**A Study of Mixed-Flow Human–Machine Collaborative Disassembly Line Balancing Problem Based on Improved Artificial Fish Swarm Algorithm †**

**Gaofei Wang, Yarong Chen \*, Jabir Mumtaz and Lixia Zhu \***

**\*** Correspondence: yarongchen@126.com (Y.C.); m18200289139@163.com (L.Z.)

† Presented at the Third International Conference on Advances in Mechanical Engineering 2023 (ICAME-23), Islamabad, Pakistan, 24 August 2023.

**Abstract:** A mixed-flow human–machine collaborative disassembly line balancing problem is introduced, considering the various recycling methods for waste products and the relationship between the attributes of each product part and the corresponding disassembly operator. The problem aims to optimize the number of workstations, balance the idle time, and minimize the disassembly cost. To address this, an Improved Artificial Fish Swarming Algorithm (IAFSA) was designed based on the combination of the problem characteristics, and the IAFSA algorithm was applied to a mixed-flow television (TV) disassembly example and compared with two different algorithms. The solution shows that the proposed algorithm optimizes the proposed algorithm by 14.3%, 52.3%, and 9.8%, respectively, on the three objectives. Finally, the performance of the three algorithms is compared using Non-dominant rate (NR) and Generation distance (GD) metrics.

**Keywords:** mixed-flow disassembly; human–machine collaboration; disassembly line balancing; IAFSA algorithm

### **1. Introduction**

Disassembly is the key to the recycling of waste products, and efficient disassembly methods are of great significance to achieving sustainable economic development. With the advancement of science and technology, the human–machine collaborative disassembly method gradually replaces the traditional manual disassembly method, which has greater production potential.

In a related literature study, Ci et al. [1] demonstrated that robots have great potential to be applied to disassembly lines by proposing a heuristic algorithm based on ant colony optimization to solve the single-operator robot disassembly line balancing problem. Yin et al. [2] proposed an incomplete disassembly line balancing problem for multi-product multi-robot disassembly. Huang [3] proposed a new method of human–robot collaboration for disassembling stamped parts based on the active flexibility of collaborative robots, and the feasibility of the method was proven through practical cases. Liu et al. [4] studied the task classification and task assignment of human–robot disassembly, and considered the safety strategy between the operator and the robot to ensure the safety of human–robot disassembly in a workstation. Xu et al. [5] studied the human–machine collaborative disassembly line balancing problem, considering the safety of workers' operations, constructed a multi-objective mathematical model for this problem, and solved this multi-objective optimization problem using an improved discrete bee colony algorithm.

The above-mentioned literature mainly focuses on improving the disassembly efficiency and safety of disassembly workers, with less consideration given to human–machine collaborative disassembly of hybrid products and the assignment of disassembly operators

**Citation:** Wang, G.; Chen, Y.; Mumtaz, J.; Zhu, L. A Study of Mixed-Flow Human–Machine Collaborative Disassembly Line Balancing Problem Based on Improved Artificial Fish Swarm Algorithm. *Eng. Proc.* **2023**, *45*, 40. https://doi.org/10.3390/ engproc2023045040

Academic Editors: Mohammad Javed Hyder, Muhammad Mahabat Khan, Muhammad Irfan and Manzar Masud

Published: 14 September 2023

School of Mechanical and Electrical Engineering, Wenzhou University, Wenzhou 325035, China; highfly1998@163.com (G.W.); jabirmumtaz@live.com (J.M.)

based on the characteristic properties of parts. Thus, this paper proposes a mixed-flow human–machine collaborative disassembly line balancing problem (MHMC\_DLBP) with the minimization of the number of workstations, the idle time balance index and the disassembly costs as the optimization objectives, and designs an improved artificial fish swarm algorithm to solve it.

#### **2. Problem Description**

The mixed-flow human–machine collaborative disassembly line balancing problem studied in this paper involves the construction of a mixed-product disassembly information model as well as the categorization and assignment of human/machine task operators with different attributes of parts, in addition to the need to satisfy general DLBP constraints. The disassembled parts are classified into three categories according to their characteristic properties: hazardous parts, complex parts and common parts, where hazardous parts correspond to machines, complex parts correspond to humans and common parts are without restrictions. Respectively, where the machine and human disassembly times are different for the same disassembly task, only one type of operator can be assigned to each workstation.

#### **3. IAFSA Algorithm**

This paper proposes an improved artificial fish swarming algorithm for the studied problem, which includes foraging behavior, clustering behavior and tailgating behavior.

### *3.1. Foraging Behavior*

To guide the artificial fish to converge in the optimal direction, the crossover operator of the genetic algorithm is introduced, and the crossover operation is performed on it to guide the artificial fish to forage. First, generate 2 random crossover points, *P*<sup>1</sup> and *P*2, on *X*1, and the sequence before and after the crossover point satisfies the disassembly priority relationship. Then, a reference fish, *X*2, is randomly generated, and the sequence between *P*<sup>1</sup> and *P*<sup>2</sup> is obtained by mapping *X*<sup>2</sup> with the remaining sequence of *X*<sup>1</sup> to form a new artificial fish,*Xnew*.

#### *3.2. Clustering Behavior*

With artificial fish, *X*<sup>1</sup> = (*a*1, *a*2,... *a*n),*X*<sup>2</sup> = (*b*1, *b*2,... *b*n), the distance between two artificial fish is defined by combining the DLBP problem features as

$$D(X\_1, X\_2) = \sum\_{i}^{n} \text{sgn} |X\_1 - X\_2| \tag{1}$$

where sgn is a 0–1 variable indicating the similarity and difference between vectors *ai* and *bi* in *X*<sup>1</sup> and *X*2.

If the artificial fish horizon is *V*, the crowding degree is *delta* and the population size is *fish*\_*num*. When *D*(*X*1, *X*2) ≤ *V*, it is determined that *X*<sup>2</sup> is an artificial fish searched by *X*<sup>1</sup> in its field of view. Find all artificial fish *fishall* in the fields of view, judge whether the conditions are satisfied by the crowding degree calculation formula *delta* = *fishall*/ *fish*\_*num*, choose NSGA-II crowding distance mechanism to sort the artificial fish that satisfy the conditions and select the one with the largest crowding degree as the central fish *Xcenter* obtained from the clustering behavior.

#### *3.3. Tailgating Behavior*

Explore the number of partners *Nf* within *X*<sup>1</sup> field of view *V*, determine whether the tail-chasing condition is satisfied and then place the current artificial fish in the tail-chasing behavior bulletin board *Qt* for non-dominated sorting to filter out the non-inferior solutions in the bulletin board. The tail-chasing behavior accelerates the movement of the artificial fish towards a more optimal state.

#### **4. Example and Analysis**

The proposed algorithm is applied to the human–machine collaborative disassembly example of a hybrid TV product to verify the solution performance. The algorithm parameters are *CT* = 100 s, *fish*\_*num* = 50, *Gen* = 500, *V* = 30, *try*\_*number* = 10, *delta* = 0.8. The Genetic Simulated Annealing Algorithm (GASA) [6], and Teaching Optimization (HTLBO) algorithm [7] were introduced for comparison, and the parameters of the comparison algorithms can be referred to in the literature.

From Figure 1, it can be seen that for *F*1, the value obtained via the IAFSA algorithm is 6, the GASA algorithm is 7 and the HTLBO algorthim is 8; for objective *F*2, the three algorithms converge at the 219th, the 385th and the 485th generations, respectively; for *F*3, the IAFSA algorithm converges to 78.69 at the 250th generation and the HTLBO converges to 99.08 at the 390th generation; the GASA algorithm converges to 87.19 at the 489th generation. Thus, the convergence speed and the convergence results of each optimization objective for the proposed IAFSA algorithm are all better than the other two comparison algorithms. Figure 2 shows the Gantt chart of the disassembly task sequence for a solution in the Pareto solution set solved by the IAFSA algorithm.

**Figure 1.** Single-objective convergence curves of the three algorithms at 500 iterations.


**Figure 2.** Gantt chart of disassembly task sequence assignment for hybrid TV products.

The three algorithms were executed five times for an equal duration to evaluate the effectiveness of the algorithms and assess the convergence and distribution of the Pareto solutions. This allowed us to determine the non-dominance rate (NR) and generation distance (GD) metrics. As given in Table 1, in the five runs, the NR metrics of the IAFSA were larger than those of the HTLBO and GASA algorithms, and the GD metrics were smaller than those of the other two comparison algorithms. In summary, the NR and GD metrics verify that the IAFSA algorithm is superior in terms of solution diversity and convergence.


**Table 1.** Multi-objective evaluation values via three algorithms for the same time.

### **5. Conclusions**

A mixed-flow human–machine collaborative disassembly line balancing problem was studied in this paper, and an improved IAFSA algorithm was designed according to the problem characteristics, in order to solve the disassembly instances of two kinds of TVs mixing, and the effectiveness and the superiority of the IAFSA algorithm was verified by comparing it with the GASA and HTLBO algorithms from a convergence performance perspective as well as by the NR and GD two metrics. Subsequently, research can also be carried out on the layout form of the human–machine disassembly line, and multi-operator joint disassembly.

**Author Contributions:** Conceptualization, G.W. and Y.C.; methodology, J.M. and L.Z.; software, G.W. and J.M.; validation, G.W. and J.M.; formal analysis, G.W. and Y.C.; writing—review and editing, Y.C. and L.Z.; visualization, L.Z.; supervision, G.W.; funding acquisition, Y.C. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research was funded by National Natural Science Foundation of China, grant number [No. 51705370].

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data that support the findings of this study are available from the corresponding author upon reasonable request.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

