Mathematical Problems in Engineering

Volume 2017, Article ID 7964545, 11 pages

https://doi.org/10.1155/2017/7964545

## A Study on the Optimization of Chain Supermarkets’ Distribution Route Based on the Quantum-Inspired Evolutionary Algorithm

^{1}School of Intelligent Manufacturing, Sichuan University of Arts and Science, No. 400, Nanba Road, Dachuan, Dazhou, Sichuan, China^{2}School of Computer Science, Beijing University of Posts and Telecommunications, No. 10, Xitucheng Road, Haidian, Beijing, China^{3}School of Computer Science and Engineering, University of Electronic Science and Technology of China, No. 2006, Xiyuan Road, Gaoxin, Chengdu, Sichuan, China

Correspondence should be addressed to Bi Liang; moc.621@6ibgnail

Received 22 June 2017; Accepted 7 November 2017; Published 28 November 2017

Academic Editor: Thomas Hanne

Copyright © 2017 Bi Liang and Fengmao Lv. 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

The chain supermarket has become a major part of China’s retail industry, and the optimization of chain supermarkets’ distribution route is an important issue that needs to be considered for the distribution center, because for a chain supermarket it affects the logistics cost and the competition in the market directly. In this paper, analyzing the current distribution situation of chain supermarkets both at home and abroad and studying the quantum-inspired evolutionary algorithm (QEA), we set up the mathematical model of chain supermarkets’ distribution route and solve the optimized distribution route throughout QEA. At last, we take Hongqi Chain Supermarket in Chengdu as an example to perform the experiment and compare QEA with the genetic algorithm (GA) in the fields of the convergence, the optimal solution, the search ability, and so on. The experiment results show that the distribution route optimized by QEA behaves better than that by GA, and QEA has stronger global search ability for both a small-scale chain supermarket and a large-scale chain supermarket. Moreover, the success rate of QEA in searching routes is higher than that of GA.

#### 1. Introduction

The chain operation originates from the United States. But according to the record in “Encyclopedia Americana,” in 200 BC (Before Christ), a Chinese businessman had many stores, which was to be called the earliest sprout of the chain operation [1]. In 1859, the world’s first chain store was born in the United States—the Great Atlantic and Pacific Tea Co. In 1969, the Wal-Mart supermarket, ranking first in the world’s retail industry, built its first distribution center, which showed chain supermarkets began to pay attention to the management of logistics links [2]. At present, the United States, Japan, Germany, and other developed countries have conducted a lot of studies on the distribution mode of chain supermarkets, and their theories and practices are more mature. For example, for wholesalers, retailers, warehouses, transportation, and other main subjects, the United States constructs different sorts of distribution centers for different subjects to expand distribution business. Its goal is to reduce the logistics cost and increase the efficiency of supermarket operation. Self-supporting distribution centers are built for large-scale chain supermarkets in Japan, and also distribution centers that can be used commonly are built for distribution business of small-scale retailers, which play an effective role in improving the distribution mode of chain supermarkets [3].

Compared with foreign countries, China’s chain operation started later. In the late 1980s, the chain operation in our country just started quietly. In 1990s, the chain operation bloomed in medium or large cities as well as in coastal areas, such as Xifu in Beijing, Lianhua in Shanghai, Meijia in Dongguan, and Hongqi in Chengdu. In recent years, with the rapid development of the chain operation in China, our country’s chain supermarkets have implemented the “unified procurement, unified accounting, unified distribution, centralized management” business model [4]. Relying on the fine scale economy, low logistics cost, and other advantages, it has become the major retail format in current domestic circulation. The unified procurement and distribution of chain supermarkets are mainly achieved through the operation of distribution centers, and the speed of working efficiency directly reflects the core competitiveness of chain supermarkets.

However, the distribution system of chain supermarkets in our country is imperfect and there are still many problems, such as unreasonable transport phenomena (e.g., repeat transport, detour transport, convective transport, empty vehicles return, and backward transport), inappropriate truck arrangement and low distribution efficiency, and high transportation cost. The basic cause of these problems is unreasonable distribution routes. With the intensification of market competition, it is necessary that the chain supermarket operation should have a set of efficient logistics distribution system to carry out scientific and reasonable optimization design for distribution routes and transport the required distribution goods to the designated chain stores in the shortest time, at the fastest speed, and with the lowest cost. Therefore, the optimization design of distribution routes has been the focus of the distribution research of chain supermarkets.

At present, there are two kinds of algorithms for the optimization design of distribution routes, that is, the traditional heuristic algorithm and the modern heuristic algorithm [5]. The traditional heuristic algorithms are mainly the saving mileage algorithm, the nearest neighbor algorithm, the nearest insertion algorithm, the scanning algorithm, and so on. The modern heuristic algorithms are mainly GA, the ant colony algorithm, the simulated annealing algorithm, the taboo search algorithm, the neural network algorithm, and so on. QEA is a modern heuristic algorithm, which is based on the concept of quantum computing and absorbs the characteristics of quantum superposition, quantum entanglement, and quantum coherence [6]. Through the quantum bit encoding chromosome, it introduces the quantum rotation, the crossover, the mutation, and other operators to realize the evolution of the population. Meanwhile, it uses the latest information to update the quantum rotation gate in order to accelerate the convergence of the algorithm.

In recent years, QEA has attracted lots of attention. Han and Kim [7] carry out experiments on the knapsack problem, a classic combinatorial optimization problem, to demonstrate the effectiveness and the applicability of QEA. The results show that QEA performs well, even with a small population, without premature convergence as compared to the conventional GA. Feng et al. [8] solve the traveling salesman problem (TSP) based on QEA. It adopts quantum bit (Q-bit) individual to encode the visited sequence of the cities and employs the quantum rotation gate to adjust the population dynamically. The experiment results of 14 cities show that the proposed approach is feasible and effective for the small-scale TSP. Lau et al. [9] apply QEA to handle the unit-scheduling problem. Studies on the application demonstrate the superior performance and feasibility of QEA.

Unlike previous genetic algorithms based on crossovers, QEA adopts Q-bit representation to codify the solution. Using observations to generate new solutions instead of crossovers, QEA can avoid permutation problems. In addition, QEA decreases the risk of throwing away potential solutions since it just modifies the Q-bits rather than discarding the subsolutions when bad fitness values are found [10]. Additionally, in terms of loss of diversity, scalability, solution quality, and robustness to fitness noise, QEA performs better when compared with other evolutionary algorithms. Presently, QEA, with the advantages of good robustness, parallel processing, and high efficiency, has been widely used in various fields, especially in the combinatorial optimization problem, and good results have been obtained, so in this paper the algorithm is adopted to optimize the distribution routes of chain supermarkets.

#### 2. The Background of QEA

##### 2.1. Q-Bit and Q-Gate

QEA is a kind of new intelligent optimization algorithm, which is a combination of the quantum computing and the evolutionary algorithm. The smallest unit of information stored in a two-state quantum computer is called a quantum bit or Q-bit. A Q-bit may be in the “0” state, in the “1” state, or in any superposition of the two [11]. The state of a Q-bit can be represented aswhere and are complex numbers that specify the probability amplitudes of the corresponding states. gives the probability that the Q-bit will be found in the “0” state and gives the probability that the Q-bit will be found in the “1” state. Normalization of the state to unity guarantees

And, a Q-bit individual as a string of Q-bits is defined as where . If there is a system of Q-bits, the system can represent 2^{m} states at the same time. However, in the act of observing a quantum state, it collapses to a single state.

The state of a Q-bit can be changed by the operation with a quantum rotation gate or Q-gate, and the following rotation gate is used as a basic Q-gate in QEA, such as and then where is a rotation angle of each Q-bit toward either 0 or 1 state depending on its sign, and . Figure 1 depicts the polar plot of the rotation gate for Q-bit individuals. At the same time, the angle parameters used for the rotation gate are shown in Table 1, where is the profit, is the sign of , and and are the th bits of the best solution and the binary solution , respectively. The value of has an effect on the speed of convergence, and the sign determines the direction of convergence to a global optimum [12].