Optimization of Multi-Operator Human–Robot Collaborative Disassembly Line Balancing Problem Using Hybrid Artificial Fish Swarm Algorithm ^†

Abstract

This paper addresses the multi-operator human–robot collaborative disassembly line balancing problem aimed at minimizing the number of workstations, workstation idle time, and disassembly costs, considering the diversity of end-of-life products and the characteristics of their components. A hybrid artificial fish swarm algorithm (HAFSA) is designed in accordance with the problem characteristics and applied to a disassembly case of a hybrid refrigerator. Comparative experiments with the non-dominated sorting genetic algorithm II (NSGA-II) and teaching–learning-based optimization (TLBO) algorithms demonstrate the superiority of the proposed algorithm. Finally, the performance of the three algorithms is evaluated based on non-dominated rate (NR), generational distance (GD), and inverted generational distance (IGD) metrics.

1. Introduction

With the advancement of the green economy and sustainable development, recycling end-of-life products has become increasingly important. Traditional disassembly methods are inefficient and costly, and manual disassembly poses safety risks while lacking flexibility. Human–robot collaborative disassembly combines the advantages of manual and automated disassembly, enhancing both disassembly efficiency and ensuring flexibility and safety in the process. Therefore, optimizing the human–robot collaborative disassembly line balancing problem for shared workstations is of significant importance.

In the relevant literature, Huang et al. [1] introduced an innovative approach for the disassembly of stamped parts using human–robot collaboration, leveraging the active flexibility of collaborative robots. The practicality of this approach was validated through a case study that involved a collaborative robot and a human operator working together to disassemble an automobile water pump. Wu et al. [2] introduced a bilateral disassembly line balancing problem with human–robot interaction constraints. By modeling and developing algorithms, they addressed disassembly instances under these constraints, providing new insights into the application of human–robot interaction technology in disassembly line production. Qu et al. [3] developed a human–robot collaborative disassembly environment with both virtual and real interaction capabilities. By promoting real-time human–robot collaboration strategies in dynamic production processes, they significantly enhanced the flexibility of disassembly operations. Xu Peiyu et al. [4] introduced a parallel disassembly line balancing problem for shared human–robot workstations. They addressed the limitations of existing research on task allocation constraints in human–robot shared workstation disassembly. By optimizing the number of workstations, number of operators, workstation balance index, and disassembly cost, they constructed a complete multi-objective mixed integer programming model that can be solved precisely. Xu et al. [5] explored the issue of balancing human–robot collaborative disassembly lines, with a focus on worker safety. They developed an HRC-DLBP information model that incorporates safety measures and addressed this problem using an enhanced discrete bee algorithm to manage safety protocols between human operators and robots. Wu et al. [6] considering the hazardous and complex nature of used batteries and proposed an integrated human–robot collaborative disassembly model for battery modules. They solved the model using the battery pack of a Tesla Model S as a case study, resulting in two distinct disassembly schemes.

These studies enhance disassembly efficiency and safety but focus less on task allocation and multi-product disassembly. This paper introduces a multi-operator human–robot collaborative disassembly line balancing problem (MHRC_DLBP). The main objectives are to minimize the number of workstations (F₁), reduce idle time (F₂), and lower disassembly costs (F₃). To address this problem, we employ a hybrid artificial fish swarm algorithm.

2. Problem Description

The MHRC_DLBP studied in this paper is a multi-layered, multi-dimensional, complex decision-making problem that integrates three sub-problems: operator allocation during the disassembly process, sequencing of disassembly tasks, and assignment of disassembly tasks to workstations. This problem not only requires adherence to the general constraints of disassembly line balancing problems (DLBPs) but also entails developing a hybrid product disassembly information model. Additionally, it involves classifying and assigning tasks to human and robot operators based on the varying characteristics of components.

The disassembled components are categorized into three types based on their characteristics: hazardous components, complex components, and ordinary components. Robots execute the disassembly tasks for hazardous components; human workers execute the disassembly tasks for complex components; and there are no restrictions for ordinary components, which either workers or robots can disassemble. Within the same task, the disassembly times for robots and workers differ. Each workstation includes two types of disassembly operation objects, allowing for simultaneous disassembly operations by humans and robots within the same station.

3. HAFSA

In response to the problem characteristics studied in this paper, a hybrid artificial fish swarm algorithm is proposed, incorporating adaptive visual behavior, chemotactic behavior, and opposition-based learning behavior.

3.1. Adaptive Visual Behavior

In the artificial fish swarm algorithm, selecting an appropriate visual range is crucial for convergence performance. A smaller visual range enhances search capability while a larger range broadens the search space but slows convergence. Thus, an adaptive visual method is proposed:

• Set a larger visual range initially to facilitate searching.
• Before each iteration, each fish calculates the average distance to other fish within its visual range, which becomes the visual range for the next iteration.

3.2. Chemotactic Behavior

This paper integrates the chemotaxis operation from the bacterial foraging algorithm into the artificial fish swarm algorithm. This enhances local optimization and helps to escape local optima to find the global solution. Chemotaxis involves bacteria moving randomly and comparing fitness values to determine their direction. When the artificial fish swarm’s foraging fails, chemotaxis is applied to the current solution, updating it through fragment exchanges until the maximum iterations are reached.

The chemotaxis operation for bacterium i with a unit step length is described as follows:

$${\theta }^i(j+1,k,l)={\theta }^i(j,k,l)+C\left(i\right)\varnothing \left(i\right)$$

(1)

$$\varnothing (j)={\displaystyle \frac{∆\left(i\right)}{\sqrt{{∆}^T\left(i\right)∆\left(i\right)}}}$$

(2)

Equations (1) and (2) are explained below:

Let ${\theta }^i(j,k,l)$ denote the position of the ith bacterium during the jth chemotactic operation, the kth reproduction operation, and the lth migration operation. $C\left(i\right)$ represents the swimming step length of the chemotactic operation and $\varphi \left(j\right)$ is a random unit-length direction vector for the chemotactic operation. $\mathsf{\Delta }\left(i\right)$ is a random number between [−1, 1], and ${\theta }^i(j+1,k,l)$ represents the ith bacterium’s position after the j + 1th swim.

3.3. Opposition-Based Learning Behavior

The opposition-based learning mechanism is designed to effectively expand the search space and cover more feasible solution regions. It has achieved significant success in the application of intelligent algorithms. This mechanism generates an opposite solution based on the current solution and then compares the fitness values of the original and opposite solutions. If the fitness value of the opposite solution is better, the opposite solution is chosen for optimization in subsequent iterations; if the original solution has a better fitness value, the original solution continues to be used for optimization. This process enhances the diversity and breadth of the search by introducing the opposite solution, helping to avoid local optima and thereby improving the algorithm’s overall performance.

3.4. Integrated Optimization Strategies for Enhanced AFSA Performance

The design of these three behaviors aims to optimize the artificial fish swarm algorithm (AFSA) by employing diverse strategies to enhance search efficiency and convergence performance while overcoming local optima issues. Firstly, the adaptive visual behavior initiates with a larger visual range to expand the search space, ensuring comprehensive early exploration. This range is dynamically adjusted in each iteration based on the average distance between fish, gradually focusing the search to improve convergence speed. Secondly, the chemotactic behavior, inspired by the bacterial foraging algorithm, enhances local optimization capabilities by allowing for random movement and fitness value comparison. This helps the fish swarm escape local optima and discover global solutions. When the foraging behavior fails, chemotaxis updates the current solution through fragment exchanges until the maximum number of iterations is reached. Lastly, the opposition-based learning behavior generates opposite solutions based on the current solution and compares their fitness values, selecting the better solution for subsequent optimization. This expands the search space and prevents the algorithm from getting stuck in local optima, thereby enhancing search diversity and overall performance. In summary, these behavior designs effectively integrate extensive exploration and precise search strategies, significantly improving the AFSA’s global search capability and local optimization performance, ensuring the algorithm’s stability and effectiveness.

4. Example and Analysis

To verify the effectiveness of the proposed algorithm, we implemented it on a human–robot collaborative disassembly scenario involving a hybrid refrigerator product. The parameters for the algorithm were configured as follows [7]: fish_num = 80, max_gen = 100, try_num = 15, n_step = 8, CT = 100 s. We introduced the NSGA-II algorithm [8] and the TLBO algorithm [4] for comparison, using the parameters provided in the literature for the comparison algorithms.

To assess the performance of the algorithms and analyze the convergence and distribution of the obtained Pareto solutions, we executed each of the three algorithms five times within the same time period. We calculated the non-dominated rate (NR), generational distance (GD), and inverted generational distance (IGD) indicators.

The disassembly flowchart for the hybrid refrigerator product is illustrated in Figure 1. This hybrid refrigerator consists of two parts, with Part 1 on the left side and Part 2 on the right side. In the flowchart, tasks highlighted in green indicate those that can only be assigned to workers while tasks highlighted in blue can only be assigned to machines. Tasks shown in white indicate those that can be assigned to either workers or machines. The arrows in the figure represent the precedence constraints between the tasks of this product.

Box plots corresponding to the case mentioned above are drawn to present the simulation results more intuitively. Figure 2 shows the box plots of the three algorithms’ NR, GD, and IGD indicators. In each plot, the number next to the box represents the median value for that algorithm.

For the NR indicator, the HAFSA achieves a median value of 0.524, which is higher than the medians of 0.281 and 0.138 for NSGA-II and TLBO, respectively. This indicates that the HAFSA consistently finds more non-dominated solutions. For the GD and IGD indicators, the HAFSA achieves lower median values compared to NSGA-II and TLBO, indicating that the solutions generated by the HAFSA are closer to the true Pareto front and more evenly distributed.

Overall, the HAFSA demonstrates superior performance across all three evaluation metrics, as reflected by the positions and medians of the box plots.

Figure 3 presents a Gantt chart depicting the disassembly task sequence for one of the Pareto-optimal solutions generated by the HAFSA. As shown in the figure, the proposed HAFSA generated four human–robot workstations for the disassembly tasks, labeled station1 to station4. Each workstation includes one worker and one robot. The green squares represent workers and the blue squares represent robots. The numbers inside the squares correspond to specific tasks within the disassembly process. For example, in station1, tasks 26, 27, 4, and 14 are performed by the worker while tasks 2, 3, 1, 21, and 16 are performed by the robot.

As shown in

Table 1. Multi-objective evaluation metrics for five runs of the three algorithms within the same runtime.

Algorithm	HAFSA			NSGA-II			TLBO			Time (s)
	NR	GD	IGD	NR	GD	IGD	NR	GD	IGD	/
1	0.546	14.33	0.427	0.215	21.05	0.606	0.139	27.19	0.693	500
2	0.524	13.46	0.305	0.305	24.28	0.457	0.124	27.48	0.582	500
3	0.416	18.40	0.806	0.335	24.44	0.923	0.138	36.58	1.29	500
4	0.560	11.55	0.601	0.243	26.09	0.753	0.094	29.28	1.102	500
5	0.457	17.27	1.201	0.281	23.72	1.389	0.183	35.03	1.601	500

, the HAFSA achieves the best performance in the NR indicator, with a value of 0.560, compared to 0.335 for NSGA-II and 0.183 for TLBO. This indicates that the HAFSA consistently finds more non-dominated solutions than the other two algorithms. Furthermore, the GD and IGD indicators for the HAFSA are consistently lower across five runs than those of NSGA-II and TLBO. For instance, the HAFSA achieves a GD value of 11.55 in one of the runs, which is significantly better than the lowest GD value of NSGA-II at 21.05 and TLBO at 27.19. Similarly, the HAFSA’s IGD value in one of the runs is 0.305, whereas the lowest values for NSGA-II and TLBO are 0.606 and 0.582, respectively. These lower GD and IGD values indicate that the solutions obtained by the HAFSA are closer to the true Pareto front and more evenly distributed.

Table 2. Multi-objective results of the three algorithms.

Algorithm	HAFSA			NSGA-II			TLBO			Time (s)
	F1	F2	F3	F1	F2	F3	F1	F2	F3	/
4	4	101	64.48	5	158	70.24	5	132	92.63	500

presents the multi-objective results from one run of each algorithm. For the F1 objective, the HAFSA achieves a value of 4, which is lower than the corresponding values of 5 for both NSGA-II and TLBO. This indicates that the HAFSA is more effective in optimizing the F1 objective. For the F2 objective, the HAFSA’s value is 101, also lower than NSGA-II’s 158 and TLBO’s 132, demonstrating the HAFSA’s superiority in optimizing this objective as well. Similarly, for the F3 objective, the HAFSA achieves a value of 64.48, compared to 70.24 for NSGA-II and 92.63 for TLBO, further highlighting the HAFSA’s effectiveness.

These results collectively indicate that the HAFSA outperforms both NSGA-II and TLBO in solving the multi-objective optimization problem described in this paper. The consistently better performance in the NR, GD, and IGD indicators suggests that the HAFSA provides a more robust and efficient solution approach. Additionally, the superior results in the F₁, F₂, and F₃ objectives demonstrate the HAFSA’s capability to effectively balance the trade-offs between different objectives, making it a more suitable choice for the problem at hand.

5. Conclusions

This paper focuses on balancing human–robot collaborative disassembly lines and introduces an enhanced hybrid artificial fish swarm algorithm (HAFSA) to address disassembly scenarios involving a hybrid refrigerator. By comparing the results with NSGA-II and TLBO algorithms, the effectiveness and superiority of the HAFSA are validated using key performance indicators: non-dominated rate (NR), generational distance (GD), and inverted generational distance (IGD). The HAFSA consistently outperforms the other two algorithms across these metrics, indicating its robust capability in generating high-quality, non-dominated solutions closer to the true Pareto front and more evenly distributed.

The enhanced efficiency and flexibility brought about by the human–robot collaborative disassembly approach ensure safer and more adaptable disassembly processes. The superior performance of the HAFSA in multi-objective results for F₁, F₂, and F₃ demonstrates its ability to balance competing goals effectively, making it suitable for complex disassembly line balancing problems. Future research could explore the layout and spatial arrangement of human–robot disassembly lines and the real-world implementation of the HAFSA to fully assess its practical applicability and impact.