Geometric Programming Technique Research Articles

A GEOMETRIC PROGRAMMING APPROACH TO CONVEX MULTI-OBJECTIVE PROGRAMMING PROBLEMS

Over the past few years, convex optimization has played a vital role in the study of complex engineering problems in different fields. Geometric programming is one of the available techniques particularly used for solving nonconvex programming problems. But in this article, a suitable attempt has been made to solve a real-life model on convex multi-objective using geometric programming technique with help of the E-constraint method and result is compared with the solutions obtained by fuzzy technique. Finally, a conclusion is presented by analyzing the solutions to a numerical problem.

AoI Minimization for WSN Data Collection With Periodic Updating Scheme

In this paper, we consider the design of a wireless sensor network (WSN) that aims at monitoring the environment and collecting data periodically. In view of the limited energy and computational capability of the sensor nodes, a mobile edge computing (MEC) server is deployed in the WSN as a data processing unit. The goal of the design is to maintain the freshness of the data, which is characterized by the criterion of the age of information (AoI). Therefore, we analyze the long-term average AoI of the considered network. Then, the energy and time constraints for the WSN are modeled with consideration of transmission and computation. Next, a non-convex average AoI minimization problem is formulated subject to the energy and time constraints by jointly optimizing the sampling rate, computing scheduling, and transmit power. To tackle the challenging problem, the geometric programming and successive convex approximation (SCA) technique are applied to develop an algorithm with convergence guarantee. Moreover, to exhibit the benefits of the MEC server, a joint design is investigated for the WSN without the MEC server. Finally, the numerical results demonstrate the efficiency of our proposed SCA-based algorithm and show the impact of the sampling rate on the AoI performance.

Solving geometric programming problems with triangular and trapezoidal uncertainty distributions

The geometric programming problem is an important optimization technique that is often used to solve different nonlinear optimization problems and engineering problems. The geometric programming models that are commonly used are generally based on deterministic and accurate parameters. However, it is observed that in real-world geometric programming problems, the parameters are frequently inaccurate and ambiguous. In this paper, we consider chance-constrained geometric programming problems with uncertain coefficients and with geometric programming techniques in the uncertain-based framework. We show that the associated chance-constrained uncertain geometric programming problem can be converted into a crisp geometric programming problem by using triangular and trapezoidal uncertainty distributions for the uncertain variables. The main aim of this paper is to provide the solution procedures for geometric programming problems under triangular and trapezoidal uncertainty distributions. To show how well the procedures and algorithms work, two numerical examples and an application in the inventory model are given.

IRS-Aided SWIPT: Joint Waveform, Active and Passive Beamforming Design Under Nonlinear Harvester Model

The performance of Simultaneous Wireless Information and Power Transfer (SWIPT) is mainly constrained by the received Radio-Frequency (RF) signal strength. To tackle this problem, we introduce an Intelligent Reflecting Surface (IRS) to compensate the propagation loss and boost the transmission efficiency. This paper proposes a novel IRS-aided SWIPT system where a multi-carrier multi-antenna Access Point (AP) transmits information and power simultaneously, with the assist of an IRS, to a single-antenna User Equipment (UE) employing practical receiving schemes. Considering harvester nonlinearity, we characterize the achievable Rate-Energy (R-E) region through a joint optimization of waveform, active and passive beamforming based on the Channel State Information at the Transmitter (CSIT). This problem is solved by the Block Coordinate Descent (BCD) method, where we obtain the active precoder in closed form, the passive beamforming by the Successive Convex Approximation (SCA) approach, and the waveform amplitude by the Geometric Programming (GP) technique. To facilitate practical implementation, we also propose a low-complexity design based on closed-form adaptive waveform schemes. Simulation results demonstrate the proposed algorithms bring considerable R-E gains with robustness to CSIT inaccuracy and finite IRS states, and emphasize the importance of modeling harvester nonlinearity in the IRS-aided SWIPT design.

Baseline Design for Multibaseline InSAR System: A Review

Multibaseline (MB) synthetic aperture radar (SAR) interferometry (InSAR) is an exciting and growing remote sensing technique, which can improve the traditional InSAR from the ill-posed problem to the well-posed problem. Baseline lengths play an important role in the MB InSAR system design. It is fair to say that the baseline lengths of the MB InSAR system directly determine the quality of the MB InSAR products. In this article, we present an overview of the established MB baseline design criteria and requirements for the MB InSAR digital elevation model (DEM) generation, which includes the effect of the baseline lengths and their estimation errors on ambiguity height, DEM accuracy, decorrelation, and MB phase unwrapping robustness. In addition, we prospectively apply the geometric programming technique to combine those effects together for obtaining the global optimal baseline lengths of the MB InSAR system. It is our hope that this review will provide guidelines to future researchers to enhance further the new airborne and spaceborne MB InSAR system developments.

Multi Objective Geometric Programming with Interval Coefficients: A Parametric Approach

When we talk of optimization in industry we need to pay attention in searching for very powerful and flexible optimization techniques. One of such techniques which has attracted the interest of many researchers in the last few decades is called geometric programming that provides a powerful tool for solving nonlinear problems. As we know in the real world, many applications of geometric programming are engineering design problems. Generally, engineering design problems deal with multi-objective functions, in which their objectives are often in conflicts with each other. This paper considers a solution method when the cost, the constraint coefficients, and the right-hand sides in the multi-objective geometric programming problems are imprecise and represented as interval values. This problem is reduced with the method of weighted sum to a single objective function and further by applying interval-valued function, we solve the problem by geometric programming technique. The ability of calculating the bounds of the objective value developed in this paper might help lead to more realistic modeling efforts in engineering optimization areas. Finally a numerical example is given to illustrate the methodology of solution and efficiency of the present approach.

Effects of Pilot Contamination Attacks in Multi-Cell Multi-User Massive MIMO Relay Networks

The detrimental effects of pilot contamination attacks by active eavesdroppers are investigated for multi-cell multi-user massive multiple-input multiple-output (MIMO) relay networks. To this end, secure transmission strategies are designed for both users-to-relay and relay-to-destination channels in the presence of active pilot attacks with imperfect legitimate user channel state information (CSI) and with no eavesdropper CSI knowledge at the relay. The excess degrees-of-freedom offered by the massive MIMO relay are exploited to mitigate detrimental effects of cooperative jamming (CJ) signals and to generate artificial noise (AN) during the first and second time-slots, respectively. Thereby, the achievable secrecy rate lower bounds for active attacks are derived in the finite/infinite relay antenna regimes. The secrecy rates for passive eavesdropping are deduced and compared to that of active attacks. A joint optimal power allocation scheme for the pilot, payload data, and AN and CJ signals is formulated and solved by using geometric programming techniques. Rigorous numerical and simulation results are provided to obtain valuable insights, which are useful in designing secure physical layer transmission strategies for multi-cell multi-user massive MIMO relay networks.

Geometric programming technique to optimize power distribution system

Geometric programming is an important tool for solving certain optimization problems. In this paper, multi objective geometric programming with $$\epsilon $$ -constraint method is used to find the maximum radius of a circular power supply substation to supply power in a particular region. The main aim of the proposed method is to formulate a mathematical model for the efficient distribution of the power supply to maximum area from a circular substation with least investment and minimum waste. The proposed multi-objective optimization model has been solved to generate Pareto optimal solutions using weighted sum method. The results so obtained have been compared with that of $$\epsilon $$ -constraint method by considering suitable numerical examples.

Joint power allocation and subcarrier assignment for device to device in 5G time division duplex networks

The explosive demands for mobile broadband service bring a major challenge to 5G wireless networks. Device-to-device communication, adopting side links for user-direct communication, is regarded as a main technical source for offloading large volume of mobile traffic from cellular base station. This article investigates the joint power and subcarrier allocation scheme for device-to-device communication in 5G time division duplex systems. In time division duplex system, instead of utilizing an exclusive portion of the precious cellular spectrum, device-to-device pairs reuse the subcarriers occupied by cellular users, thus producing harmful interference to cellular users in both uplink and downlink communication, and strongly limiting the spectrum efficiency of the system. To this end, we focus on the maximization of device-to-device throughput while guaranteeing both uplink and downlink channel quality of service of cellular users as well as device-to-device pairs. The problem is formulated as a mixed integer non-linear programming (MINLP) problem. To make it tractable, we separate the original MINLP problem into two sub problems: power allocation and sub-carrier reusing. The former is to develop optimal power allocation for each device-to-device pair and each cellular user, with the constraints of maximum power and quality of service. It is solved by geometric programming technique in convex optimization method. The latter is derived as a one-to-many matching problem for scheduling multiple subcarriers occupied by cellulars to device-to-device pairs. It is solved by Hungarian method. Simulation results show that the proposed scheme significantly improves system capacity of the device-to-device underlay network, with quality of service of both device-to-device users and cellular users guaranteed.

Performance Analysis and Power Control for Multi-Antenna V2V Underlay Massive MIMO

Device-to-device (D2D) communication has been considered a promising solution for vehicle-to-vehicle (V2V) communication. In V2V underlay massive MIMO cellular networks, V2V has the potential to increase spectral efficiency (SE) by reusing cellular spectrum. However, the interference between cellular and V2V transmissions may be serious if not designed properly. In this paper, we first derive the analytical lower bounds on multi-antenna V2V and cellular SEs under both perfect and imperfect channel state information for maximum-ratio combining and zero-forcing detection. Using these lower bounds, performance analysis is given to provide more insights and guide practice. Then, we formulate a large-scale fading-based power control problem to guarantee the SE constraints of V2V pairs while maximizing the sum SE of cellular users. Moreover, the geometric programming technique is applied to solve the optimal power control problem. Numerical results show that the proposed SE-constrained power control scheme can greatly increase the reliability and achievable SE of V2V communications while the achievable sum SE is slightly degraded, compared with the fixed maximum power scheme.

Neutrosophic Goal Geometric Programming Problem based on Geometric Mean Method and its Application

This paper describes neutrosophic goal geometric programming method, a new concept to solve multi-objective non-linear optimization problem under uncertainty. The proposed method is described here as an extension of fuzzy and intuitionistic fuzzy goal geometric programming technique in which the degree of acceptance , degree of indeterminacy and degree of rejection is simultaneously considered.

Neutrosophic Goal Geometric Programming Problem and Its Application to Multi-objective Reliability Optimization Model

This paper presents the goal geometric programming method in neutrosophic environment. Neutrosophic set is one of the most useful tools to express uncertainty, impreciseness in a more general way compare to fuzzy set and intuitionistic fuzzy set. Thus, the proposed approach is described here as an extension of fuzzy goal geometric programming and intuitionistic fuzzy goal geometric programming. To demonstrate the methodology and applicability of the proposed approach, a multi-objective nonlinear reliability optimization model is taken here and it is evaluated comparing the result obtained by the proposed method with the solution obtained in intuitionistic fuzzy goal geometric programming technique at the end of this paper.

Fuzzy E.O.Q model with constant demand and shortages: A fuzzy signomial geometric programming (FSGP) approach

In this paper, a fuzzy economic order quantity (E.O.Q) model with shortages under fully backlogging and constant demand is formulated and solved. Here the model is solved by fuzzy signomial geometric programming (FSGP) technique. Fuzzy signomial geometric programming (FSGP) technique provides a powerful technique for solving many non-linear problems. Here we have proposed a new idea that is fuzzy modified signomial geometric programming (FMSGP) and some necessary theorems have been derived. Finally, these are illustrated by some numerical examples and applications.

A fuzzy inventory model with unit production cost, time depended holding cost, with-out shortages under a space constraint: a parametric geometric programming approach

In this paper, an Inventory model with unit production cost, time depended holding cost, with-out shortages is formulated and solved. We have considered a single objective structural optimization model. In most real world situation, the objective and constraint function of the decision makers are imprecise in nature. Hence the coefficients, indices, the objective function and constraint goals are imposed here in fuzzy environment. Geometric programming provides a powerful tool for solving a variety of imprecise optimization problems. Here we use nearest interval approximation method to convert a triangular fuzzy number to an interval number. In this paper, we transform this interval number to a parametric interval-valued functional form and then solve the parametric problem by geometric programming technique. Numerical example is given to illustrate the model through this Parametric Geometric-Programming method.

A fuzzy inventory model with unit production cost, time depended holding cost, with-out shortages under a space constraint: a parametric geometric programming approach

In this paper, an Inventory model with unit production cost, time depended holding cost, with-out shortages is formulated and solved. We have considered here a single objective inventory model. In most real world situation, the objective and constraint function of the decision makers are imprecise in nature, hence the coefficients, indices, the objective function and constraint goals are imposed here in fuzzy environment. Geometric programming provides a powerful tool for solving a variety of impreciseoptimization problem. Here we have used nearest interval approximation method to convert a triangular fuzzy number to an interval number then transform this interval number to a parametric interval-valued functional form and solve the parametric problem by geometric programming technique. Here two necessary theorems have been derived. Numerical example is given to illustrate the model through this Parametric Geometric-Programming method.

A Fuzzy E.O.Q Model With Unit Production Cost, Time Depended Holding Cost, With-Out Shortages Under A Space Constraint: A Fuzzy Geometric Programing (FGP) Approach

In this paper, an Economic Order quantity (E.O.Q) model with unit production cost, time depended holding cost, with-out shortages is formulated and solved. In most real world situation, the objective and constraint function of the decision makers are uncertainty in nature so the coefficients, indices the objective function and constraint goals are imposed here in fuzzy environment The problem is then solved using both Fuzzy Max-Min Geometric-Programming technique and Fuzzy parametric Geometric-Programming. Sensitivity analysis is also presented here.

A Geometric Programming Solution for the Mutual-Interference Model in HetNets

It is well known that the use of heterogeneous networks and densification strategies will be crucial to handle the wireless cellular traffic increase that is foreseen in the forthcoming years. Hence, the scientific community is putting effort into the proposal and assessment of radio resource management solutions for this type of deployments. For that, an accurate modeling of the underlying resources is mandatory. In this letter, we propose a mutual-interference model, which enables a precise estimation of the signal-to-interference and noise ratio (SINR), compared with the widespread constant-load alternative. This is of utter relevance, since the SINR has a direct influence on the spectral efficiency and, consequently, on the resources to be allocated. We also propose a transformation of the corresponding resource assignment problem, so that it can be solved using geometric programming techniques. The validity of this transformation is assessed by comparing the corresponding solution with the one that would have been obtained exploiting a heuristic approach (simulated annealing).

Optimization of Industrial Wastewater Treatment Using Intuitionistic Fuzzy Goal Geometric Programming Problem

This paper describes a design of industrial wastewater treatment plant, operating on pulp and paper manufacturing waste. The main objective is to formulate cost effective biological treatment process on industrial wastewater. In terms of the percent of five-day bio-chemical oxygen demand removed, the required final effluent quality has been maximized. Also, the cost involved has been minimized in five-day bio-chemical oxygen demand removal. To optimize remaining five-day bio-chemical oxygen demand in wastewater spending minimum money, a goal geometric programming is used here. Moreover, goal geometric programming is described incorporating imprecision in it. A model of intuitionistic fuzzy goal geometric programming problem is given in this paper. We have solved intuitionistic fuzzy goal programming model using geometric programming technique. The algorithm of the approach is discussed in this paper. It is also shown that the usefulness of intuitive fuzzy environment in goal geometric programming is compared to fuzzy goal geometric programming using a numerical example.

English

English

Optimization of Structural Design by Fuzzy Geometric Programming Technique

Optimization of Structural Design by Fuzzy Geometric Programming Technique