# Optimization of Transportation Routing Problem for Fresh Food by Improved Ant Colony Algorithm Based on Tabu Search

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## Abstract

**:**

_{2}emissions. The fresh degree and CO

_{2}emissions are involved in the vehicle routing optimization problem in the cold chain logistics. In order to meet the quality requirement for fresh agricultural products and low carbon logistics, a novel routing optimization model considering the costs of quality deterioration and carbon emissions (Low Carbon and Freshness Degrees Vehicle Routing Problem (LCFD-VRP)) for cold chain distribution was established in this study. This model takes into account the fixed cost, fuel cost and time window penalty cost. An improved ant colony algorithm (IACA) is used to optimize the whole vehicle distribution routing with its strong global search ability. Tabu Search (TS) algorithm is used to search the single vehicle distribution routing with its good local search ability. An IACA combined with TS (IACATS) was proposed to solve the above LCFD-VRP model. The practicability of the model and the effectiveness of the above improved algorithm are verified using a real case study. The results of Zhoushan Dayang Refrigerated Logistics Co., Ltd. showed that, compared with the traditional algorithm, IACATS could reduce the dispatching of two refrigerated vehicles, thus lowering the total cost by 4.94%, shortening the actual transportation distance by 5.50% and cutting the total CO

_{2}emissions by 8.9%. Therefore, the LCFD-VRP model can effectively help to achieve the low carbon emissions, multi-variety and low-cost distribution of fresh agricultural products. The proposed model and IACATS algorithm would be used to optimize VRP in cold chain enterprises. The results of this study also provide management suggestions for cold chain enterprises to effectively balance economic cost and environmental cost.

## 1. Introduction

_{2}emissions and other greenhouse gases generated from distribution vehicles in the process of delivery. It leads to an increase in greenhouse gases and, as a result, air pollution and greenhouse effect will be intensified. The increased carbon emissions not only pollute the environment, but also raise the cost of logistics enterprises due to the implementation of national carbon-taxing policies [3]. Therefore, how to reduce carbon emissions in cold chain logistics, thereby alleviating the global warming caused by the greenhouse effect, has become a popular issue in the research field of cold chain logistics distribution routes [4].

## 2. Literature Review

#### 2.1. Research Considering the VRP Model in Cold Chain Logistics

_{2}emissions. Even though many experts and scholars achieved fruitful achievements in the VRP issue in the past several decades, by reviewing the previous literature, we draw the conclusion that the academic research of VRP in cold chain logistics is relatively sufficient. What remains to be proved is that VRP has extensive application value in cold chain logistics.

#### 2.2. Research Considering Fresh Degrees

#### 2.3. Research Considering Carbon Emissions

_{2}, NO

_{x}and CO as three major gas emissions in the open time-dependent vehicle routing problem. Liu et al. [35] proposed a method for calculating carbon emissions and established an integer programming model based on the load and working time constraints of the open pollution routing problem. Fornell et al. [36] investigated the vehicle travel time and carbon emissions, and established a non-linear mixed integer programming model for vehicle scheduling and routing assignment in urban distribution using the improved multi-objective particle swarm optimization algorithm. Zeng et al. [37] taking Zhuhai Express Company as an example, established a distribution route optimization model by treating vehicle load as a factor affecting fuel consumption and CO

_{2}emissions. Parasuraman et al. [38] constructed a distribution route optimization model with the lowest carbon emissions as the objective and based on the necessity of energy saving in cold chain logistics vehicle distribution. Wang et al. [39] considered the differences in energy consumption between the transportation and unloading processes caused by the opening of the refrigerated door, and established the optimal distribution route model of fresh agricultural products in terms of carbon emissions and with the objective of generating the lowest cost.

#### 2.4. Research Considering the Optimization Algorithms

## 3. Model

#### 3.1. Problem Description

**Assumptions:**

- (1)
- Each customer can only be distributed to by one distribution center (DC), and all vehicles have the same loading ability.
- (2)
- The fresh products would deliver from DC and then to customers, with the assumption that each route begins and ends at the same DC.
- (3)
- We do not need to consider the customer’s request ahead of time. The demand of the customers is known or can be estimated in advance.

**Notations:**

#### 3.2. Objective Function of the LCFD-VRP

^{kj}

_{jk}is the total load at the departure time of vehicle k minus the total demand of customer points that have been served. Equation (6) suggests that the quantity of goods carried by each distribution vehicle when it sets out from the distribution center is equal to the total demand of the customer points for which the vehicle provides services.

_{i},l

_{j}] for service.

#### 3.3. Factors Considered in the Model

#### 3.3.1. Cost Profile

#### 3.3.2. Fixed Cost

_{k0}j0j

_{k}= 1, it means that vehicle k travels from the distribution center to the customer point j (otherwise 0). Then sigma j = 1nxk

_{j}, where sigma indicates whether vehicle k is used, so the fixed cost of the vehicle is as follows [52]:

#### 3.3.3. Fuel Cost and Carbon Cost

_{2}emissions coefficient, fuel consumption and carbon trading price. The fuel consumption of the vehicle is related to the vehicle engine model, driving speed and load, and the specific parameters are shown in Table 2. The fuel consumption of delivery vehicle k from customer point i to customer point j can be calculated as follows [53]:

_{tf}η), α = T + g sin ε + gC

_{r}cosε, β = 0.5C

_{d}PS.

_{0}. Both the vehicle acceleration T and road slope ε were zero, namely α = gCr.

#### 3.2.4. Penalty Cost for Freshness Degradation

_{j}point j is the earliest time acceptable for the customer, and Tj is the time before the distribution vehicle reaches the customer’s deadline, which can be calculated as follows:

#### 3.2.5. Time Window Penalty Cost

## 4. Solving the Model Using IACATS

#### 4.1. Improved Ant Colony Algorithm

_{ij}denotes that Ant k on the edge (i,j) is the length of the path pheromone amount; ${p}_{ij}^{k}$ refers probability of ant k moving from node i to neighborhood node j; both α and β are parameters supporting regulation, which describe the weight of accumulated pheromones and self-heuristics in the path of ant movement. ‘Allowed k’ represents the random value of ant k within the allowed range.

_{k}(i) specifically describes the set of nodes visited by the number Ant k after the visit of node I. The q parameter is a random number in the range of [0, 1]. Q

_{0}can be determined before calculation. By adjusting this parameter, the algorithm can achieve a balance between diversified search and centralized search. At this point, when the ant selects the next node for transfer, a random parameter in the interval of [0, 1] will be generated, and the direction of ant transfer will be determined according to the size of this parameter.

#### Resetting the Rules of Updated Pheromone

_{min}. While, if pheromone values are over τ

_{max}we defined as τ

_{max}. In this way, it can avoid the pheromone in a certain path more than any other path pheromone, which quickly avoids all ants close to the path.

_{ij}(t) = C, and its positioning for maximum τ

_{max}. After completing 1 cycle, the ants who find the shortest path have right to release the pheromones from their passed path and keep the below rules:

#### 4.2. Local Optimization and Improvement

#### 4.3. Calculation Steps of the Algorithm

**Step 1**:

**Initialize**. set the parameters of the Nc = 0, ${\tau}_{ij}(0)$ = ${\tau}_{\mathrm{max}}$, then carry out parameter initialization of ${\tau}_{ij}^{k}$, α, β, ρ. The initial point should be included in the current disaggregation model and then be evaluated. The value of output is defined as Z;

**Step 2:**If the tabu list is not full, then improved ant colony algorithm is carried out. Except for the initial point, if it is not able to reach the vehicle quality time window required by vertex j in other remaining points, then it goes directly to the next step and calculate the total loading (

**Sum**). On the contrary, if it is meet the requirements of vehicle quality and time window in the remaining points, it will select point j in a random manner to solve the transition probability P

^{k}ij parameter and combine this parameter with random number (0–1) for comparative analysis. If the requirements are met, transfer Ant k to Point j and place point j in the disaggregation model set. If the requirements are not met, the vertex needs to be selected again;

**Step 3:**when all points are in the disaggregation model set, solve z

_{ki}. Then record the number of ants as m←k; otherwise, there is k←k+1, and then skip to

**step 2**and re-operate;

**Step 4:**if the

**Sum**generated in

**step 2**is less than

**Q**, select tabu local search mechanism to realize ant path optimization;

**Step 5:**solve the objective function value and updated pheromone.

**If Nc = Nc**then turn back

_{max}, then end the iterations. If not,**step 2**and reserve the current non-inferior solution;

**Step 6:**The next ant selects the different edges and update the tabu list. Given the edges (I,j) is the optimal path, it is analyzed to further solve ${\tau}_{ij}$(t+n) = $(1-\rho ){\tau}_{ij}(t)+\Delta {\tau}_{ij}^{\mathrm{min}}$; given the edges (I,j) is the non-optimal path, it is analyzed to solve ${\tau}_{ij}(t+n)=(1-\rho ){\tau}_{ij}(t)$; finally, analyze all edges (I,j) and set $\Delta {\tau}_{ij}^{\mathrm{min}}$$\leftarrow $0, Nc $\leftarrow $ Nc + 1 to update the tabu list;

**Step 7**: If the N

_{c}parameter value is lower than the set number of iterations, go to

**step 2**;

**Step 8**: If the N

_{c}parameter value is lower than the set number of iterations, output to the optimal results.

**Step 9: End**. The above calculation process in schematic illustration is in Figure 2.

## 5. Case Study

#### Parameter Profile

_{2}emissions coefficient was 2.63 kg/L, the fuel price was 6.95 Yuan/L, the CO

_{2}emissions price was 5 Yuan/kg and the biggest car load was 10 t.

## 6. Results

_{2}emissions was 44.48 kg. One of the most optimal distribution schemes is to use six transport vehicles to perform the distribution task with a total cost of 3602.73 Yuan. In addition, the total time spent was 477.33 min, and the total CO

_{2}emissions was 43.02 kg. The specific distribution routing information is shown in Table 5. If the traditional method was employed, the distribution scheme would be as follows: eight transport vehicles would be used to complete the distribution task, and the total cost, total time and total CO

_{2}emissions would be, respectively, 3840.55 Yuan, 505.12 min and 47.26 kg. In comparison, the improved genetic algorithm would reduce the dispatching of two refrigerated vehicles, cut the total cost by 4.94%, shorten the actual transportation distance by 5.50% and decrease the total CO

_{2}emissions by 8.9%.

#### 6.1. The Influences of Different Parameters on the Stability Performance of IACATS

#### 6.2. Parameter Sensitivity Analysis

_{2}emissions price and between carbon emissions and total cost in the optimization of cold chain distribution routing to fresh agricultural products, we adjusted different prices of fuel oil and CO

_{2}emissions, as shown in Figure 3 and Figure 4.

_{2}emissions will decrease. Figure 4 shows that when the carbon price rises, the freshness degree will be decreased generally and the carbon emissions will decline. Therefore, in order to encourage the adoption of low carbon cold chain logistics distribution, it is necessary to appropriately raise the fuel price or carbon price. It not only can reduce CO

_{2}emissions and energy consumption, but also decrease enterprises’ total costs. These experimental results would offer useful information to the government when figuring out corresponding policies and regulations. Moreover, these simulated results would serve as a reference for the selection of vehicle routing optimization of low carbon cold chain logistics.

#### 6.3. Effectiveness Analysis of IACATS Algorithm

## 7. Discussion

_{2}emissions by 8.9% compared with the traditional ant algorithm mode. Therefore, the LCFD-VRP model we proposed can effectively help to achieve the low carbon emissions and low cost of fresh agricultural products. This suggests that the proposed model and IACATS algorithm would be used to design and operate food distribution systems with high-quality fresh food and less environmental pollution.

_{2}emissions and fresh food. In addition, the influence of the energy consumption of refrigeration equipment on carbon emissions is often ignored. This paper aims to deal with optimization of VRP with CO

_{2}emission and fresh food. Most of the models only considered CO

_{2}emissions from the generation of fuel consumption [49]. CO

_{2}emissions in this paper are derived from two parts: the generation of fuel consumption and the energy consumption of refrigeration equipment. In order to achieve the lowest cost as the objective function, we considered costs such as the fixed costs, carbon emissions cost, time window penalty cost and freshness penalty cost. These costs cover most of the costs in cold chain logistics. Even though we considered the above-mentioned cost factors in the proposed model, more cost factors, such as fresh food damage costs, fresh food shortage costs and waiting time costs, should be included in the future model from the perspective overall consideration.

_{2}emissions reduced by 8.9% in our study shows that LCFD-VRP model can effectively reduce carbon emissions. From the government’s consideration, this method could be promoted in other similar cold chain logistics to raise the awareness of low carbon logistics. On the other hand, from cold chain logistics enterprise’s consideration, this method should be introduced into the daily routing optimization of cold chain logistics, because it can reduce the operation cost and can fulfill enterprise’s social responsibility, which inversely improve the competitiveness of enterprises in the marketplace.

## 8. Conclusions

_{2}emissions and raise the food fresh degree. The experimental results of this paper provide management suggestions for logistics enterprises to effectively balance economic costs and environmental costs in vehicle routing problems.

_{2}emissions by 8.9%. Therefore, the LCFD-VRP model can effectively help cold chain logistics enterprises to reduce the low carbon emissions and increase high quality fresh agricultural products.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

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Symbols | Descriptions |
---|---|

${x}_{ij}^{k}$ | 0–1 are decision variables. If k car serves customer point i, and goes to serve customer point j, ${x}_{ij}^{k}$ = 1, otherwise ${x}_{ij}^{k}$ = 0. |

d_{ij} | The distance from customer point i to customer point j/km |

P_{1} | The price of fresh agricultural products transported/(RMB t^{−1}) |

P_{2} | The price of fuel used by distribution vehicles/(RMB L^{−1}) |

P_{3} | Real-time carbon trading prices on the carbon exchange/(RMB t^{−1}) |

P_{4} | Fixed cost of the delivery vehicle/(RMB car number^{−1}) |

S_{i} | Service time/min of the delivery vehicle at customer point i |

$\left[{\ell}_{i},{l}_{i},{\overline{l}}_{i}\right]$ | Time window requirements of customer point i. Particularly, $\left[{\ell}_{i},{l}_{i}\right]$ is the best receiving time for customers, and ${\overline{l}}_{i}$ is the latest receiving time that customers can tolerate. |

$\overline{K}$ | Distribution vehicle collection $\overline{K}$= {1,2,3, ⋯,Κ}, where K represents the maximum number of vehicles in the distribution center |

Q | Maximum load of the distribution vehicle/t |

q_{i} | Quantity demanded/t at customer point i |

ρ | CO_{2} emissions index |

F_{i} | Requirement of customers order i on fresh agricultural products |

v_{0} | Delivery vehicle speed/(km h^{−1}) |

∂ | The freshness decreasing coefficient of produce |

θ | Time window penalty coefficient |

Parameter | Description |
---|---|

ξ | Fuel to air mass ratio |

κ | Calorific value of the fuel engine/(kJ g^{−1}) |

ψ | Conversion coefficient/(from g s-1 to L s^{−1}) |

b | Engine friction coefficient |

M | Engine speed |

ω | Without loading in the vehicle/kg |

g | Acceleration of gravity |

ε | Road slope |

Cr | Rolling resistance coefficient |

v | Vehicle speed |

Cd | Air resistance coefficient |

n_{tf} | Vehicle transmission efficiency |

η | Fuel engine efficiency parameters |

τ | Vehicle acceleration |

${U}_{j}^{k}$ | Load when vehicle k reaches customer point j |

P | Air density/(kg m^{−3}) |

V | Engine capacity/VL |

S | Frontal surface area |

No. | Horizontal Axis/m | Vertical Axis/m | Fixed Time Window | Acceptable Time Window | Quantity Demanded/t | Service Time/min |
---|---|---|---|---|---|---|

0 | 0 | 0 | 5:30–17:00 | 5:00–17:00 | 0 | 0 |

1 | −189.2 | 455 | 6:00–7:00 | 6:00–7:30 | 0.8 | 15 |

2 | 103.8 | 1452 | 6:20–7:30 | 6:20–8:00 | 3.35 | 19 |

3 | 1103.5 | 426 | 6:00–6:50 | 6:00–7:20 | 2.95 | 17 |

4 | 1264.7 | 1289 | 7:00–8:00 | 7:00–8:20 | 2.4 | 11 |

5 | 1221.2 | −1842 | 6:40–7:30 | 6:40–8:00 | 2.75 | 14 |

6 | 1436.6 | −2025 | 6:00–7:00 | 6:00–7:40 | 3.3 | 20 |

7 | 245.6 | −672 | 6:30–7:00 | 6:30–7:30 | 2.8 | 15 |

8 | 2350.0 | −1189 | 6:20–7:30 | 6:20–8:00 | 3.25 | 10 |

9 | 1148.7 | −425 | 6:00–7:30 | 6:00–8:30 | 2.15 | 15 |

10 | 1025.2 | −27 | 6:20–8:00 | 6:20–9:00 | 3.05 | 18 |

11 | 863.6 | −1214 | 6:20–7:40 | 6:20–8:00 | 3.2 | 16 |

12 | 1785.6 | −957 | 7:30–8:50 | 7:30–9:20 | 3.5 | 11 |

13 | 682.4 | −3356 | 6:00–7:30 | 6:00–8:00 | 0.55 | 15 |

14 | 134.6 | −2879 | 6:40–7:50 | 6:40–8:30 | 2.7 | 19 |

15 | −485.4 | −1689 | 6:20–7:00 | 6:20–8:00 | 1.7 | 14 |

16 | 423.1 | −2196 | 6:00–7:00 | 6:00–7:30 | 2.25 | 10 |

17 | 444.3 | −983 | 6:00–6:40 | 6:00–7:10 | 2.75 | 15 |

18 | 1168.7 | −1786 | 7:00–8:00 | 7:00–9:00 | 1.9 | 20 |

19 | −568.3 | −622 | 6:00–6:50 | 6:00–7:20 | 3.15 | 14 |

20 | −722.4 | −2089 | 6:50–7:30 | 6:50–8:10 | 1 | 11 |

Parameter | Implication | Value |
---|---|---|

ω | Vehicle weight/kg | 6350 |

ξ | Fuel-to-air-mass ratio | 1 |

b | Engine friction coefficient | 0.2 |

M | Engine speed | 33 |

V | Engine capacity/L | 5 |

g | Acceleration of gravity | 9.81 |

Cr | Rolling resistance coefficient | 0.01 |

η | Fuel engine efficiency parameters | 0.9 |

κ | Calorific value of fuel engine/(kJ·g^{−1}) | 44 |

ψ | Conversion coefficient | 737 |

n_{tf} | Vehicle transmission efficiency | 0.4 |

Cd | Coefficient of air resistance | 0.7 |

P | Air density/(kg m^{−3}) | 1.2041 |

S | Frontal surface are/m^{2} | 3.912 |

Number of Vehicles | Distribution Routing | Cost/RMB | Loading Rate/% | CO_{2} Emissions/kg | Total Time/min |
---|---|---|---|---|---|

1 | 0-19-2-8-0 | 528.22 | 96.87 | 9.23 | 63.78 |

2 | 0-17-15-14-0 | 534.25 | 72.52 | 5.01 | 66.89 |

3 | 0-1-10-6-20-0 | 658.72 | 83.20 | 8.96 | 83.56 |

4 | 0-16-11-4-0 | 632.02 | 79.68 | 7.25 | 74.25 |

5 | 0-13-5-12-0 | 589.36 | 68.79 | 7.95 | 105.23 |

6 | 0-9-3-7-18-0 | 657.85 | 99.03 | 7.02 | 83.87 |

(α,β) | K | Z |
---|---|---|

(1,1) | 4 | 3587 |

(1,2) | 3 | 3581 |

(1,3) | 3 | 3576 |

(2,1) | 3 | 3590 |

(2,2) | 3 | 3586 |

(2,3) | 3 | 3598 |

Type | Research Time/s | Search Success Rate/% | Average Numberof Iterations |
---|---|---|---|

NSGA | 2 722.6 | 76 | 48 |

MACOA | 2 692.8 | 85 | 30 |

this work | 2534.3 | 98 | 16 |

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Chen, J.; Gui, P.; Ding, T.; Na, S.; Zhou, Y.
Optimization of Transportation Routing Problem for Fresh Food by Improved Ant Colony Algorithm Based on Tabu Search. *Sustainability* **2019**, *11*, 6584.
https://doi.org/10.3390/su11236584

**AMA Style**

Chen J, Gui P, Ding T, Na S, Zhou Y.
Optimization of Transportation Routing Problem for Fresh Food by Improved Ant Colony Algorithm Based on Tabu Search. *Sustainability*. 2019; 11(23):6584.
https://doi.org/10.3390/su11236584

**Chicago/Turabian Style**

Chen, Jing, Pengfei Gui, Tao Ding, Sanggyun Na, and Yingtang Zhou.
2019. "Optimization of Transportation Routing Problem for Fresh Food by Improved Ant Colony Algorithm Based on Tabu Search" *Sustainability* 11, no. 23: 6584.
https://doi.org/10.3390/su11236584