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In order to improve the working efficiency of automated guided vehicles (AGVs) and the processing efficiency of fulfilling orders in intelligent warehouses, a novel parallel ant colony optimization algorithm for warehouse path planning is proposed. Through the interaction of pheromones among multiple subcolonies, the coevolution of multiple subcolonies is realized and the operational capability of the algorithm is improved. Then, a multiobjective function with the object of the shortest path and the minimum number of turns of the AGV is established. And the path satisfying this objective function is obtained by the proposed algorithm. In addition, the path is further smoothed by reducing the number of intermediate nodes. The results show that the stability and convergence rate of the algorithm are faster and more stable, compared to other algorithms, in generating paths for different complexity maps. The smoothing treatment of the path significantly reduces the number of turns and the path length in the AGV driving process.

Nowadays, automated guided vehicles (AGVs) are often used to move goods in common logistics storage spaces such as intelligent warehouses and automated wharfs. AGVs are required to search for a best path in a given working environment according to certain goals (e.g., shortest time, shortest energy consumption, shortest distance). A reasonable AGV driving path not only improves the goods turnover rate and order fulfillment efficiency of the warehouse, but also makes the AGV more stable during driving. Therefore, the path planning of AGVs in intelligent warehouses is mainly studied in this paper.

In path planning, the goal is to find a collision-free path from the starting position to the target position while optimizing one or more objectives (e.g., path length, smoothness, security) with a reasonable method [

The ant colony optimization (ACO) algorithm, initially proposed by Marco Dorigo, is a metaheuristic approach inspired by ants’ foraging behavior and used to solve the traveling salesman problem (TSP) [

The previous work about improving the operation effect of the ACO algorithm focused on the intervention of certain parameters to change the node selection mode of ants in the population or to influence the pheromone updating mode of the ant population. Less consideration has been given to the pheromone interactions between multiple ant colonies and the cogrowth of multiple subcolonies in the iteration process, so as to improve the overall path search capability of the ant colonies by using the search capability of the subcolonies themselves. Furthermore, most of the relevant research only pursues the shortest path of the AGV and does not consider the problem that the AGV is not smooth enough due to too many turns in the operation process. Therefore, research is needed to effectively reduce the number of turns in the AGV driving process.

Based on the above analysis, a warehouse map model is firstly built and a novel algorithm is proposed to generate the shortest AGV path with the least number of turns. It is a parallel-ranking ant colony optimization (P-RACO) algorithm. Compared with other algorithms, it is proven that the algorithm has faster convergence speed and better stability. Then, on the basis of the first stage of the path generation, the algorithm proved to be faster and more stable. By reducing the intermediate nodes, the path is smoothed, the number of turns and the length of the path are reduced, and the actual driving path of AGV is more stable and feasible.

In an intelligent warehouse, when receiving the task, an AGV is required to begin from the starting point, bypassing barriers to complete the order. Therefore, a shortest path with minimum number of turns is needed to ensure the efficiency of the warehouse operation and the driving stability of the AGV.

The following four assumptions are made in this research: ① the warehouse map is known; ② the warehouse grid map is divided into passable and nonpassable grids; ③ the AGV is in good condition; ④ the starting point and end point of a task are known.

The objective function is to minimize the number of turns and the length of the path. A multiobjective path optimization model is established. The P-RACO is used to solve the problem to obtain the path which can meet the requirements of these two constraints to the greatest extent.

Through the analysis of an actual warehouse environment, the AGV working environment is determined to be a two-dimensional static environment that is divided into shelves (barriers) and AGV driving channels. The grid method is simple and effective; the use of a grid map can greatly reduce the complexity of the warehouse environment modeling. Therefore, the grid method is used to divide the working environment. In the simulation program, the driving channel is a passable grid, which is identified by 0, and the obstacle is represented by a nonpassable grid, which is represented by 1. The grids are marked (passable, nonpassable) and identified using two-dimensional rectangular coordinates. Figure

Grid coordinates and grid number arrangement.

The barrier grids are black, barrier-free grids are white, S is the grid’s identifying number, and

In practical environments, fewer turns on paths can reduce the overall mechanical loss and prolong the service life of an AGV. The objective function is as follows:

In practical environments, an AGV can save time and improve the efficiency of the whole warehouse by seeking the shortest driving path. The objective function is as follows:

In order to simplify the model, the length of each grid in the grid map is set to be one unit length (the dimension of the objective function should be unified according to the actual unit length in its practical application). The objective function is calculated by linear weighting, so that the solution can satisfy both the shortest path and the minimum number of turns. The relationship between the above two objective functions and the utility function

As an evolutionary algorithm, the ACO algorithm has shown great potential to solve combinatorial optimization problems. However, like other evolutionary algorithms, it has shortcomings in terms of its convergence speed and its ease of falling into a local minimum solution. In order to address these problems, it is necessary to redesign the search strategy of the ant colony.

In genetic algorithm, a ranking selection mechanism is used to improve the search speed. First, the population is classified according to fitness; then, the probability of being selected depends on the order of the individuals. The higher the fitness, the better the individual is, and the higher the probability of it being selected in the next iteration. This ranking and selection concept of genetic algorithms is extended to the ant colony algorithm. After all of the ants complete an iteration, a selection is made. The

However, an ant colony algorithm based on the ranking optimization accumulates numerous pheromones in the local area very early. Although the speed is improved, it reduces the diversity of solutions in each generation. Consequently, the algorithm can readily fall into a local optimum. To address this problem, the ant colony is divided into several subcolonies to grow together, and the pheromone of the better individual in a subcolony is transmitted to another subcolony. This is accomplished through an information interaction between the subcolonies. The transmission ensures that the pheromone accumulation of each subcolony has the correct direction. The flowchart of the algorithm for a single subcolony is shown in Figure

Single sub-ant colony operational flowchart.

Diagram of subcolony information interactions.

Before the path construction, a large ant colony is divided into several subcolonies such that each subcolony has

If the node has been accessed,

When each ant generates a path, it volatilizes part of the pheromone that exists on the path before updating the pheromone, as follows:_{1} ≤ _{2} ≤ … ≤ _{m}). At the same time, according to the length of the path constructed by the ants in the subcolony, ^{bs}. Otherwise,

Warehouse environments vary with the complexity of their functions. In a complex environment, ants may fall into a dead corner state in the process of searching for solutions (i.e., no target point is found and no mobile nodes are present). This state is illustrated in Figure

Dead corner of a path state diagram.

Figure

This solution can improve the global search capability of the algorithm and effectively avoid ants falling into the dead corner at the same location.

A smooth and executable path with less turns is an important part of warehouse AGV path planning. Too many turns during the operation of the AGV will significantly increase the mechanical wear of the machine and reduce its service life. In order to reduce this impact and make the obtained path more applicable to the actual robot, it is necessary to smooth the path [

As the warehouse map model is a grid map, the path generated in the first stage is a broken line composed of straight lines; these connect the centers of each grid. In practice, when there are no barriers on the road, several grids can be crossed directly. The center points of nonadjacent grids can be connected to reduce the number of turns and the length of the path, so as to improve the overall efficiency of the warehouse. The flowchart is shown in Figure

Path smoothing processing flowchart.

Firstly, the path solving process is introduced, and the performance of the proposed algorithm is tested with the classical TSP model and compared with other algorithms. Then, the proposed algorithm is used to solve the AGV path planning in the 30 ∗ 30 and 35 ∗ 35 warehouse grid graphs and compared with other multiobjective algorithms. Finally, the generated path is smoothed and the data before and after the path smoothing is compared. The computing environments are Windows 10, i5 CPU, 8 GB memory, and MATLAB 2018.

The TSP is a typical NP-hard problem, and it is often used to test the performance of various optimization algorithms. Most of the research on picking operations abstracts the picking path into the TSP model.

Firstly, the TSP model is used to test the optimization performance of the P-RACO algorithm. The test results are compared with those of ACO, RACO, and the improved ant colony (IAC) proposed in the literature [

Each algorithm runs 50 times and records the maximum value (Max), minimum value (Min), average value (Avg), and standard deviation (Sd) of the runs.

When solving the TSP, it can be seen from Table

50-simulation results of four algorithms for the TSP model.

Path length | The number of iteration | |||||||
---|---|---|---|---|---|---|---|---|

Max | Min | Avg | Sd | Max | Min | Avg | Sd | |

ACO | 3369.457 | 3198.345 | 3141.356 | 58.754 | 96 | 13 | 17.65 | 15.678 |

RACO | 3280.290 | 3089.658 | 3189.875 | 29.747 | 57 | 7 | 10.35 | 5.869 |

IAC | 3179.658 | 3086.897 | 3124.121 | 27.864 | 25 | 6 | 8.64 | 5.786 |

P-RACO | 3154.785 | 3048.856 | 3104.457 | 21.654 | 18 | 3 | 5.89 | 3.879 |

After each iteration of the RACO algorithm, pheromones are rewarded to the ants with higher contributions. Although this behavior makes ants approach the optimal solution faster through the rapid accumulation of pheromones, it also reduces the diversity of the ant solutions. In this paper, P-RACO uses a multiple-ant-colony search to increase the diversity of the whole ant colony solution.

The standard deviation

Diversity curve.

Figure

In this section, multiobjective path planning is carried out on the simplified two-dimensional grid map of the warehouse, and the model is established according to the common warehouse size. The warehouse maps are set to 30 ∗ 30 and 35 ∗ 35 sizes. The number of barrier grids is 200 and 400, respectively. Four algorithms (ACO, TACO, IAC, and P-RACO) are used to solve the problem.

For the 30 ∗ 30 environment, Figure

Path planning result diagrams of the four algorithms in the 30 ∗ 30 map. (a) ACO. (b) RACO. (c) IAC. (d) P-RACO.

Convergence curves of the four algorithms in the 30 ∗ 30 map.

50-simulation results of the four algorithms in the 30 ∗ 30 map.

Max | Min | Avg | Sd | The number of iterations | ||||
---|---|---|---|---|---|---|---|---|

Max | Min | Avg | Sd | |||||

ACO | 36.578 | 30.726 | 32.889 | 1.446 | 33 | 20 | 24.98 | 3.346 |

RACO | 34.768 | 30.890 | 32.776 | 1.267 | 25 | 17 | 17.49 | 2.879 |

IAC | 34.960 | 30.352 | 31.097 | 1.188 | 26 | 14 | 16.75 | 2.245 |

P-RACO | 34.086 | 29.872 | 30.463 | 0.902 | 10 | 8 | 8.89 | 0.508 |

From Figure

For the 35 ∗ 35 environment, Figure

Path planning result diagrams of the four algorithms in the 35 ∗ 35 map. (a) ACO. (b) RACO. (c) IAC. (d) P-RACO.

Path planning result diagrams of the four algorithms in the 35 ∗ 35 map.

50-simulation results of the four algorithms in the 35 ∗ 35 map.

Max | Min | Avg | Sd | The number of iterations | ||||
---|---|---|---|---|---|---|---|---|

Max | Min | Avg | Sd | |||||

ACO | 49.345 | 40.125 | 45.430 | 3.568 | 42 | 27 | 32.49 | 2.970 |

45.384 | 40.345 | 42.456 | 2.346 | 34 | 19 | 24.60 | 2.097 | |

47.293 | 38.872 | 42.236 | 1.870 | 28 | 19 | 23.34 | 1.083 | |

P-RACO | 43.986 | 38.262 | 40.346 | 0.866 | 12 | 9 | 10.20 | 0.533 |

With the increase of map complexity, the stability of the ACO algorithm becomes worse. Figure

The experimental results show that the algorithm in this paper converges after 100 iterations at most when solving the path planning problem of different size warehouses. After 100 iterations, the ACO algorithm does not search for even better paths, and the value of the minimum utility function does not change any more. Therefore, the maximum number of iterations of the experimental results is set to 100.

In this experiment, the turning center of the generated optimal path is processed to reduce the number of invalid paths and the number of turns of the AGV. The intermediate nodes of the generated optimal path are processed as illustrated in Figure

Smoothing route comparison. (a) Comparison of route smoothing in the 30 ∗ 30 map. (b) Comparison of route smoothing in the 30 ∗ 35 map.

Data comparison before and after the path smoothing.

Map size | Length before smoothing | Length after smoothing | Reduction rate | Turns before smoothing | Turns after smoothing | Reduction rate (%) |
---|---|---|---|---|---|---|

30 ∗ 30 | 42.3553 | 39.8410 | 5.9 | 13 | 11 | 15.3 |

35 ∗ 35 | 51.1838 | 47.5159 | 7.2 | 18 | 11 | 39.0 |

For the 30 ∗ 30 and the 35 ∗ 35 maps, Table

The research of this paper is based on a general practical warehouse that is simplified to a two-dimensional grid map model. Therefore, the algorithm in this paper is universal in the warehouse AGV path planning domain. This path planning method can be applied to a variety of different types and sizes of warehouses, which can effectively improve the efficiency of warehouse operation.

Aimed at the problem of AGV path planning in automated warehouses, a P-RACO for path planning is proposed. The method of reducing invalid intermediate nodes is used to smooth the generated path. Firstly, the TSP problem is used to test the performance of the algorithm, and then the algorithm is verified on the two-dimensional grid warehouse map model. The following conclusions are drawn:

When the P-RACO is used to solve the path planning multiobjective problem of the warehouse model, the path obtained can integrate two objectives: the shortest path and the least number of turns. Compared with approaches that only consider the shortest path, the P-RACO algorithm improves the efficiency and reduces the number of turns.

Compared with the ACO, RACO, and IAC algorithms, the P-RACO algorithm proposed in this paper accumulates more pheromones in the early stage of solving the path planning problems under the TSP and for warehouses with different complexities. The P-RACO algorithm has better directionality, which can avoid the algorithm falling into a local optimum; from the standard deviation of many experiments, the proposed algorithm has better stability.

By analyzing the standard deviation of the first 100 iterations when the P-RACO algorithm solves the TSP, it can be seen that the solutions of each generation of the algorithm have better diversity and the algorithm does not appear to stagnate.

In this paper, the initial path is smoothed by reducing the intermediate nodes. This method significantly reduces the number of turns and the length of path in AGV driving. Consequently, it improves the overall operational efficiency of the warehouse and the service life of the AGVs.

In this paper, we mainly consider the operation of a single AGV in a warehouse. The dynamic collision avoidance problem resulting from multiple AGVs working simultaneously in an environment is an interesting and valuable direction for future research.

The data used to support the findings of this study are included in the supplementary information file.

The authors declare that they have no conflicts of interest.

This paper was supported by the Key R&D Projects in Shaanxi Province (2017ZDCXL-SF-03-02); National Key Research and Development Project of China, entitled “New Generation Intelligent Building Platform Techniques” (No. 2017YFC0704100); Shaanxi Provincial Science and Technology Department Special Research Project (2017JM6106); and Brain Research Fund of the University (JC1706).

The data used to support the findings of this study are included in the supplementary information file.