# A Cyclical Non-Linear Inertia-Weighted Teaching-Learning-Based Optimization Algorithm
## 1 Introduction  
As is well known, the research and application of swarm intelligence optimization mostly focus on nature-inspired algorithms. In the past decades, many classical nature-inspired optimization algorithms based on population have been proposed. These algorithms have been proven effective in solving global optimization problems and specific types of engineering optimization problems, such as GA (genetic algorithm) [1; 2], ACO (ant colony optimization) [3; 4], PSO (particle swarm optimization) [5; 6], ABC (artificial bee colony) [7; 8; 9] and DE (differential evolution) [10; 11; 12], etc. However, any algorithm has its own merits and demerits in solving diverse problems. In order to solve the demerits, such as easily being trapped into a local optimum and slow convergence, numerous improved algorithms for various swarm intelligence algorithms are presented, including the variants of various algorithms or their hybrid algorithms. In general, the quality of an optimization algorithm depends on three basic factors, i.e., the ability obtaining the true global optima value, the fast convergence speed and a minimum of control parameters. Therefore, our ultimate aim in the practical optimization applications is that the optimization algorithms should have higher calculation accuracy, faster convergence speed and a minimum of control parameters for ease of use in program. The teaching-learning-based optimization (TLBO) algorithm is a swarm intelligence algorithm, which simulates the phenomenon of teaching and learning in a class. A few years ago, the TLBO algorithm was first proposed by [PERSON] et al. [13; 14]. The TLBO is a parameter-less algorithm [15] requiring only the common control parameters, such as population size and numbers of generation, and does not need any other specific control parameters. Therefore, there is no burden of tuningcontrol parameters in the TLBO algorithm. So, the TLBO algorithm is simpler, more effective, and its computational cost is relatively less. Because the TLBO algorithm has the ability to achieve better results at faster convergence speed than other algorithms mentioned above, it has been successfully applied in many diverse optimization fields [16; 17; 18; 19; 20]. Of course, TLBO also has some disadvantages too. Although TLBO has high search accuracy and fast convergence speed, but it has poor exploiting ability and is easy to fall into the local optimum and appeared premature convergence in multimodal function. Therefore, many improved algorithms for TLBO have been presented so far. To improve the performance of TLBO, some variants of the TLBO have been presented. [PERSON] et al. proposed an ETLBO (elitist TLBO) algorithm [15] for solving complex constrained optimization problems, and applied a modified TLBO algorithm [17] to the multi-objective optimization problem. Aiming at neural network training in portable AI (artificial intelligence) devices, [PERSON] et al. [21] proposed the CTLBO (compact teaching-learning-based optimization) algorithm to solve global continuous problems, which can reduce the memory requirement while maintaining the high performance. [PERSON] et al. [22] presented an improved TLBO algorithm. In order to balance the diversity and convergence, an efficient subpopulation was employed in the teacher phase and a ranking differential vector was used in the learner phase. To improve the convergence solution, the neighbor learning and differential mutation is introduced into the basic TLBO by [PERSON] et al. [23]. Combining TLBO and ABC, [PERSON] et al. [24] propose a new hybrid teaching-learning-based artificial bee colony (TLABC) to solve the parameters estimation problems of solar photovoltaic. Furthermore, some other improved TLBO algorithms [25; 26; 27; 28] have been presented for solving the global function optimization problem. We have even proposed a non-linear inertia weighted teaching-learning-based optimization algorithm (NIWTLBO) [29], which has a fast convergence rate and high accuracy. However, its exploiting ability is weaker.