Computational Intelligence and Neuroscience

Volume 2017, Article ID 1583847, 11 pages

https://doi.org/10.1155/2017/1583847

## Chaos Quantum-Behaved Cat Swarm Optimization Algorithm and Its Application in the PV MPPT

^{1}Information Engineering School, Nanchang University, Nanchang, Jiangxi Province 330031, China^{2}Economics Management School, Nanchang University, Nanchang, Jiangxi Province 330031, China

Correspondence should be addressed to Xiaohua Nie; moc.361@hoaixein

Received 14 January 2017; Revised 23 March 2017; Accepted 11 September 2017; Published 17 October 2017

Academic Editor: Athanasios Voulodimos

Copyright © 2017 Xiaohua Nie 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

Cat Swarm Optimization (CSO) algorithm was put forward in 2006. Despite a faster convergence speed compared with Particle Swarm Optimization (PSO) algorithm, the application of CSO is greatly limited by the drawback of “premature convergence,” that is, the possibility of trapping in local optimum when dealing with nonlinear optimization problem with a large number of local extreme values. In order to surmount the shortcomings of CSO, Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed in this paper. Firstly, Quantum-behaved Cat Swarm Optimization (QCSO) algorithm improves the accuracy of the CSO algorithm, because it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper. Secondly, CQCSO has been applied in the simulation of five different test functions, showing higher accuracy and less time consumption than CSO and QCSO. Finally, photovoltaic MPPT model and experimental platform are established and global maximum power point tracking control strategy is achieved by CQCSO algorithm, the effectiveness and efficiency of which have been verified by both simulation and experiment.

#### 1. Introduction

Solar energy is widely used due to the advantages of renewable and nonpolluting. Global maximum power point tracking (GMPPT) is one of the basic means to improve the overall efficiency of photovoltaic power generation system. However, the traditional maximum power point tracking (MPPT) algorithm is often ineffective because of the output power curve with multipeak problem in complex shade conditions. The problem results in efficiency reducing of photovoltaic power generation [1, 2]. Many scholars have carried out massive researches to solve these questions. Many optimization algorithms are used to realize global maximum power point tracking and achieve good results, like Particle Swarm Optimization (PSO) algorithm, evolutionary algorithm, fuzzy logic control algorithm, neural network control algorithm, chaos search algorithm, and so on [2–9].

The Cat Swarm Optimization (CSO) algorithm was proposed by Chu et al. in 2006 [10]. The experimental results showed that the CSO algorithm could find the global optimal solution in a short time, and the CSO algorithm is better than the PSO algorithm in the convergence speed and nonlinear optimization of the local extremum [11–18]. However, the CSO algorithm has the shortcoming of “premature convergence” in the practical application. If the number of iteration is increased continuously, it will cause the convergence time to multiply while the accuracy of the optimal value is not significantly improved. The same problems also occur in the PSO algorithm. A novel chaotic quantum-behaved PSO algorithm is proposed for solving nonlinear system of equations in [19]. Different chaotic maps are introduced to enhance the effectiveness and robustness of the algorithm. The comparison of results reveals that the proposed algorithm can cope with the highly nonlinear problems and outperform other algorithms. The Hybrid Chaotic Quantum-behaved Particle Swarm Optimization (HCQPSO) algorithm is used for thermal design of plate fin heat exchangers in [20]. The HCPQSO algorithm successfully combines a variant of Quantum-behaved Particle Swarm Optimization with efficient local search mechanisms to yield better results in terms of solution accuracy and convergence rate. It is also observed that the proposed algorithm successfully converges to optimum configuration with a higher accuracy. A chaotic improved Particle Swarm Optimization algorithm is proposed for photovoltaic MPPT in [21]. An improved cuckoo search (ICS) algorithm is proposed to establish the parameters of chaotic systems in [22]. The numerical results demonstrate that the algorithm can estimate parameters with high accuracy and reliability. An evolutionary approach of parking space guidance is proposed based upon a novel Chaotic Particle Swarm Optimization (CPSO) algorithm in [23]. The Chaotic Firefly algorithm using tent maps is proposed for optimally coordinating the relays in [24]. Chaos theory has been incorporated to prevent the search process from being trapped in local minima by modifying the concept of random movement factor variable.

In this paper, a Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed. The cat with the quantum behavior has no definite trajectory in tracking and has the possibility of getting rid of the local optimal point with large disturbance. Since there is only position vector in the control parameter, with no velocity vector, and the convergence time is shortened, then, the tent chaotic map is introduced to change the cat position information in the iteration process, the “premature convergence” problem of the CSO algorithm is avoided, and the precision of searching is further improved. In Section 2, the CQCSO algorithm is tested in five nonlinear function curves with multiple local extreme points. The results show that the proposed CQCSO algorithm has high tracking precision and fast convergence speed. Moreover, the proposed CQCSO algorithm has the ability to adapt to complex and different curves. In Section 3, the proposed CQCSO algorithm is applied to PV MPPT control, and a multipeak MPPT control strategy based on CQCSO algorithm is proposed. The simulation and experimental results show that the proposed control strategy more efficiently tracks the global maximum power points.

#### 2. Chaos Quantum-Behaved Cat Swarm Optimization (CQCSO) Algorithm

##### 2.1. QCSO Algorithm

The CSO algorithm is a kind of swarm intelligence algorithms based on the cat’s living habits and foraging. It is superior to the PSO in searching accuracy and convergence time [12–19]. It is widely used to solve the optimization problem. In the CSO algorithm, the cat’s position is regarded as a feasible solution to the optimization problem, and then the cat swarms are divided into two groups according to the mixture ratio (MR), which are the searching cat group and the tracking cat group. The searching cat group refers to the genetic algorithm to complete the cat’s location update. The cats with the highest fitness value are selected to replace the current cat position by copying and mutating individuals. The tracking cat groups are similar to the PSO algorithm and use the cat’s own speed and the current position information to update the position of the cat continuously, so that each individual can move closer to the global optimal solution. Although the search of the global optimal solution can be realized, there exists shortcoming of “premature convergence” problem like other swarm intelligent algorithms.

Quantum-behaved Cat Swarm Optimization (QCSO) algorithm is a combination of CSO algorithms and quantum mechanics. In the evolutionary process, each tracing cat has a -centered DELTA potential well, which makes each tracing cat converge to an attractor . It continuously updates the location of the cat by tracking individual extremes and global extremes, so that the cat’s speed and location are uncertain. So, it can be distributed in a certain probability to search space at any position. It is possible to get rid of the local optimal points in disturbing environment. As a result, the QCSO algorithm can jump out of the local optimum and improve the accuracy of CSO algorithm.

The updated expression of individual position in quantum space iswhere where is population size, , is dimension, is maximum number of iterations, , is maximum number of traces, , is the cat group optimal position center of the th iteration, is the optimal position of the th cat for the th iteration, is the optimal position of the th cat for the th iteration, is the global optimal position of the population at the th iteration, is the th iteration expansion contraction factor, , are the initial compression factor and the termination value, respectively, , , and are random numbers with uniform distribution in the interval.

##### 2.2. CQCSO Algorithm

The QCSO algorithm improves the accuracy of the CSO algorithm, because the cat in the evolutionary process continues to move closer to the optimal position of the population, the diversity of the population gradually decreases, and it is easy to fall into the local optimum in the later stage. Chaos Quantum-behaved Cat Swarm Optimization (CQCSO) algorithm is proposed by introducing tent map for jumping out of local optimum in this paper.

The individual location update expression of tent map is as follows:where , , . can be mutually mapped transformation with the chaotic variables through

Detailed CQCSO algorithm steps are as follows.

*Step 1. *Initialize the cat swarm, set the population size , the maximum iteration number , and the mixture ratio (MR) of the cat optimization algorithm, and randomly initialize position of the cat population between ; it is expressed with the row vector .

*Step 2. *The fitness value of all cats in the population was calculated, and the cat with the greatest fitness was selected and recorded.

*Step 3. *According to MR, cats swarms are randomly grouped. MR represents the proportion of the number of cats in the tracking group in the entire cat population. MR is generally a smaller value to ensure that most of the cats in the swarm are in search mode and a few cats are in tracking mode.

*Step 4. *When the cat is in the search group, it replicates its position according to the size of seeking memory pool (SMP), executes the selection operator, updates SMP, and replaces the position of the current cat with the candidate point with the highest fitness value. In the end, the optimal value updating is completed. The cat of tracking group updates its own position information according to formula (1).

*Step 5. *The cat with the best fitness is recorded in the reserved populations.

*Step 6. *It is judged whether the termination condition is satisfied, and if so, the program ends and the optimal solution is output. If it is not satisfied, it is judged whether the position of the global optimal cat is the same after the th and iterations, and if not, Steps 3–6 are repeated. If it is the same, it means that it has fallen into local optimum and needs to deal with chaos. The mapping of the normal variable is performed by using formula (4). The chaotic variables after mapping are in the range . Chaos variable is mapped to get using formula (3). And then through formula (5), chaos variable mapping transformation, the next iteration of the conventional variables is obtained. Steps 2–6 are repeated to optimize iteration.

##### 2.3. Verification for CQCSO Algorithm

In order to verify the superiority of the CQCSO algorithm, five kinds of nonlinear functions with multiple local extremum peaks such as Schaffer, Shubert, Griewank, Rastrigrin, and Rosenbrock are compared for seeking optimization. In simulation, the total number of cat groups is set to 20; each function program runs 50 times.

*(1) Schaffer Function*where ; Schaffer function is a two-dimensional complex function with numerous small points. The minimum value 0 is obtained at (0, 0). Because this function has strong concussion, it is hard to find the global optimal value. The seeking optimization result is obtained and shown in Figure 1(a).