Global convergence analysis of the bat algorithm using a markovian framework and dynamical system theory

The bat algorithm (BA) has been shown to be effective to solve a wider range of optimization problems. However, there is not much theoretical analysis concerning its convergence and stability. In order to prove the convergence of the bat algorithm, we have built a Markov model for the algorithm and proved that the state sequence of the bat population forms a finite homogeneous Markov chain, satisfying the global convergence criteria. Then, we prove that the bat algorithm can have global convergence. In addition, in order to enhance the convergence performance of the algorithm and to identify the possible effect of parameter settings on convergence, we have designed an updated model in terms of a dynamic matrix. Subsequently, we have used the stability theory of discrete-time dynamical systems to obtain the stable parameter ranges for the algorithm. Furthermore, we use some benchmark functions to demonstrate that BA can indeed achieve global optimality efficiently for these functions

Energy Efficient Uplink Transmission in Cooperative mmWave NOMA Networks with Wireless Power Transfer

In 5G wireless networks, cooperative non-orthogonal multiple access (NOMA) and wireless power transfer (WPT) are efficient ways to improve the spectral efficiency (SE) and energy efficiency (EE). In this paper, a new cooperative NOMA scheme with WPT is proposed, where EE optimization with a constrained maximum transmit power and minimum required SE is considered for the user grouping and transmit power allocation of users. We obtain a sub-optimal solution by decoupling the original problem in two sub-problems: an iterative algorithm is considered for the user grouping, while, in addition, we utilize the Bat Algorithm (BA) for solving the power allocation problem, where BA was proved to be able to achieve a higher accuracy and efficiency with respect to other meta-heuristic algorithms. Furthermore, to validate the performance of the proposed system, analytical expressions for the energy outage probability and outage probability of users are derived, confirming the effectiveness of the simulation results. It is demonstrated that the proposed cooperative NOMA with WPT offers a considerable improvement in terms of SE and EE of the network compared to other methods. Finally, the effectiveness of BA in solving the EE optimization problem is demonstrated through a high convergence speed by comparing it with other methods