# Shortest Path Selection Algorithm for Cold Chain Logistics Transportation Based on Improved Artificial Bee Colony

Authors: Zhihuan Liu
Journal: Scientific Programming
 (2021)

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## Abstract

Aiming at the problems of low shortest path selection accuracy, longer response time, and poor selection effect in current cold chain logistics transportation methods, a cold chain logistics transportation shortest path selection algorithm based on improved artificial bee colony is proposed. The improved algorithm is used to initialize the food source, reevaluate the fitness value of the food source, generate a new food source, optimize the objective function and food source evaluation strategy, and get an improved artificial bee colony algorithm. Based on the improved artificial bee colony algorithm, the group adaptive mechanism of particle swarm algorithm is introduced to initialize the position and velocity of each particle randomly. Dynamic detection factor and octree algorithm are adopted to dynamically update the path of modeling environment information. According to the information sharing mechanism between individual particles, the group adaptive behavior control is performed. After the maximum number of cycles, the path planning is completed, the shortest path is output, and the shortest path selection of cold chain logistics transportation is realized. The experimental results show that the shortest path selection effect of the cold chain logistics transportation of the proposed algorithm is better, which can effectively improve the shortest path selection accuracy and reduce the shortest path selection time.


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## Body

## 1. Introduction

Cold chain logistics means that every circulation link of fresh frozen food must be preserved in a certain low temperature environment from production to consumption, so as to ensure food freshness or reduce food deterioration and loss [1]. The strict time limit, high storage cost, and high service quality of fresh agricultural products put forward high distribution requirements for cold chain logistics transportation [2]. Therefore, it is very important for the cold chain logistics transportation to scientifically plan the cold chain logistics transportation route, reasonably formulate the cold chain logistics transportation scheme so as to ensure the distribution efficiency of fresh agricultural products, as well as the freshness and low loss rate of food, and improve the service quality level. It is also an urgent problem to be solved on the development road of fresh agricultural products [3]. The path planning problem is to find an optimal path from the starting point to the target point in a given network graph. The shortest path problem has always been a research hotspot in traffic engineering, computer science, geographic information science, and other disciplines. Therefore, it is of great significance to study the shortest path of cold chain logistics transportation.At present, scholars in related fields have studied the shortest path of cold chain logistics transportation and achieved some theoretical results. Reference [4] proposed an online planning algorithm of cold chain logistics distribution route in cloud computing environment based on shortest path optimization control. In the cloud computing environment, the shortest path search model is used to optimize the ship path of cold chain logistics distribution, and the location of cold chain logistics distribution path nodes is designed. Based on the load balancing model of distribution network, the ship routing and distribution routing planning of cold chain logistics in cloud computing environment are carried out. The algorithm has the advantages of low route cost, good distribution network balance, and high cold chain logistics distribution output. Reference [5] proposed a port logistics distribution path planning algorithm based on artificial fish swarm algorithm. According to the port logistics distribution path planning framework, the expression form of port demand point node is designed, and the path planning constraints are set. According to the constraints and VPR mathematical model, the distribution path planning model is constructed. The artificial fish swarm algorithm is used to simulate the distribution process as a fish swarm foraging process, select the optimal travel direction and distance, and optimize the above set path planning model. The algorithm can effectively reduce the transportation cost. However, the above methods still have the problems of low precision, long time, and poor effect.To contribute to the solution of the above problems, we propose a shortest path selection algorithm for cold chain logistics transportation based on improved artificial bee colony. The improved algorithm initializes the food source, generates a new food source, and optimizes the objective function and food source evaluation strategy. The population adaptive mechanism of particle swarm optimization algorithm is introduced to randomly initialize the position and velocity of each particle. The dynamic detection factor and octree algorithm are used to model the dynamic update path of environmental information. The group adaptive behavior control is carried out according to the information sharing mechanism between particles. The algorithm introduces the population adaptive mechanism of particle swarm optimization algorithm. Particles dynamically control the path through interaction and dynamically update the path according to the dynamic detection factor.After the maximum number of cycles, the shortest path of cold chain logistics transportation is output. The shortest path selection effect of this method is good, which can effectively improve the shortest path selection accuracy and shorten the shortest path selection time.


## 2. Improvement of Artificial Bee Colony Algorithm

In this section, we are going to explain artificial bee colony algorithm and its working mechanism.


### 2.1. Artificial Bee Colony Algorithm

Artificial bee colony algorithm solves the function optimization problem by simulating bee colony to find excellent honey source [6]. Because the algorithm has the advantages of simple and easy implementation, few control parameters, and strong robustness and is suitable for dealing with high-dimensional optimization problems in engineering, it is widely used in the fields of signal and image processing, communication, control, data mining, and so on.


#### 2.1.1. Foraging Model of Artificial Bee Colony Algorithm

The design of artificial bee colony algorithm originates from the foraging behavior of bees in nature. The bee foraging model has three components, food sources, employed bees, and unemployed bees, and two basic behavior patterns, recruiting bees to collect nectar and giving up food sources. Among them, nonhired bees include onlooker bees and scout bees. The foraging model of artificial bee colony algorithm is shown in Figure1.Figure 1
Foraging model of artificial bee colony algorithm.The three components of the foraging model of the artificial bee colony algorithm are introduced as follows:(1)
Food source: the food source is the honey source to be searched by bees when foraging. The fitness value calculated by the food source indicates the advantages and disadvantages of the obtained solution. In the standard artificial bee colony algorithm, the value of food source is expressed by its fitness value.(2)
Employed bees: employed bees are also called leading bees, which carry current nectar source information and share the obtained nectar source information with other bees with a certain probability. After other bees obtain the information shared by the hired bees, they will conduct selective foraging based on this information. At the same time, the hired bee will optimize the food source based on the current food source information.(3)
Unemployed bees: according to the different division of labor of unemployed bees, they can be divided into two types: observation bees and reconnaissance bees. The first task of these bees is to search for and optimize the source of nectar. Observing bees choose to forage near the hive based on the food source information provided by the hired bees.The foraging model of artificial bee colony algorithm has two basic behavior patterns: one is to recruit bees to collect nectar, and the other is to give up food sources. The introduction is as follows:(1)
Recruiting bees to collect nectar: when hired bees find a nectar-rich food source, they will use swing dances at the hive to exchange food source information with other bees, attracting other bees to collect nectar. In this way, more and more bees will come to gather nectar near this food source, and this food source will be optimized. This is a recruitment behavior for the food source. This behavior forms the positive feedback effect of bee foraging.(2)
Abandon food source: when the reconnaissance bee finds that the nectar content of a food source is very scarce compared with other food sources through comparison, the reconnaissance bee will actively abandon this food source and search for a new food source, which is the behavior of abandoning food source in artificial bee colony algorithm. This behavior forms a negative feedback effect of bee foraging.The role conversion relationship of the three types of bees in the artificial bee colony algorithm is shown in Figure2.Figure 2
Role transformation relationship of honey bee.Whether bees can quickly find high-quality food sources is closely related to their internal food source selection mechanism. In the process of collecting honey, the reconnaissance bee will return to the hive after searching for a new food source and exchange information with the observation bee waiting in the hive through swing dance. Observing bees have two choices after watching the swing dance of reconnaissance bees: First, if the food source information meets their own expectations, they will collect nectar based on the nectar source information of the reconnaissance bees. Second, if the food source information is not within the scope of its own expectations, they continue to wait in the hive for new food source information. The roles of the three types of bees are not fixed and will change according to the nectar collection situation. In addition to observing bees transforming into hired bees to collect nectar, when the corresponding food source is exhausted, hired bees will also transform into scout bees to find new high-quality food sources.


#### 2.1.2. Algorithm Model of Artificial Bee Colony Algorithm

The algorithm model of artificial bee colony algorithm can be abstracted from the foraging model of natural bees. As an intelligent optimization algorithm, artificial bee colony algorithm can rely on the self-organization ability of bees to realize the positive and negative feedback mechanism of the algorithm [7]. In the following section, we present the algorithm model of artificial bee colony algorithm:(1)
Initialization strategy: the initialization process of the artificial bee colony algorithm will form an initial food source. The algorithm produces a set of initial solutionsx1,x2,...,xn,...,xN; the vector xn is the solution that needs to be optimized during each iteration:(1)xni=rand0,1×ubi−lbi+lbi.In formula (1), lbi is the minimum value that xni can achieve, ubi is the maximum value that xni can achieve, rand0,1 refers to generating a random number between 0,1, and n∈1,2,...,FoodNumber, where FoodNumber is the number of food sources.(2)
Food source evaluation strategy: after the food source is initialized, it is necessary to use the food source evaluation strategy to evaluate its fitness value. The purpose of the food source evaluation strategy is to compare different food sources in order to preserve the food sources rich in nectar and to abandon the food sources lacking in nectar. Another function of the food source evaluation strategy is to calculate the attraction of the food source to the observer bee. A food source evaluation method of artificial bee colony algorithm is as follows:(2)fitnessnxn=11+fnxn,fnxn≥0,1+fnxn,fnxn<0.In formula (2), fnxn is the objective function value corresponding to the solution vector xn, n∈1,2,...,FoodNumber.(3)
Employed bee foraging strategy: employed bees will remember the location of food sources rich in nectar and find better food sources based on this memory. The methods for hiring bees to find new food sources near nectar sources are as follows:(3)xni′=ubi,xni+εnixni−xki>ubi,lbi,xni+εnixni−xki<lbi,xni+εnixni−xki,otherwise.In formula (3), xni′ is the newly generated food source, xni is the current food source location, εni is the search coefficient, which is between −1,1, and xki is a randomly selected food from all food sources which is different from xni source. Among them, k∈1,2,...,FoodNumber. When a new source of nectar is found, the hired bee will evaluate the newly generated food source, calculate its fitness value, and decide whether to abandon the nectar source in the original memory.(4)
Observing bee foraging strategy: observing bees will wait near the hive, and they will search for food based on the food source information brought by the hired bees when they return. First, they use the fitnessfitnessxn of the food source to calculate the possibility probabilityn of choosing each food source. The calculation method is as follows:(4)probabilityn=fitnessxn∑n=1Nfitnessxn.If the calculation result meets the expected value of the observation bee, the observation bee will turn into a hired bee and select this food source for foraging. This is the positive feedback link of the artificial bee colony algorithm.(5)
Scout bee foraging strategy: scout bees will select those food sources that have not been improved after the maximum number of selections oflimit times of nectar collection, abandon these food sources, and randomly generate new food sources as follows:(5)xnik+1=rand0,1×ubi−lbi+lbi,trial>limit,xnik,trial≤limit.In formula (5), trial is the number of times the bee optimizes the food source. Through the reconnaissance bee foraging strategy, the diversity of food sources can be increased, and the artificial bee colony algorithm can jump out of the local optimal value. This is the negative feedback link of the artificial bee colony algorithm. The artificial bee colony algorithm process is shown in Figure 3.Figure 3
Flowchart of artificial bee colony algorithm.


### 2.2. Improved Artificial Bee Colony Algorithm

In the subsequent subsections, the improved artificial bee colony algorithm is explained. The working mechanism and its technical details are provided.


#### 2.2.1. Optimization Method of Artificial Bee Colony Algorithm

(1)
A star algorithm: a star algorithm is a typical heuristic search algorithm, which has been widely used in games, robot path planning, and other fields. The evaluation function of the A star algorithm is as follows:(6)fn=gn+hn.In formula (6), gn is the path cost from the initial node to node n , and hn is the estimated minimum path cost from node n to the target node, which is called the heuristic function. If the heuristic function hn satisfies certain conditions and has sufficient time and space information, the A star search is complete and optimal.(2)
Particle swarm algorithm: the particle swarm algorithm is an intelligent algorithm that simulates the foraging and flight behavior of bird swarms in nature. The algorithm is carried out according to the process of initialization, iterative update, and finding the optimal solution [8]. In the iterative process, the particle updates its own state by tracking two extreme values: one is the individual extreme value, that is, the current optimal solution of the particle itself, and the other is the global extreme value, that is, the current optimal solution of the entire population. The particle updates its speed and position according to the following formula:(7)vk+1=vk+c1r1pbestk−xk+c2r2gbestk−xk,xk+1=xk+vk+1.In formula (7), xk is the current position of the particle, vk is the current velocity vector of the particle, pbestk is the optimal solution position currently found by the particle, gbestk is the optimal solution position currently found for the entire population, c1 and c2 are learning factors and social cognition factor, respectively, and r1 and r2 are random numbers between 0,1.(3)
Octree algorithm: the octree algorithm is also called a hierarchical tree structure, which is a tree-like data structure that describes a three-dimensional space [9]. The application of octree is mainly concentrated in the fields of computer graphics, computer vision, and image processing. The octree algorithm has a simple structure and easy set operations. During the path planning process, the group can easily detect target points and obstacles based on the correlation information between nodes, so as to react quickly. According to the characteristics of the shortest path selection of cold chain logistics transportation, the octree data structure is constructed as follows:(8)ClassOctreeintindex;intdepth;Obbbox;Octree∗parent;Octree∗child8;Meshmeshn;//Member function.In formula (8), index is the sequence number of the tree node, depth is the depth information of the octree node, box describes the information of the constructed Obb bounding box, parent stores the parent node information of the node, and child stores the 8-child-node information of the node. If the node is a leaf node, child is empty and mesh is the member variable of the node.


#### 2.2.2. Improved Artificial Bee Colony Algorithm

In order to improve the performance of the artificial bee colony algorithm and to make the algorithm suitable for solving the shortest path selection task of cold chain logistics transportation, the artificial bee colony algorithm is optimized [10], and the optimization content is as follows:(1)
Improvement of algorithm initialization: in order to ensure that cold chain logistics and transportation will not collide with obstacles and to ensure the safety of cold chain logistics and transportation [11], in the food source initialization method in this paper, the quality of the initial food source is higher than that of the path point obtained when obstacles are included, the algorithm convergence speed is accelerated, the search space of the algorithm is reduced, and the running speed is increased. The newly proposed food source is initialized as follows:(9)xni=rand0,1×ubi−lbi+lbi,subjectto:xni⊄areaA.In formula (9), areaA refers to the range where obstacle A is located. If it is an environment with multiple obstacles, A in areaA refers to the range of all obstacles.(2)
New food source generation method: in order to speed up the convergence speed of the algorithm, the random selection factor is improved. The new random selection factor should have a tendency to decrease with the number of iterations of the algorithm, but it should not make the random selection factor of the algorithm too small. The new random selection factors are as follows:(10)ε=e−Loop/MaxLoop×rand−1,1.In formula (10), Loop is the current iteration number of the algorithm, and MaxLoop is the maximum iteration number of the algorithm.(3)
Objective function and food source evaluation strategy: the artificial bee colony algorithm applied to the shortest path selection of cold chain logistics transportation needs to design a suitable objective function. The objective function considers three optimization goals: the shortest path length goal of cold chain logistics transportation, the shortest path safety goal of cold chain logistics transportation, and the shortest path smoothness goal of cold chain logistics transportation [12]. The objective function of each path designed after weighted synthesis is as follows:(11)Objv=∑i=1Stepω1×dist_goali+ω2×dist_obsi+ω3×∑i=2Stepθi−θi−1=∑i=1Stepω1×fii×xi−xgoal2+yi−ygoal2+ω2×∑k=1obstf2qixi−Oxk2+yi−Oyk2+ω3×∑i=2Stepθi−θi−1.In formula (11), dist_goali represents the distance from the shortest point xi,yi of cold chain logistics transportation to the target point xgoal,ygoal, dist_obsi is the distance from the shortest point xi,yi of cold chain logistics transportation to the obstacle Oxk,Oyk , obst is the number of obstacles, and ω1,ω2,ω3 is the weight coefficient.


## 2.1. Artificial Bee Colony Algorithm

Artificial bee colony algorithm solves the function optimization problem by simulating bee colony to find excellent honey source [6]. Because the algorithm has the advantages of simple and easy implementation, few control parameters, and strong robustness and is suitable for dealing with high-dimensional optimization problems in engineering, it is widely used in the fields of signal and image processing, communication, control, data mining, and so on.


### 2.1.1. Foraging Model of Artificial Bee Colony Algorithm

The design of artificial bee colony algorithm originates from the foraging behavior of bees in nature. The bee foraging model has three components, food sources, employed bees, and unemployed bees, and two basic behavior patterns, recruiting bees to collect nectar and giving up food sources. Among them, nonhired bees include onlooker bees and scout bees. The foraging model of artificial bee colony algorithm is shown in Figure1.Figure 1
Foraging model of artificial bee colony algorithm.The three components of the foraging model of the artificial bee colony algorithm are introduced as follows:(1)
Food source: the food source is the honey source to be searched by bees when foraging. The fitness value calculated by the food source indicates the advantages and disadvantages of the obtained solution. In the standard artificial bee colony algorithm, the value of food source is expressed by its fitness value.(2)
Employed bees: employed bees are also called leading bees, which carry current nectar source information and share the obtained nectar source information with other bees with a certain probability. After other bees obtain the information shared by the hired bees, they will conduct selective foraging based on this information. At the same time, the hired bee will optimize the food source based on the current food source information.(3)
Unemployed bees: according to the different division of labor of unemployed bees, they can be divided into two types: observation bees and reconnaissance bees. The first task of these bees is to search for and optimize the source of nectar. Observing bees choose to forage near the hive based on the food source information provided by the hired bees.The foraging model of artificial bee colony algorithm has two basic behavior patterns: one is to recruit bees to collect nectar, and the other is to give up food sources. The introduction is as follows:(1)
Recruiting bees to collect nectar: when hired bees find a nectar-rich food source, they will use swing dances at the hive to exchange food source information with other bees, attracting other bees to collect nectar. In this way, more and more bees will come to gather nectar near this food source, and this food source will be optimized. This is a recruitment behavior for the food source. This behavior forms the positive feedback effect of bee foraging.(2)
Abandon food source: when the reconnaissance bee finds that the nectar content of a food source is very scarce compared with other food sources through comparison, the reconnaissance bee will actively abandon this food source and search for a new food source, which is the behavior of abandoning food source in artificial bee colony algorithm. This behavior forms a negative feedback effect of bee foraging.The role conversion relationship of the three types of bees in the artificial bee colony algorithm is shown in Figure2.Figure 2
Role transformation relationship of honey bee.Whether bees can quickly find high-quality food sources is closely related to their internal food source selection mechanism. In the process of collecting honey, the reconnaissance bee will return to the hive after searching for a new food source and exchange information with the observation bee waiting in the hive through swing dance. Observing bees have two choices after watching the swing dance of reconnaissance bees: First, if the food source information meets their own expectations, they will collect nectar based on the nectar source information of the reconnaissance bees. Second, if the food source information is not within the scope of its own expectations, they continue to wait in the hive for new food source information. The roles of the three types of bees are not fixed and will change according to the nectar collection situation. In addition to observing bees transforming into hired bees to collect nectar, when the corresponding food source is exhausted, hired bees will also transform into scout bees to find new high-quality food sources.


### 2.1.2. Algorithm Model of Artificial Bee Colony Algorithm

The algorithm model of artificial bee colony algorithm can be abstracted from the foraging model of natural bees. As an intelligent optimization algorithm, artificial bee colony algorithm can rely on the self-organization ability of bees to realize the positive and negative feedback mechanism of the algorithm [7]. In the following section, we present the algorithm model of artificial bee colony algorithm:(1)
Initialization strategy: the initialization process of the artificial bee colony algorithm will form an initial food source. The algorithm produces a set of initial solutionsx1,x2,...,xn,...,xN; the vector xn is the solution that needs to be optimized during each iteration:(1)xni=rand0,1×ubi−lbi+lbi.In formula (1), lbi is the minimum value that xni can achieve, ubi is the maximum value that xni can achieve, rand0,1 refers to generating a random number between 0,1, and n∈1,2,...,FoodNumber, where FoodNumber is the number of food sources.(2)
Food source evaluation strategy: after the food source is initialized, it is necessary to use the food source evaluation strategy to evaluate its fitness value. The purpose of the food source evaluation strategy is to compare different food sources in order to preserve the food sources rich in nectar and to abandon the food sources lacking in nectar. Another function of the food source evaluation strategy is to calculate the attraction of the food source to the observer bee. A food source evaluation method of artificial bee colony algorithm is as follows:(2)fitnessnxn=11+fnxn,fnxn≥0,1+fnxn,fnxn<0.In formula (2), fnxn is the objective function value corresponding to the solution vector xn, n∈1,2,...,FoodNumber.(3)
Employed bee foraging strategy: employed bees will remember the location of food sources rich in nectar and find better food sources based on this memory. The methods for hiring bees to find new food sources near nectar sources are as follows:(3)xni′=ubi,xni+εnixni−xki>ubi,lbi,xni+εnixni−xki<lbi,xni+εnixni−xki,otherwise.In formula (3), xni′ is the newly generated food source, xni is the current food source location, εni is the search coefficient, which is between −1,1, and xki is a randomly selected food from all food sources which is different from xni source. Among them, k∈1,2,...,FoodNumber. When a new source of nectar is found, the hired bee will evaluate the newly generated food source, calculate its fitness value, and decide whether to abandon the nectar source in the original memory.(4)
Observing bee foraging strategy: observing bees will wait near the hive, and they will search for food based on the food source information brought by the hired bees when they return. First, they use the fitnessfitnessxn of the food source to calculate the possibility probabilityn of choosing each food source. The calculation method is as follows:(4)probabilityn=fitnessxn∑n=1Nfitnessxn.If the calculation result meets the expected value of the observation bee, the observation bee will turn into a hired bee and select this food source for foraging. This is the positive feedback link of the artificial bee colony algorithm.(5)
Scout bee foraging strategy: scout bees will select those food sources that have not been improved after the maximum number of selections oflimit times of nectar collection, abandon these food sources, and randomly generate new food sources as follows:(5)xnik+1=rand0,1×ubi−lbi+lbi,trial>limit,xnik,trial≤limit.In formula (5), trial is the number of times the bee optimizes the food source. Through the reconnaissance bee foraging strategy, the diversity of food sources can be increased, and the artificial bee colony algorithm can jump out of the local optimal value. This is the negative feedback link of the artificial bee colony algorithm. The artificial bee colony algorithm process is shown in Figure 3.Figure 3
Flowchart of artificial bee colony algorithm.


## 2.1.1. Foraging Model of Artificial Bee Colony Algorithm

The design of artificial bee colony algorithm originates from the foraging behavior of bees in nature. The bee foraging model has three components, food sources, employed bees, and unemployed bees, and two basic behavior patterns, recruiting bees to collect nectar and giving up food sources. Among them, nonhired bees include onlooker bees and scout bees. The foraging model of artificial bee colony algorithm is shown in Figure1.Figure 1
Foraging model of artificial bee colony algorithm.The three components of the foraging model of the artificial bee colony algorithm are introduced as follows:(1)
Food source: the food source is the honey source to be searched by bees when foraging. The fitness value calculated by the food source indicates the advantages and disadvantages of the obtained solution. In the standard artificial bee colony algorithm, the value of food source is expressed by its fitness value.(2)
Employed bees: employed bees are also called leading bees, which carry current nectar source information and share the obtained nectar source information with other bees with a certain probability. After other bees obtain the information shared by the hired bees, they will conduct selective foraging based on this information. At the same time, the hired bee will optimize the food source based on the current food source information.(3)
Unemployed bees: according to the different division of labor of unemployed bees, they can be divided into two types: observation bees and reconnaissance bees. The first task of these bees is to search for and optimize the source of nectar. Observing bees choose to forage near the hive based on the food source information provided by the hired bees.The foraging model of artificial bee colony algorithm has two basic behavior patterns: one is to recruit bees to collect nectar, and the other is to give up food sources. The introduction is as follows:(1)
Recruiting bees to collect nectar: when hired bees find a nectar-rich food source, they will use swing dances at the hive to exchange food source information with other bees, attracting other bees to collect nectar. In this way, more and more bees will come to gather nectar near this food source, and this food source will be optimized. This is a recruitment behavior for the food source. This behavior forms the positive feedback effect of bee foraging.(2)
Abandon food source: when the reconnaissance bee finds that the nectar content of a food source is very scarce compared with other food sources through comparison, the reconnaissance bee will actively abandon this food source and search for a new food source, which is the behavior of abandoning food source in artificial bee colony algorithm. This behavior forms a negative feedback effect of bee foraging.The role conversion relationship of the three types of bees in the artificial bee colony algorithm is shown in Figure2.Figure 2
Role transformation relationship of honey bee.Whether bees can quickly find high-quality food sources is closely related to their internal food source selection mechanism. In the process of collecting honey, the reconnaissance bee will return to the hive after searching for a new food source and exchange information with the observation bee waiting in the hive through swing dance. Observing bees have two choices after watching the swing dance of reconnaissance bees: First, if the food source information meets their own expectations, they will collect nectar based on the nectar source information of the reconnaissance bees. Second, if the food source information is not within the scope of its own expectations, they continue to wait in the hive for new food source information. The roles of the three types of bees are not fixed and will change according to the nectar collection situation. In addition to observing bees transforming into hired bees to collect nectar, when the corresponding food source is exhausted, hired bees will also transform into scout bees to find new high-quality food sources.


## 2.1.2. Algorithm Model of Artificial Bee Colony Algorithm

The algorithm model of artificial bee colony algorithm can be abstracted from the foraging model of natural bees. As an intelligent optimization algorithm, artificial bee colony algorithm can rely on the self-organization ability of bees to realize the positive and negative feedback mechanism of the algorithm [7]. In the following section, we present the algorithm model of artificial bee colony algorithm:(1)
Initialization strategy: the initialization process of the artificial bee colony algorithm will form an initial food source. The algorithm produces a set of initial solutionsx1,x2,...,xn,...,xN; the vector xn is the solution that needs to be optimized during each iteration:(1)xni=rand0,1×ubi−lbi+lbi.In formula (1), lbi is the minimum value that xni can achieve, ubi is the maximum value that xni can achieve, rand0,1 refers to generating a random number between 0,1, and n∈1,2,...,FoodNumber, where FoodNumber is the number of food sources.(2)
Food source evaluation strategy: after the food source is initialized, it is necessary to use the food source evaluation strategy to evaluate its fitness value. The purpose of the food source evaluation strategy is to compare different food sources in order to preserve the food sources rich in nectar and to abandon the food sources lacking in nectar. Another function of the food source evaluation strategy is to calculate the attraction of the food source to the observer bee. A food source evaluation method of artificial bee colony algorithm is as follows:(2)fitnessnxn=11+fnxn,fnxn≥0,1+fnxn,fnxn<0.In formula (2), fnxn is the objective function value corresponding to the solution vector xn, n∈1,2,...,FoodNumber.(3)
Employed bee foraging strategy: employed bees will remember the location of food sources rich in nectar and find better food sources based on this memory. The methods for hiring bees to find new food sources near nectar sources are as follows:(3)xni′=ubi,xni+εnixni−xki>ubi,lbi,xni+εnixni−xki<lbi,xni+εnixni−xki,otherwise.In formula (3), xni′ is the newly generated food source, xni is the current food source location, εni is the search coefficient, which is between −1,1, and xki is a randomly selected food from all food sources which is different from xni source. Among them, k∈1,2,...,FoodNumber. When a new source of nectar is found, the hired bee will evaluate the newly generated food source, calculate its fitness value, and decide whether to abandon the nectar source in the original memory.(4)
Observing bee foraging strategy: observing bees will wait near the hive, and they will search for food based on the food source information brought by the hired bees when they return. First, they use the fitnessfitnessxn of the food source to calculate the possibility probabilityn of choosing each food source. The calculation method is as follows:(4)probabilityn=fitnessxn∑n=1Nfitnessxn.If the calculation result meets the expected value of the observation bee, the observation bee will turn into a hired bee and select this food source for foraging. This is the positive feedback link of the artificial bee colony algorithm.(5)
Scout bee foraging strategy: scout bees will select those food sources that have not been improved after the maximum number of selections oflimit times of nectar collection, abandon these food sources, and randomly generate new food sources as follows:(5)xnik+1=rand0,1×ubi−lbi+lbi,trial>limit,xnik,trial≤limit.In formula (5), trial is the number of times the bee optimizes the food source. Through the reconnaissance bee foraging strategy, the diversity of food sources can be increased, and the artificial bee colony algorithm can jump out of the local optimal value. This is the negative feedback link of the artificial bee colony algorithm. The artificial bee colony algorithm process is shown in Figure 3.Figure 3
Flowchart of artificial bee colony algorithm.


## 2.2. Improved Artificial Bee Colony Algorithm

In the subsequent subsections, the improved artificial bee colony algorithm is explained. The working mechanism and its technical details are provided.


### 2.2.1. Optimization Method of Artificial Bee Colony Algorithm

(1)
A star algorithm: a star algorithm is a typical heuristic search algorithm, which has been widely used in games, robot path planning, and other fields. The evaluation function of the A star algorithm is as follows:(6)fn=gn+hn.In formula (6), gn is the path cost from the initial node to node n , and hn is the estimated minimum path cost from node n to the target node, which is called the heuristic function. If the heuristic function hn satisfies certain conditions and has sufficient time and space information, the A star search is complete and optimal.(2)
Particle swarm algorithm: the particle swarm algorithm is an intelligent algorithm that simulates the foraging and flight behavior of bird swarms in nature. The algorithm is carried out according to the process of initialization, iterative update, and finding the optimal solution [8]. In the iterative process, the particle updates its own state by tracking two extreme values: one is the individual extreme value, that is, the current optimal solution of the particle itself, and the other is the global extreme value, that is, the current optimal solution of the entire population. The particle updates its speed and position according to the following formula:(7)vk+1=vk+c1r1pbestk−xk+c2r2gbestk−xk,xk+1=xk+vk+1.In formula (7), xk is the current position of the particle, vk is the current velocity vector of the particle, pbestk is the optimal solution position currently found by the particle, gbestk is the optimal solution position currently found for the entire population, c1 and c2 are learning factors and social cognition factor, respectively, and r1 and r2 are random numbers between 0,1.(3)
Octree algorithm: the octree algorithm is also called a hierarchical tree structure, which is a tree-like data structure that describes a three-dimensional space [9]. The application of octree is mainly concentrated in the fields of computer graphics, computer vision, and image processing. The octree algorithm has a simple structure and easy set operations. During the path planning process, the group can easily detect target points and obstacles based on the correlation information between nodes, so as to react quickly. According to the characteristics of the shortest path selection of cold chain logistics transportation, the octree data structure is constructed as follows:(8)ClassOctreeintindex;intdepth;Obbbox;Octree∗parent;Octree∗child8;Meshmeshn;//Member function.In formula (8), index is the sequence number of the tree node, depth is the depth information of the octree node, box describes the information of the constructed Obb bounding box, parent stores the parent node information of the node, and child stores the 8-child-node information of the node. If the node is a leaf node, child is empty and mesh is the member variable of the node.


### 2.2.2. Improved Artificial Bee Colony Algorithm

In order to improve the performance of the artificial bee colony algorithm and to make the algorithm suitable for solving the shortest path selection task of cold chain logistics transportation, the artificial bee colony algorithm is optimized [10], and the optimization content is as follows:(1)
Improvement of algorithm initialization: in order to ensure that cold chain logistics and transportation will not collide with obstacles and to ensure the safety of cold chain logistics and transportation [11], in the food source initialization method in this paper, the quality of the initial food source is higher than that of the path point obtained when obstacles are included, the algorithm convergence speed is accelerated, the search space of the algorithm is reduced, and the running speed is increased. The newly proposed food source is initialized as follows:(9)xni=rand0,1×ubi−lbi+lbi,subjectto:xni⊄areaA.In formula (9), areaA refers to the range where obstacle A is located. If it is an environment with multiple obstacles, A in areaA refers to the range of all obstacles.(2)
New food source generation method: in order to speed up the convergence speed of the algorithm, the random selection factor is improved. The new random selection factor should have a tendency to decrease with the number of iterations of the algorithm, but it should not make the random selection factor of the algorithm too small. The new random selection factors are as follows:(10)ε=e−Loop/MaxLoop×rand−1,1.In formula (10), Loop is the current iteration number of the algorithm, and MaxLoop is the maximum iteration number of the algorithm.(3)
Objective function and food source evaluation strategy: the artificial bee colony algorithm applied to the shortest path selection of cold chain logistics transportation needs to design a suitable objective function. The objective function considers three optimization goals: the shortest path length goal of cold chain logistics transportation, the shortest path safety goal of cold chain logistics transportation, and the shortest path smoothness goal of cold chain logistics transportation [12]. The objective function of each path designed after weighted synthesis is as follows:(11)Objv=∑i=1Stepω1×dist_goali+ω2×dist_obsi+ω3×∑i=2Stepθi−θi−1=∑i=1Stepω1×fii×xi−xgoal2+yi−ygoal2+ω2×∑k=1obstf2qixi−Oxk2+yi−Oyk2+ω3×∑i=2Stepθi−θi−1.In formula (11), dist_goali represents the distance from the shortest point xi,yi of cold chain logistics transportation to the target point xgoal,ygoal, dist_obsi is the distance from the shortest point xi,yi of cold chain logistics transportation to the obstacle Oxk,Oyk , obst is the number of obstacles, and ω1,ω2,ω3 is the weight coefficient.


## 2.2.1. Optimization Method of Artificial Bee Colony Algorithm

(1)
A star algorithm: a star algorithm is a typical heuristic search algorithm, which has been widely used in games, robot path planning, and other fields. The evaluation function of the A star algorithm is as follows:(6)fn=gn+hn.In formula (6), gn is the path cost from the initial node to node n , and hn is the estimated minimum path cost from node n to the target node, which is called the heuristic function. If the heuristic function hn satisfies certain conditions and has sufficient time and space information, the A star search is complete and optimal.(2)
Particle swarm algorithm: the particle swarm algorithm is an intelligent algorithm that simulates the foraging and flight behavior of bird swarms in nature. The algorithm is carried out according to the process of initialization, iterative update, and finding the optimal solution [8]. In the iterative process, the particle updates its own state by tracking two extreme values: one is the individual extreme value, that is, the current optimal solution of the particle itself, and the other is the global extreme value, that is, the current optimal solution of the entire population. The particle updates its speed and position according to the following formula:(7)vk+1=vk+c1r1pbestk−xk+c2r2gbestk−xk,xk+1=xk+vk+1.In formula (7), xk is the current position of the particle, vk is the current velocity vector of the particle, pbestk is the optimal solution position currently found by the particle, gbestk is the optimal solution position currently found for the entire population, c1 and c2 are learning factors and social cognition factor, respectively, and r1 and r2 are random numbers between 0,1.(3)
Octree algorithm: the octree algorithm is also called a hierarchical tree structure, which is a tree-like data structure that describes a three-dimensional space [9]. The application of octree is mainly concentrated in the fields of computer graphics, computer vision, and image processing. The octree algorithm has a simple structure and easy set operations. During the path planning process, the group can easily detect target points and obstacles based on the correlation information between nodes, so as to react quickly. According to the characteristics of the shortest path selection of cold chain logistics transportation, the octree data structure is constructed as follows:(8)ClassOctreeintindex;intdepth;Obbbox;Octree∗parent;Octree∗child8;Meshmeshn;//Member function.In formula (8), index is the sequence number of the tree node, depth is the depth information of the octree node, box describes the information of the constructed Obb bounding box, parent stores the parent node information of the node, and child stores the 8-child-node information of the node. If the node is a leaf node, child is empty and mesh is the member variable of the node.


## 2.2.2. Improved Artificial Bee Colony Algorithm

In order to improve the performance of the artificial bee colony algorithm and to make the algorithm suitable for solving the shortest path selection task of cold chain logistics transportation, the artificial bee colony algorithm is optimized [10], and the optimization content is as follows:(1)
Improvement of algorithm initialization: in order to ensure that cold chain logistics and transportation will not collide with obstacles and to ensure the safety of cold chain logistics and transportation [11], in the food source initialization method in this paper, the quality of the initial food source is higher than that of the path point obtained when obstacles are included, the algorithm convergence speed is accelerated, the search space of the algorithm is reduced, and the running speed is increased. The newly proposed food source is initialized as follows:(9)xni=rand0,1×ubi−lbi+lbi,subjectto:xni⊄areaA.In formula (9), areaA refers to the range where obstacle A is located. If it is an environment with multiple obstacles, A in areaA refers to the range of all obstacles.(2)
New food source generation method: in order to speed up the convergence speed of the algorithm, the random selection factor is improved. The new random selection factor should have a tendency to decrease with the number of iterations of the algorithm, but it should not make the random selection factor of the algorithm too small. The new random selection factors are as follows:(10)ε=e−Loop/MaxLoop×rand−1,1.In formula (10), Loop is the current iteration number of the algorithm, and MaxLoop is the maximum iteration number of the algorithm.(3)
Objective function and food source evaluation strategy: the artificial bee colony algorithm applied to the shortest path selection of cold chain logistics transportation needs to design a suitable objective function. The objective function considers three optimization goals: the shortest path length goal of cold chain logistics transportation, the shortest path safety goal of cold chain logistics transportation, and the shortest path smoothness goal of cold chain logistics transportation [12]. The objective function of each path designed after weighted synthesis is as follows:(11)Objv=∑i=1Stepω1×dist_goali+ω2×dist_obsi+ω3×∑i=2Stepθi−θi−1=∑i=1Stepω1×fii×xi−xgoal2+yi−ygoal2+ω2×∑k=1obstf2qixi−Oxk2+yi−Oyk2+ω3×∑i=2Stepθi−θi−1.In formula (11), dist_goali represents the distance from the shortest point xi,yi of cold chain logistics transportation to the target point xgoal,ygoal, dist_obsi is the distance from the shortest point xi,yi of cold chain logistics transportation to the obstacle Oxk,Oyk , obst is the number of obstacles, and ω1,ω2,ω3 is the weight coefficient.


## 3. Shortest Path Selection Algorithm of Cold Chain Logistics Transportation

In this paper, the improved artificial bee colony algorithm is used to select the shortest path of cold chain logistics transportation. The algorithm introduces the population adaptive mechanism of particle swarm optimization algorithm. Particles dynamically control the path through interaction and dynamically update the path according to the dynamic detection factorρ and octree modeling environment information, so as to improve the convergence of the algorithm [13]. The reconnaissance bee carries out local optimal detection under the control of abandoning the honey source threshold to avoid the algorithm falling into local optimization. The shortest path selection algorithm flow of cold chain logistics transportation is as shown in Figure 4.Figure 4
Flowchart of the shortest path selection algorithm.The specific execution process of the shortest path selection algorithm for cold chain logistics transportation is as follows:(i)
Step 1: particle coding: for ad-dimensional optimization problem, the algorithm first randomly initializes the position and velocity of each particle(ii)
Step 2: static environment preprocessing: imprecise grid division of the environment of the group, that is, spatial division using the octree method, and at the same time setting attributeμ and weight ω to the node(iii)
Step 3: dynamic path planning: the hired bees randomly select a new nectar source to collect nectar, and the observing bees select the nectar source information of the hired bee through the greedy selection mechanism and environmental coding information(iv)
Step 4: group behavior control: the individual particles use the information sharing mechanism to control the group adaptive behavior, learn from each other's experience to control the individual path, and interact with the environment through the octree node information and the dynamic detection factorρ(v)
Step 5: afterlimit cycles, judge whether there is a solution that needs to be discarded; if it exists, the scout bee will generate a new solution instead; otherwise, return to step 3 to continue execution(vi)
Step 6: after the maximum number of cycles, the path planning is completed, and the global optimal solution and the shortest path are output


### 3.1. Algorithm Initialization

For ad-dimensional optimization problem, the algorithm first initializes each individual's position, velocity, and m possible solutions (i.e., honey) Yi=yi1,yi2,...,yid,i=1,2,...,m. Set the group size to N, and randomly generate individual position matrix X and velocity matrix V within a limited range:(12)X=x11x12x13x21x22x23⋯⋯⋯xN1xN2xN3,V=v11v12v13v21v22v23⋯⋯⋯vN1vN2vN3.In order to avoid the problem that the performance of the algorithm is affected by the possible uneven distribution of the randomly generated initial solution, the intercell generation method is used to initialize the possible solution, and the equivalent interval is taken between cells; that is, the optimization range is evenly divided intoN cells. The intercell generation method can accelerate the convergence speed of the algorithm.


### 3.2. Dynamic Path Update

When selecting the target point, the hired bee uses the formulavij=xij+ϕijxij−xkj+ϕijD to generate a new target point around the target point. Among them, k is randomly selected from 1,2,...,m and k≠i, j∈1,2,...,d , and D represents the initial setting of the size of the octree node, ϕij∈−1,1. In this way, the particles dynamically adjust with the octree node as the unit in the process of selecting the target point. After the new honey source vij is generated, the fitness of vij and xij is judged as follows:(13)fitnessyi=αyi12+yi22+⋯+yid2+βSN+δωij.In formula (13), α,β,δ is the influence factor, S is the nectar content of the nectar source, and N is the number of particles that select the target point in this iterative operation. ω represents the weight of the octree node [14].After the hired bees complete the search, they inform the observation bees of the location and fitness of the nectar source, and the observation bees select the nectar source based on their fitness as follows:(14)pi=expfitnessi/T∑i=1SNexpfitnessi/T,T=T00.99c−1.In formula (14), fitnessi is the fitness of the i solution and pi is the probability of selecting the nectar source xi.


### 3.3. Adaptive Behavior Control

After the observation bee selects the nectar source,n individuals of the same nectar source yij are selected to form a small bee colony, and individual path planning is carried out through the information sharing mechanism to avoid individual collisions [15]. First, initialize the position xi, speed vi, individual extreme value pbest, and global extreme value gbest of each individual bee. When ω=0, calculate the individual fitness fxi according to fxi=αd+βfyij. Further environmental decomposition is done according to the octree modeling decomposition strategy, until the optimal path is found. Comprehensive consideration is given to factors such as the distance between the individual particle and the target position, the pros and cons of the target point, and the difficulty of the walking path. The position and velocity of the updated particles are as follows:(15)vid=ω′vid+c1randpid−xid+c2randpgd−xid,xid=xid+vid.In formula (15), ω′ is the inertia weight, c1 is the weight coefficient of the particle's own acceleration, c2 is the weight coefficient of the global acceleration, and rand is the random function on 0,1.


### 3.4. Fitness Function Control

In the nectar-collecting behavior of bees, the distance between the nectar source and the hive is used as the nectar source fitness evaluation standard as follows:(16)fitnessxi=xi1−yi12+xi2−yi22+⋯+xid−yid2.The distance between the individual bee and the nectar source and the average honey content of the individual are used as the fitness evaluation criteria of the individual bee as follows:(17)fitnessyi=αyi12+yi22+⋯+yid2+βSn.In formula (17), xi is the position of the particle, yi is the position of the nectar source, S is the nectar content, n is the number of individuals in the nectar source, and α,β is the influence factor.


### 3.5. Parameter Control

Afterlimit iterations, if the fitness of a nectar source xi is still at a low level, the nectar source is abandoned, and the scout bee generates a new solution to replace xi as(18)xij=xminj+randxmaxj−xminj.Observation bees and hired bees perform local searches, and observation bees and reconnaissance bees perform global searches, so as to achieve a balance between global decentralized search and local chemotaxis search. Through the above steps, the shortest path selection of cold chain logistics transportation is realized.


## 3.1. Algorithm Initialization

For ad-dimensional optimization problem, the algorithm first initializes each individual's position, velocity, and m possible solutions (i.e., honey) Yi=yi1,yi2,...,yid,i=1,2,...,m. Set the group size to N, and randomly generate individual position matrix X and velocity matrix V within a limited range:(12)X=x11x12x13x21x22x23⋯⋯⋯xN1xN2xN3,V=v11v12v13v21v22v23⋯⋯⋯vN1vN2vN3.In order to avoid the problem that the performance of the algorithm is affected by the possible uneven distribution of the randomly generated initial solution, the intercell generation method is used to initialize the possible solution, and the equivalent interval is taken between cells; that is, the optimization range is evenly divided intoN cells. The intercell generation method can accelerate the convergence speed of the algorithm.


## 3.2. Dynamic Path Update

When selecting the target point, the hired bee uses the formulavij=xij+ϕijxij−xkj+ϕijD to generate a new target point around the target point. Among them, k is randomly selected from 1,2,...,m and k≠i, j∈1,2,...,d , and D represents the initial setting of the size of the octree node, ϕij∈−1,1. In this way, the particles dynamically adjust with the octree node as the unit in the process of selecting the target point. After the new honey source vij is generated, the fitness of vij and xij is judged as follows:(13)fitnessyi=αyi12+yi22+⋯+yid2+βSN+δωij.In formula (13), α,β,δ is the influence factor, S is the nectar content of the nectar source, and N is the number of particles that select the target point in this iterative operation. ω represents the weight of the octree node [14].After the hired bees complete the search, they inform the observation bees of the location and fitness of the nectar source, and the observation bees select the nectar source based on their fitness as follows:(14)pi=expfitnessi/T∑i=1SNexpfitnessi/T,T=T00.99c−1.In formula (14), fitnessi is the fitness of the i solution and pi is the probability of selecting the nectar source xi.


## 3.3. Adaptive Behavior Control

After the observation bee selects the nectar source,n individuals of the same nectar source yij are selected to form a small bee colony, and individual path planning is carried out through the information sharing mechanism to avoid individual collisions [15]. First, initialize the position xi, speed vi, individual extreme value pbest, and global extreme value gbest of each individual bee. When ω=0, calculate the individual fitness fxi according to fxi=αd+βfyij. Further environmental decomposition is done according to the octree modeling decomposition strategy, until the optimal path is found. Comprehensive consideration is given to factors such as the distance between the individual particle and the target position, the pros and cons of the target point, and the difficulty of the walking path. The position and velocity of the updated particles are as follows:(15)vid=ω′vid+c1randpid−xid+c2randpgd−xid,xid=xid+vid.In formula (15), ω′ is the inertia weight, c1 is the weight coefficient of the particle's own acceleration, c2 is the weight coefficient of the global acceleration, and rand is the random function on 0,1.


## 3.4. Fitness Function Control

In the nectar-collecting behavior of bees, the distance between the nectar source and the hive is used as the nectar source fitness evaluation standard as follows:(16)fitnessxi=xi1−yi12+xi2−yi22+⋯+xid−yid2.The distance between the individual bee and the nectar source and the average honey content of the individual are used as the fitness evaluation criteria of the individual bee as follows:(17)fitnessyi=αyi12+yi22+⋯+yid2+βSn.In formula (17), xi is the position of the particle, yi is the position of the nectar source, S is the nectar content, n is the number of individuals in the nectar source, and α,β is the influence factor.


## 3.5. Parameter Control

Afterlimit iterations, if the fitness of a nectar source xi is still at a low level, the nectar source is abandoned, and the scout bee generates a new solution to replace xi as(18)xij=xminj+randxmaxj−xminj.Observation bees and hired bees perform local searches, and observation bees and reconnaissance bees perform global searches, so as to achieve a balance between global decentralized search and local chemotaxis search. Through the above steps, the shortest path selection of cold chain logistics transportation is realized.


## 4. Experimental Analysis

In this section, we are going to validate the proposed method using experimentation. The algorithm is simulated in MATLAB.


### 4.1. Experimental Environment and Parameter Setting

In order to verify the effectiveness of the shortest path selection algorithm for cold chain logistics transportation based on the improved artificial bee colony, the simulation experiment uses MATLAB to write code to initialize the shortest path selection environment for cold chain logistics transportation as shown in Figure5.Figure 5
Environmental diagram of the shortest path selection of cold chain logistics transportation.The shortest path selection environment of cold chain logistics transportation is divided into 15 × 15 grids. The starting point of the shortest path of cold chain logistics transportation is grid 1, which is represented by the symbol ○, and the target point of the shortest path of cold chain logistics transportation is grid 211. Represented by the symbol △, the black part is an obstacle, and the white part is a free space. Applying the improved artificial bee colony algorithm to the shortest path selection of cold chain logistics transportation involves many parameters, and these factors have an impact on the optimization ability and convergence speed. The parameters of the improved artificial bee colony algorithm mainly include the size of the bee colonypopSize, the proportion of bees collected ratio, the maximum number of search times of the nectar source limit, the maximum number of iterations maxGen, and the length of the taboo table maxLen; the specific values are shown in Table 1.Table 1
Algorithm parameter setting table.
ParameterMeaningValuepopSizeColony size80ratioPercentage of bees collected0.5limitMaximum search times of honey source50maxGenMaximum number of iterations500maxLenLength of taboo table20


### 4.2. Experimental Evaluation Criteria

The selection of the shortest path of cold chain logistics transportation is to follow certain evaluation criteria in an environment with obstacles: path selection effect, accuracy, and required time. Find the collision-free optimal or suboptimal path from the starting point to the target point for cold chain logistics transportation. Generally, the shortest path is used as the evaluation criterion in path planning. The fitness function for establishing the path is as follows:(19)fit=k×L+1−k×E.In formula (19), k is the weight, L is the path length, and E is the collision penalty function of the path. The smaller the fit value, the shorter the planned path selection and the better the path selection effect.


### 4.3. Selection Effect of the Shortest Path of Cold Chain Logistics Transportation

In order to verify the shortest path selection effect of the proposed algorithm for cold chain logistics transportation, the algorithms in [4] and the algorithms in [5] are compared with the proposed algorithm, respectively, and the comparison results of the shortest path selection effects of different algorithms are obtained as shown in Figure 6.Figure 6
Comparison results of the shortest path selection effect of cold chain logistics transportation with different algorithms.Analysis of Figure6 shows that when the number of iterations is 500, the average fitness function of the algorithm of [4] is 0.75, the average fitness function of the algorithm of [5] is 0.6, and the average fitness function of the proposed algorithm is 0.1. It can be seen that, compared with the algorithm of [4] and the algorithm of [5], the average fitness function of the proposed algorithm is smaller, the selected path is shorter, and the path selection effect is better.


### 4.4. Time Required for the Shortest Path Selection of Cold Chain Logistics Transportation

In order to further verify the time required for the shortest path selection of cold chain logistics transportation of the proposed algorithm, the algorithms proposed in [4] and [5] and our proposed algorithm are tested to obtain the time required for the shortest path selection of cold chain logistics transportation. The results are shown in Figure 7.Figure 7
Comparison of the time required for selection of the shortest path.It is obvious from Figure7 that as the number of iterations increases, the time required to select the shortest path of cold chain logistics transportation with different algorithms increases. When the number of iterations is 500, the shortest path selection time of cold chain logistics transportation in the algorithm of [4] is 47 s, the shortest path selection time of cold chain logistics transportation in the algorithm of [5] is 56.5 s, and the shortest path selection time of cold chain logistics transportation in the proposed algorithm is only 22 s. It can be seen that, compared with the algorithm of [4] and the algorithm of [5], the shortest path selection time of the cold chain logistics transportation of the proposed algorithm is shorter.


### 4.5. Selection Accuracy of the Shortest Path of Cold Chain Logistics Transportation

On this basis, the shortest path selection accuracy of the proposed algorithm is further verified. The standard deviation of the shortest path selection of cold chain logistics transportation compared with the algorithm of [4], the algorithm of [5], and the proposed algorithm is given in Table 2.Table 2
Comparison results of the standard deviation of the shortest path selection of cold chain logistics transportation with different algorithms.
Number of iterations (time)The proposed algorithm (m)The algorithm of reference [4] (m)The algorithm of reference [5] (m)1000.212.431.422000.343.5917.93000.593.972.124000.774.983.225000.815.434.54According to the data in Table2, as the number of iterations increases, the standard deviation of the shortest path selection for cold chain logistics transportation of different algorithms increases. When the number of iterations is 500, the standard deviation of the shortest path selection of cold chain logistics transportation in the algorithm of [4] is 5.43 m, the standard deviation of the shortest path selection of cold chain logistics transportation in the algorithm of [5] is 4.54 m, and the standard deviation of the shortest path selection of cold chain logistics transportation in the proposed algorithm is only 0.81 m. It can be seen that, compared with the algorithm of [4] and the algorithm of [5], the standard deviation of the shortest path selection of cold chain logistics transportation of the proposed algorithm is smaller, which can effectively improve the accuracy of the shortest path selection of cold chain logistics transportation.


## 4.1. Experimental Environment and Parameter Setting

In order to verify the effectiveness of the shortest path selection algorithm for cold chain logistics transportation based on the improved artificial bee colony, the simulation experiment uses MATLAB to write code to initialize the shortest path selection environment for cold chain logistics transportation as shown in Figure5.Figure 5
Environmental diagram of the shortest path selection of cold chain logistics transportation.The shortest path selection environment of cold chain logistics transportation is divided into 15 × 15 grids. The starting point of the shortest path of cold chain logistics transportation is grid 1, which is represented by the symbol ○, and the target point of the shortest path of cold chain logistics transportation is grid 211. Represented by the symbol △, the black part is an obstacle, and the white part is a free space. Applying the improved artificial bee colony algorithm to the shortest path selection of cold chain logistics transportation involves many parameters, and these factors have an impact on the optimization ability and convergence speed. The parameters of the improved artificial bee colony algorithm mainly include the size of the bee colonypopSize, the proportion of bees collected ratio, the maximum number of search times of the nectar source limit, the maximum number of iterations maxGen, and the length of the taboo table maxLen; the specific values are shown in Table 1.Table 1
Algorithm parameter setting table.
ParameterMeaningValuepopSizeColony size80ratioPercentage of bees collected0.5limitMaximum search times of honey source50maxGenMaximum number of iterations500maxLenLength of taboo table20


## 4.2. Experimental Evaluation Criteria

The selection of the shortest path of cold chain logistics transportation is to follow certain evaluation criteria in an environment with obstacles: path selection effect, accuracy, and required time. Find the collision-free optimal or suboptimal path from the starting point to the target point for cold chain logistics transportation. Generally, the shortest path is used as the evaluation criterion in path planning. The fitness function for establishing the path is as follows:(19)fit=k×L+1−k×E.In formula (19), k is the weight, L is the path length, and E is the collision penalty function of the path. The smaller the fit value, the shorter the planned path selection and the better the path selection effect.


## 4.3. Selection Effect of the Shortest Path of Cold Chain Logistics Transportation

In order to verify the shortest path selection effect of the proposed algorithm for cold chain logistics transportation, the algorithms in [4] and the algorithms in [5] are compared with the proposed algorithm, respectively, and the comparison results of the shortest path selection effects of different algorithms are obtained as shown in Figure 6.Figure 6
Comparison results of the shortest path selection effect of cold chain logistics transportation with different algorithms.Analysis of Figure6 shows that when the number of iterations is 500, the average fitness function of the algorithm of [4] is 0.75, the average fitness function of the algorithm of [5] is 0.6, and the average fitness function of the proposed algorithm is 0.1. It can be seen that, compared with the algorithm of [4] and the algorithm of [5], the average fitness function of the proposed algorithm is smaller, the selected path is shorter, and the path selection effect is better.


## 4.4. Time Required for the Shortest Path Selection of Cold Chain Logistics Transportation

In order to further verify the time required for the shortest path selection of cold chain logistics transportation of the proposed algorithm, the algorithms proposed in [4] and [5] and our proposed algorithm are tested to obtain the time required for the shortest path selection of cold chain logistics transportation. The results are shown in Figure 7.Figure 7
Comparison of the time required for selection of the shortest path.It is obvious from Figure7 that as the number of iterations increases, the time required to select the shortest path of cold chain logistics transportation with different algorithms increases. When the number of iterations is 500, the shortest path selection time of cold chain logistics transportation in the algorithm of [4] is 47 s, the shortest path selection time of cold chain logistics transportation in the algorithm of [5] is 56.5 s, and the shortest path selection time of cold chain logistics transportation in the proposed algorithm is only 22 s. It can be seen that, compared with the algorithm of [4] and the algorithm of [5], the shortest path selection time of the cold chain logistics transportation of the proposed algorithm is shorter.


## 4.5. Selection Accuracy of the Shortest Path of Cold Chain Logistics Transportation

On this basis, the shortest path selection accuracy of the proposed algorithm is further verified. The standard deviation of the shortest path selection of cold chain logistics transportation compared with the algorithm of [4], the algorithm of [5], and the proposed algorithm is given in Table 2.Table 2
Comparison results of the standard deviation of the shortest path selection of cold chain logistics transportation with different algorithms.
Number of iterations (time)The proposed algorithm (m)The algorithm of reference [4] (m)The algorithm of reference [5] (m)1000.212.431.422000.343.5917.93000.593.972.124000.774.983.225000.815.434.54According to the data in Table2, as the number of iterations increases, the standard deviation of the shortest path selection for cold chain logistics transportation of different algorithms increases. When the number of iterations is 500, the standard deviation of the shortest path selection of cold chain logistics transportation in the algorithm of [4] is 5.43 m, the standard deviation of the shortest path selection of cold chain logistics transportation in the algorithm of [5] is 4.54 m, and the standard deviation of the shortest path selection of cold chain logistics transportation in the proposed algorithm is only 0.81 m. It can be seen that, compared with the algorithm of [4] and the algorithm of [5], the standard deviation of the shortest path selection of cold chain logistics transportation of the proposed algorithm is smaller, which can effectively improve the accuracy of the shortest path selection of cold chain logistics transportation.


## 5. Conclusion

The shortest path selection algorithm of cold chain logistics transportation based on improved artificial bee colony proposed in this paper gives full play to the advantages of improved artificial bee colony algorithm. Its shortest path selection accuracy of cold chain logistics transportation is high, which can effectively shorten the time required for the shortest path selection of cold chain logistics transportation, and has a good effect on the shortest path selection of cold chain logistics transportation. However, this method does not consider the influencing factors of transportation cost, carbon emission, and customer satisfaction in the process of selecting the shortest path of cold chain logistics transportation. Therefore, in the next research, we need to fully consider the factors affecting the objective function, such as traffic congestion, vehicle speed change, and customer dynamic demand change in the transportation process, so as to define and calculate the multiobjective optimization function, and further study is needed to improve the effectiveness of the proposed algorithm.



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*Source: 9007162-2021-11-10.xml*