Nonlinear Fractional Programming Research Articles

Energy-efficient resource allocation for bidirectional wireless power and information transfer over interference channels

Energy efficiency is an important performance metric for the sustainable operation of energy-limited communication networks. This study investigates an energy-efficient resource allocation strategy to maximize the energy efficiency of wireless-powered bidirectional communication over interference channels. The receivers in the system harvest energy and decode information simultaneously using a time switching or power splitting policy from data signals sent by transmitters in the forward link. The harvested energy is subsequently used to send response signals back to the transmitters in the backward link. Our objective is to jointly optimize the transmit power of the transmitters and the energy harvesting ratio of the receivers to maximize the energy efficiency of the entire system while maintaining the minimum required data rates in both the forward and backward links. Considering the non-convexity and NP-hardness of this optimization problem, we first apply nonlinear fractional programming and a dual method to derive an analytical expression for each control parameter and then propose an iterative algorithm to find suboptimal solutions with low computational complexity. The simulation results show that the proposed algorithm adjusts both the transmit power and energy harvesting ratio adaptively considering the co-channel interference and thus achieves near-optimal energy efficiency performance within a short computation time.

Energy-Efficiency Optimization With Model Convexification for Wireless Ad Hoc Networks With Multi-Packet Reception Capability

Energy efficiency is a significant requirement of resource management and design optimization in information networks. In this work, we propose an iterative fractional programming framework embedded with a distributed primal-dual extra-gradient projection algorithm, which addresses a wide class of the energy-efficiency optimization problems in wireless ad hoc networks with full-duplex radios and multi-packet reception capability. Specifically, we propose a model convexification mechanism by joining an affine transformation and an exponential transformation into the nonlinear fractional programming, which enables us to deal with the challenge arising from the complexity and non-convex structure of the original problem. With the model convexification, we can map the non-convex power control space into a convex space and equivalently derive a sequence of convex subproblems, which relaxes the convexity assumption widely adopted in the existing literature. We further propose a distributed primal-dual algorithm based on extra-gradient projection to solve the convex subproblem at each iteration of the fractional programming. The convergence of the proposed iterative fractional programming and the distributed optimization method is theoretically proven. Numerical results also verify the proposed method and demonstrate its superior performance over other representative distributed and centralized schemes in terms of achieving global energy efficiency.

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.

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.

Distributed Multi-Agent Approach for Achieving Energy Efficiency and Computational Offloading in MECNs Using Asynchronous Advantage Actor-Critic

Mobile edge computing networks (MECNs) based on hierarchical cloud computing have the ability to provide abundant resources to support the next-generation internet of things (IoT) network, which relies on artificial intelligence (AI). To address the instantaneous service and computation demands of IoT entities, AI-based solutions, particularly the deep reinforcement learning (DRL) strategy, have been intensively studied in both the academic and industrial fields. However, there are still many open challenges, namely, the lengthening convergence phenomena of the agent, network dynamics, resource diversity, and mode selection, which need to be tackled. A mixed integer non-linear fractional programming (MINLFP) problem is formulated to maximize computing and radio resources while maintaining quality of service (QoS) for every user’s equipment. We adopt the advanced asynchronous advantage actor-critic (A3C) approach to take full advantage of distributed multi-agent-based solutions for achieving energy efficiency in MECNs. The proposed approach, which employs A3C for computing offloading and resource allocation, is shown through numerical results to significantly reduce energy consumption and improve energy efficiency. This method’s effectiveness is further shown by comparing it to other benchmarks.

An Investigation of Linear Diophantine Fuzzy Nonlinear Fractional Programming Problems

The linear Diophantine fuzzy set notion is the main foundation of the interactive method of tackling nonlinear fractional programming problems that is presented in this research. When the decision maker (DM) defines the degree α of α level sets, the max-min problem is solved in this interactive technique using Zimmermann’s min operator method. By using the updating technique of degree α, we can solve DM from the set of α-cut optimal solutions based on the membership function and non-membership function. Fuzzy numbers based on α-cut analysis bestowing the degree α given by DM can first be used to classify fuzzy Diophantine inside the coefficients. After this, a crisp multi-objective non-linear fractional programming problem (MONLFPP) is created from a Diophantine fuzzy nonlinear programming problem (DFNLFPP). Additionally, the MONLFPP can be reduced to a single-objective nonlinear programming problem (NLPP) using the idea of fuzzy mathematical programming, which can then be solved using any suitable NLPP algorithm. The suggested approach is demonstrated using a numerical example.

Energy Efficient Resource Allocation for UAV-Served Energy Harvesting-Supported Cognitive Industrial M2M Networks

In this letter, the resource allocation problem for Energy Harvesting-supported Cognitive Industrial Machine-to-Machine (EH-CI-M2M) network underlaying Unmanned Aerial Vehicles (UAVs) communication is investigated with the objective of maximizing the average energy efficiency by jointly considering the EH time slot assignment, transmit power control and bandwidth allocation under the constraints of Quality of Service (QoS) and the available energy status of the EH-CMNet devices. Nevertheless, the optimization problem is difficult to be tackled directly since it is non-convex and NP-hard. We first transform the primitive objective problem into a convex form equivalently by non-linear fractional programming and variable relaxation approach. Based on Dinkelbach and Lagrangian theory, an iterative algorithm is proposed to solve the optimization problem. Extensive simulation results demonstrate that the proposed scheme outperforms the benchmark schemes in terms of energy efficiency in different network settings.

Cross-Layer Design for Energy-Efficient Reliable Multi-Path Transmission in Event-Driven Wireless Sensor Networks.

In event-driven wireless sensor networks (WSNs), a reliable, efficient, and scalable routing solution is required for the reliable delivery of sensory data to the base station (BS). However, existing routing algorithms rarely address the issue of energy efficiency under multi-path conflicts for multi-event-driven scenarios. In order to maximize energy efficiency while maintaining a manageable conflict probability, this paper investigates a cross-layer design of routing and power control for multi-event-driven WSNs. We first develop a mathematical characterization of the conflict probability in multi-path routing, and we then formulate the energy efficiency maximization problem as a non-convex combinatorial fractional optimization problem subject to a maximum conflict probability constraint. By utilizing non-linear fractional programming and dual decomposition, an iterative search algorithm was used to obtain near-optimal power allocation and routing solutions. Extensive results demonstrate that our proposed algorithm achieved a gain of 9.09% to 35.05% in energy efficiency compared to other routing algorithms, thus indicating that our proposed algorithm can avoid unnecessary control overhead from multi-path conflicts with a lower conflict probability and can ensure maximum energy efficiency through routing and power control design.

A Study of Coverage Probability-Based Energy-Efficiency Analysis for UAV-Aided THz-Enabled 6G Networks

Reliable and flexible emergency communication is a crucial challenge for search and rescue in the circumstance of disasters, specifically for the situation when base stations (BS) are no longer functioning. Unmanned aerial vehicle (UAV)-aided networking is becoming a prominent solution to establish emergency networks, which also should be energy-efficient. The Terahertz (THz) frequency-enabled communication system is also envisioned as enabling technology for Sixth-Generation (6G) communication systems. To this end, we consider a THz UAV network for our investigation. In this article, we study energy-efficiency (EE) analysis for UAV-Aided Terahertz-Enabled 6G Networks. The metric coverage probability (CP) is adopted as EE analysis given the QoS requirement. Using stochastic geometry tools, we derive a CP. Afterward, considering that CP, we study a network EE optimization method. Borrowing the idea from the existing literature, we reformulate the actual EE optimization problem into a solvable Dinkelbach nonlinear fractional programming. However, the optimization problem turns into a nondeterministic polynomial hard (NP-hard) problem. Eventually, we transform that NP-hard problem into a convex optimization problem using the ConCave-Convex procedure (CCCP), which is more tractable and feasible to find a solution for the optimization.

Bistatic MIMO DFRC System Waveform Design via Fractional Programming

The Cramér-Rao lower bound (CRLB) and sum-rate (SR) are widely-used metrics in the radar parameter estimation performance evaluation and communication quality-of-service (QoS) assessment, respectively. In this paper, we adopt these two metrics in waveform design for bistatic multiple-input multiple-output dual-function radar-communication (MIMO DFRC) systems, which is different from existing methods where only suboptimal optimization criteria are employed. However, both of the design formulations result in nonconvex and nonlinear fractional programming (FP) problems with complex fractional constraint and objective function. Especially, the CRLB for direction-of-departure (DOD) and direction-of-arrival (DOA) in bistatic DFRC MIMO system is a fraction with quadratic polynomial in the numerator and quartic polynomial in the denominator; whereas the SR expression corresponds to a summation-log-fraction function. By fractional function transformation and convexification, complex function design and simplification, and summation-log-fraction function separation, this paper derives an FP framework to solve these complicated problems. Numerical results demonstrate the excellent performance of our design solutions.

Maximizing the energy efficiency in intelligent reflecting surface‐aided unmanned aerial vehicle data collection system in presence of malicious jammers

AbstractIn this article, intelligent reflecting surface (IRS) aided an unmanned aerial vehicle (UAV) data collection system is investigated, where an IRS is deployed to assist in the communication from a cluster of Internet‐of‐Things (IoT) devices to a UAV in the presence of a jammer. We aim to improve the energy efficiency (EE) via the joint design of UAV trajectory, IRS passive beamforming, device power allocation and communication scheduling. However, the formulated nonlinear fractional programming problem is challenging to solve due to its nonconvexity and coupled variables. To overcome the difficulty, we propose an alternating optimization based algorithm to solve it sub‐optimally by leveraging the Dinkelbach's algorithm, successive convex approximation (SCA) technique, and block coordinate descent (BCD) method. Extensive simulation results show that the proposed design can significantly improve the anti‐jamming performance. In particular, for the remote jammer case, the proposed design can largely shorten the flight path and thus decrease the energy consumption via the signal enhancement; while for the local jammer case, which is deemed highly challenging in conventional systems without IRS since the retreating away strategy becomes ineffective, our proposed design even achieves a higher performance gain owing to the efficient jamming signal mitigation.

Dual-Hop Hybrid IRS-Aided Outdoor-to-Indoor mmWave Communications

In this letter, we design a dual-hop hybrid intelligent reflecting surface (IRS)-aided millimeter-wave (mmWave) system with one passive and one active IRS. In this system, we aim to maximize the user received signal-to-noise ratio (SNR) by jointly optimizing the reflecting coefficients of the reflecting elements (REs) at the cascaded IRSs and the active beamforming vector at the base station. To achieve this target, we formulate a nonlinear fractional programming problem. However, it is difficult to be solved. Since it is non-convex and all the three design variables are deeply coupled. To address this problem, we decouple all variables using an alternating optimization method and divide the original problem into three sub-problems. By solving the three sub-problems iteratively until convergence, we obtain a sub-optimal solution. Simulation results show that the proposed scheme outperforms the traditional schemes.

An Adaptive Projection Gradient Method for Solving Nonlinear Fractional Programming

In this study, we focus on solving the nonlinear fractional optimization problem in which the numerator is smooth convex and the denominator is smooth concave. To achieve this goal, we develop an algorithm called the adaptive projection gradient method. The main advantage of this method is that it allows the computations for the gradients of the considered functions and the metric projection to take place separately. Moreover, an interesting property that distinguishes the proposed method from some of the existing methods is the nonincreasing property of its step-size sequence. In this study, we also prove that the sequence of iterates that is generated by the method converges to a solution for the considered problem and we derive the rate of convergence. To illustrate the performance and efficiency of our algorithm, some numerical experiments are performed.

Energy Efficient Resource Allocation for eHealth Monitoring Wireless Body Area Networks With Backscatter Communication

Electronic Health (eHealth) monitoring systems with wireless body area networks (WBANs) have recently emerged as promising solutions to provide sustainable and high-quality health services. In this paper, we propose an optimization framework to maximize the energy efficiency (EE) of a WBAN assisted by backscatter communication (BackCom) and energy harvesting technologies, subject to quality-of-service and power budget constraints. More specifically, the optimization problem jointly optimizes the transmit power of the aggregator, transmission time, and backscatter time of the WBAN consisting of energy-constrained sensor nodes (SNs) which have the ability to harvest energy from the signals transmitted by the aggregator. A generalized gamma distribution is adopted to characterize the channel propagation characteristics of patients under different arbitrary body movements and their corresponding transmission requirements during daily life activities. It is shown that the formulated EE optimization problem is a quasi-concave nonlinear fractional program, and it is transformed to an equivalent parametric problem by using the Dinkelbach algorithm to obtain the solution. We exploit the structure of the optimization problem and propose a low-complexity iterative-based suboptimal heuristic with performance fairly close to the optimized solution. Simulation results demonstrate the effectiveness of the proposed schemes in maximizing EE of the WBAN, whereas the comparisons with the related work from the literature reaffirm the superiority of the proposed algorithms.

Using Geometric Arithmetic Mean to Solve Non-linear Fractional Programming Problems

Using Geometric Arithmetic Mean to Solve Non-linear Fractional Programming Problems

VIKOR approach for bi-level multi-criteria nonlinear fractional programming problems: new insights

PurposeThe paper aims to introduce a novel concept to solve the bi-level multi-criteria nonlinear fractional programming (BL-MCNFP) problems. Bi-level programming problem (BLPP) is rigorously flourished and studied by several researchers, which deals with decentralized decisions by comprising a sequence of two optimization problems, namely upper and lower-level problems. However, on the other hand, many real-world decision-making problems involve multiple objectives with fraction aspects, called fractional programming problems that reflect technical and economic performance.Design/methodology/approachThis paper introduces a VIKOR (“VlseKriterijumska Optimizacija I Kompromisno Resenje”) approach to solve the BL-MCNFP problem. In this approach, an aggregating function based on LP metrics is formulated on the basis of the “closeness” scheme from the “ideal” solution. The three steps perform the solution process: First, a new concept is attempted to minimize and maximize of the numerators and denominators from their respective ideal solutions and anti-ideal values simultaneously. Second, for each level, the K-dimensional objective space of each level is converted to a one-dimensional space by an aggregating function. Third, to obtain the final solution, all levels are combined into single-level model where the decision variables of upper levels are interrelated with other levels through fuzzy strategy-based linear and nonlinear membership functions.FindingsThe effectiveness of the proposed VIKOR is demonstrated by numerical examples, where the reported results affirm that the extended VIKOR method provides superior results in comparison with the same methods in the literature, and it is a good alternative to BL-MCNFP problems.Originality/valueIn terms of the assistance-based right decision, a parametric analysis for the weight of the majority is provided to exhibit a wide range of compromise solutions for the decision-maker.

Energy Efficiency Maximization for UAV-Enabled Hybrid Backscatter-Harvest-Then-Transmit Communications

Wireless powered communication via backscatter and/or harvest-then-transmit (HTT) has been considered a promising solution to connecting nodes in the Internet-of-things (IoT) networks. However, the harvested energy at an IoT node is heavily limited by the distance between the node and the power beacon (PB) due to the high propagation loss. In this paper, we propose to employ an unmanned aerial vehicle (UAV) as a mobile PB to provide energy signals on demand to the IoT nodes, which convey their information to a reader via backscattering or active transmission using the harvested energy. We maximize the total energy efficiency (EE) of all the IoT nodes powered by the UAV by jointly optimizing the UAV’s transmit power and trajectory, the IoT nodes’ backscatter reflection coefficients and their transmit power for active transmission, and the time allocation between backscattering and active transmission. To solve the formulated non-linear fractional programming problem, we use the generalized fractional programming theory and a block coordinated decent method to decompose it into two sub-problems: one optimizes the communication resource allocation under a fixed UAV trajectory, and the other optimizes the UAV trajectory for given communication resource allocation. We then devise a Dinkelbach-based iterative algorithm to solve the two sub-problems by employing a Lagrangian dual method and a successive convex programming technique, respectively and iteratively. Simulation results show that our proposed iterative algorithm converges very fast, and the optimized UAV-enabled hybrid backscatter-HTT communication achieves a much higher EE of all the IoT nodes than the benchmark schemes including the UAV-enabled backscatter, UAV-enabled HTT, and hybrid BackCom-HTT with a fixed PB.

Terahertz Meets Untrusted UAV-Relaying: Minimum Secrecy Energy Efficiency Maximization via Trajectory and Communication Co-Design

Unmanned aerial vehicles (UAVs) and Terahertz (THz) technology are envisioned to play paramount roles in next-generation wireless communications. In this paper, we present a novel secure UAV-assisted mobile relaying system operating at THz bands for data acquisition from multiple ground user equipments (UEs) towards a destination. We assume that the UAV-mounted relay may act, besides providing relaying services, as a potential eavesdropper called the untrusted UAV-relay (UUR). To safeguard end-to-end communications, we present a secure two-phase transmission strategy with cooperative jamming. Then, we devise an optimization framework in terms of a new measure $-$ secrecy energy efficiency (SEE), defined as the ratio of achievable average secrecy rate to average system power consumption, which enables us to obtain the best possible security level while taking UUR's inherent flight power limitation into account. For the sake of quality of service fairness amongst all the UEs, we aim to maximize the minimum SEE (MSEE) performance via the joint design of key system parameters, including UUR's trajectory and velocity, communication scheduling, and network power allocation. Since the formulated problem is a mixed-integer nonconvex optimization and computationally intractable, we decouple it into four subproblems and propose alternative algorithms to solve it efficiently via greedy/sequential block successive convex approximation and non-linear fractional programming techniques. Numerical results demonstrate significant MSEE performance improvement of our designs compared to other known benchmarks.

Energy-Efficient Joint Task Assignment and Power Control in Energy-Harvesting D2D Offloading Communications

In this article, we investigate the joint task assignment and power control problems for Device-to-Device (D2D) offloading communications with energy harvesting. Exploiting the D2D links for data offloading allows reducing the traffic load of the cellular base stations. The energy consumed by the D2D transmitters for data offloading can be compensated by energy harvesting. The main objective is to maximize the energy efficiency (EE) under energy causality and delay constraints, assuming a harvest–transmit model. Hence, the proposed model results in a nonconvex problem. We first derive an equivalent and more tractable optimization problem by exploiting nonlinear fractional programming, also known as the Dinkelbach method. We propose a layered optimization method by decoupling the EE maximization problem into power allocation and offloading assignment. The first step consists of computing the optimal power values by applying the conjugate gradient method. In the second step, the problem of the D2D pair formation for data offloading amounts to the bipartite graph matching. It can be solved to optimality using the Hungarian algorithm. Extensive simulations were performed on various network scenarios. Numerical results show that the proposed resource allocation scheme achieves remarkable improvements in terms of network EE.

Social-aware relay selection and energy-efficient resource allocation for relay-aided D2D communication

How to improve the flexibility of limited communication resources to meet the increasing requirements of data services has become one of the research hotspots of the modern wireless communication network. In this paper, a novel social-aware motivated relay selection method is put forward to allocate the energy efficiency (EE) resources for the device-to-device (D2D) communication. To improve system flexibility, a D2D user is selected to act as a relay named D2D-relay instead of the traditional cellular relay. The optimal relay selection strategy is formulated by searching the maximum trust value that is obtained by assessing the link stability and social connections between two users. Then, the resource allocation problem, which turns out to be a mixed-integer nonlinear fractional programming (MINLFP) problem, is solved by maximizing the total EE under physical constraint and social constraint synthetically. To improve the solution efficiency, a novel iterative algorithm is proposed by integrating the Dinkelbach theory and Lagrange dual decomposition method. Simulation results demonstrate the effectiveness of the proposed scheme. Compared with the existing social-blind and social-aware schemes, it significantly improves the probability of successful relay selection and total EE of the D2D pairs.