Computational Intelligence and Neuroscience

Volume 2015, Article ID 851863, 13 pages

http://dx.doi.org/10.1155/2015/851863

## Improved Quantum Artificial Fish Algorithm Application to Distributed Network Considering Distributed Generation

^{1}Department of Mathematics, Science College, China Three Gorges University, Yichang 443002, China^{2}Hubei Province Key Laboratory of System Science in Metallurgical Process, Wuhan University of Science and Technology, Wuhan 430081, China

Received 28 May 2015; Revised 2 August 2015; Accepted 10 August 2015

Academic Editor: José Alfredo Hernandez

Copyright © 2015 Tingsong Du 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

An improved quantum artificial fish swarm algorithm (IQAFSA) for solving distributed network programming considering distributed generation is proposed in this work. The IQAFSA based on quantum computing which has exponential acceleration for heuristic algorithm uses quantum bits to code artificial fish and quantum revolving gate, preying behavior, and following behavior and variation of quantum artificial fish to update the artificial fish for searching for optimal value. Then, we apply the proposed new algorithm, the quantum artificial fish swarm algorithm (QAFSA), the basic artificial fish swarm algorithm (BAFSA), and the global edition artificial fish swarm algorithm (GAFSA) to the simulation experiments for some typical test functions, respectively. The simulation results demonstrate that the proposed algorithm can escape from the local extremum effectively and has higher convergence speed and better accuracy. Finally, applying IQAFSA to distributed network problems and the simulation results for 33-bus radial distribution network system show that IQAFSA can get the minimum power loss after comparing with BAFSA, GAFSA, and QAFSA.

#### 1. Introduction

Distributed generation (DG) is small-scale and radial generating facilities, which are placed in the vicinity of the load, delivering electricity to consumers independently. Compared with the traditional and centralized power, DG has many advantages [1, 2] such as being near to the center of the users and having high energy efficiency and lower cost of construct. Studies show that DG grid connection has significant impact on the distributed network, including power flow, voltage profile, system losses, and reliability, the extend of which has something to do with the location of DG intimately [3–5]. On the one hand, the suitable installation position and capacity can improve the voltage quality effectively and reduce the active loss; on the other hand, unsuitable configuration turns out to be just the opposite wish and threat to the safe and stable operation of the power network. There are many approaches for deciding the optimum sizing and sitting of DG units in distribution systems. Some of them rely on conventional optimization methods and others use artificial intelligence-based optimization methods [6]. The new methods of distribution network programming, Genetic Algorithm (GA) [7, 8], Ant Colony Algorithm (ACA) [9], Particle Swarm Algorithm (PSA) [10], and Chaos Algorithm (CA), have advantages and disadvantages, respectively. The robustness of the GA is strong in addition to its ability to be trapped in a local minimum. Initial particles generated by CA have property of ergodicity but slower convergence speed. Therefore, how to effectively combine the merits of different intelligent algorithms to improve the performance among search algorithm is a worth studying direction [11–13].

Basic artificial fish swarm algorithm (BAFSA) is a kind of intelligence optimization algorithm based on animal behavior by Li et al. in 2002 [14]. According to the characteristics of the fish swarm and its animal autonomous model, it simulates behavior of fish to achieve the purpose of the group global optimization by each individual in the local optimization. The main fish behaviors are the following: foraging, huddling, following, and being random. In almost all the cases, the BAFSA is easy to avoid falling into local optimum and obtain the global optimum. Although the algorithm with the merits of strong robustness and good convergence performance is not sensitive to initial value and parameter selection, it has the weakness with search efficiency such as the poor ability to keep balance of exploration and development, late blind search, slow arithmetic speed, and low accuracy of optimization results.

Quantum computing that is different from the traditional calculation model of classical physics has incomparable advantages such as quantum super parallelism and exponential storage capacity [15]. The combination of quantum computing and intelligent optimization algorithm injected new life into the intelligent optimization computing source, by using quantum computing in a new mode of representing and processing information, and so forth [16, 17]. Intelligent optimization algorithm can be designed from another angel to enrich the theory of intelligent computing and improve the traditional method of intelligent search performance as a whole.

In the present paper, the improved quantum artificial fish swarm algorithm (IQAFSA) is proposed in consideration of the slow speed and low accuracy of BAFSA and randomness and blindness of quantum computing [18, 19]. The proposed algorithm improves the coding way of the quits artificial fish and uses quantum revolving door, artificial fish following, artificial fish preying, and variation of update strategy to complete self-renewal, resulting in a new artificial fish. IQAFSA is then applied to solve high dimensional and complex nonconvex programming and distributed network programming considering distributed generation. By simulation experiment among BAFSA, the global edition artificial fish swarm algorithm (GAFSA) has been put forward in [20] and quantum artificial fish swarm algorithm (QAFSA). The simulation results indicate that IQAFSA has great convergence and superiority in function optimization; meanwhile, they illustrate the validity and feasibility of IQAFSA applied to optimal configuration of DG in distributed network system.

The rest of this paper is organized as follows. We devote Section 2 to a discussion of those aspects of basic idea of BAFSA. The detail on quantum computing is then discussed in Section 3. The update of the quantum bit needs to make use of the transformation of quantum gates. In Section 4, the QAFSA has been formulated. The IQAFSA given in Section 5 is encoded by quantum bits and updated by quantum revolving gate. Artificial fish perform preying behavior and following behavior. In Section 6, the effectiveness of the algorithm compared with those of BAFSA, GAFSA, and QAFSA for three multidimensional and box constraints programming systems is demonstrated except for one two-dimensional box constraint programming. Section 7 deals with the distributed network modeling and the effect of DGs on system losses. Finally, Section 8 is devoted to drawing of the conclusions.

#### 2. Description of BAFSA

Artificial fish complete update and obtain the optimal value mainly through the following four behaviors: being random, preying, swarming, and following in the process of iterative calculation.

##### 2.1. AF-Random

Random behavior is to randomly select a new state in its visual field and then move a step in the direction. It is actually a default behavior.

##### 2.2. AF-Prey

Preying is a kind of the basic behavior of artificial fish, which move to the direction of food with high concentration. The AF-preying behavior is described as follows:where is element of state vector; is elements of ; is the next step state vector; is a random number between 0 and step .

##### 2.3. AF-Swarm

AF-swarm refers to the fact that every fish moves to the center of the adjacent partners in the process of swimming as fast as possible and avoids overcrowding. Suppose that is the current state of artificial fish . is the number of partners and is the central position in the current field . If , it shows that there are more food around the partner and its not too crowded. Then, the fish moves a step forward to the central position of this partner. The AF-swarming behavior is described as follows: Otherwise, the fish performs preying behavior.

##### 2.4. AF-Follow

AF-follow illustrates that each artificial fish moves to the current optimal direction in the range of vision. Suppose that is the current state of artificial fish . is the greatest partner in the current field . If , it turns out to be that there are more food around while being not too crowded. Then, the fish moves a step forward to the direction of . The AF-following behavior is described as follows: Otherwise, the fish performs preying behavior.

In the problem of function optimization. Suppose that in a -dimensional search space goal, the number of artificial fish is . The state of the individual artificial fish can be denoted by vector and which is the optimization variable. The food concentration of the artificial fish in the current location can be expressed as , where denotes the objective function value. is the distance between the fish and the fish . The idea of BAFSA is that it firstly initializes a swarm of artificial fish randomly; secondly the fish complete update by four basic behaviors mentioned above. Each of the artificial fish explores the current environment conditions (including the change of the objective function and partners). Then, select an appropriate behavior and move in the direction of optimal areas. Finally, artificial fish gather around several local optimal, especially in some better optimal areas, which are generally able to rally more artificial fish, namely, the optimal value of objective function.

#### 3. Quantum Computing

Physical media acting as the information storage unit are a two-state quantum systems in quantum computing, to be referred to as quantum bit. A quantum bit can be in a state of quantum superposition represented by , where and denote quantum bit probability amplitude. The probability of is represented by , and the probability of is represented by ; furthermore, . Each quantum state in system can be expressed as the superposition of the basic state; as and approach to be 1 or 0, the quantum bit will converge to a specific state.

The update of the quantum bit needs to make use of quantum gates which include the xor gate, the controlled xor gate, Hadamard transform gate, and the revolving gate. The quantum revolving gate [21, 22] was adopted in this paper to change its phase by interference and the basic state probability amplitude. The revolving gate is described as follows:where denotes the rotation angle of the quantum gate; the update process is as follows:

The rotation angle of quantum gate is adjusted dynamically with the evolutionary process, whilst rotation angle is set larger at the beginning of the algorithm. With the increase of evolution generation, the rotation angle is gradually reduced by formula , where is a coefficient influencing the speed and is the direction of rotation angle. Emphasis here is on the fact that if is very large, the search step length will be very big in each iteration in the process of calculation. It is easy to fall into local optimal value. On the other hand, if the convergence speed is slow, the computation time will be too long. In this paper, , where denotes the current evolution generation, and is the biggest evolution generation. is to make the algorithm get the optimal solution, the principle of which is to use the current solution to approach to the best solution , determining the direction of rotation of the quantum revolving gate. An adjusting strategy which is general and has nothing to do with the problem [23] is adopted in this paper. These strategies are described in Table 1.