Swiss Round Selection Algorithm for Multi-Robot Task Scheduling

Abstract

Efficient and stable control and task assignment optimization in electronic commerce logistics and warehousing systems involving multiple robots executing multiple tasks is highly challenging. Hence, this paper proposes a Swiss round selection algorithm for multi-robot task allocation to address the challenges mentioned. Firstly, based on the shipping process of electronic commerce logistics and warehousing systems, the tasks are divided into packaging and sorting stages, and a grid model for the electronic commerce warehousing system is established. Secondly, by increasing the probabilities of crossover and mutation in the population and adopting a full crossover and full mutation approach, the search scope of the population is expanded. Then, a Swiss round selection mechanism with burst probability is proposed, which ensures the smooth inheritance of high-quality individuals while improving the diversity of the population. Finally, 12 comparative experiments are designed with different numbers of robots and tasks. The experimental results demonstrate that the Swiss round selection algorithm outperforms the genetic algorithm in terms of maximum task completion time and convergence time to reach the optimal value. Thus, the effectiveness of the Swiss round selection algorithm in solving the multi-robot task allocation problem is verified.

1. Introduction

With the development of internet technology and the continuous improvement of people’s living standards, shopping methods have significantly changed. In recent years, owing to the vigorous development of the e-commerce industry [1], an increasing number of people shop online, easily placing orders at home using a smartphone and having their goods delivered to their doorstep., benefiting from a new shopping experience. Additionally, to expand their sales channels, merchants have turned to online e-commerce for business expansion [2]. Against this backdrop, the popularity of online shopping has brought immense pressure and new challenges to the logistics industry [3].

The traditional logistics industry currently relies on manual handling, which is costly and inefficient. The e-commerce logistics industry faces challenges, such as large orders, long delivery distances, and short delivery times. Therefore, the traditional manual dispatching method can no longer meet the rapidly growing demand. As logistics costs rise, e-commerce enterprises are increasingly eager to improve efficiency and reduce costs, with multi-robot dispatch effectively reducing labor costs and improving operational efficiency. Moreover, e-commerce logistics warehouses often have complex environments [4], including various goods, packages of different sizes, and shelves of different heights, increasing the complexity of task scheduling. At the same time, the e-commerce logistics industry requires orders to be delivered quickly and accurately, thus placing high demands on the real-time nature of task scheduling, necessitating timely dispatch decisions. With the continuous development and application of artificial intelligence, machine learning, and automation technologies, the feasibility and effectiveness of multi-robot dispatch in practical applications have been enhanced [5], providing technical support for further research and application.

Therefore, using advanced robots to perform some of the work in the logistics system is a necessary step for future development. However, existing robots mostly use a proximity principle for goods distribution, which is less efficient under high task volumes [6]. Hence, studying the robot dispatch system in the logistics system is necessary. Multi-robot multi-task scheduling refers to allocating multiple tasks to multiple robots for execution, optimizing the sequence in which each robot performs the tasks to reduce the overall system work time and improve the work efficiency of the e-commerce logistics warehouse [7]. Task scheduling is a typical NP problem [8,9], and although exhaustive methods can achieve optimal solutions, they are unfeasible as the problem size increases. Therefore, research on multi-robot multi-task scheduling has attracted significant attention.

This paper proposes a dispatch model based on the Swiss Round Selection Algorithm for the complex problem of multi-robot multi-task scheduling. The proposed algorithm has achieved significant advantages in the multi-robot multi-task scheduling environment by comparing several common genetic algorithms. The main contributions of this paper are:

(1)

Model Construction: Based on the dispatch process of the e-commerce logistics and warehousing system, a grid model including two packaging and distribution stages is established, providing a theoretical framework for the multi-robot task allocation problem;

(2)

Algorithm Innovation: A new multi-robot task allocation algorithm, the Swiss Round Selection Algorithm (RCG), is proposed. It expands the search range of the population through full crossover and full mutation operations using a Swiss Round Selection operation with a cold explosion probability to screen the population, ensuring the inheritance of high-quality individuals and population diversity;

(3)

Problem Solving: The Swiss Round Selection Algorithm is used to solve the multi-robot task allocation problem, effectively reducing the overall system work time and improving the work efficiency of the e-commerce logistics warehouse;

(4)

Performance Verification: Through 12 sets of comparative experiments with different numbers of robots and tasks, it is verified that the Swiss Round Selection Algorithm is superior to traditional genetic algorithms regarding maximum task completion time and the number of convergences to the optimal value, proving the effectiveness and superiority of the algorithm;

The remainder of this paper is organized as follows. Section 2 introduces the current research on multi-robot multi-task scheduling in the logistics industry. Section 3 presents the task scheduling model of the e-commerce logistics and warehousing system. Section 4 describes the improvements made to the Swiss Round Genetic Algorithm, and Section 5 compares the improved algorithm proposed in this paper with traditional genetic algorithms. Finally, Section 6 concludes this paper.

2. Related Work

With the development of the e-commerce industry, automated logistics systems have also attracted increasing research attention from scholars and companies. The primary key point of the related research is the logistics system’s effective modeling. Logistics system modeling is a complex issue [10] involving multiple factors, such as network structure, information interaction, task processing, resource scheduling, and equipment performance. For instance, Marchet et al. [11] proposed a logistics model for traditional commerce that effectively reduces a company’s logistics costs and enhances its profitability. An alternative logistics modeling approach uses drones for goods distribution within the logistics system, involving the planning and describing of low-altitude space [12]. Traditional logistics companies wish to plan the logistics distribution system in detail from the source factory, incorporating Internet of Things (IoT) sensors into the logistics system to improve the accuracy of goods tracking [13]. With the development of big data, IoT has played an important role in modeling the logistics industry, further improving the accuracy of the model and system efficiency [14,15]. For example, Zarbakhshnia et al. [16] introduced a multi-objective model for green forward and reverse logistics network design for multi-target tracking systems that effectively track and coordinate multiple machine targets.

Research on robot scheduling and collaboration has also progressed. In [17], the authors develop a distributed market-oriented algorithm that improves work efficiency by exchanging tasks without considering global optimal scheduling. Qin et al. proposed an improved ant colony algorithm to solve the task allocation problem for multiple robots [18]. However, their method suffers from poor stability, a tendency to fall into local optima, and slow computation speed. Wang et al. developed an improved algorithm to solve task scheduling and path optimization for robots in a warehousing logistics system [19]. Still, their method applies only to small-scale robot scheduling. Yang et al. proposed an immune ant colony optimization algorithm that integrates immune algorithms with ant colony algorithms to address the multi-target allocation problem for warehouse robots [20]. This scheme has a relatively high complexity and resource consumption. Jiang et al. suggested an improved particle swarm algorithm to solve the scheduling problem of order tasks [21], fully considering the collaborative transportation between multiple orders and improving the efficiency of intelligent warehousing. However, it does not consider the utilization rate of individual robots, leading to an excessively high utilization rate of single robots.

The genetic algorithm is the most commonly used for multi-robot multi-task scheduling [22,23,24]. Genetic algorithms are widely applied in multi-robot task allocation and scheduling due to their simplicity, strong operability, and good global convergence ability [25,26]. Research on algorithm parameters and operators is currently the focus of genetic algorithms [27]. Regarding their parameters, the self-adaptive genetic algorithm proposed by Zheng et al. utilizes hormone regulation technology to judge the algorithm’s state [28], effectively improving its performance. Considering the algorithm operators, the main focus is on the three basic operators of genetic algorithms: selection [29], crossover [30], and mutation [31]. Most research on multi-robot task scheduling only focuses on certain aspects and lacks overall planning.

In response to the problems for task scheduling of robots in the e-commerce logistics and warehousing system, this paper proposes a Swiss Round Selection Algorithm for multi-robot distribution scheduling. Firstly, based on the actual delivery scenario of the e-commerce logistics and warehousing system, a task scheduling model for the e-commerce logistics and warehousing system is established, analyzing the constraints and objective functions. In addition, the Swiss Round Selection Algorithm outputs the optimal scheduling results, thus achieving task allocation and scheduling for multiple robots. Finally, the Swiss Round Selection Algorithm is compared with the tournament selection strategy, elitist selection strategy, and roulette wheel selection strategy in genetic algorithms under the same conditions through comparative experiments, verifying the superiority of the proposed method for robot task scheduling.

3. E-Commerce Logistics and Warehousing System Task Scheduling Model

3.1. Problem Description

Table 1. Definition of Research Subjects.

Object	Robot	Shelf	Phase	Task	Packing Workstation	Distribution Workstation
Definition	R	S	P	T	W	F

reports the main research subjects’ parameters to describe better the workflow of the e-commerce logistics and warehousing system.

The dispatch process of the e-commerce logistics and warehousing system comprises two stages. When the system receives a set of order tasks, robot R1 first moves from the initial position to the position of the task shelf S1, taking 10 s. Then, R1 picks up the goods from the shelf and transports them to the packaging workstation W to complete the first stage of distribution work P1. The transportation takes 15 s, and P1 takes 30 s to complete. After P1 is completed, R1 returns to a free state and carries out other scheduled tasks. Subsequently, robot R2 transports the goods to the distribution workstation F to perform the second stage of distribution work P2. The transportation process takes 25 s, and P2 takes 40 s to complete. After the second stage of distribution work is completed, the dispatch process of task T1 is finished. The entire T1 requires 120 s. Figure 1 illustrates the Gantt chart of this example, presenting the working status of the robots and various workstations as the system executes tasks. Under multiple robots and tasks, optimizing the order of task execution and the distribution scheduling for each phase becomes particularly important.

3.2. Task Scheduling Model

The grid model of the e-commerce logistics and warehousing system is established using the grid method [32]. Figure 2 illustrates the e-commerce logistics and warehousing system comprising robots, packaging workstations, distribution workstations, and shelves. Robots are free to move in the aisles between the shelves, with one staff member at each workstation, and robots can transport shelves to different workstations for packaging and distribution tasks.

Since the grid model allows the robot to choose only the next target point in four directions—forward, backward, left, and right—the path distance traveled by the robot is calculated using the Manhattan distance:

$$L_{ij}=\left|x_i-x_j\right|+\left|y_i-y_j\right|,$$

(1)

where $L_{ij}$ represents the Manhattan distance between a point $i$ and $j$, $(x_i,y_i)$ is the two-dimensional coordinate of $i$, and $(x_j,y_j)$ is the two-dimensional coordinate of $j$. The robot is assumed to travel at a constant speed $v$ without considering the acceleration and deceleration processes during the start and stop phases. Therefore, the relationship between the time required during the robot’s work process and the distance traveled is as follows:

$$t_{ij}=\frac{L_{ij}}{v},$$

(2)

where $t_{ij}$ is the time the robot requires to travel from point $i$ to point $j$.

3.3. Assumptions of the Model

(1)

The robots are always in a state of full battery charge, and energy consumption is not considered;

(2)

The robots operate under the condition that the paths are clear, with no traffic congestion or other special circumstances;

(3)

There is an ample supply of goods on the shelves, which can meet the demand of orders;

(4)

The robots return to their initial positions by default after completing all tasks;

(5)

Throughout the execution of system tasks, all robots maintain uniform operational velocities;

(6)

A single robot is capable of processing one task per instance.

3.4. Constraint Conditions

3.4.1. Workstation Constraints

The packaging and distribution tasks of Task T should be completed by the packaging workstation W and the distribution workstation F, respectively. Each workstation can only perform its corresponding task and handle the packaging or distribution of one item of goods at any given moment.

3.4.2. Time Constraints

Completing Task T involves two stages. Task T must undergo packaging P1 at the packaging workstation W before proceeding to the distribution workstation F for distribution P2. This means that the completion time of Task T for the P1 phase must be before the start of the P2 phase. The time constraints for the task are as follows:

$$t_c(P_{i1})<t_c(P_{i2}),$$

(3)

where $t_c$ represents a certain point during the task process, $t_c(P_{i1})$ is the completion time point of the first stage of Task $i$, and $t_c(P_{i2})$ is the completion time point of the second stage of Task $i$.

A workstation can only proceed to Task $T_2$ after completing the previous task $T_1$. The time constraint for the workstation is the following:

$$\left\{\begin{array}{l}\forall t_c=c\\ count(T_M)\le 1\\ count(T_F)\le 1\end{array}\right.,$$

(4)

where $T_M$ represents the task executed by the packaging workstation, $T_F$ is the task executed by the distribution workstation, and $count()$ is the task counting function.

If the robot $R_x$ has been scheduled to perform the $P_2$ phase of Task $T$, but the $P_1$ phase of Task $T$ has not yet been completed, then $R_x$ must wait for $P_1$ to finish before executing $P_2$. The time constraint for the robot is:

$$\left\{\begin{array}{l}\forall t_c<t_c(P_{ij})\\ \forall R_i\in R\\ count(T_{R_i})=0\end{array}\right.,$$

(5)

where $t_c$ represents a certain point in time during the task process and $count()$ is the counting function.

3.4.3. Task Constraints

All tasks $T$ issued by the system must be completed, and the same task cannot be executed more than once. The decision variables of the model are as follows: when $P_{1_{Ri}}=1$, robot $R$ is executing the $P_1$ phase of task $i$, otherwise it is considered not executed. When $P_{2_{Rij}}=1$, robot$R$ executes the $P_2$ phase of task $j$ after completing the $P_1$ phase of task $i$, otherwise it is considered not executed. The constraints for the tasks are presented below:

$${\displaystyle \sum _{i=1}^T{P}_{1_{Ri}}}=1,$$

(6)

$${\displaystyle \sum _{i=1}^T{P}_{2_{Rij}}}=P_{1_{Rj}},$$

(7)

$${\displaystyle \sum _{j=1}^T{P}_{2_{Rij}}}=P_{1_{Ri}},$$

(8)

where $P_{1_{Ri}}$ represents the first phase $P_1$ of the task $i$ being executed by the robot $R$. At the time when $P_2$ is considered, robot $R$ executes the second phase $P_{2_{Rij}}$ of task $j$ after completing the $P_1$ phase of task $i$. The constraints of Equations (6) to (8) ensure that each task is performed and executed only once.

3.5. Objective Function

The optimization goal of the e-commerce logistics warehouse scheduling model is to minimize the total time required for all robots to complete all tasks. The objective function is as follows:

$$C_{total}=\min ({\displaystyle \sum _{i=1}^n{\displaystyle \sum _{j=1}^{m_i}C(T_i,P_{ij}))}},$$

(9)

where $C_{total}$ represents the objective function, $T_i$ denotes the task $i$ pending execution, where $i$ ranges from 1 to $n$, and $P_{ij}$ refers to the $j$th phase within a task $T_i$, where $j$ ranges from 1 to 2.

4. Swiss Round Genetic Algorithm

4.1. Overall Algorithm Process

The Swiss Round Selection Algorithm is inspired by the Swiss system tournament format used in chess championships. The main idea of the algorithm is to expand the search range of the population through full crossover and full mutation operations, followed by a Swiss Round Selection operation with a cold explosion probability for population screening. This screening method ensures that high-quality individuals successfully advance to the next generation while maintaining the diversity of the population, thereby enhancing the algorithm’s rapid global search capability. The flowchart of the algorithm is depicted in Figure 3.

4.2. Encoding

Chromosome encoding uses a dual-chromosome encoding method, with one chromosome for task encoding and the other for robot encoding. Both task encoding and robot encoding use real-number encoding, and the chromosome length is twice the total number of tasks to be performed. In the task chromosome encoding, each task gene appears twice. The first occurrence represents the execution of the first phase (P1) packaging task, and the second occurrence represents the execution of the second phase (P2) distribution task. The order of the task encoding from left to right represents the sequence in which tasks are to be executed, while the robot chromosome encoding indicates the robot numbers corresponding to the sequence of tasks to be executed. For example, with five tasks and three robots, the encoding of a certain chromosome is presented in Figure 4.

4.3. Fitness Function

The adaptability of a chromosome is evaluated based on the following fitness function:

$$f_{fit}=\frac{1}{C_{total}},$$

(10)

where $f_{fit}$ represents the fitness function of the chromosome.

4.4. Crossover

This paper does not set a crossover probability, and all parent chromosomes are involved in the crossover operation. This is because the two-phase tasks of the e-commerce logistics and warehouse have time constraints, and through this strategy, we aim to reduce the time overhead of the crossover operation. The specific process of the crossover operation is as follows:

(1)

Randomly select two endpoints from the parent robot chromosome encoding;

(2)

Perform the crossover operation between these endpoints while keeping the task chromosome encoding unchanged.

The crossover operation aims to randomly explore individual populations, improving the algorithm’s search efficiency. The process of crossover operation is presented in Figure 5.

4.5. Mutation

This paper does not set a mutation probability, and all parent chromosomes are involved in the mutation operation. This approach aims to reduce the time overhead associated with the mutation operation. The specific process of the mutation operation is as follows:

(1)

Randomly select a robot encoding gene from the parent robot chromosome;

(2)

Perform a single-point mutation on this gene.

The mutation operation aims to achieve diversity among the individuals in the population, thereby enhancing the search efficiency of the algorithm. The process of mutation operation is presented in Figure 6.

4.6. Selection

After the genetic operations of crossover and mutation, the population can produce new individuals with different genetic characteristics, providing new candidate solutions for the algorithm’s search and promoting the convergence of the population toward the optimal solution. The selection operation is a key step in the algorithm’s search process. By comparing and screening new and old individuals, better individuals are selected to enter the next generation population, gradually approaching the optimal solution. The subsequent selection operation will maintain the population’s stability, and the offspring’s quality will significantly impact the future iterations of the population. If only high-quality individuals are selected for the next generation, the search process is prone to the “premature convergence” phenomenon, where the algorithm easily falls into a local optimum, lacking stability. However, if random selection is performed, it may lead to the loss of high-quality individuals, thereby greatly reducing the algorithm’s efficiency. Therefore, this paper introduces a Swiss Round Selection method with a cold explosion probability to ensure the population’s diversity and expand the algorithm’s search range.

Taking an initial population size of 80 as an example, 160 offspring individuals are produced after crossover and mutation operations. Subsequently, the parents and offspring are merged to form a population of 240 individuals. We define a cold explosion probability P = 0.1. In order to ease understanding, we divide the population into four groups: Group A (corresponding to Group 0), Group B (Group 1), Group C (Group 2), and Group D (Group 3).

The specific selection steps are as follows:

Step 1: Randomly select two individuals from the population and evaluate them based on the fitness function PK. The winning individual will receive 1 point and advance to Group B, while the losing individual will not receive any points and will go to Group A. At this point, Group A contains 120 individuals, all with a score of 0, and Group B also contains 120 individuals, all with a score of 1.

Step 2: Randomly select two individuals from Group B and evaluate them based on the fitness function PK. The winning individual will receive 1 point and advance to Group C, while the losing will remain in Group B. At the same time, we also randomly select two individuals from Group A and evaluate them based on the fitness function PK. In each round of PK, we generate a random number Z with a range of 0–1. If an individual wins in PK and Z is greater than or equal to PK, or if the individual loses in PK and Z is less than PK, then that individual will receive 1 point and advance to Group B. Otherwise, the individual will not receive any points and remain in Group A. After this step, Group C will contain 60 individuals, all with a score of 2. Group B will contain 120 individuals, all with a score of 1, and Group A will contain 60 individuals, all with a score of 0.

Step 3: Randomly select two individuals from Group C and evaluate them based on the fitness function PK. The winning individual will receive 1 point and advance to Group D, while the losing individual will remain in Group C. At the same time, we also randomly select two individuals from Group B and evaluate them based on the fitness function PK. In each round of PK, we generate a random number Z with a range of 0–1. If an individual wins in PK and Z is greater than or equal to PK, or if the individual loses in PK and Z is less than PK, then that individual will receive 1 point and advance to Group C. Otherwise, the individual will not receive any points and remain in Group B. We randomly select two individuals from Group A and evaluate them based on the fitness function PK. In each round of PK, we generate a random number Z with a range of 0–1. If an individual wins in PK and Z is greater than or equal to PK, or if the individual loses in PK and Z is less than PK, then that individual will receive 1 point and advance to Group B. Otherwise, the individual will not receive any points and remain in Group A. After this step, Group D will contain 30 individuals, all with a score of 3. Group C will contain 90 individuals, all with a score of 2. Group B will contain 90 individuals, all with a score of 1, and Group A will contain 30 individuals, all with a score of 0. All individuals in Group D are advanced, and all in Group A are eliminated.

Step 4: Select ((G-D)×2)-C individuals from Group B and advance them to Group C directly. In this example, there are 10 individuals. At this point, Group C has a total of 100 individuals. Randomly select two individuals from Group C and evaluate them based on the fitness function PK. In each round of PK, we generate a random number Z within the range 0–1. If an individual wins in PK and Z is greater than or equal to PK, or if the individual loses in PK and Z is less than PK, then that individual will receive 1 point and advance to Group D. Otherwise, the individual will not receive any points and will remain in Group C. After this step, Group D will have 80 individuals, all with a score of 3. All individuals in Group D will participate in the next iteration process or output the optimal scheduling result.

The selection process ends here, and the specific operation is illustrated in Figure 7.

5. Experimental Analysis

5.1. Experimental Environment

Next, we constructed a simulation environment and conducted experiments to evaluate the performance of the proposed algorithm. All experiments were executed on a computer equipped with an Intel Core i9 processor, 128 GB of RAM, and two NVIDIA RTX4090 GPUs with 24GB of video memory each, using Python programming.

The experimental environment was set up as a 50 m × 50 m grid map, which included one packaging workstation and one distribution workstation. The time taken to complete tasks at each workstation was 20 s. In our experiments, we set the initial population size to 80 and the Swiss Round (RCG) cold explosion probability to 0.1. The crossover probability for all genetic algorithms was set to 0.6, and the mutation probability was set to 0.1. The maximum number of iterations for all algorithms was 100.

5.2. Comparative Experiments

To assess the effectiveness of the Swiss Round Selection Algorithm (hereinafter referred to as RCG) in solving multi-robot task scheduling problems, we conducted comparative experiments with several other selection strategies commonly used in Genetic Algorithms (GAs). In our experiments, we utilized three selection strategies: Tournament Selection (TS), Elitist Selection (ES), and Roulette Wheel Selection (RS).

We set up 12 groups of experimental conditions corresponding to different numbers of robots and tasks. For each set of conditions, we conducted 10 independent repetitions of the experiment and recorded the final scheduling results and the number of iterations required for the algorithm to reach the optimal value. After analyzing the experimental results, we calculated the average values and presented the results in

Table 2. Objective Function Values with R = 3 and Various Task Quantities.

Algorithm	Number of Tasks
	15	20	25	30	35	40	45	50
RCG	488.66	675.6	801.4	940.01	1079.35	1222.01	1356.3	1506.23
TS	490.43	677	804.6	944.53	1084.32	1227.33	1362.8	1513.18
ES	501.86	690	819.86	962	1113	1257.5	1402.23	1558.13
RS	513.2	704.8	835.2	981	1135	1281.2	1428.26	1588.31

and Figure 8.

Table 2 compares the objective function values for a scenario that involves three robots and 15 to 50 tasks. Figure 8 shows the number of iterations required for the algorithm to reach the optimal value under different conditions.

Table 3. Objective Function with T = 80, Under Different Numbers of Robots.

Algorithm	Number of Robots
	3	4	5	6
RCG	2393.4	1838.8	1677	1677
TS	2408.9	1848.1	1678.3	1677
ES	2480.5	1890.5	1678.6	1677
RS	2530.9	1928.2	1679.8	1677

compares the objective function values for 80 tasks, and the number of robots ranges from three to six.

Table 2 highlights that for the same number of robots but varying numbers of tasks, the optimization effect of RCG on the objective function is significantly better than that of TS, ES, and RS. When the number of tasks is 15, the objective function of RCG decreased by 0.36%, 2.63%, and 4.78%, compared to TS, ES, and RS, respectively. When the number of tasks increased to 50, the objective function of RCG decreased by 0.45%, 3.33%, and 5.16%, compared to TS, ES, and RS, respectively. This indicates that as the number of tasks increases, the gap between RCG and TS, ES, and RS widens, and the optimization effect of RCG on the objective function is better.

Figure 8 reveals that under different task quantity conditions, the number of iterations required for RCG to reach the optimal value is superior to other algorithms. The experimental results indicate that the RCG algorithm outperforms other algorithms regarding solution speed and convergence capability.

Table 3 infers that for the same number of tasks but varying numbers of robots, the optimization effect of RCG on the objective function is significantly better than that of TS, ES, and RS. When the number of robots is three, the objective function of RCG decreased by an average of 0.64%, 3.51%, and 5.43%, compared to TS, ES, and RS, respectively. When the number of robots is four, the objective function of RCG decreased by an average of 0.5%, 2.73%, and 4.63%, compared to TS, ES, and RS, respectively. As the number of robots continues to increase until saturation, the objective function output by all algorithms remains consistent. Increasing the number of robots further will not reduce the maximum completion time of the system.

The experimental verification confirmed that the RCG algorithm performs better in solving multi-robot multi-task scheduling problems. Under the strategy of full crossover and full mutation, the RCG algorithm expands the population’s search range and enhances the population’s diversity. At the same time, using the Swiss Round Selection strategy ensures the inheritance of high-quality solutions and the inheritance of some medium- and low-quality individuals, thereby maintaining the diversity of the population. The Swiss Round Selection algorithm achieves a smaller objective function value and better convergence than other algorithms. Therefore, the Swiss Round Selection algorithm can more quickly and effectively obtain an optimized solution for multi-robot collaborative scheduling.

6. Conclusions

In addressing the multi-robot multi-task scheduling problem within the context of e-commerce logistics and warehousing systems, this paper has established a two-stage scheduling grid model that includes packaging and distribution based on the actual dispatch scenarios of e-commerce logistics and warehousing. This model provides a theoretical foundation for solving the multi-robot scheduling problem. Furthermore, in response to the low efficiency and susceptibility to local optima of genetic algorithms when solving multi-robot scheduling problems, this paper has proposed and applied the RCG (Robust Crossbreeding and Genetic) method to effectively address these issues.

Initially, during the algorithm’s iterative process, a full crossover and full mutation strategy was adopted, with all parent individuals participating in crossover and mutation operations, thereby enhancing the search scope of the population. Subsequently, a Swiss Round Selection mechanism with a cold explosion probability was proposed, ensuring that high-quality individuals are smoothly inherited while also passing on some medium- and low-quality individuals to the next generation. This approach increases the diversity of the population and effectively prevents the traditional genetic algorithm from easily falling into local optima, thereby improving the performance of the algorithm.

Furthermore, to verify the feasibility of the RCG algorithm, this paper designed 12 comparative experiments with different numbers of robots and tasks and analyzed the advantages of RCG over TS (Tournament Selection), ES (Elitist Selection), and RS (Roulette Wheel Selection). The results show that when the number of robots is the same, RCG performs better than TS, ES, and RS regarding the objective function and the number of iterations required to reach the optimal value under different task quantities. When the number of tasks is the same, the gap between RCG and TS, ES, and RS decreases as the number of robots continuously increases. When the number of robots increases, the maximum completion time of the system tasks will first decrease and then increase, eventually reaching saturation. At this point, even if the number of robots is further increased, the maximum completion time of the system tasks will not change significantly.

However, this study still has some shortcomings, as the issue of path conflicts during the robots’ travel has not yet been considered. Additionally, in cases with many tasks, this paper did not consider the energy consumption and sudden failure of robots during the scheduling process, nor did it address the problem of optimal path planning for robots. Given the existence of these issues, future research will delve into path conflict resolution, robot failure handling and optimal robot path planning, aiming to further enhance the reliability of the entire system.