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Overview of Cyber-Physical Systems and Cybersecurity
Published in Chong Li, Meikang Qiu, Reinforcement Learning for Cyber-Physical Systems, 2019
Another example of resource allocation for industrial cyber-physical IoT systems based on 5G technologies is presented in [87]. A framework that multiple sensors and actuators establish communication links with a central controller in full-duplex mode with low bandwidth requirement is considered. In [87], the authors segregated the non-convex optimization problem with the objective to maximize the sum energy efficiency of the system into two sub-problems: power allocation and channel allocation. Various techniques are employed to tackle these subproblems, including Dinkelbach’s algorithm, the Hungarian algorithm, and game-theoretic methods. Dinkelbach’s algorithm is a method for solving convex fractional programming [37]. The Hungarian algorithm is a polynomial algorithm for solving the linear assignment problem [72].
Design and Simulation of New Beamforming
Published in Mohammed Usman, Mohd Wajid, Mohd Dilshad Ansari, Enabling Technologies for Next Generation Wireless Communications, 2020
Tanzeela Ashraf, Javaid A. Sheikh, Sadaf Ajaz Khan, Mehboob-ul-Amin
F1 being a problem of Fractional Programming (FP) has a fractional nonconcave function and constraints that are nonlinear, making it tricky to uncover the most favorable solution. Therefore, F1 is transformed in a diminution problem, which is defined as:
Application of fuzzy random-based multi-objective linear fractional programming to inventory management problem
Published in Systems Science & Control Engineering, 2022
Hamiden Abd El-Wahed Khalifa, Pavan Kumar, Sultan S. Alodhaibi
Fractional programming, i.e. the optimization of a fraction of two functions subject to some prescribed conditions, plays important role in modelling and optimization in the field of management, engineering, finance, economics and science. Recently, huge developments have taken place in this area. Charnes and Cooper (1962) proposed the programming with linear fractional functions, termed as fractional programming problem (FPP). Normally, FPP is a decision making model that aims to optimize the ratio subject to some constraints. In real-life situations, the decision maker (DM) sometimes may face to compute the ratio between stock of goods and sales, output and employee etc., with both denominator and numerator are linear. When one ratio is considered as an objective function under linear constraints, the problem is referred as linear FPP. As per applications scenario, FPP is used in the fields of traffic planning (Dantzig et al., 1966), and many more. In the meantime, some applications of FPP and the algorithms to solve this kind of problems were presented by Dinkelbach (1967). Luhandjula (1984) developed some fuzzy approaches to solve the multi-objective linear FPP. Sakawa and Yano (1988) proposed an approach for multi-objective linear FPPs. Guzel (2013) suggested a proposal for solving a multi-objective linear FPP.
Energy-efficient power allocation scheme for distributed MISO system with transmit correlation
Published in International Journal of Electronics, 2018
Benben Wen, Xiangbin Yu, Ying Wang, Xiaoyu Dang
According to these analyses in the preceding paragraphs, the EE optimization in DAS has been studied well over spatially-independent channels; but, only single antenna is considered in each RAU for analysis convenience. Hence, the presented PA algorithms lack of generality and the corresponding EE performance will be also limited. Besides, spatial correlation is not considered, whereas the antennas in a RAU may be correlated due to insufficient spacing. However, the EE optimization in distributed MISO system over spatially-correlated channels is addressed much less. Considering these reasons, composite channels including shadowing fading, path loss and spatially-correlated small-scale Rayleigh fading are presented for distributed MISO system, where each RAU employs multiple transmit antennas. By maximizing the EE subject to the maximum transmit power constraint of each RAU, the optimal PA scheme is developed, and then the energy-efficient PA problem can be formulated as nonlinear fractional programming problem. For this, fractional programming theory is first used to convert the nonconvex optimization problem in fractional form to an equivalent convex problem in subtractive form, and an iterative algorithm based on Dinkelbach method is presented for calculating the optimal PA coefficients iteratively. To reduce the complexity of the iterative algorithm from the optimal scheme, a simplified PA scheme and the corresponding algorithm are proposed by choosing the best antenna of each RAU and determining optimal number of active RAUs employed for transmitting signals, this simplified scheme can provide a closed-form PA. Moreover, the two proposed schemes can be reduced to those under spatially-independent fading channel. Computer simulations indicate that the two proposed schemes can achieve almost the same EE performance, and the simplified scheme has lower complexity than the optimal one because of closed-form PA calculation.
Parametric approach for multi-objective enhanced interval linear fractional programming problem
Published in Engineering Optimization, 2023
Mridul Patel, Jyotirmayee Behera, Pankaj Kumar
The fractional programming problem is also known as the ratio programming problem (Sivri, Albayrak, and Temelcan 2018), in which objective functions are in the ratio of two functions. The fractional programming problem has extensive applications in production planning, financial problems, health care, hospital planning, traffic planning, etc. There are many real-world problems in which more than one ratio of conflicting objectives are optimized simultaneously. In order to deal with such a case, a multi-objective linear fractional programming problem () is used. Several approaches — see Isbell and Marlow (1956), Charnes and Cooper (1962) and Stancu-Minasian (2012) — have been suggested in preceding studies for solving linear fractional programming problems. Tantawy (2008) has described an iterative method for solving linear fractional programming problems for sensitivity analysis when a scalar parameter is introduced in the objective function coefficients. A detailed overview of fractional programming is done by Schaible (2002). In the earlier days of fractional programming modelling, the model's parameters were considered a fixed quantity. But in reality, such parameters cannot be estimated precisely in real situations owing to uncertainty in the environment. Therefore, the concept of randomness or fuzziness is used to estimate the uncertainty involved parameters of fractional programming by many researchers — see Stanojevic, Dzitac, and Dzitac (2020) and Khalifa and Kumar (2022). A parameter's distribution function or membership function is assumed in advance to estimate it in these studies. Estimation of the parameters in the form of a closed interval is also one of the ways to represent the uncertainty involved in the problem (Moore 1966), which avoids the earlier assumptions about the distribution function or membership function. Programming problems are designed and analysed using the interval optimization method in this scenario.