straightforward solutions in several settings gives the proposed algorithm high computational efficiency while delivering reliable results: our theoretical analysis demonstrates that the proposed algorithm asymptotically computes critical angles. Numerical experiments validate the efficiency of our approach, even when dealing with problems of relatively large dimensions: only a few seconds are necessary to compute critical angles between different types of cones in spaces of dimension 1000. [ABSTRACT FROM AUTHOR]

The design (decision) variables in the presented article of a multi-objective interval fractional optimization problem based on a linear function are assumed to take the form of a closed interval using the concept of the parametric form of an interval. The original problem is initially changed into equivalent multi-objective interval linear programming with the design variables as closed intervals. Further, it is made free from interval uncertainty by changing into a classical single-objective problem using the weighted-sum method. The solutions of the model are theoretically justified by its existence. Finally, a numerical example and a case study on the agricultural planting structure optimization problem with hypothetical data are presented to support the recommended technique for the model. [ABSTRACT FROM AUTHOR]

The main objective of our research was to explore and develop a fractional-order derivative within the predator-prey framework. The framework includes prey refuge and selective nonlinear harvesting, where the harvesting progressively approaches a threshold value as the density of the harvested population advances. For memory effect, a non-integer order derivative is better than an integer-order derivative. The solutions to the fractional framework were shown to be existence, uniqueness, non-negativity, and boundedness. Matignon's condition was used for analysing local stability, and a suitable Lyapunov function provided global stability. While discussing the Hopf bifurcation's existence condition, we explored derivative order and refuge as bifurcation parameters. We aimed at redefining the predator-prey framework to incorporate fractional order, refuge, and harvesting. This kind of nonlinear harvesting is more realistic and reasonable than the model with constant yield harvesting and constant effort harvesting. The Adams-Bashforth-Moulton PECE algorithm in MATLAB software was used to simulate the proposed outcomes, investigate the impact on various factors, and analyse harvesting's effect on non-integer order predator-prey interactions. [ABSTRACT FROM AUTHOR]

This paper investigates energy-efficient communication within an integrated sensing and communication system. The system employs a dual-function radar-communication base station. This base station concurrently serves multiple mobile users for communication purposes while also performing target sensing within a designated range cell. An active reconfigurable intelligent surface (RIS) is utilized to enhance communication efficiency. The focus of this work is to optimize the communication energy efficiency by jointly allocating the transmit power and configuring the RIS elements. This optimization is achieved while satisfying constraints on both the probing power required for target sensing and the quality-of-service demands of the communication users. Two novel optimization methods are proposed, combining techniques from alternating optimization, sequential programming, and fractional programming. Through numerical simulations, the effectiveness of the developed algorithms is validated. Additionally, the performance of the system utilizing an active RIS is compared to that of a system with a passive RIS, specifically in terms of their respective communication energy efficiencies. [ABSTRACT FROM AUTHOR]

Simultaneous wireless information and power transfer (SWIPT) has been advocated as a highly promising technology for enhancing the capabilities of 5G and 6G devices. However, the challenge of dealing with large propagation path loss poses a significant hurdle. To address this issue, massive multiple-input multiple-output (MIMO) is employed to enhance the efficiency of SWIPT in cellular-based networks with multiple small cells, and especially increase the energy for cell-edge users. In addition, by leveraging a large set of spatially distributed base stations to collaboratively serve SWIPT-enabled user equipment, the cell-free massive MIMO has the potential to provide even better performance than the conventional small-cell systems. In this work, we extend the investigation to include the application of SWIPT technology with alternating current (AC) logic in the cell-free networks and the small-cell networks and propose joint beamforming and power splitting optimization frameworks to maximize the system sum-rate, subject to the constraints on harvested energy, AC logic energy supply, and total transmit power. The optimization problem is shown to be non-convex, posing a significant challenge. To address this challenge, we resort to a two-stage decomposition approach. Specifically, we first introduce quadratic transform-based fractional programming (FP) algorithms to iteratively solve the non-convex optimization problems in the first stage, achieving near-optimal solutions with low time complexities. To further reduce the complexities, we also incorporate conventional schemes such as zero forcing, maximum ratio transmission, and signal-to-leakage-and-noise ratio for the design of beamforming vectors. Second, to determine the optimal power splitting ratio within the framework, we develop a one-dimensional (1-D) search algorithm to tackle the single variable optimization problem reduced in the second stage. These algorithms are then evaluated in the context of cell-free MIMO and small-cell networks with numerical experiments. The results show that the FP-based algorithms can consistently outperform those utilizing the conventional beamforming schemes, and the solutions of this work can achieve up to fivefold improvement in the system sum-rate than the small-cell counterpart while providing different but comparable performance trends in energy harvesting (EH). [ABSTRACT FROM AUTHOR]

Amidst uncertainty, decision-making in manufacturing becomes a central focus due to its complexity. This study explores complex transportation constraints and uses novel ways to guide manufacturers. The Multi-objective Stochastic Linear Fractional Transportation Problem (MOSLFTP) is a crucial tool for managing supply chains, manufacturing operations, energy distribution, emergency routes, healthcare logistics, and other related areas. It adeptly addresses uncertainty, transforming efficiency and effectiveness in several domains. Stochastic programming is the process of converting theoretical probabilities into concrete certainties. The artistic compromise programming technique acts as a proficient mediator, reconciling opposing objectives and enabling equitable decision-making. This novel approach also addresses the Multi-objective Stochastic Linear plus Linear Fractional Transportation Problem (MOSLPLFTP), which involves two interconnected issues. The effectiveness of these principles is clearly shown with the help of the LINGO® 18 optimization solver. This study uses a ranking method to compare the similar methods to solve the current problems. A meticulously designed example acts as a significant achievement, shedding light on our method in a practical setting. It serves as a distinctive instrument, leading manufacturers through the maze of uncertainty and assisting them in determining the most advantageous course of action. This journey involves subtle interactions between complexity and simplicity, uncertainty is overcome by decisiveness, and invention is predominant. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surface (RIS)-assisted cell-free (CF) massive Multiple-Input Multiple-Output (MIMO) technology exhibits significant potential in enhancing the energy efficiency of 6G mobile communications. Nevertheless, recent studies suggest that both access points (APs) and RISs encounter challenges related to a high energy consumption during operation. To address this issue, strategies involving AP hibernation and RIS shut-off are proposed. Subsequently, an optimization problem is formulated to jointly optimize RISs, beamforming vectors, and AP selection with the aim of maximizing the energy efficiency (EE). Initially, the non-convex optimization problem for maximizing energy efficiency is decomposed into three sub-problems. These sub-problems are subsequently reformulated using fractional programming and variational programming techniques and then solved using the successive convex approximation (SCA) algorithm, Dinkelbach algorithm, and greedy algorithm, respectively. Subsequently, an alternate optimization algorithm based on block gradient descent is introduced to iteratively solve the four-variable optimization problem, thereby obtaining an approximate solution to the original problem. The simulation results demonstrate that the algorithm significantly reduces energy consumption. Specifically, compared to the scheme without the hibernation strategy, the energy efficiency (EE) is enhanced by 35%. [ABSTRACT FROM AUTHOR]

Interval linear fractional programming problem (ILFPP) approaches uncertainties in real-world systems such as business, manufacturing, finance, and economics. In this study, we propose solving the interval linear fractional programming (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 without converting the problem into its conventional form. This paper compares the range, solutions, and approaches of ILFP with fuzzy linear fractional programming (FLFP) in solving real-world optimization problems. The illustrated numerical examples show a better range of interval solutions on practical applications of ILFPs and uncertain parameters. [ABSTRACT FROM AUTHOR]

Zero-shot learning enables the recognition of new class samples by migrating models learned from semantic features and existing sample features to things that have never been seen before. The problems of consistency of different types of features and domain shift problems are two of the critical issues in zero-shot learning. To address both of these issues, this paper proposes a new modeling structure. The traditional approach mapped semantic features and visual features into the same feature space; based on this, a dual discriminator approach is used in the proposed model. This dual discriminator approach can further enhance the consistency between semantic and visual features. At the same time, this approach can also align unseen class semantic features and training set samples, providing a portion of information about the unseen classes. In addition, a new feature fusion method is proposed in the model. This method is equivalent to adding perturbation to the seen class features, which can reduce the degree to which the classification results in the model are biased towards the seen classes. At the same time, this feature fusion method can provide part of the information of the unseen classes, improving its classification accuracy in generalized zero-shot learning and reducing domain bias. The proposed method is validated and compared with othermethods on four datasets, and fromthe experimental results, it can be seen that the method proposed in this paper achieves promising results. [ABSTRACT FROM AUTHOR]

The surge in technology is driving demands for real-time interactive applications and high-speed transmissions, necessitating improved network throughput and energy efficiency (EE) for immersive experiences. The rise in industrial automation has led to higher connectivity needs, straining fifth-generation networks. Sixth-generation networks aim to address these demands, potentially maximizing throughput and EE through enhanced coverage. This paper introduces innovative techniques like phone user clustering-based downlink hybrid multiple access in unmanned aerial vehicle-assisted heterogeneous networks (HetNets) to jointly optimize phone user (PU) admission, cell association, throughput, and EE while ensuring PU fair association with cell (PUFAC) and quality of service (QoS), i.e., minimum rate requirement of PUs. An outer approximation algorithm solves the mixed integer non-linear programming (MINLP) optimization problem arising from the transformation of the concave fractional programming optimization problem using the Charnes-Cooper transformation. The method's effectiveness is assessed, showcasing its superiority over existing macro-cell-only networks and HetNets concerning throughput, EE, PU admission, PU-cell association, PUFAC, and QoS. [ABSTRACT FROM AUTHOR]

We discuss an extragradient projectionmethod for dealing with equilibrium problems involving bifunctions which are strongly quasiconvex on its second argument. The algorithm combines a proximal step with a subgradient projection step using a generalized subdifferential, which is especially useful for dealing with this class of generalized convex functions, and with a line search. As a consequence, the usual assumption regarding the relationship between the Lipschitz-type parameter and the modulus of strong quasiconvexity is no longer needed for ensuring the convergence of the generated sequence to the solution of the problem. Furthermore, numerical experiments for classes of nonconvex mixed variational inequalities based on fractional programming problems are given in order to show the performance of our proposed method. [ABSTRACT FROM AUTHOR]

In next‐generation wireless communications, reconfigurable intelligent surface (RIS) has emerged as a cost‐effective technique for enhancing physical layer security (PLS) in millimeter‐wave (mmWave) communications, especially under challenging scenarios with adversarial entities and obstructions. However, the primary studies for RIS incorporation in mmWave communication systems utilized static deployments, lacking adaptability and efficiency in complex environments. To address this problem, a dynamic RIS deployment design framework is introduced for PLS enhancement in mmWave systems against jamming and eavesdropping attacks. For the design, it is aimed to maximize the secrecy rate by jointly optimizing the RIS selection with the beamforming design. The resulting optimization problem is challenging to solve due to the coupling of the RIS control factor, joint beamforming design, and non‐convex constraints. To tackle these issues, an efficient multi‐RIS‐aided PLS enhancement algorithm is proposed. It transforms the objective into a series of subproblems and employs the fractional programming technique and prox‐linear block coordinate descent updating method to solve them alternatively and obtain the optimal solution. The simulations demonstrate the advantage of the dynamic deployment, which exhibits enhanced security performance with reduced complexity compared with benchmarks. Further examinations also provide insight into optimal RIS activation configurations, achieving optimal balance for securing mmWave communications against emerging threats while maintaining system efficiency. [ABSTRACT FROM AUTHOR]

In this article, we employ advanced techniques of convex analysis and $ \mathcal {C} $ C -differentiation to examine KKT-type robust necessary and sufficient optimality conditions and robust duality for an uncertain multiobjective programming problem under uncertainty sets, where $ \mathcal {C} $ C denotes the set of all $ \mathcal {G} $ G -derivatives which are positively homogeneous and convex with respect to the second argument. We first provide the robust constraint qualification of the (RCQ) type via the $ \mathcal {C} $ C -derivatives of uncertain constraint functions. We second establish KKT-type robust necessary conditions for robust (weakly) efficient solutions via the subdifferentials of $ \mathcal {C} $ C -derivatives to such problems. We third propose two new kinds of generalized $ \mathcal {C} $ C -convex functions via the subdifferentials of $ \mathcal {C} $ C -derivatives involving max-functions. Under suitable assumptions on the generalized $ \mathcal {C} $ C -convexity, KKT-type robust necessary optimality conditions become robust sufficient optimality conditions. Furthermore, we formulate as some applications a dual multiobjective programming problem to the underlying programming and examine weak, strong, and converse duality theorems for the same. Some illustrative examples are also provided for our findings. [ABSTRACT FROM AUTHOR]

This article demonstrates techniques to solve the linear fractional programming (LFP) problem using an interval approach. This approach addresses uncertainties as intervals and employs interval arithmetic for robustness. In this paper, a reasonable attempt is made to construct a mathematical model of interval linear fractional programming, and various approaches were employed to solve it. The proposed process emphasizes solving the ILFP problem in different optimization techniques and uses interval arithmetic to obtain a better range of intervals. The study illustrates the practical aspects of this approach and its effectiveness in solving real-world situations when uncertainties are significant. The methods, process, solutions, and time consumption are analyzed later to show our proposed method's real-life application and efficiency. [ABSTRACT FROM AUTHOR]

This paper is devoted to applying the inverse Data Envelopment Analysis (InvDEA) in the simultaneous presence of desirable and undesirable factors. One of the most common ways to improve units' performance in the business environment is through activity synergies called units' merging. The present study models how to identify the inherited input/output from the units participating in the merger process to achieve the desired efficiency goal. The proposed models are established based on the InvDEA approach and multiple-objective programming tools. Sufficient conditions to estimate desirable and undesirable data are obtained using Pareto solutions to multi-objective programming problems. The theory extended in the study is explained by an application in the banking sector. [ABSTRACT FROM AUTHOR]

We trained a long short-term memory (LSTM) network based on a pooled dataset made of hundreds of liquid stocks aiming to forecast the next daily realized volatility for all stocks. Showing the consistent outperformance of this universal LSTM relative to other asset-specific parametric models, we uncovered nonparametric evidence of a universal volatility formation mechanism across assets relating past market realizations, including daily returns and volatilities, to current volatilities. A parsimonious parametric forecasting device combining the rough fractional stochastic volatility and quadratic rough Heston models with fixed parameters resulted in the same level of performance as the universal LSTM, which confirmed the universality of the volatility formation process from a parametric perspective. [ABSTRACT FROM AUTHOR]