Fractional Programming Research Articles

Dynamic reconfigurable intelligent surface deployment for physical layer security enhancement in mmWave systems

AbstractIn 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.

Fractional Programming-Based Uplink Transmission Power Allocation for User-Centric Cell-Free Massive MIMO Systems

Fractional Programming-Based Uplink Transmission Power Allocation for User-Centric Cell-Free Massive MIMO Systems

An ordered multi-objective fuzzy stochastic approach to sustainable water resources management: a case study from Taiyuan City, China

Abstract 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.

Optimizing air conditioning loads scheduling: A bi‐objective dynamic optimization algorithm considering life loss impact

AbstractAir conditioning loads (ACLs) can actively contribute to optimizing energy usage and increasing renewable energy utilization rate through scheduling. Existing studies on the participation of ACLs in DR have mainly focused on developing ON/OFF strategies, little consideration has been given to the impact of DR on the life loss of ACLs. In light of this, the present study first introduces an equation for quantifying the life loss of ACLs. Building upon this, an optimizing ACLs scheduling model is established considering life loss impact. As the relationship between life loss and refrigeration power is a complex non‐linear high‐order fractional function, it cannot be solved by conventional commercial solvers. Therefore, a bi‐objective dynamic optimization algorithm is proposed based on non‐linear fractional programming (NFP) to address this problem. To assess the effectiveness of our algorithm, it is used in a microgrid case with three schemes. Scheme 3 is aquatinted to consider the economic cost and the life loss of ACLs simultaneously, aiming to maximize the comprehensive benefit of the scheduling scheme. The results confirm the efficiency and superiority of the proposed algorithm.

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.

Deep Unfolded Fractional Programming-Based Beamforming in RIS-Aided MISO Systems

Deep Unfolded Fractional Programming-Based Beamforming in RIS-Aided MISO Systems

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

An Outer Space Approach to Tackle Generalized Affine Fractional Program Problems

An Outer Space Approach to Tackle Generalized Affine Fractional Program Problems

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.

Power Allocation Based on Multi-Agent Deep Deterministic Policy Gradient for Underwater Acoustic Communication Networks

This paper proposes a reinforcement learning-based power allocation for underwater acoustic communication networks (UACNs). The objective function is formulated as maximizing channel capacity under constraints of maximum power and minimum channel capacity. To solve this problem, a multi-agent deep deterministic policy gradient (MADDPG) approach is introduced, where each transmitter node is considered as an agent. Given the definition of a Markov decision process (MDP) model for this problem, the agents learn to collaboratively maximize the channel capacity by deep deterministic policy gradient (DDPG) learning. Specifically, the power allocation of each agent is obtained by a centralized training and distributed execution (CTDE) method. Simulation results show the sum rate achieved by the proposed algorithm approximates that of the fractional programming (FP) algorithm and improves by at least 5% compared with the DQN (deep Q-learning network) -based power allocation algorithm.

Joint Active and Passive Beamforming in RIS-Assisted Secure ISAC Systems.

This paper investigates joint beamforming in a secure integrated sensing and communications (ISAC) system assisted by reconfigurable intelligent surfaces (RIS). The system communicates with legitimate downlink users, detecting a potential target, which is a potential eavesdropper attempting to intercept the downlink communication information from the base station (BS) to legitimate users. To enhance the physical-layer secrecy of the system, we design and introduce interference signals at the BS to disrupt eavesdroppers' attempts to intercept legitimate communication information. The BS simultaneously transmits communication and interference signals, both utilized for communication and sensing to guarantee the sensing and communication quality. By jointly optimizing the BS active beamformer and the RIS passive beamforming matrix, we aim to maximize the achievable secrecy rate and radiation power of the system. We develop an effective scheme to find the active beamforming matrix through fractional programming (FP) and semi-definite programming (SDP) techniques and obtain the RIS phase shift matrix via a local search technique. Simulation results validate the effectiveness of the proposed methods in enhancing communication and sensing performance. Additionally, the results demonstrate the effectiveness of introducing the interference signals and RIS in enhancing the physical-layer secrecy of the ISAC system.

Improving efficiency and sustainability of water-agriculture-energy nexus in a transboundary river basin under climate change: A double-sided stochastic factional optimization method

In this study, a double-sided stochastic fractional programming (DSFP) method is developed for identifying optimal water-allocation schemes of water-agriculture-energy nexus (WAEN) system under considering climate change impact. The advantages of DSFP are (i) handling complex uncertainty of double-sided randomness, (ii) addressing conflicting objectives with optimal system efficiency, and (iii) achieving trade-off between marginal benefit and system risk. Then, a DSFP-based water-agriculture-energy nexus (DSFP-WAEN) model is formulated for water resources allocation in a transboundary river basin of Central Asia, where 48 scenarios are designed to examine the impacts of climate change, irrigation efficiency, and system risk over a long-term planning horizon (2026–2050). Results reveal that: (i) among all agricultural activities, cash crop cultivation shows the greatest change in adaption to climate change, with the share of cash crop cultivation increasing to 70.7% by 2050 under RCP4.5; (ii) Kazakhstan, which has the largest irrigation needs and is the county most sensitive to water supply risk, should be the first to be constrained in the case of severe water shortages and poor delivery levels; (iii) the improvement of irrigation efficiency can increase the inflow to the Aral Sea by 2.7%, and reduce water loss of infield irrigation by 11.3% even under severe water shortage (i.e. p = 0.01). Compared with the models based on the traditional stochastic programming and single-objective methods, DSFP-WAEN has advantages in optimizing water-use efficiency and reflecting system complexity with flexible solutions. To coordinate transboundary water conflicts, strategies from both demand and supply sides related to quota management and water-saving techniques are suggested for the Syr Darya River basin, such as clean energy transition, drip irrigation promotion and canal system improvement. From a long-term planning perspective, WAEN schemes should be adapted to risk attitude and climate change, which can help address water scarcity and achieve future sustainability.

Radar Waveform Design Based on Target Pattern Separability via Fractional Programming

Radar Waveform Design Based on Target Pattern Separability via Fractional Programming

Towards neutrosophic Circumstances goal programming approach for solving multi-objective linear fractional programming problems

Indeterminacy is common in practical decision-making circumstances. So the mathematical models of decision making represent the situations in a better way if the parameters are considered as neutrosophic. This article studies a general framework of multi-objective neutrosophic linear fractional programming problem (MONLFPP) and proposes unique approach. The issue's parameters are thought of as triangular neutrosophic numbers. The problem is converted into an equal crisp multi-objective linear programming problem (MOLPP) with the help of variable transformation technique and a ranking function. Fuzzy goal programming is used to solve the MOLPP that has been obtained. Finally, the usefulness of the proposed technique is established using two mathematical models.

A Mathematical Approach to Solve Multi-Objective Pentagonal Fuzzy Linear Plus Linear Fractional Programming Problems

A Mathematical Approach to Solve Multi-Objective Pentagonal Fuzzy Linear Plus Linear Fractional Programming Problems

The Composite Approach for Linear Fractional Programming Problem in Fuzzy Environment

The Composite Approach for Linear Fractional Programming Problem in Fuzzy Environment

Weighted Sum-Rate Maximization with Transceiver and Passive Beamforming Design for IRS-Aided MIMO-BC Communications via Matrix Fractional Programming

Weighted Sum-Rate Maximization with Transceiver and Passive Beamforming Design for IRS-Aided MIMO-BC Communications via Matrix Fractional Programming

A New Framework of RIS-Aided User-Centric Cell-Free Massive MIMO System for IoT Networks

With its merit of inter-cell interference elimination and enhanced throughput, cell-free (CF) massive multiple-input multiple-output (MIMO) system, has attracted considerable interests in evolution of 6G Internet-of-Things (IoT) networks. Meanwhile, reconfigurable intelligent surface (RIS) has shown its potential benefit in enhancing both capacity and energy efficiency (EE). In this paper, a new framework of RIS-aided CF massive MIMO system is proposed for IoT networks, in which extra active APs are deployed closely to the passive RISs, in that way, the RIS-user channels can be approximately obtained by parameters estimated at those extra APs with acceptable loss. To avoid extra power consumption, user-centric AP selection strategy in CF system is suggested, on the basis of which, an optimization problem related to power control, precoding and RIS phase shift is formulated to maximize the sum rate. To deal with this tough three-variable optimization, a Lagrangian dual transformation and fractional programming based algorithm is proposed. In particular, the proposed algorithm can extend to optimize EE and well adapt to other RIS-aided CF systems. Simulation results reveal that the proposed algorithm can achieve superior performance in terms of both sum rate (SR) and EE.

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

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

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

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