To improve the efficiency of warehouse operations, reasonable optimization of picking operations has become an important task of the modern supply chain. For the purpose of optimization of order picking in warehouses, a new fruit fly optimization algorithm, particle swarm optimization, random weight, and weight decrease model are used to solve the mathematical model. Further optimization is achieved through the analysis of the warehouse shelves and screening of the optimal solution of the picking time. In addition, simulation experiments are conducted in the MATLAB environment through programming. The shortest picking time is found out and chosen as an optimized method by taking advantage of the effectiveness of these six algorithms in the picking optimization and comparing the data obtained under the simulation. The result shows that the optimization capacity of RWFOA is better and the picking efficiency is the best.
As a part of the logistics, the efficiency of the automated warehouse is largely dependent on the efficiency of order picking. Therefore, the picking plays an important role in the automated warehouse for improving the efficiency of picking operation. Although the automated stereoscopic warehouse provides more orderly and standardized management and the error rate is also small, for small batch warehouse, frequent warehousing, and warehouses with various products, logistics storage becomes more stringent, and requirements for the efficiency of the logistics are higher, and thus, the efficiency of picking needs to be improved.
There are a lot of algorithms for optimization of order picking, all of which have made minor or major contributions to the optimization of order picking [
The main structure of this paper is as follows: Section
Across the various operations in a warehouse, order picking is the most time-consuming operation in general [
Order picking is a particular case of the traveling salesman problem (TSP). This problem, introduced by Dantzig et al. [
To most order-picking research studies, optimization algorithms are still the center of routing studies [
The dedicated algorithms include dynamic programming, integer programming, and branch and bound method. Although this kind of algorithm can get the exact solution, the calculation time is long and it is seldom used in the practical application [
At present, the shelves of the automatic stereoscopic warehouse are mainly fixed shelves, and each row of shelves in the warehouse is equipped with a stacker, which is responsible for picking up a cargo on the shelf. This paper takes some of the shelves in the warehouse as the object of study. In an automated warehouse, the stacker enters from the entrance, performs order picking, and chooses goods according to the programmed procedure. Assuming that there are
This study refers to the high-level rack model designed by Professor Ning and Hu [
Structural model of high-level rack.
Where, the position of the column
Assuming that the velocity in the horizontal direction of the stacker is
Since the horizontal and vertical movements of the stacker occur at the same time, the time of operation at the adjacent cargo space is
Then, the
If the picking time spent by the stacker is the same each time, that is,
Thus, the total time
Under above circumstances, we will ask for the total time of operation of the automated warehouse stacker and the minimum value
Particle swarm optimization is a new algorithm in recent years, which solves the TSP problem, and a good result is obtained [
The original FOA was invented by Professor Pan [ Set initial location of fruit flies at random ( Random directions and distance of fruit flies searching for food relying on good sense of smell, which is equivalent to the initial location of the fruit flies plus random flight distance: As the location of food cannot be obtained, estimate the distance ( Substitute decision value of Smelli ( Locate the fruit fly with the best Smelli from fruit flies (max): Retain the smell best and Enter into iterative optimization, repeat steps 2–5, and judge whether the Smelli is superior to the Smelli of the previous iteration, if yes, execute step 6.
The foraging process of a fruit fly group is illustrated in Figure
Foraging process of a fruit fly group.
In view of the optimization of picking in this paper, we know that the range of search distance of the original fruit fly in the coordinates is limited, which leads to the weak optimal performance. If the weight is added to the original FOA, the search range of fruit flies will be enlarged, which will greatly enhance the optimization ability of fruit flies.
Particle swarm algorithm [ Suppose in a D-dimensional target search space, The “flying” velocity of the The optimal position of the The optimal position of the whole particle swarm searched so far is called the global extremum, denoted as follows:
When these two optimal values are found, the particles will update their speed and position according to the following two formulas:
The foraging process of a particle swarm group is illustrated in Figure
Process of a Particle swarm group.
In this paper, we refer to the weight decrease and random weight algorithm mentioned by Gao [
The weight decrease method can adjust the global and local search capabilities of PSO and FOA, but it still has two shortcomings: first, the local search ability of early iterations is relatively weak, even if the initial particles are close to the global optimal point, it will be missed, and the global search ability will become weak at the later stage, so the program is caught in the local optimal value; second, the maximum number of iterations is difficult to predict, which will affect the adjustment function of the algorithm [
The random weight algorithm is based on the original PSO and FOA. In this paper, the RW refers to taking
Suppose the length of the shelf is 80 m, the height is 8 m, and a complete shelf has 40 rows and 5 tiers. The lateral movement speed Va of the stacker is 1 m/s and longitudinal velocity Vb is 0.2 m/s. The picking time of each cargo space is assumed to be 10 s. According to the above optimization algorithms, Popsize1 = 5 and Popsize2 = 10, that is, the number of all populations is Popsize1 × Popsize2 = 50. The largest number of iterations of six algorithms is 1000 times. In terms of FOA parameter, the random initial position of a fruit fly swarm is [−5, 5], fruit flies searching for food randomly, and the distance interval is [−50, 50]; in terms of PSO parameter,
We apply the RW and WD mathematical model to FOA and PSO and take the individual position as the encoding object, and the length of the code is a randomly generated cargo space number. We then assume that the number of subpopulations is Popsize1, the number of individuals in each population is Popsize2, and the number of individuals in all populations is Popsize1 × Popsize2, and then the population quantity is Popsize1 × Popsize2. If
Coding scheme of fruit flies randomly generated.
Cargo space | 1 | 2 | … | 7 | 8 | ||
---|---|---|---|---|---|---|---|
Tier | xab1 | xab2 | … | xab7 | xab8 | xab ( | xabn |
Row | yab1 | Yab2 | … | yab7 | yab8 | yab ( | yabn |
Smell | Sab1 | Sab2 | … | Sab7 | Sab8 | Sab ( | Sabn |
In order to check the optimization capability of the proposed FOA and PSO, two groups of 10 cargo spaces and 20 cargo spaces are randomly generated, as shown in Tables
10 cargo spaces in Group 1.
Tier | 24 | 32 | 40 | 26 | 17 | 12 | 38 | 15 | 7 | 29 |
---|---|---|---|---|---|---|---|---|---|---|
Row | 4 | 1 | 4 | 5 | 3 | 2 | 2 | 3 | 5 | 1 |
10 cargo spaces in Group 2.
Tier | 22 | 32 | 12 | 28 | 40 | 12 | 25 | 34 | 17 | 27 |
---|---|---|---|---|---|---|---|---|---|---|
Row | 2 | 1 | 3 | 3 | 1 | 5 | 3 | 2 | 2 | 4 |
20 cargo spaces in Group 1.
Tier | 20 | 32 | 42 | 35 | 22 | 6 | 19 | 43 | 18 | 38 |
---|---|---|---|---|---|---|---|---|---|---|
Row | 3 | 2 | 3 | 5 | 1 | 3 | 2 | 1 | 4 | 5 |
Tier | 25 | 10 | 44 | 16 | 41 | 17 | 28 | 3 | 7 | 15 |
Row | 1 | 5 | 2 | 4 | 4 | 2 | 1 | 3 | 5 | 4 |
20 cargo spaces in Group 2.
Tier | 8 | 20 | 22 | 6 | 12 | 13 | 28 | 14 | 34 | 4 |
---|---|---|---|---|---|---|---|---|---|---|
Row | 4 | 3 | 2 | 4 | 2 | 1 | 3 | 6 | 3 | 1 |
Tier | 33 | 11 | 32 | 3 | 36 | 27 | 40 | 4 | 22 | 25 |
Row | 4 | 2 | 2 | 5 | 3 | 1 | 3 | 4 | 2 | 6 |
The results (subfigures) are shown below in proper order: PSO (upper left), WDPSO (center left), RWPSO (lower left), FOA (upper right), WDFOA (center right), and RWFOA (lower right).
According to the data of Figure
Iterative changes of 10 cargo spaces in Group 1: (a) PSO; (b) FOA; (c) WDPSO; (d) WDFOA; (e) RWPSO; (f) RWFOA. Note:
According to the data of Table
Average of picking time of 10 cargo spaces in Group 1.
Algorithm | Original (s) | WD (s) | RW (s) | Average (s) |
---|---|---|---|---|
PSO | 243 | 235 | 234 | 237 |
FOA | 236 | 228 | 226 | 230 |
Average | 234.5 | 232 | 231 |
From the standard deviation in Table
Standard deviation of picking time of 10 cargo spaces in Group 1.
Algorithm SD | |||
---|---|---|---|
Algorithm | Original | WD | RW |
PSO | 6.6 | 6.4 | 6.2 |
FOA | 4.9 | 3.8 | 3.7 |
The optimal picking time of 10 cargo spaces is 226 s, and the corresponding picking order is as follows: 8–5–6–9–2–1–10–7–4–3.
According to the data of Figure
Iterative changes of 10 cargo spaces in Group 2: (a) PSO; (b) FOA; (c) WDPSO; (d) WDFOA; (e) RWPSO; (f) RWFOA. Note:
According to the data of Table
Average of picking time of 10 cargo spaces in Group 2.
Algorithm | Original (s) | WD (s) | RW (s) | Average (s) |
---|---|---|---|---|
PSO | 216 | 214 | 212 | 214 |
FOA | 209 | 208 | 207 | 208 |
Average | 212.5 | 211 | 209.5 |
From the standard deviation in Table
Standard deviation of picking time of 10 Cargo spaces in Group2.
Algorithm SD | |||
---|---|---|---|
Algorithm | Original | WD | RW |
PSO | 6.3 | 5.9 | 5.5 |
FOA | 4.8 | 4.7 | 4.6 |
The optimal picking time of 10 cargo spaces is 207 s, and the corresponding picking order is as follows: 3–2–1–8–5–7–6–10–9–4.
According to the data of Figure
Iterative changes of 20 cargo spaces in Group 1: (a) PSO; (b) FOA; (c) WDPSO; (d) WDFOA; (e) RWPSO; (f) RWFOA. Note:
According to the data of Table
Average of picking time of 20 cargo spaces in Group 1.
Algorithm | Original (s) | WD (s) | RW (s) | Average (s) |
---|---|---|---|---|
PSO | 553 | 550 | 549 | 550 |
FOA | 545 | 543 | 541 | 543 |
Average | 549 | 546.5 | 545 |
From the standard deviation in Table
Standard deviation of picking time of 20 cargo spaces in Group 1.
Algorithm SD | |||
---|---|---|---|
Algorithm | Original | WD | RW |
PSO | 18.4 | 15.3 | 15.0 |
FOA | 15.6 | 14.3 | 11.2 |
The optimal picking time of 20 cargo spaces is 541 s, and the corresponding picking order is as follows: 9–12–19–13–20–15–4–17–8–1–10–2–16–5–14–3.
According to the data of Figure
Iterative changes of 20 cargo spaces in Group 2: (a) PSO; (b) FOA; (c) WDPSO; (d) WDFOA; (e) RWPSO; (f) RWFOA. Note:
According to the data of Table
Average of picking time of 20 cargo spaces in Group 2.
Algorithm | Original (s) | WD (s) | RW (s) | Average (s) |
---|---|---|---|---|
PSO | 544 | 542 | 540 | 542 |
FOA | 531 | 528 | 514 | 524 |
Average | 537 | 535 | 527 |
From the standard deviation in Table
Standard deviation of picking time of 20 cargo spaces in Group 2.
Algorithm SD | |||
---|---|---|---|
Algorithm | Original | WD | RW |
PSO | 15.7 | 14.5 | 13.2 |
FOA | 21.3 | 15.5 | 14.7 |
The optimal picking time of 20 cargo spaces is 514 s, and the corresponding picking order is as follows: 8–18–19–4–5–1–12–2–10–6–16–15–20–14–11–7–9–3–13–17.
With the increasing pursuit of efficiency in logistics warehousing, order picking has also become an important research, and it is constantly proposed to apply a variety of different algorithms to optimize picking time. This paper assumes a model of automated warehouse shelves. By referring to previous studies, the study is designed to set the picking route to get the optimal picking time so as to improve the efficiency of order picking. It has been widely used in various industries, including electronic appliances, pharmaceutical logistics, tobacco logistics, machinery automation, and food industry.
A new FOA, PSO, RW, and WD are used to improve FOA and PSO and to look for the optimal order picking time. The result shows that the optimization capacity of RWFOA is better and the picking efficiency is the best. Therefore, it can be applied to the order picking in automated warehouses, thereby improving warehouse operation efficiency and reducing the time cost of order picking.
RWFOA is a more effective local search method which can be used in future work. The proposed RWFOA could be applied to other variations of the TSP; for example, fixed edges are listed that are required to appear in each solution to the problem, path problem, or vehicle routing problem etc. Therefore, future work could focus on the development of adaptive algorithms with the implementation of other problem-specific features that could improve the performance of the RWFOA.
This study also has certain limitations. For example, the paper assumes that the stacker is moving at a constant speed, but the speed in the actual operating conditions is uncertain. Secondly, this paper takes part of the shelves as the object of study instead of shelf-to-shelf, which means it is the local optimal in the warehouse rather than the global optimal.
The data used to test the algorithm are randomly generated, readers need to pay more attention to intelligent algorithms. Anyway, the data used to support the findings of this study are available from all the authors upon request.
The authors declare there are no conflicts of interest regarding the publication of this paper.
This research was financially supported by the 2018 Social Science Planning Project of Guangzhou “Research on the Construction and Development of Guangzhou Smart International Shipping Center Based on the One Belt One Road Strategy” (Grant no. 2018GZGJ169) and 2016 Humanities and Social Sciences Research Projects of Universities in Guangdong Province “Construction of key disciplines in business administration” (Grant no. 2015WTSCX126).