Computational Intelligence and Neuroscience

Volume 2018, Article ID 5671709, 12 pages

https://doi.org/10.1155/2018/5671709

## A Novel Teaching-Learning-Based Optimization with Error Correction and Cauchy Distribution for Path Planning of Unmanned Air Vehicle

College of Mechanical and Equipment Engineering, Hebei University of Engineering, Handan, Hebei 056038, China

Correspondence should be addressed to Zhibo Zhai; moc.mot@obihziahz

Received 9 May 2018; Accepted 25 June 2018; Published 1 August 2018

Academic Editor: David M. Powers

Copyright © 2018 Zhibo Zhai et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Teaching-learning-based optimization (TLBO) algorithm is a novel heuristic method which simulates the teaching-learning phenomenon of a classroom. However, in the later period of evolution of the TLBO algorithm, the lower exploitation ability and the smaller scope of solutions led to the poor results. To address this issue, this paper proposes a novel version of TLBO that is augmented with error correction strategy and Cauchy distribution (ECTLBO) in which Cauchy distribution is utilized to expand the searching space and error correction to avoid detours to achieve more accurate solutions. The experimental results verify that the ECTLBO algorithm has overall better performance than various versions of TLBO and is very competitive with respect to other nine original intelligence optimization algorithms. Finally, the ECTLBO algorithm is also applied to path planning of unmanned aerial vehicle (UAV), and the promising results show the applicability of the ECTLBO algorithm for problem-solving.

#### 1. Introduction

Global optimization is a universal issue to the entire scientific community. It has been applied widely in many different fields such as chemical engineering [1], molecular biology [2], the training of neural networks [3], job shop scheduling [4], and network design [5]. However, in most cases, global optimization problems are nonlinear and nondifferentiable and, hence, gradient-based methods cannot be used. In recent years, a lot of effective optimization algorithms have been developed and used to successfully solve global optimization problems that are nonlinear and nondifferentiable. Typical algorithms include particle swarm optimization (PSO) [6] proposed by Kennedy and Eberhart in 1995 and inspired by swarm behavior of fish schooling and bird flocking, differential evolution (DE) [7] which mimics Darwinian evolution, group search optimizer (GSO) [8] which is inspired by animal searching behaviors, artificial bee colony (ABC) [9] which simulates the foraging behavior of honey bees, water cycle algorithm (WCA) [10] which is based on the observation of water and cycle processes and how rivers and streams flow to the sea in the real world, cuckoo search (CS) [11] which mimics the brooding behavior of some cuckoo species, backtracking search algorithm (BSA) [12] which is developed from the differential evolution algorithm, differential search algorithm (DSA) [13] which is inspired by the migration of superorganisms utilizing the concept of stable motion, and interior search algorithm (ISA) [14] which is inspired by interior design and decoration.

Recently, Rao et al. [15] proposed the teaching-learning-based optimization (TLBO) algorithm inspired by the teaching-learning process in a classroom. The algorithm simulates two fundamental phases of learning consisting of the “Teacher Phase” and the “Learner Phase.” One of the remarkable advantages of the TLBO algorithm is its simple computation. The other important advantage of the TLBO algorithm is that it does not require specific controlling parameters (the crossover and mutation probability, etc.) except for the common controlling parameters (the size of population and the problem dimensional), which makes the TLBO algorithm easy to implement and more quickly convergence speed. Hence, it has been extended to engineering optimization [15], physics-biotechnology optimization [16], multiobjective optimization [17], heat exchanger design [18], dynamic economic emission dispatch [19], and so on.

Although the TLBO algorithm has some advantages, it has some undesirable dynamical properties that degrade its searching ability. One of the most important issues is that there exists the lower exploitation ability and the smaller scope of solutions in the later stages of evolution. Another issue is regarding the ability of the TLBO algorithm to balance exploration and exploitation [20]. Exploration is the ability that the TLBO algorithm develops global solution space, and the exploitation is the ability that the TLBO algorithm searches the approximately optimization solution in local solution space. Overemphasize of exploration process prevents the population converging, while too much emphasis on the exploitation process tends to cause the premature convergence of the population. In practice, the exploration and exploitation processes contradict each other and, in order to achieve good solutions, the two processes should be properly trade-off. To improve the performance of the TLBO, modified or improved algorithms are proposed in recent years, such as an elitist teaching-learning-based optimization (ETLBO) algorithm [21], teaching-learning-based optimization with neighborhood search (NSTLBO) [22], and teaching-learning-based optimization with dynamic group strategy (DGSTLBO) [20].

Although the modified TLBO algorithms have better performance than the TLBO for some classical problems, some important issues are not considered such as there are still the lower exploitation ability and the smaller scope of solutions in the later stages of evolution. To address these issues, this paper proposes a novel version of TLBO that is augmented with error correction and Cauchy distribution (ECTLBO) in which the Cauchy distribution is utilized to expand the searching space and error correction to avoid detours to achieve more accurate solutions.

The rest of this paper is organized as follows. Section 2 first briefly introduces the TLBO algorithm and the details of its implementation. Section 3 presents TLBO with error correction and Cauchy distribution (ECTLBO). Section 4 analyzes the results of ECTLBO and several related optimization algorithms via a comparative study. Section 5 applies ECTLBO algorithm to path planning of unmanned aerial vehicle (UAV). Finally, the work is summarized in Section 6.

#### 2. Teaching-Learning-Based Optimization

The teaching-learning-based optimization algorithm is a nature-inspired algorithm analogous to the teaching-learning process in a class between a teacher and learners. The process of implementing TLBO consists of two phases, “Teacher Phase” and “Learner Phase.” The “Teacher Phase” stands for learning from the teacher while the “Learner Phase” denotes learning through the interaction between learners.

##### 2.1. Teacher Phase

During the Teacher Phase, the updating formula of the learning for a learner (*i* = 1, 2, *N*, where *N* is the number of learners), is a vector of a learner which includes *x*_{ij} consisting of various subjects such as literature, mathematics, and English (*j* = 1, 2, *D*, *X*_{i} (*x*_{i1}, *x*_{i2},, *x*_{iD}, where *D* is the number of subjects which a learner studied)), iswhere is a newly generated individual according to , is the best individual of current population, is the current mean value of all individuals, *r* is a vector whose elements are distributed randomly in [0, 1], and is a teaching factor deciding the value of the to be changed. The value of is either 1 or 2, indicating the learner learns something or nothing, respectively, from the teacher. The value of is decided randomly with equal probability:

##### 2.2. Learner Phase

During the Learner Phase, each learner interacts with other learners to improve his or her knowledge. A learner *X*_{i} learns something new if the other learner *X*_{j} has more knowledge than him or her. *f*(*X*_{i}) is the summary of all the scores of subjects for the *i*th learner, and the updating formula of the learning for a learner *X*_{i} is

#### 3. A Novel Teaching-Learning-Based Optimization

In this study, a novel version of TLBO that is augmented with an error correction strategy and Cauchy distribution (ECTLBO) is proposed.

##### 3.1. Error Correction Strategy

Some learners who have a bad result because of the bad study method should be guided correctly. Because the study method of some learners toward the teacher is wrong, this time if this is not corrected in time, there will be a detour phenomenon. The study method has problems even wrong, and this leads to opposite. Although each learner spends a lot of efforts, the effect is not too obvious. So, it must have correction function to avoid detours to achieve faster convergence speed and the precision of the optimization as long as the learner who has back phenomenon is corrected in a timely manner. The updating equation of the Teacher Phase is

##### 3.2. Cauchy Distribution

Cauchy distribution is a common distribution in probability theory and mathematical statistics, and the probability density function in dimension is as follows:

It is the standard Cauchy distribution when the parameter *t* equals 1. Figure 1 is the probability density curves of standard Gauss distribution, standard Cauchy distribution, and standard uniform distribution, respectively. As can be seen from Figure 1, the peak of Cauchy distribution at the origin is the smallest of three different distributions, while the velocity of the long flat shape near to zero is the slowest. So, if the mutation strategy of Cauchy distribution is used in the Teacher Phase and Learner Phase, its disturbance ability or self-adjustment ability is the strongest of three different distributions, and the basic TLBO algorithm is more likely to jump out of the local optimum and improve the search speed. The updating equation of the Learner Phase is