On the Optimality and Duality in Nonsmooth Multiobjective Fractional Optimization Problems via Higher-Order E-Convexity

This paper presents optimality criteria for fuzzy-valued fractional multi-objective optimization problem. There are numerous optimality criteria which have been established for the deterministic fractional multi-objective optimization problems. Very few studies are available on the establishment of optimality criteria for fuzzy-valued multi-objective optimization problem. So, Karush–Kuhn–Tucker optimality criteria for fuzzy-valued fractional multi-objective problem are established by using Lagrange multipliers. First, the original problem is modified using the parametric approach of Dinkelbach into multi-objective non-fractional optimization problem, and then, the optimality conditions are established for the modified problem using the Hukuhara derivative. The established optimality criteria are verified by two numerical examples.

A fuzzy based branch and bound approach for multi-objective linear fractional (MOLF) optimization problems

Most existing optimization objectives considered in non-orthogonal multiple access (NOMA) power allocation schemes are non-delay-sensitive metrics. In order to apply NOMA to various Internet of Things scenarios, the delay must be considered. The effective capacity of users, which characterizes the capacity under specific expiration probabilities, can potentially be a performance metric of statistical delay quality of service (QoS). In this paper, we propose two novel dynamic power allocation schemes with statistical delay QoS guarantee in the uplink NOMA system with paired users. One of the schemes maximizes the sum effective capacity (SEC) of the strong and weak users, which is a non-convex nonlinear optimization problem and is solved by Lagrangian dual decomposition and successive convex approximation (SCA). The other one maximizes the effective energy efficiency (EEE) of uplink NOMA, which is a fractional optimization problem and is solved by integrating the Dinkelbach method, SCA, and Lagrangian dual decomposition. Numerical results show that the SEC and EEE can be significantly improved by the proposed schemes, compared to the existing NOMA and orthogonal multiple access power allocation schemes.

In this paper, the secure energy-efficient transmission problem for an artificial-noise (AN)-aided simultaneous wireless information and power transfer (SWIPT) and vehicle-to-infrastructure (V2I) communication system with the imperfect channel state information (CSI) is studied. The secure energy efficiency problem is formulated with the imperfect CSI, where the constraints contain the minimum secrecy rate request of the legitimate vehicle (LV), the minimum energy harvesting (EH) request, the maximum transmit power, and the power splitting (PS) value. By exploiting the maximum ratio transmission (MRT) scheme and the norm-bounded matrix theory, we convert the original intractable problem to a fractional optimization one with three variables. Then, a two-level optimization algorithm is presented for the nonconvex fractional optimization problem. By introducing an auxiliary slack variable, the first level problem can be solved via one-dimensional optimization algorithm. The second level fractional optimization problem was furhther converted into an integer optimization one by the Dinkelbach method, and the closed-form solutions of the transmit power and the AN power are provided. Simulation results are given to verify the performance of our presented algorithm.

Sequential efficiency optimality conditions for Robust multiobjective fractional optimization problems

This paper presents two new theorems on Geoffrion's properly efficient solutions and seven examples illustrating their applications to linear fractional vector optimization problems with unbounded constraint sets. Provided that all the components of the objective function are properly fractional, the first theorem gives sufficient conditions for the efficient solution set to coincide with the Geoffrion properly efficient solution set. Admitting that the objective function can have some affine components, in the second theorem we give sufficient conditions for an efficient solution to be a Geoffrion's properly efficient solution. The recession cone of the constraint set, the derivatives of the scalar objective functions, but no tangent cone to the constraint set at the efficient point, are used in the second theorem.

This paper aims at optimizing the downlink system energy efficiency of time division duplex (TDD) small cell networks with wireless backhaul constraints. The consistency of the wireless backhaul link and access link is taken into consideration. The system energy efficiency maximization problem is formulated as a fractional mixed integer optimization problem which is NP-hard and needs the jointly optimization of transmission power, scheduling and time slots selection. A suboptimal scheme named as energy efficient slot selection (EESS) is proposed to improve the system energy efficiency in a non-decreasing manner. Simulation results indicate that EESS can efficiently improve the system energy efficiency.

This paper investigates the optimal energy-efficient transmission policy of multi-channels in energy harvesting systems. We configure the transmitter with the active mode in which the energy cost includes the basic operation cost and transmission cost and signal processing cost, while with the sleep mode only counting the basic operation cost. Then the energy efficiency maximization problem of joint transmission time and power allocation is formulated and studied in the offline manner. Based on the fractional optimization theory, we transform the original fractional optimization problem into a series of subtractive-form optimization problems which are then further transformed into convex optimization problems. Then characteristics of the optimal solution are described based on the analysis of transmission time and power allocation. Finally, a special case without considering the basic operation cost as previous works assumed is studied. We find that the optimal policy results a best subchannel scheduling which can be viewed as the peaky transmission. Through this, the energy cost of the sleep mode in previous case can be interpreted as the switching operation cost.

Resource optimization is investigated for an unmanned aerial vehicle (UAV)-mounted relay assisted Internet-of-Things (U-IoT) network. A comprehensive network structure is proposed by incorporating laser-driven adaptive wireless-power-transfer at the UAV relay, wirelessly powered backscatter communication in the radio-frequency access links, and modulating retro-reflector based free space optical backhaul link in an optimization framework. Our objective is to maximize the number of the connected IoT devices with the UAV relay for uplink data transmission while satisfying the heterogeneous quality-of-service requirements of the IoT devices. Towards this objective, a novel optimization problem is formulated by considering queueing-overflow probability constraints of the IoT devices with stochastic data arrival, backhaul capacity constraint, and energy causality constraint at the UAV relay. The considered resource optimization is NP-hard, and an iterative solution is proposed by exploiting structure of the optimization problem. Furthermore, a three-stage optimization is devised to solve an NP-complete fractional optimization problem at each iteration of the proposed solution. An algorithm of polynomial computational complexity is developed for joint connectivity maximization and resource allocation, and convergence of the developed algorithm is proved. Using extensive simulations, efficiency of the proposed algorithm is demonstrated for improving the supportable arrival rate per IoT device and the number of the connected IoT devices in uplink of a U-IoT network.

Here, we propose a new variable neighbourhood search (VNS) algorithm for solving fractional fuzzy number linear programming problems (FFNLPPs). We make use of modified Kerre’s inequality for comparison of LR fuzzy numbers. In our proposed algorithm, we introduced a new local search defined based on descent directions, which are found by solving four crisp mathematical programming problems. In several methods, a fuzzy fractional optimization problem is converted to a crisp problem. Still, in our proposed method, using modified Kerre’s inequality, the fuzzy optimization problem is solved directly, without changing it to a crisp program. To show the effectiveness of our method, we compare our proposed algorithm with other available methods.

In this paper, we study secrecy and energy-efficiency optimization in a distributed antenna system (DAS)-based IoT network with energy harvesting nodes. Considering simultaneous wireless information and power transfer (SWIPT), we define secure energy efficiency (SEE) as ratio of the achievable secrecy rate to the total consumed power. Our goal is to maximize SEE subject to maximum transmit power constraint of distributed antenna (DA) ports and minimum energy-harvesting requirement of the IoT devices. For a single IoT device and single eavesdropper, maximizing SEE is formulated as a constrained fractional optimization problem, and the optimal solution is derived by solving Karush–Kuhn–Tucker (KKT) conditions. We also consider the case of an energy-harvesting eavesdropper and attempt to restrain it from harvesting the energy from the radio signal. This is achieved by introducing one more constraint into the optimization problem corresponding to the energy harvesting requirement of the eavesdropper. Further, we also consider a general case of multiple IoT devices and multiple eavesdroppers in an N-port DAS.KeywordsWireless power transferDistributed antenna systemPhysical layer securityWireless energy harvesting

To step beyond the first-generation deployments of attacker-defender security games -- for LAX Police, US FAMS and others -- it is critical that we relax the assumption of perfect rationality of the human adversary. Indeed, this assumption is a well-accepted limitation of classical game theory and modeling human adversaries' bounded rationality is critical. To this end, quantal response (QR) has provided very promising results to model human bounded rationality. However, in computing optimal defender strategies in real-world security games against a QR model of attackers, we face difficulties including (1) solving a nonlinear non-convex optimization problem efficiently for massive real-world security games; and (2) addressing constraints on assigning security resources, which adds to the complexity of computing the optimal defender strategy. This paper presents two new algorithms to address these difficulties: Gosaq can compute the globally optimal defender strategy against a QR model of attackers when there are no resource constraints and gives an efficient heuristic otherwise; Pasaq in turn provides an efficient approximation of the optimal defender strategy with or without resource constraints. These two novel algorithms are based on three key ideas: (i) use of a binary search method to solve the fractional optimization problem efficiently, (ii) construction of a convex optimization problem through a non-linear transformation, (iii) building a piecewise linear approximation of the non-linear terms in the problem. Additional contributions of this paper include proofs of approximation bounds, detailed experimental results showing the advantages of Gosaq and Pasaq in solution quality over the benchmark algorithm (Brqr) and the efficiency of Pasaq. Given these results, Pasaq is at the heart of the PROTECT system, which is deployed for the US Coast Guard in the port of Boston, and is now headed to other ports.

<p>Device-to-device (D2D) communication can effectively use cognitive radio network approach to coexist with cellular users. For such a cognitive D2D system, two approaches (underlay and overlay) are considered to manage the spectrum sharing among the cellular (primary) users and the D2D (secondary) users. Energy efficiency (EE) is crucial in both these cases due to limited battery capacity and quality of service requirements of the D2D users. This study effectively models the power allocation problem of such a cognitive D2D system by maximising the EE of the D2D users subject to a minimum rate requirement for both the D2D users and the cellular users. This leads to a non-linear fractional optimisation problem which is more complicated and computationally intractable. Alternatively, geometric water-filling approach have been utilised for power allocation to solve this optimisation problem which results in an ‘exact’ and ‘low complexity’ solution. Simulation results reveal the benefits of the proposed algorithm.</p> <p><br></p>

This paper investigates the resource allocation issue between downlink training stage and data transmission stage for the frequency division duplexing (FDD) massive multiple-input multiple-output system from the viewpoint of energy efficiency (EE). For a given total energy budget during a coherence period, how to jointly select the training duration, training power and data power is of great significance for the system EE. Thus, an optimization problem of energy-efficient resource allocation is put forward. Since the analytical expression of the involved average spectral efficiency (SE) is intractable, a closed-form approximation of the SE is deduced using deterministic equivalent. Based on the simplified expression, the original non-convex fractional optimization problem is transformed into an equivalent problem in subtractive form by the means of fraction programming, which includes an achievable solution. Then, an iterative algorithm is proposed. Numerical results validates the benefits of the proposed resource allocation scheme.

This article addresses a special class of non-linear programming problems, viz., linear fractional programming problems having multiple objectives. In solving the real-life linear fractional optimization problems, the ambiguity and hesitation in the decision are inherent and ever-present, therefore, it is perfectly viable to formulate and solve these optimization models using the intuitionistic fuzzy environment. The purpose of this study is to propose a simple and computationally efficient approach to obtain the solution of multiple objective linear fractional programming problems having all the decision variables and parameters expressed in terms of triangular intuitionistic fuzzy numbers. The proposed solution algorithm is primarily based on the goal programming approach, fuzzy-based linearization technique, and a membership function strategy. The original linear fractional programming problem is first converted to its equivalent deterministic/crisp multi-objective linear fractional optimization problem using the weighted goal programming methodology along with the linear membership technique to resolve the intuitionistic fuzzy constraints into the crisp one. Finally, the variable transformation technique for the under- and over-deviational variables of the goal programming model is employed to linearize all the fractions involved in the problem so as to convert the original problem to an equivalent linear optimization problem. Further, this linear programming problem can be solved using any available commercial packages. Moreover, a numerical illustration is provided to demonstrate the steps of the proposed technique followed by the analysis and solution of an E-education set-up problem. The discussion and comparisons of the practical case establish the relevancy and usefulness of the proposed model.