As the energy conservation and emission reduction and sustainable development have become the hot topics in the world, low carbon issues catch more and more attention. Logistics, which is one of the important economic activities, plays a crucial role in the low carbon development. Logistics leads to some significant issues about consuming energy and carbon emissions. Therefore, reducing energy consumption and carbon emissions has become the inevitable trend for logistics industry. Low carbon logistics is introduced in these situations. In this paper, from the microcosmic aspects, we will bring the low carbon idea in the path optimization issues and change the amount of carbon emissions into carbon emissions cost to establish the path optimization model based on the optimization objectives of the lowest cost of carbon emissions. According to different levels of air pollution, we will establish the double objectives path optimization model with the consideration of carbon emissions cost and economy cost. Use DNAant colony algorithm to optimize and simulate the model. The simulation indicates that DNAant colony algorithm could find a more reasonable solution for low carbon logistics path optimization problems.
As the energy conservation and emission reduction and sustainable development has become the hot topics in the world, low carbon issues catch more and more attention. Logistics, which is one important economic activity, plays a crucial role in the low carbon development. Logistics leads to some significant issues about consuming energy and carbon emissions. Therefore, reducing energy consumption and carbon emissions have become the inevitable trend for logistics industry. Low carbon logistics is introduced in these situations. Low carbon logistics means that the processes of logistics, based on the goals of low energy consumption, low pollution, and low emissions, use the technology of energy efficiency, renewable energy, and reducing greenhouse gas emissions to restrain the harm to environment, which would be also helpful for the purification of the logistics environment and get the full use of logistics resources. It includes logistics operation part and the whole process of low carbon logistics management [
Low carbon logistics is one frontier domain of research, which catches more and more attention of scholars. Most low carbon logistics researches are focused on the macroscopic aspects, which are the qualitative researches of low carbon logistics, including low carbon logistics itself analysis [
In this paper, from the microcosmic aspects, we bring the low carbon idea in the path optimization issues and change the amount of carbon emissions into carbon emissions cost to establish the path optimization model based on the optimization objectives of lowest cost of carbon emissions. According to different levels of air pollution, we establish the double objectives path optimization model with the consideration of carbon emissions cost and economy cost. We will use DNAant colony algorithm to optimize and simulate the model. The simulation indicates that DNAant colony algorithm could find a more reasonable solution for low carbon logistics path optimization problems.
Low carbon logistics is a kind of low energy cost and low pollution logistics whose goal is to achieve the highest efficiency of logistics with the lowest greenhouse gas emissions [
As the vehicles pickup or delivery goods in the different order crossing all customers, the car load changes. With the increase of vehicle load, the unit distance fuel consumption rises, leading to the increase of carbon emissions cost [
The unit distance fuel consumption
When vehicles are full, the unit distance fuel consumption is
When vehicles are empty, the unit distance fuel consumption is
Thus, the carbon emissions cost
For the convenience of model establishment, assume that there is only one distribution center whose location is known. All the vehicles start from the distribution center and return to distribution center after delivery. The vehicles’ load is known. The location and the demand of customer are known. One vehicle is for one customer.
According to the above assumption, establish the minimizing carbon emissions cost model:
The number of distribution center is 0. The numbers of customers are
Formula (
Since the increasing pollution problems, the government considers the logistics network planning from the aspect of the whole area low carbon development to minimize the carbon emissions of the whole area. But transportation enterprises will choose the logistics lines based on the logistics network system according to their target and determine the allocation on each line. To achieve the goal of the government and the transport enterprises winwin, this paper establishes the double target distribution optimization model based on “pay attention to carbon emissions and also give consideration to economy.” The basic thought of a multiobjective optimization problem is to transfer multiobject into a numerical target evaluation function, which generally uses the linear weighted sum method [
Firstly, the goods are delivered to the distribution center. Then, the goods are sent to each customer by through highways, waterways, air transport, and a variety of other ways. In the whole distribution process, the situation is complicated, in which there exists not only the transformation of multiple transportation modes but also multiple layers of distribution network. In a variety of transportation modes, highway transportation is the largest one of carbon dioxide emissions. Thus, for the convenience of model establishment, only consider one level of distribution network, which is from distribution center to customer delivery and only consider the highway transportation mode.
For the convenience of model establishment, make the following assumptions.
Only consider the distribution center whose location is known. All the vehicles start from the distribution center. After the delivery mission, all the vehicles come back to the distribution center waiting for unified deployment.
The delivery goods can be mixed. Each customer’s goods will not exceed the maximum load of the vehicle.
The location and demand of customers are known. One vehicle is for one customer.
Load is known.
The vehicle serves for each affected point service, and on the way only discharges without loading.
According to the degree of pollution, the air pollution index is divided into five levels: top grade, good, light pollution, moderate pollution, and high level of pollution. Top level and good level include normal activities. Light pollution includes longterm exposure to this level air, vulnerable groups’ symptoms will be slightly worse, and healthy people will have irritation symptoms. Moderate pollution includes contacting with the air after a certain period of time, symptoms of the people with heart disease and pulmonary disease significantly will increase, exercise tolerance decreases, and common symptoms happen in healthy people. In high level of pollution, healthy exercise tolerance is reduced and it has obvious symptoms and diseases. According to different level of air pollution index, the values of weight coefficients of evaluation function
Scientists, who study social insect behavior characteristic, found that the insect at the community level of cooperation is basically selforganizing. This kind of collective behavior produced by the social organism, which is a kind of swarm intelligence, catches the eyes of many researchers in the fields of management science and engineering. Ant colony algorithm is a typical example of the use of swarm intelligence to solve combinatorial optimization problems. Ant colony algorithm as a new bionic evolutionary algorithm is published by Dorigo and Gambardella [
Ant colony algorithm is a kind of parallel algorithm. The searching process is not starting from a point, but from the multiple points simultaneously. The distributed parallel model greatly improves the whole operation efficiency and quick reaction capability of the algorithm, which not only increases the reliability of the algorithm but also makes the algorithm have a stronger global searching ability. Ant colony algorithm has positive feedback characteristics, which can strengthen the optimal solution of pheromones to speed up the convergence speed of the algorithm. Ant colony algorithm has robustness, whose result is not dependent on the initial route choice, and does not need manual adjustment in the process. Ant colony algorithm is easily combined with other heuristic algorithms to improve the algorithm performance. Although the ant colony algorithm has many advantages, there are still some defects such as long searching time, slow convergence speed, slow evolution, stagnation happening easily, and precocious phenomena.
Assume that there are
With time passing by, the new pheromone is added and old pheromones evaporate.
The basic ant colony algorithm to achieve the process is that
The numerous studies of ant colony algorithm have shown its significance in the optimization combination problem, but there are still some shortcomings, such as seeking to local optimal solution rather than the global optimal solution and convergence lag. In particular, for the selection of basic ant colony algorithm parameters, there is no theoretical derivation but relying on the results of experiments. The selection of ant colony algorithm parameters is directly related to the effectiveness of the algorithm’s solution. If the parameter selection is improper, it will seriously affect the performance of the ant colony algorithm. DNAant colony algorithm controls the parameter selection by the crossover and mutation idea of DNA algorithm to optimize the performance of ant colony algorithm, which will overcome the shortcomings of ant colony algorithm to improve the convergence rate and search the global optimal solution.
DNA, the socalled deoxyribonucleic acid, is the most important biological macromolecules of organisms in the nature and the main genetic materials for all creatures. The discovery of DNA double helix structure marks the development of biological science which has entered the phase of molecular biology. DNA is a kind of high molecular compound, which is the basic unit of DNA nucleotides. Each deoxyribonucleotide is composed of a molecular phosphate, molecular DNA nucleotides, and a molecule nitrogenous base. Nitrogenous base includes adenine deoxynucleotide (A), guanine oligodeoxynucleotides (G), cytosine deoxyribonucleotide (C), and thymidine nucleotide (T). Modern molecular biology believes that DNA is the main material basis of biological inheritance which stored the genetic information. It transfers genetic information from parent to offspring by selfcopy transfer and generates the RNA transcription (ribonucleic acid) to translate into specific proteins to control the phenomenon of life [
The crossover and mutation in DNA algorithm is different from genetic algorithm. Crossover and mutation in DNA algorithm is based on gene level with a different encoding method, which is two digits binary encoding instead of unit binary encoding. The crossover operation of DNA algorithm is based on the twopoint crossover method with a certain probability
Transform coding method of DNA algorithm into two binary coding method can be recognized by computers, which is A00, T01, C10, G11, and 00 with 01 and 10 with 11 (see Figure
Mutation of DNA algorithm is based on purine replacing purine and pyrimidine replacing pyrimidine, with A changing into G and C changing into T. Bases correspond to binary machines coding method, with 00 changing with 11, and 10 changing with 01. In the mutation, the base sequences mutation operates in a certain probability
DNAant colony algorithm optimizes the parameters
The basic ant colony algorithm parameters initialization is as follows:
The DNA ant colony algorithm parameters initialization is as follows:
Operate crossover and mutation of DNA algorithm are as follows:
for 1 to
repeat Steps (3)~(8);
operate crossover and mutation of DNA algorithm;
for 1 to
repeat Steps (4)~(7).
Put
while
for
calculate the transition probability of ants according to Formula (
if
ant
else
ant
repeat Step (5) until all the cities have travelled through and then check whether
for
calculate the path length
if
then clean up
Choose the better
The model solution flow chart of DNAant colony algorithm.
Assume the distribution center has 16 customers whose coordinate is (0,0). Table
Demand of customer.
Customer  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16 

Demand  15  18  20  8  15  10  25  30  17  6  2  24  19  20  7  1 
Coordinate of customer.
Customer  1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16 


2  8  18  34  −25  35  42  −10  −8  −12  −32  28  −18  −9  −18  8 

8  33  20  28  15  −5  10  20  10  −32  −40  7  0  25  8  10 
Table
Carbon emissions cost: the minimum carbon emissions cost of basic ant colony algorithm is 426.5, and the cost of DNAant colony algorithm is 398.8. The DNAant colony algorithm saves 6.4% of minimum carbon emissions cost compared with basic ant colony algorithm. The average carbon emissions cost of basic ant colony algorithm is 546.2. The average cost of DNAAnt colony algorithm is 470.34. For the average carbon emissions cost, the DNAant colony algorithm saves 13.8% compared with basic ant colony algorithm. Thus, for the solution of minimum carbon emissions cost distribution model, DNAant colony algorithm can find the path with less carbon emissions cost, which is better for environmental protection.
The number of final generation: the average number of final generation of basic ant colony algorithm is 133.7. The average number of final generation of DNAant colony algorithm is 81. From the average number of final generation, we can find that the DNAant colony algorithm has a better convergence.
The difference with minimum carbon emissions cost: the average difference between basic ant colony algorithm and minimum carbon emissions cost is 119.7. The average difference between DNAant colony algorithm and minimum carbon emissions cost is 71.54. From the difference with minimum carbon emissions cost, we can find that the DNAAnt colony algorithm is more stable in the process of search minimum carbon emissions.
Distribution Center
Distribution Center
Distribution Center
Distribution Center
The results of basic ant colony algorithm (minimum carbon emissions cost).
No.  1  2  3  4  5  6  7  8  9 

Ave.  

Carbon emissions cost  572.3  544.1  580.9  592.6  572.5  544.2  520.7  559.9  548.3 

546.2  
Vehicles  4  4  4  4  4  4  4  4  4  4  4  
End iteration  68  180  144  140  188  79  193  182  67  96  133.7  
Deviations  145.8  117.6  154.4  166.1  146  117.7  94.2  133.4  121.8  0  119.7 
The results of DNAant colony algorithm (minimum carbon emissions cost).
No.  1  2  3  4  5  6  7  8  9 

Ave.  

Carbon emissions cost  516.2  444.6  493.6  489.1  461.3  484.4  456.4  485.3  473.7 

470.34  
Vehicles  4  4  4  4  4  4  4  4  4  4  4  
End iteration  174  144  79  16  16  46  65  175  34  61  81  
Deviations  117.4  45.8  94.8  90.3  62.5  85.6  57.6  86.5  74.9  0  71.54 
Distribution path basic ant colony algorithm (minimum carbon emissions cost).
Figure
Distribution Center
Distribution Center
Distribution Center
Distribution Center
Distribution path DNAant colony algorithm (minimum carbon emissions cost).
Figure
Minimum carbon emissions cost optimization curve.
When the air pollution level is good level, vehicles are only considered the distribution cost, and the carbon emissions cost is ignored, which means that
Table
Distribution cost: the minimum distribution cost of basic ant colony algorithm is 400.7 and the cost of DNAant colony algorithm is 398. The DNAant colony algorithm saves 0.67% of minimum distribution cost comparing with basic ant colony algorithm. The average distribution cost of basic ant colony algorithm is 405.04. The average cost of DNAant colony algorithm is 400.33. For the average distribution cost, the DNAant colony algorithm saves 1.16% compared with basic ant colony algorithm. Thus, for the good air pollution level, DNAant colony algorithm can find the path with less distribution cost compared with basic ant colony algorithm.
The number of final generation: the average number of final generation of basic ant colony algorithm is 111.3. The average number of final generation of DNAant colony algorithm is 53.6. From the average number of final generation, we can find the DNAant colony algorithm has a better convergence speed.
The difference with minimum values: the average difference between basic ant colony algorithm and minimum values is 4.34. The average difference between DNAant colony algorithm and minimum values is 2.33. From the difference with minimum values, we can find that the DNAant colony algorithm is more stable in the process of search the best solution.
The results of basic ant colony algorithm (top or good air pollution level).
No.  1  2  3  4  5  6 

8  9  10  Ave.  

Cost  403.1  402.7  403.9  404.5  407.5  405.3 

405.3  409.5  407.9  405.04  
Vehicles  4  4  4  4  4  4  4  4  4  4  4  
End iteration  186  159  125  15  178  123  196  5  63  63  111.3  
Deviations  2.4  2  3.2  3.8  6.8  4.6  0  4.6  8.8  7.2  4.34 
The results of DNAant colony algorithm (top or good air pollution level).
No.  1  2  3  4  5  6  7  8  9  10  Ave  

Cost  400  398  400.7 


404 

400.7 

407.9  400.33  
Vehicles  4  4  4  4  4  4  4  4  4  4  4  
End iteration  19  145  77  13  33  16  16  163  27  27  53.6  
Deviations  2  0  2.7  0  0  6  0  2.7  0  9.9  2.33 
Figure
The distribution path figure of basic ant colony algorithm.
Vehicle 
Distribution path 

1  Distribution Center–10–11–13–Distribution Center 
2  Distribution Center–1–16–3–2–14–Distribution Center 
3  Distribution Center–9–15–5–8–Distribution Center 
4  Distribution Center–12–6–7–4–Distribution Center 
The distribution path figure of DNAant colony algorithm.
Vehicle 
Distribution path 

1  Distribution Center–13–11–10–Distribution Center 
2  Distribution Center–1–16–3–2–14–Distribution Center 
3  Distribution Center–9–8–5–15–Distribution Center 
4  Distribution Center–12–6–7–4–Distribution Center 
Distribution path basic ant colony algorithm (top or good air pollution level).
Distribution path DNAant colony algorithm (top or good air pollution level).
Figure
Distribution cost optimization curve (top or good air pollution level).
Assume that the air pollution level is moderate or high level pollution; set
Objective evaluation function value: the minimum objective evaluation function value of basic ant colony algorithm is 417.5 and the cost of DNAant colony algorithm is 402.6. The DNAant colony algorithm saves 3.5% of minimum objective evaluation function value compared with basic ant colony algorithm. The average objective evaluation function value of basic ant colony algorithm is 431.22. The average cost of DNAant colony algorithm is 414.09. For the average objective evaluation function value, the DNAant colony algorithm saves 3.97% compared with basic ant colony algorithm. Thus, for the moderate or high level pollution, DNAant colony algorithm can find the path with less objective evaluation function value to find the more effective distribution paths and reduce air pollution and distribution cost.
The number of final generation: the average number of final generation of basic ant colony algorithm is 163.3. The average number of final generation of DNAant colony algorithm is 86.9. From the average number of final generation, we can find that the DNAant colony algorithm has a better convergence speed.
The difference with minimum values: the average difference between basic ant colony algorithm and minimum values is 13.72. The average difference between DNAant colony algorithm and minimum values is 11.49. From the difference with minimum values, we can find that the DNAant colony algorithm is more stable in the process of search the best solution.
The results of basic ant colony algorithm (moderate or high level pollution).
No.  1  2  3  4  5  6  7  8  9  10  Ave.  

W  430.3  422.4 

423.2  458.4  433.2  443.4  437.4  418.4  428  431.22  
Vehicles  4  4  4  4  4  4  4  4  4  4  4  
End iteration  160  175  193  150  155  162  182  161  163  132  163.3  
Deviations  12.8  4.9  0  5.7  40.9  15.7  25.9  19.9  0.9  10.5  13.72 
The results of DNAant colony algorithm (moderate or high level pollution).
No.  1  2  3  4  5  6  7  8  9  10  Ave.  

W  418.6 


409  412.6  428.7  414.8  421.1  415.8  415.1  414.09  
Vehicles  4  4  4  4  4  4  4  4  4  4  4  
End iteration  126  30  133  68  20  133  26  46  131  156  86.9  
Deviations  16  0  0  6.4  10  26.1  12.2  18.5  13.2  12.5  11.49 
Figure
Vehicle 1: Distribution Center
Vehicle 2: Distribution Center
Vehicle 3: Distribution Center
Vehicle 4: Distribution Center
Distribution path basic ant colony algorithm (moderate or high level pollution).
Figure
Vehicle 1: Distribution Center
Vehicle 2: Distribution Center
Vehicle 3: Distribution Center
Vehicle 4: Distribution Center
Distribution path DNAant colony algorithm (moderate or high level pollution).
Figure
Distribution cost optimization curve (moderate or high level pollution).
In this paper, starting from the actual requirements of low carbon logistics, microscopic quantitative analysis was used for low carbon logistics. The minimum cost of carbon emissions model and the double target distribution optimization model with considering the cost of carbon emissions were established to find the reasonable distribution routes to achieve energy conservation and emissions reduction based on the solution of DNAant colony algorithm. According to the simulation of MATLAB, DNAant colony algorithm had a better effectiveness than the basic ant colony algorithm on the issue of low carbon logistics distribution route optimization. But this is the preliminary research on the low carbon logistics distribution route optimization problem. It is the exploration stage for low carbon logistics distribution route optimization model. The models are established based on the ideal situation without consideration of many complex factors and real situations in the constraints of the models. In future study, there is a to optimize the model to make the model more accord with the actual needs.
The authors declare that there is no conflict of interests regarding the publication of this paper.
This work was supported by Soft Science Research Project in Shanxi Province (no. 20100410773).