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 quantuminspired 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 smallscale chain supermarket and a largescale chain supermarket. Moreover, the success rate of QEA in searching routes is higher than that of GA.
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 [
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 [
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 [
In recent years, QEA has attracted lots of attention. Han and Kim [
Unlike previous genetic algorithms based on crossovers, QEA adopts Qbit 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 Qbits rather than discarding the subsolutions when bad fitness values are found [
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 twostate quantum computer is called a quantum bit or Qbit. A Qbit may be in the “0” state, in the “1” state, or in any superposition of the two [
And, a Qbit individual as a string of
The state of a Qbit can be changed by the operation with a quantum rotation gate or Qgate, and the following rotation gate is used as a basic Qgate in QEA, such as
The angle parameters used for the rotation gate.












0  0  False  0  0  0  0  0 
0  0  True  0  0  0  0  0 
0  1  False  0  0  0  0  0 
0  1  True 

−1  +1 

0 
1  0  False 

−1  +1 

0 
1  0  True 

+1  −1  0 

1  1  False 

+1  −1  0 

1  1  True 

+1  −1  0 

The polar plot of the rotation gate.
QEA is a kind of evolutionary algorithm based on population, so it is similar to the traditional evolutionary algorithm. Its solution to the problem depends on the evolutionary population consisting of quantum chromosomes, mainly including population initialization, quantum chromosome observation, evaluation, update, and other operations. The basic procedure of QEA is described as follows [
According to literatures, QEA, apart from its application to the knapsack problem, the traveling salesman problem, the flow shop scheduling problem, and other ordering problems [
Hu and Wu [
However, QEA is not applied to solve the chain supermarket distribution route optimization problem at present, whose general solutions are the Dynamic Planning Algorithm, the Saving Algorithm, the ant colony algorithm, and so on. Due to the fact that the chain supermarket distribution route optimization problem is similar to the vehicle routing problem, we take QEA in this paper to cope with it.
This paper adopts QEA to optimize the distribution routes of chain supermarkets. Its mathematical model is described as follows: given that a distribution center of a supermarket chain uses at most
First define two variables:
and the range of each variable is
The designed model is as follows:
the target function:
Each truck’s load capability:
The truck must deliver goods for each chain store with orders.
The goods of each chain store with orders are delivered by only one truck.
To avoid the subloop of truck driving route,
Moreover, the chain store has certain requirements on the departure and arrival time of the truck to transport goods, so the time constraints (that is time window) need to be added to the model. Its specific details are as follows [
The main parameters involved in the model and their meanings are listed in Parameters.
Only the weight of goods to be delivered is taken into account instead of their size and shapes, and they can be mixed up. Besides, traffic condition is good during the period of transporting goods (that is to say, there are no traffic jams, traffic accidents, or other undesirable conditions).
According to the basic procedure of QEA, in this paper QEA is adopted to effectively solve the distribution route model of chain supermarkets and obtain the optimal distribution route. Before the optimization of distribution routes, there are several preconditions:
The location of the distribution center, the warehouse, and the chain store is determined.
The number of trucks, the truck speed, and its load capacity in the distribution center are known.
The demand for the goods of each chain store is known.
The time window of each chain store is known.
All distributed goods are shipped uniformly from the distribution center on time.
All distributed goods can be mixed together in the same truck.
In the process of distribution route optimization, in order to avoid the local optimum of the classical QEA, this paper introduces the cataclysm operator and sets the evolutionary step “distance.” If the generation of the continuous “distance” of the optimal value stays the same, the evolution falls into premature convergence. Then the current optimal individual needs to be stored, and other individuals are supposed to be reinitialized, so as to enter the next generation evolution as well as jump over the local optimum. The specific solution procedure is as follows [
In Step
Procedure Update
begin
while
begin
determine
obtain
if (
then
else
end
end
And, the flow chart for solving optimization distribution route is shown in Figure
The algorithm design flow chart by QEA.
This study adopts QEA and GA to make a comparative experiment for the same case (Hongqi Chain Supermarket in Chengdu). QEA is a kind of improved evolutionary algorithm, which has been mentioned in detail in Section
The genetic algorithm procedure.
Hongqi Chain Supermarket in Chengdu was founded on June 22, 2000, which was renamed Chengdu Hongqi Chain Joint Stock Limited Company on June 9, 2010. At present, the company has developed into a largest commercial chain enterprise in the western region of China with chain operation, logistics distribution, and ecommerce as a whole. There are four logistics distribution centers and more than 8600 chain stores in Sichuan Province. It has established a good winwin business cooperation relationship with thousands of suppliers and has become a key connection enterprise for essential life necessities of Sichuan Province. In order to bring to consumers a more relaxing and convenient life and make them enjoy it, this enterprise makes full use of the company’s huge market network and information technology resources and other advantages, following the “commodity + service” business strategy to be the pioneer in constructing a convenient and multifunctional service platform for the consumer. As a result the unanimous praise from consumers is won.
We take Hongqi Chain Supermarket in a Town of Chengdu city as an example. There are 1 distribution center, 10 trucks (the load capacity of each truck is 5 t, the maximum travel distance is 150 km, and the average distribution speed is 50 km/h), and 12 chain stores. The average speed of loading or unloading is 0.3 h/t, the demanding for goods of every chain store is
The demanding of every chain store and the service time constraint.
Chain stores  1  2  3  4  5  6  7  8  9  10  11  12 

1.5  2.2  0.5  1.6  2.7  3.2  1.3  0.8  0.8  1.5  2.4  4.1 

0.45  0.66  0.15  0.48  0.81  0.96  0.39  0.24  0.24  0.45  0.72  1.23 













The distance between the distribution center and the chain store and the distance between one chain store and another chain store is
The distance between distribution centers and chain stores and the distance between one chain store and another.
According to the distribution route model of chain supermarkets constructed above, we take the corresponding data into the model and get the distribution route model of Hongqi Chain Supermarket in the Town; for example, the target function is
The population size of QEA is equal to 10, a Qbit chromosome is updated by the rotation gate
Using QEA to solve the problem of route optimization requires at least 5 trucks, the shortest total distance for traveling is 142.9 kilometers, and the minimum total time is 2.86 hours. Its optimization routes are as follows.
Truck 1: the center→4→5→the center
Truck 2: the center→7→6→the center
Truck 3: the center→3→2→1→the center
Truck 4: the center→9→10→11→the center
Truck 5: the center→8→12→the center.
But using GA to solve the problem of route optimization requires at least 6 trucks, the shortest total distance for traveling is 168.2 kilometers, and the minimum total time is 3.37 hours. Its optimization routes are as follows.
Truck 1: the center→10→9→8→7→the center
Truck 2: the center→4→the center→11→the center
Truck 3: the center→3→the center→1→2→the center
Truck 4: the center→5→the center
Truck 5: the center→6→the center
Truck 6: the center→12→the center
The results show that, in solving the optimization route of the smallscale Hongqi Chain Supermarket, the number of trucks taken by QEA is less than that of trucks taken by GA by one. Besides, the total traveling distance of QEA is 25.3 kilometers, less than that of GA. Moreover, the solution made by QEA helps to save the time of 0.50 hours when compared with that made by GA. And the convergence of two algorithms is shown in Figure
The convergence effect diagram of algorithms.
From Figure
Comparison of smallscale case experimental results.
Algorithms  The best value  The worst value  The average value  The search success rate  The convergence generation 

GA  168.2  175.5  170.9  20.8%  49.7 
QEA  142.9  164.3  151.7  55.1%  36.2 
From Table
We take Hongqi Supermarket Chain in Chengdu, China, as an example. There are 4 distribution centers, 684 trucks (most of the load capacity of trucks is 5 t), and 8607 chain stores. Other conditions are similar to the smallscale Hongqi Chain Supermarket, and the data of distance among chain stores and that of demanding of every chain store come from the data management center of Hongqi Supermarket Chain. We still adopt QEA and GA to solve it and their parameters are defined like the smallscale case above. Among them, the population size of QEA is equal to 10; the angle value is set to
At last, we obtain the optimal distribution route for a certain distribution center of Hongqi Supermarket Chain on the day as shown in Figures
The optimal route of QEA.
The optimal route of GA.
The convergence of QEA.
The convergence of GA.
And, we get the results of the experiments as shown in Table
The comparison of largescale case experimental results: the number of chain stores is 8607, the maximum number of generations 1000, the population size 10, the evolutionary step “distance” 10, and the number of runs 30.
Case  Known best solution  QEA  GA  

BE  DE (%)  BE  DE (%)  
(1)  662  671  1.36  674  1.81 
(2)  695  704  1.29  708  1.87 
(3)  778  785  0.90  814  4.63 
(4)  786  786  0  820  4.33 
(5)  830  846  1.93  871  4.94 
(6)  924  952  3.03  969  4.87 
(7)  933  971  4.07  985  5.57 
(8)  1002  1028  2.59  1055  5.29 
(9)  1353  1406  3.92  1419  4.88 
(10)  1773  1862  5.02  1882  6.15 
From Table
It can be seen from the distribution route optimization experimental results of the smallscale and the largescale Hongqi Chain Supermarket in Chengdu, for smallscale chain supermarkets, QEA and GA are not caught in local convergence and the success rate of QEA search is higher than that of GA [
At present, the business competition of domestic chain supermarkets is further intensified, and the logistics distribution of chain supermarkets has become the focus of competition. Whether the distribution route is scientific or reasonable will directly affect the logistics cost and market competition of chain supermarkets. This paper takes Hongqi Chain Supermarket in Chengdu as an example and adopts QEA to optimize the distribution route of the chain supermarket. First of all, we set up a mathematical model of the distribution route of the chain supermarket. Then we design the process of solving the model according to QEA idea and adopt the 01 matrix encoding method and the decoding scheme in which we firstly arrange the route and then group the route. At the same time, we use the quantum rotation gate to realize the evolution and introduce the cataclysm operator to ensure the diversity of solution space. Finally, we compare QEA with GA in the fields of the convergence, the optimal solution, the search ability, and so on.
The experiment results show that the optimization distribution route of chain supermarkets by QEA is better than that of GA. It makes the number of trucks rather smaller and the total traveling distance of trucks much shorter. It not only shortens the time to transport the goods and decreases the cost of truck’s transportation, but also effectively improves the economic benefits of chain supermarkets, enhances the quality of their service, strengthens the core competitive ability of the market, and boosts the healthy and stable development of chain supermarkets. However, in this paper, we do not take the uncertainty of parameters into consideration like the actual freight volume of every chain store, transport time, and so on caused by the economic fluctuations, holidays, traffic restrictions, competitors, and other uncertain factors. And these uncertainties also affect the distribution route optimization, which is the focus of upcoming research.
To sum up, the logistics distribution of chain supermarkets is a systematic project and the distribution route optimization needs combination of the distribution center location of chain supermarkets, the network layout of chain supermarkets, the reasonable scheduling of drivers, and the current road conditions as well as other constraint factors to achieve greater efficiency.
The total number of trucks
The total number of chain stores
The truck
The chain store
The warehouse of the distribution center
The load capacity of the truck
The demand for the goods of the chain store
The shortest distance from the chain store
The time it takes from the chain store
The truck
The truck
The target function
The earliest beginning time that the chain store
The latest beginning time that the chain store
The beginning time of the distribution task of the chain store
The end time of the distribution task of the chain store
Bi Liang and Fengmao Lv declare that there are no conflicts of interest regarding the publication of this paper.
This work is supported by the National Natural Science Foundation of China in 2014 (61375029) and the General Project of Education Department of Sichuan Province in 2016 (16ZB0362).