Fuzzy scheduling optimization system for multi-objective transportation path based on ant colony algorithm

Abstract

The key algorithm of the traditional system is aimed at the minimum of a certain factor, but does not consider the uncertain conditions and various modes of transportation, and the result of the scheduling is not excellent. To this end, a new fuzzy scheduling optimization system based on ant colony algorithm for multi-objective transportation path is designed. Based on the GPS module, a fuzzy scheduling optimization system based on ant colony algorithm for multi-objective transportation path is designed, and the overall structure of the system is given. The scheduling optimization problem of freight transport lines is described, and the volume of demand, the total volume of delivery and the remaining number of vehicles are made fuzzy processing. The goal is to minimize the total time of the advance or tardiness of the transportation and the total cost, so that the fuzzy scheduling model of transportation path is built. According to the principle of ant colony algorithm, the built multi-objective model will be transformed into a single objective model, and combined with the objective function, the index heuristic information and the performance of ant colony algorithm are set, and the optimal solution of that the deviation is minimum with the ideal solution is calculated by using ant colony algorithm, so as to achieve the multi-objective transportation path scheduling. The experimental results show that the total transportation distance of the designed system is short, the total cost is low, and the goods can be delivered in time.

Keywords

Ant colony algorithm multi-objective transportation path fuzzy scheduling

1 Introduction

With the gradual improvement of the economic level, the logistics industry has developed rapidly. The route scheduling of transportation has become a key problem for the logistics and transportation management system [1]. In the long term development process, the logistics transportation scheduling has not been properly solved, resulting in the fact that the information feedback is not in time and the cost is high. To a large extent, it affects the development of China’s logistics enterprises [2]. Most of the existing transportation path scheduling studies assume that information about demand information, supply information and roads are accurate, and only one target is considered, which is not suitable for practical application [3]. How to effectively realize the design of fuzzy scheduling optimization system for multi-objective transportation path has become an urgent problem to be solved.

Literature [4] used the goal programming method to put forward multi-rule of transportation, including cost, response time, fairness, priority, reliability and safety, and establish a multi-rule optimization model. However, in the face of large-scale demand, the general situation is that the demand for goods is large and various, the demand points are scattered and numerous, and different points of demand need different kinds of goods and quantities, which cannot guarantee the optimization of the scheduling results. Literature [5] designed a spatio-temporal network of pattern conversion, proposed a network flow problem with time windows, but the model was only aimed at minimizing the total cost. In an another literature, Literature [6] proposed a multimode hierarchical network that simplifies the transport model, which was also the objective of minimizing the total cost. Moreover, the above two literatures all assume that the path transport time is the integer multiple of the length of the scheduling cycle, and the length of the cycle is fixed value. In essence, it is a multi-cycle static decision making model with poor adaptability. Literature [7] proposed a dynamic decision model from multiple supply points to demand centers, but it only considered the shortest path from supply point to assembly center, and the scheduling result was not the optimal. To aim at minimizing the total cost, minimizing the total running time and maximizing the minimum satisfaction rate, a multi-objective model of emergency material distribution system was established [8], but the model did not consider the uncertain conditions and multiple transportation modes.

In view of the disadvantages of the above methods, a new fuzzy scheduling optimization system based on ant colony algorithm for multi-objective transportation path is proposed. The transport scheduling system is designed to describe the problem of transportation path scheduling and to establish a fuzzy scheduling model of multi-objective transportation path. The model is solved by ant colony algorithm, and the optimal scheduling path is obtained. It is verified by experiments that the scheduling results of the designed system are better than those of other systems.

2 Material and methods

2.1 Overall design of the system

The designed fuzzy scheduling optimization system based on ant colony algorithm for multi-objective transportation route is based on GPS module. It is mainly composed of microcontroller LPC2368, GPS module GPS9805, communication module SIM300C, data acquisition module, etc. the detailed structure is described in Fig. 1.

Fig.1

Overall structure of the system.

2.2 Description of key algorithm problem

In this paper, the transport line model from multiple supply points to multiple demand points is mainly studied.

The problem is described as follows: in the first stage, there are n_g supply points and n_x demand points. The supply vehicles start from the supply point, transport a certain quantity of goods to the demand point, and then return to the supply point, and each vehicle can only be used for one time, as shown in Fig. 2. In the second stage, demand points have fuzziness for the needs of acquisition, so after a period of time t, it is likely that there is a shortage or surplus of the demand point goods. Therefore, in the case of satisfying the optimal of the first stage, the goods is transferred from the supply point or the demand point having the surplus goods to the demand point which still need the goods, as shown in Fig. 3. The fuzzy scheduling model of transportation path is considered on the condition of meeting the demand of transportation and the minimum transportation cost. There are h_n (n = 1, 2, …, n_g) vehicles at each supply point. The transport capacity of each vehicle is s_z. Each demand point can be transported by any vehicle, but it can only be transported by any vehicle for one time. The time required for point i to point j is t_ij, and the demand quantity of point i is a fuzzy number of $\tilde{D_{i}}$ .

Fig.2

The transport path in the first stage.

Fig.3

The transport path in the second stage.

For the fuzzy number $\tilde{D_{i}}$ , the trigonometric fuzzy number $\tilde{D_{i}} = (d_{1 i}, d_{2 i}, d_{3 i})$ is used to express, as shown in Fig. 4. Where, d_1i and d_3i represent the left and right boundaries of the fuzzy number, and d_2i represent a point that the membership degree is 1. The membership function of the fuzzy number is expressed as follows: $μ_{D} (x) = {\begin{matrix} 0, x \leq d_{1 i}, x \geq d_{3 i} \\ \frac{x - d_{1 i}}{d_{2 i} - d_{1 i}}, d_{1 i} \leq x \leq d_{2 i} \\ \frac{d_{3 i} - x}{d_{3 i} - d_{2 i}}, d_{2 i} \leq x \leq d_{3 i} \end{matrix}$ (1)

Fig.4

Trigonometric fuzzy function.

When one vehicle finishes the transportation of n_g - 1 demand points, the total amount ${\tilde{S}}_{n_{g} - 1}$ of goods delivered is also fuzzy, which can be expressed as: ${\tilde{S}}_{n_{g} - 1} = \sum_{i = 1}^{n_{g} - 1} \tilde{D_{i}} = (\sum_{i = 1}^{n_{g} - 1} d_{1 i}, \sum_{i = 1}^{n_{g} - 1} d_{2 i}, \sum_{i = 1}^{n_{g} - 1} d_{3 i})$ (2)

The remaining quantity of the existing goods of the vehicle is also fuzzy, that is: ${\tilde{C}}_{n_{g} - 1} = (s - \sum_{i = 1}^{n_{g} - 1} d_{3 i}, s - \sum_{i = 1}^{n_{g} - 1} d_{2 i}, s - \sum_{i = 1}^{n_{g} - 1} d_{1 i})$ (3)

2.3 The establishment of fuzzy scheduling model for multi-objective transportation path

The fuzzy scheduling model of multi-objective transportation path is divided into the followinglevels:

The first level objective is to deliver the goods on time in order to improve the quality of logistics service according to the customer’s requirements. The following is called punctuality to complete the distribution task. The second level objective is to optimize the logistics distribution path reasonably to achieve the lowest total cost, and the following is the lowest cost. This is a requirement for logistics companies to improve their economic performance. The total cost includes the total cost of transportation routes, the total operation cost of start-up facilities, and the total cost of goods tardiness [9, 10]. Therefore, the goal programming model is asfollows: $\begin{matrix} F_{1} (x) \\ = min [δ \sum_{i, j \in K} \sum_{a \in U} {({rt}_{ij} - t_{ij})}^{2} + ɛ \sum_{i, j \in K} \sum_{a \in U} {(t_{ij} - {et}_{ij})}^{2}] \end{matrix}$ (4) $\begin{matrix} F_{2} (x) \\ = min [\sum_{i = 1}^{K} C_{k} \sum_{i = 1}^{N} \sum_{j = 1}^{N} X_{ijk} q_{j} + \sum_{i = 1}^{r} F_{i} Z_{i} + \sum_{i = 1}^{K} C_{k} \sum_{i = 1}^{R + N} \sum_{j = 1}^{R + N} X_{ijk} C_{ijk} q_{j} d_{ij}] \end{matrix}$ (5)

In the formula, δ and ɛ are used to describe the weight coefficient of the first and second level objectives. et_ij and rt_ij are used to describe the upper and lower limits of customer periods from customer i to customer j, and K represent customers who need to serve. U represents the route of the U vehicles of transportation to reach the supply point; and C_k represents the cost of the average punishment cost per unit time that is not delayed according to the requirements of the customer [11]. X_ijk represents the k_th vehicle to provide services for the customer i and the customer j from the warehouse r; q_j represents the average number of customer needs; $Z_{i} = {\begin{matrix} 1, set up the facilities in warehouse \\ 0, otherwise \end{matrix};$

C_ijk is the transport cost of the k_th average per unit distance from customer i to the customer j. d_ij is the distance from the customer i to the customer j.

The objective function (4) is a minimum of the total time for the advance/tardiness penalty for transportation, so that the goods are delivered to the customers on time. The objective function (5) is the total cost (including the cost of the transport path, the cost of the conveyance, the cost of selecting and operating the warehouse) to find the minimum.

Constraints (6) ensure that each customer is provided with only one conveyance. $\sum_{k \in V} \sum_{i \in H} x_{ijk} = 1, \forall j \in K$ (6)

Constraints (7) are constraints on the capacity of a transport tool, and each vehicle running on the path does not exceed its capacity. $\sum_{i \in H} \sum_{j \in S} q_{j} x_{ijk} \leq {\tilde{S}}_{n_{g} - 1} + {\tilde{C}}_{n_{g} - 1}$ (7)

Constraints (8) are continuous constraints for a series of paths, and refer to that the goods shipped to a certain point are shipped out by the same vehicle:

$\sum_{i \in S} x_{ipk} - \sum_{j \in S} x_{pjk} > 0, \forall k \in U, p \in S$ (8)

Constraints (9) ensure that the path of each transport vehicle is out of one warehouse at most: $\sum_{r \in G} \sum_{j \in H} x_{rjk} \leq 1, \forall k \in U$ (9)

Constraints (10) guarantee that there is no other connection between any two warehouses: $\sum_{k \in V} x_{rmk} + Z_{r} + Z_{m} \leq 2, \forall m = 1, R, r \in G$ (10) $Z_{r} = {\begin{matrix} 1, if set up a facility in r, r \in G \\ 0, otherwise \end{matrix},$ where G represents the set of potential facilities.

Constraints (11) and (12) provide that the driving of each vehicle comes from one warehouse and has only one starting point: $\sum_{k \in V} \sum_{j \in H} x_{ijk} - Z_{r} \geq 0, \forall r \in G$ (11) $\sum_{j \in K} x_{rjk} - Z_{r} \leq 0; \forall k \in V, r \in G$ (12)

Constraints (13) guarantee that any two distribution centers will not be on the same path: $\sum_{r \in G} \sum_{i \in H} x_{ijk} + \sum_{i \in H} \sum_{m \in G} x_{jmk} \leq 1, \forall k \in U$ (13)

Constraints (14) provide a mathematical expression of t_ij in the first level objective: $t_{i j} = \sum_{k \in V} \sum_{j \in H} \sum_{i \in H} x_{i j k} t_{i j k}, \forall i, j \in K, k \in U$ (14)

Constraints (15) guarantee the sequence of travel path and time. $x_{ijk} (T_{j} - T_{i}) \geq 0, \forall i, j \in K, k \in U$ (15)

Constraints (16) and (17) guarantee that the integer constraints are satisfied: $x_{ijk} = 0 or 1, \forall i, j \in S, k \in U$ (16) $Z_{r} = 0 or 1, \forall r \in G$ (17)

2.4 Ant colony algorithm

Ant colony algorithm is a new simulated evolutionary algorithm by simulating the behavior of natural ant routing. It solves a series of combinatorial optimization problems [12, 13]. The ant has the characteristics of swarm intelligence, can make full use of a material called pheromone for information transmission, resulting in the absence of any visual cues of the environment, to find the shortest path from a food source to the nest [14]. Ant colony algorithm has achieved a series of good experimental results in solving such problems, which has attracted more and more researchers’ attention and applied to practical engineering problems such as combinatorial optimization, data classification and clustering. The domestic scholars have successfully applied the ant colony algorithm to the distribution network planning, logistics distribution, production scheduling, traffic system control and other fields. Ant colony algorithm has made breakthrough progress in both theory and application research [15].

From the point of view of complex system and complexity science, ant colony system is a complex system. Searching the shortest path from the nest to the food source, is the results of interaction, interrelationship, mutual contact and mutual cooperation of large number of individual ants in ant colony system. The basic characteristics of ant colony algorithm embodies in this process: one is dynamic, the ants continue to spread biological hormones to strengthen their roles, and the new information will soon be added to the environment, but the old information will be lost, these are the biological hormone update to finish [16]; The second one is positive feedback. In ant colony algorithm, pheromone stacking is a positive feedback process, leaving more pheromones on the superior path, and more pheromones attract more ants, so that the system evolves towards the optimal solution direction. The third one is collaborative. The ants exchange information with each other according to their own releasing information, coordinate with each other. By cooperating with each other, the optimal path is gradually displayed, becoming the route selected by most ants.

The algorithm is a simulated evolutionary bionic algorithm, which simulates the foraging behavior of the real ant in the natural world. The algorithm provides a unified frame structure system model [17 –19], which has the advantages of robustness and good positive feedback characteristics. At the same time, it has the characteristics of distributed parallel computing. Therefore, this algorithm has been widely used in the field of combinatorial optimization.

In nature, ant can find the shortest path from their nest to food through the mutual cooperation, and can change with the environment changes. A large number of studies have found that ants, in the process of searching for food, ants will leave some chemicals as pheromones in the places they pass through. And the ants in the same ant colony can perceive the substance and strength, and later ants tend to move in the direction of the high concentration of pheromones. And then the pheromone left by the ants moving will strengthen the original pheromone, thus forming a positive feedback. Through this positive feedback, the more the paths go through is, the stronger the pheromones of ants are, and the more likely the ants will choose shorter paths is. Finally, all ants will take the shortest path. The principle of ant colony optimization algorithm is illustrated in Fig. 5.

Fig.5

Diagram of ant colony searching path.

It is assumed that two roads can reach the food source F from the nest of the ant (Fig. 5 (a)): N-A-B-C-F and N-A-D-C-F, and the length is 4 and 6, respectively. The ant can move a unit length within a unit time, without any pheromone on all roads at the beginning.

At the time of t = 0, 20 ants move from the nest to A (Fig. 5 (b)). They choose the path A-B-C or A-D-C at the same probability, so on average, 10 ants choose A-B-C, and the other 10 ants choose A-D-C.

At the time of t = 4, the ant that walks the path of the A-B-C will return once they reach to the food source.

At the time of t = 5, the two groups of ants will meet at C. At this point, the pheromone on the BC is the same as that on the DC, because each of the 10 ants choose BC and DC. So, five returned ants choose B, and the other five choose D.

At the time of t = 6, the ant that walks the path of A-D-C will return once they reach to the food source. At this point, the pheromone on the BC is the same as that on the DC, because each of 15 ants choose BC and DC. So, five returned ants choose B, and the other five choose D.

At the time of t = 8, only the first 5 ants that walk A-B-C return to their nests (Fig. 5 (c)). At this time, there are each of five ants on the path AD, CD and BC, respectively.

At the time of t = 9, the first five ants that walks the path of A-D-C returned to their nests. At this time, the number of pheromones on AB is 20, while the pheromone data on AD is 15, so more ants will choose A-B-C, thus increasing the pheromone of the path. As the process continues, the pheromone gap on the two roads will grow, until the vast majority of the ants have chosen the shortest path. It is because one road is shorter than the other, in the same time interval, a short path will have more opportunities to be chosen.

The essence of the fuzzy scheduling problem of transport path is a combinatorial optimization problem of a multi-objective, which is based on the minimum total cost of transportation and minimum total time of earliness/tardiness penalty as the optimization goal, looking at the optimal transport path scheduling scheme for multiple demand points in multiple supply points. Ant colony algorithm has good parallel, distributed and global search capabilities. It has some advantages in solving complex optimization problems, especially in discrete optimization problems. The solving process is as follows:

The expression of the solution.

In order to solve the problem, it needs to transform the above multi-objective problem into a single objective problem. The basic idea of solving multi-objective minimization is to build an evaluation function that transforms multi-objective into a numerical objective. There are many ways to transform multi-objective problem to single objective problem. In this section, a linear weighted sum method is adopted. In this section, the following objective function forms are selected for the problem of transportation path fuzzy scheduling: $min Z = ω_{1} (F_{1} (x) + ω_{2} (F_{2} (x)))$ (18)

In the formula, ω₁ and ω₂ are control factors, and the different values represent the degree of attention to different targets, and the application will be determined according to the actual situation of transportation scheduling.

The setting of heuristic information.

Because the minimum time and total cost between supply point and demand point play a very important role in solving the transportation path scheduling problem, this two information are used as heuristic information for the grain depots in supply point to ants. Based on the above assumptions, C_k is the average penalty cost per unit time that delayed transport the goods to the customer. C_ijk is used to describe the transport costs of k_th average unit distances from customer i to customer j. The heuristic information of the ant k from the supply point to the demand point is shown in formula (19), where ω₁ and ω₂ are the weights corresponding to the earliest time and minimum cost of the sub goal, namely the control factor. $η_{ij}^{k} = ω_{2} \cdot \frac{X_{i}}{S_{j}} + ω_{1} \cdot \frac{1}{T_{ij}}$ (19)

Setting of performance indicators.

In the multi-objective optimization problem to be solved, there is not a specific solution that all sub functions can achieve the optimal solution, therefore, the solution composed of the optimal solutions of all the sub-objective functions is called the ideal solution of the multi-objective combinatorial optimization problem. For this reason, for the demand point j, the deviation $V_{j}^{k}$ of the superior solution and the ideal solution obtained by ant k is used as the performance evaluation index of the ant colony algorithm. The transport path fuzzy scheduling scheme that corresponds to the minimum deviation of in the solution obtained by all ants is the optimal solution.

In transportation path fuzzy scheduling, only two optimization goals are needed to consider that the punctuality and the minimum total cost. For the demand point j, the deviation $V_{j}^{k}$ between the superior solution and the ideal solution obtained by the ant k is shown in the following formula. ${\begin{matrix} V_{j}^{k} = ω_{1} μ_{1 j}^{k} + ω_{2} μ_{2 j}^{k} \\ μ_{1 j}^{k} = \frac{t_{S_{j}}^{k} - t_{S_{j}}^{*}}{t_{S_{j}}^{*}} \\ μ_{2 j}^{k} = \frac{C_{ijk} + C_{k}}{{lC}_{ijk}} \end{matrix}$ (20)

Among them, $t_{S_{j}}^{k}$ is the earliest time to start delivery of that ant k searches demand point j, $t_{S_{j}}^{*}$ is the ideal earliest time to start that demand point j only in the premise of the earliest delivery time, l represents the total transport distance.

The ant colony algorithm is used to solve the implementation process.

On the basis of ant colony algorithm (ACA), the multi-objective model is transformed into a single target model. Firstly, the multi-objective model is transformed into a single objective model. Then the objective function is combined to set the heuristic information, the update rule and the transfer strategy in the ant colony algorithm. Then an ant colony algorithm is used to find the best solution to the minimum deviation from the ideal solution, that is, a scheduling scheme which satisfies the conditions, and the concrete implementation steps are described as follows. ant_max ants are set, NC_max is to define the maximum number of cycles, the ideal solution that takes the minimum time and the lowest total cost between the two optimization objectives from the supply point to the demand point, as the weight value. ω₁ = 1 and ω₂ = 1 are the special cases.

Step 1. initialization: Sett = 0, the number of cycles is NC = 0, the pheromone τ_ij (0) = τ_max of each supply point, and Δτ_ij = 0. ant_max ants are randomly placed on the m supply point; the heuristic information for each supply point is calculated by formula (19).

Step 2. Set NC = NC + 1, k = 1.

Step 3. Number of ants k = 1. the next step that should be moved to the supply point is selected according to the probability $p_{ij}^{k} (t)$ : $p_{ij}^{k} (t) = \frac{{[τ_{ij} (t)]}^{α} {[η_{ij}^{k}]}^{β}}{\sum_{j \in {allowed}_{k}} j {[τ_{ij} (t)]}^{α} {[η_{ij}^{k}]}^{β}}$ (21)

In the formula, α is the relative importance of trajectory and is the heuristic factor of information; β represents the relative importance of visibility, which is expected to be the expected heuristic factor.

Step 4. the taboo tabu_k of ant k is updated and the ant k is moved to a new supply point.

Step 5. to determine whether the requirement $\tilde{D_{j}}$ of the demand point B_j is satisfied, and if it is satisfied, it jumps to the Step 6, otherwise, goes to the Step 3.

Step 6. the deviation value of the k ant is calculated, to determine whether the solution is not inferior, and the pheromone concentration Δτ_ij on all supply points is updated.

Step 7. if all ants search finished, the deviation values of for all the ants are compared, the minimum deviation value obtained if no change in a certain period of time, then print out the results, terminate the whole procedure, and record the optimal solution, otherwise empty the tabu list and jump to Step 2.

3 Results

In this paper, the transportation path scheduling optimization of a certain logistics company is taken as an example. In order to more intuitively describe the relative location relationship between the supply point and the demand points, and facilitate the next research on transportation path scheduling optimization, according to the highway traffic sketch map and the road related data in the area, it can get the schematic diagram of distribution network, as shown in Fig. 6. The supply point is set up in position 1, and the goods are transferred from here to each demand point, that is, the position 2∼11.

Fig.6

Schematic diagram of distribution network.

The transport of freight vehicles with a load of 5 tons is limited, and the acquisition fuzzy demand for each demand point is shown in Table 1. The data in the table is about the data.

Table 1

Demand and time for delivery of goods at different demand points

Demand point	Distribution time	Distribution/t
1	–	0
2	9 : 00	1.3
3	9 : 50	1.7
4	8 : 30	1.2
5	9 : 00	2.9
6	13 : 30	1.4
7	12 : 00	1
8	12 : 30	1.9
9	9 : 20	1.4
10	11 : 10	1.6
11	10 : 40	1.3

In order to minimize the cost of freight transportation, considering that the demand of each demand point is less than the truck load capacity, so as to ensure the requirement of shortest time, we need to transport only one freight vehicle for each demand point. The geographic coordinates of the supply points and the various demand points can be measured from the schematic distribution network, as shown in Table 2.

Table 2

Geographical coordinates of supply points and different demand points

Demand point	1	2	3	4	5	6	7	8	9	10	11
x/km	40	46	46	14	22	33	32	19	6	20	19
y/km	43	31	5	42	34	30	28	24	22	15	5

In order to verify the effectiveness of the fuzzy scheduling optimization system based on ant colony algorithm for multi-target transportation path designed in this paper, the designed systems in reference [6] and reference [8] are as a comparison. The operation waiting time is set no more than 20 s, the cost per unit distance is 12.6 yuan, and the penalty cost per unit time is 5 yuan.

The transportation route scheduling results of the system in this paper are described in Fig. 7. The optimal path of transportation is: 1⟶2⟶3⟶11⟶7⟶6⟶1, 1⟶4⟶9⟶10⟶8⟶1, 1⟶5⟶0.

Fig.7

The scheduling results of system in this paper.

The total transportation distance of the proposed method is 187.1262 km, the total cost is 2511.5265 yuan, and all of them are delivered on time.

The scheduling results in the designed system of the reference [6] are described in Fig. 8. The optimal paths are 1⟶2⟶3⟶11⟶10⟶1, 1⟶4⟶8⟶9⟶5⟶1, 1⟶6⟶7⟶1.

Fig.8

System scheduling results of reference [6].

The total transport distance in the designed system of the reference [6] is 225.3626 km, the total cost is 2923.0563 yuan, the location 5, 6, 7 and 9 are not delivered on time, the distance, total cost and punctuality are all lower than the system in thispaper.

The shortest path scheduling results in the designed system of reference [8] are described in Fig. 9. The best transport paths are 1⟶2⟶3⟶7⟶6⟶1, 1⟶4⟶9⟶11⟶10⟶1, 1⟶5⟶8⟶1.

Fig.9

System scheduling results of reference [8].

The total transportation distance in the designed system of the reference [8] is 242.1269 km, the total cost is 3215.35 yuan, all is delivered on time, but the distance and the total cost are lower than the system in this paper.

Based on the above experimental results, we can see that the total transport distance of the system scheduling is the shortest and the total cost is the lowest, which ensures the timely delivery of goods, and verifies the advantages of this system for multi-objective transportation path scheduling.

4 Conclusions

In this paper, a fuzzy scheduling optimization system based on ant colony algorithm for multi-objective transportation path is studied. Combined with GIS platform, a scheduling command system is constructed, which provides intelligent decision support for transportation decision-making.

The research content of this article can be summed up as follows:

Development of a scheduling system based on GIS

The GIS is introduced into the field of transportation scheduling, and the overall structure framework of the scheduling system is analyzed and designed with the background of GIS.

Fuzzy problem of multi-objective transportation path

In this paper, the dynamic transportation scheduling problem of how to plant the supply points, distribution center and the demand of information as a whole according to the fuzzy demand per cycle of each demand point, and select a satisfactory path, point of delivery, shipment and mode of transportation in the premise of that a variety of transport modes are available is studied. The multi-objective nonlinear integer programming model is set up for the goal of minimum transportation advance/tardiness penalty time and cost minimization.

Solving by genetic algorithm

In the fuzzy scheduling for multi-objective transportation path based on ant colony algorithm, the multi-objective model is transformed into a single objective model firstly. Combined with the objective function, the heuristic information, update rules and transfer strategies of the ant colony algorithm are set. And then the optimum solution that having the minimum deviation between the ideal solution is obtained by using ant colony algorithm, that is, the scheduling scheme to meet the conditions.

In this paper, only the fuzzy scheduling problem of multi-objective transportation route is focused to study and discuss. Although, it is improved in the scheduling of scientific and automation to a certain extent, the impact of the transportation safety situation is complicated, and scheduling methods need to be constantly improved, thus there is still a lot of work to be further studied and perfected.

Footnotes

Acknowledgments

We are indebted to the China National NaturalScience Fund grant number 61502534, and Universiti Kebangsaan Malaysia under the grant GUP-2017-105 for funding this research.

References

Eaton

, Yang

and Gongora

, Ant colony optimization for simulated dynamic multi-objective railway junction rescheduling, IEEE Transactions on Intelligent Transportation Systems99(23) (2017), 1–13.

Bououden

, Chadli

and Karimi

H.R.

, An ant colony optimization-based fuzzy predictive control approach for nonlinear processes, Information Sciences299(45) (2015), 143–158.

Robert

, Martin

and Rolf

, Antarna-ant colony based rna sequence design, Bioinformatics31(23) (2015), 3114–3121.

Zheng

, Zecchin

A.C.

, Newman

J.P.

, et al., An adaptive convergence-trajectory controlled ant colony optimization algorithm with application to water distribution system design problems, IEEE Transactions on Evolutionary Computation21(11) (2017), 773–791.

K.J.

, An interactive approach for the multi-objective transportation problem with interval parameters, International Journal of Production Research53(12) (2015), 1051–1064.

Starkey

, Hagras

, Shakya

, et al., A multi-objective genetic type-2 fuzzy logic based system for mobile field workforce area optimization, Information Sciences329(56) (2016), 390–411.

Zhang

, Su

, Li

, et al., Distributed flight routing and scheduling for air traffic flow management, IEEE Transactions on Intelligent Transportation Systems18(3) (2017), 2681–2692.

Jacquillat

and Odoni

A.R.

, An integrated scheduling and operations approach to airport congestion mitigation, Operations Research63(34) (2015), 1390–1410.

Auad

and Batta

, Location-coverage models for preventing attacks on interurban transportation networks, Annals of Operations Research258(35) (2017), 1–39.

10.

Lin

, A hybrid biogeography-based optimization for the fuzzy flexible job shop scheduling problem, Knowledge-Based Systems78(45) (2015), 59–74.

11.

Ciro

G.C.

, Dugardin

, Yalaoui

, et al., Open shop scheduling problem with a multi-skills resource constraint: A genetic algorithm and an ant colony optimisation approach, International Journal of Production Research54(34) (2016), 1–28.

12.

and Qiao

, Performance of financial expenditure in China’s basic science and math education: Panel data analysis based on CCR model and BBC model, Eurasia Journal of Mathematics Science and Technology Education13(8) (2017), 5217–5224.

13.

, Liu

, Furuta

and Peng

, Adsorption characteristics of sulfur solution by acticarbon against drinking-water toxicosis, Saudi Journal of Biological Sciences24(6) (2017), 1355–1360.

14.

Ismail

, Kanwal

and Shahbaz

M.Q.

, Generalized ratio-product-type estimator for variance using auxiliary information in simple random sampling, Kuwait Journal of Science45(1) (2018), 79–88.

15.

Qin

and Xiong

, Extremal ranks of some matrix expression with applications, Journal of Interdisciplinary Mathematics20(2) (2017), 581–593.

16.

Jiang

, Liu

and Lv

, Transportation system evaluation model based on DEA, Journal of Discrete Mathematical Sciences and Cryptography20(1) (2017), 115–124.

17.

Mosconi

S.J.N.

, Optimal elliptic regularity: A comparison between local and nonlocal equations, Discrete and Continuous Dynamical Systems-Series S11(3SI) (2018), 547–559.

18.

Bortolan

M.C.

and Rivero

, Non-autonomous perturbations of a non-classical non-autonomous parabolic equation with subcritical nonlinearity, Applied Mathematics and Nonlinear Sciences2 (2017), 31–60.

19.

Lokesha

, Deepika

, Ranjini

P.S.

and Cangul

I.N.

, Operations of nanostructures via SDD, ABC4 and GA5 indices, Applied Mathematics and Nonlinear Sciences2 (2017), 173–180.