Integrated Risk-Aware Smart Disassembly Planning for Scrap Electric Vehicle Batteries

Abstract

With the increase in the production of electric vehicles (EVs) globally, a significant volume of waste power battery modules (WPBM) will be generated accordingly, posing challenges for their disposal. An intelligent scrap power battery disassembly sequence planning method, integrated with operational risk perception, is proposed to automate the planning process. Taking into consideration the risk coefficients, energy consumption, and costs during disassembly, this method maximizes profits, minimizes energy usage, and ensures safety. Utilizing an extended part priority graph, an optimized model for integrated risk-aware disassembly sequence planning (IRA-DSP) is constructed. With the Guangqi Toyota LB7A-FX1 as a case study, and using real data from resource recovery enterprises, an improved MOPSO-GA algorithm is proposed to solve the model and generate disassembly plans. The results demonstrate the method’s ability to achieve unit-level disassembly of WPBM, avoid high-risk sequences, and optimize profit and energy consumption, exhibiting its practicality and feasibility.

1. Introduction

Within the framework of the “dual carbon” targets, the rapid development of China’s new energy automotive industry heralds the approaching retirement of a large number of power batteries [1]. Used lithium-ion batteries have become a research focus due to their valuable key metal resources and potential environmental risks [2,3]. Current research primarily focuses on recovering valuable metal elements, such as cobalt and lithium, from used batteries through advanced pyrometallurgical and chemical leaching techniques [4], as well as on exploring secondary utilization technologies to maximize their resource value [5,6]. Given the aging differences among battery components over time, thorough disassembly of used power batteries becomes a crucial step in unlocking their residual value and achieving a circular economy [7]. However, the safety issues surrounding the disassembly process cannot be overlooked, as improper operations can lead to equipment failure, fires, explosions, and other severe consequences [8]. Therefore, systematically studying the disassembly sequence planning of power batteries is crucial for ensuring the safety of disassembly operations, reducing environmental and health risks, and promoting the sustainable development of the battery recycling industry [9].

Disassembly involves the orderly removal of sub-assemblies (including parts and components) from a product [10]. The disassembly sequence directly impacts disassembly efficiency and recycling benefits, making it crucial for the recovery and reuse of waste products [11,12]. Finding the optimal disassembly sequence to achieve objectives such as maximizing profits, minimizing energy consumption, and reducing risks, known as disassembly sequence planning, is essential [10,13]. Notably, traditional remanufacturing processes aim to achieve the optimal disassembly level of products, restoring their performance by replacing certain parts and balancing economic indicators with disassembly depth. However, this approach fails to fully utilize the residual value of retired power batteries, necessitating their complete disassembly.

The principal contributions of this research are outlined as follows:

• Using an extended part priority graph to clarify the constraint relationships between disassembly operations and to represent the inherent risk factors of the operations themselves;
• The formulation of an integrated risk-aware (IRA) model for intelligent sequencing in the recycling of retired power batteries, which incorporates a comprehensive risk perception approach;
• The utilization of the extended part priority graph to strategize the disassembly sequence of the battery pack, effectively reducing the complexity of the problem at hand;
• The provision of a case study on the disassembly of the Guangqi Toyota LB7A-FX1 battery pack, grounded in actual data from a resource recycling enterprise.

The subsequent sections of this study are organized as follows. Section 2 presents a comprehensive literature review, synthesizing the current state of knowledge in the relevant field. Section 3 introduces the IRA-DSP model, providing a detailed exposition of its development process and underlying assumptions. Section 4 offers an enhanced MOPSO-GA algorithm specifically tailored to efficiently address the IRA-DSP model. In Section 5, a rigorous case study analysis is conducted to validate the effectiveness of the IRA-DSP model and demonstrate the superiority of the improved MOPSO-GA algorithm, thereby verifying the accuracy and practical utility of the proposed planning methodology. Finally, Section 6 summarizes the research findings and explores potential avenues for future investigation, offering perspectives and insights that aim to catalyze further advancements in the pertinent domain.

2. Literature Review

2.1. Battery Disassembly Graph Theory Expression

Graphical tools such as part priority graphs, AND/OR graphs, Petri nets, Knowledge graph, and disassembly trees can abstract DSP problems, revealing their structure and solution space, thereby enhancing solution efficiency and quality [14,15].

Based on the part priority graph, Guo Hongfei et al. established a comprehensive evaluation model for recycling and proposed an integrated decision-making method for disassembly sequencing and disassembly depth to maximize the recycling benefits of waste products. Finally, they took the power battery as the disassembly object to verify the feasibility and effectiveness of the model and method proposed in the paper [16]. Wu Hao and his team proposed a new method for planning the disassembly sequence based on the knowledge graph of power battery. They constructed an updatable and scalable disassembly information model to capture the dynamic information and assembly relationship among battery components [17]. Tsai C. Kuo proposed an analytical method based on Petri Net to address the disassembly and recycling issues in end-of-life electronic products. By utilizing PN analysis, an optimal trade-off between the cost and environmental efficiency of the disassembly process can be determined [18]. Although priority graphs can represent the priority relationships between parts [19], they may not fully capture other component information. AND/OR graphs, knowledge graphs, and Petri nets can suffer from combinatorial explosion issues. In addition to economic and energy-efficiency objectives, this study emphasizes the hazards encountered during the comprehensive disassembly process of power batteries, including high voltage and chemical leakage. Consequently, the risk coefficient of individual battery components becomes paramount. To address this, an enhanced partial priority graph is utilized in this research, providing a clearer depiction of the priority relationship among components and their associated risk coefficients.

2.2. Power Battery Disassembly Model

Due to their complex structure, cumbersome disassembly, and high risks, power batteries require efficient and cost-effective disassembly while ensuring safety. Although recent studies, such as Alfaro-Algaba’s disassembly model for the Audi A3 hybrid system, aim to maximize profits while minimizing environmental impact [20], the assessment of disassembly sequences remains limited and lacks a comprehensive consideration of costs, profits, and risks. Kathrin Wegener et al. provided a graphical representation for the disassembly of the Audi Q5 hybrid system, but a comprehensive evaluation is still lacking [21].

Existing research has inadequate risk considerations, particularly for hazardous recycling items like power batteries. Therefore, this study proposes an integrated risk-aware disassembly sequence planning (IRA-DSP) model that comprehensively considers profit maximization, energy consumption minimization, and risk minimization to address the optimization of power battery disassembly in a more comprehensive and rigorous manner, promoting the sustainable development of power battery recycling.

2.3. The DSP Multi-Objective Optimization Algorithm

The DSP aims to find the optimal disassembly sequence, which is a combinatorial optimization problem belonging to the NP-Hard category [22]. As the number of instructions increases, the solution space expands rapidly, resulting in significant time consumption for finding the optimal solution [23]. Therefore, direct brute-force, dynamic programming, and greedy algorithms are often not preferred due to their inefficiency [24]. Instead, heuristic methods become the preferred choice as they can leverage specific knowledge or experience to find suboptimal or optimal solutions within a reasonable time [25], effectively reducing computational resource consumption, making them suitable techniques for solving the DSP [26]. Wu Tengfei and his team established a mathematical model for the specific disassembly process of power batteries, optimizing the four objectives of the number of workstations, workstation idle time, number of workers, and disassembly costs. They chose the NSGA-II algorithm to effectively solve this combinatorial optimization problem. NSGA-II employs the non-dominated sorting approach to rank individuals in the population, which results in high computational complexity, especially when dealing with large-scale populations or problems with multiple objective functions. This can significantly increase the execution time of the algorithm [27]. Chu Mengling and Chen Weida proposed a hybrid particle swarm optimization algorithm based on Q-learning to solve the human–machine collaborative disassembly model, which can dynamically adapt to the uncertainties during the disassembly process [28]. Amel Alaji et al. proposed a novel RL (reinforcement learning) technique based on the Q-Network algorithm for optimizing the DSP (disassembly sequence problem). The research focused on optimizing two disassembly strategies—partial disassembly sequence planning (PDSP) and full disassembly sequence planning (FDSP)—and applied the method to two structurally simpler industrial product components, demonstrating its effectiveness [29]. However, it requires a large amount of trial and error as well as feedback to learn the optimal strategy, resulting in the need for more computational resources and time. In battery disassembly sequence planning, due to the complexity of the problem and the need to consider multiple objectives such as disassembly efficiency, cost, and environmental impact, computational efficiency and real-time performance are crucial.

The multi-objective particle swarm optimization (MOPSO) algorithm has emerged as an ideal choice for solving such problems due to its effectiveness in obtaining the Pareto optimal solution set [30]. Based on the MOPSO algorithm, this paper introduces genetic operators and proposes an enhanced MOPSO-GA algorithm to efficiently and accurately address the integrated risk-aware disassembly sequence planning (IRA-DSP) model for retired power batteries.

3. IRA-DSP Model Construction

3.1. Problem Description

IRA-DSP refers to the integrated optimization of energy consumption, profit, and safety under the premise of meeting the fixed cost of the disassembly operation, conversion cost, safety risk factor, energy consumption of the disassembly operation, and conversion energy consumption of the disassembly operation during the process of battery disassembly.

Suppose that the old power battery pack to be dismantled is composed of $N$ subassembly and subassembly is $\left\{1,2,\dots ,N\right\}$. The disassembly of the battery pack requires $J$ disassembly operations, and the disassembly operation set is $\left\{0,1,2,\dots ,J\right\}$, where $j,k$ is the number of the disassembly operation, and operation $0$ indicates the initial disassembly operation $j,k\in \left\{0,1,2,\dots ,J\right\}$. The decision variable is ${\mathrm{x}}_j$ and $y_{im}$. If the operation is executed, then $x_j=1$; otherwise, ${\mathrm{x}}_j=0$; If operation $j$ is the $m$ in the disassembly sequence, then $y_{jm}=1$, otherwise, ${\mathrm{y}}_{jm}=0$. To construct an IRA-DSP model based on the extended part-priority graph, two basic relationship matrices are defined here, namely, the priority matrix and the association matrix.

The priority matrix $P=[p_{jk}]$ is used to describe the priority constraint relationship between subassembly/disassembly operations. When the operation is completed, the operation can be performed immediately, and the operation cannot be performed over the operation; if the operation is the tight front operation of the operation, then ${\mathrm{p}}_{jk}=1$; otherwise, ${\mathrm{p}}_{jk}=0$.

There is a correlation between the parts and the disassembly task; that is, removing each component needs to complete the corresponding disassembly operation. Disassembly operations generate costs, such as work costs and time costs, as well as the recovered components. In order to represent the recovery profits, it is necessary to define the correlation relationship of components and disassembly operations; the association matrix $G=[g_{ij}]$. If action $\mathrm{j}$, the subassembly $i$ is obtained, then $g_{ij}=1$; if action $j$, the subassembly $i$ is decomposed, then ${\mathrm{g}}_{ij}=-1$; otherwise, ${\mathrm{g}}_{ij}=0$.

3.2. IRA-DSP Model Construction

3.2.1. Profit Function

The recovery profit of the subassembly needs to consider the recovery benefit of the subassembly, the fixed cost of the disassembly operation, and the conversion cost between the disassembly operations. If the benefit of the waste power battery sub-assembly $i$ is $R_i$, the work $j$ cost (including fixed cost and time cost) is $C_{\mathrm{j}}$, and the work cost of completing the conversion from operation $j$ to operation $k$ is ${\mathrm{c}}_{jk}$, then the battery recovery profit function can be expressed as

$$f_1={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{i=1}^N{g}_{ij}{x}_j{R}_i-{\displaystyle \sum _{j=1}^J{C}_j{x}_j}}}-{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^J{\displaystyle \sum _{m=1}^{J-1}{c}_{jk}{y}_{jm}{y}_{k,m+1}}}}.$$

(1)

3.2.2. Energy Consumption Function

The energy consumption of the battery disassembly and recovery process mainly includes two parts: the fixed energy consumption of the disassembly operation and the conversion energy consumption between the disassembly operation. We set $W_j$ as the power consumed to perform the operation $j$, set the working time $T_j$ to complete the operation $j$, and the fixed energy consumption $h_{jk}$ is transferred from operation $j$ to operation $k$. The energy consumption function of battery recovery is

$$f_2={\displaystyle \sum _{j=1}^J{W}_j{T}_j{x}_j+{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^J{\displaystyle \sum _{m=1}^{j-1}{h}_{jk}{y}_{jm}{y}_{k,m+1}}}}}.$$

(2)

3.2.3. Risk Index Function

The internal structure of the power battery is crisscrossed, the adjacent components often have high coupling, and the disassembly operation of different components has different risk degrees. According to these two characteristics of the disassembly process, the risk compensation coefficient of operation $k$ is expressed by $s_k$, and the battery recovery risk function is established as

$$f_3={\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^J{\displaystyle \sum _{m=1}^{J-1}|k-j|s_k{y}_{jm}{y}_{k,m+1}}}}.$$

(3)

According to the above analysis, with the goal of the maximum recovery profit, the lowest recovery energy consumption, and the lowest risk of the disassembly process, the comprehensive risk perception of the retired power battery disassembly sequence planning (IRA-DSP) model is constructed as follows:

$$\max \hspace{0.33em}{\mathrm{f}}_1,$$

(4)

$$\min \hspace{0.33em}{f}_2,$$

(5)

$$\min \hspace{0.33em}{f}_3,$$

(6)

$$s.t. x_0=1,$$

(7)

$$x_j+x_k\le 1,j\in B_k,\hspace{1em}k=0,1,2,\dots ,J,$$

(8)

$${\displaystyle \sum _{j\in A_k}^J{\displaystyle \sum _{\mathrm{m}=1}^{n=1}{y}_{jm}}}\ge y_{kn},\hspace{1em}k=1,2,\dots ,J,$$

(9)

$$x_j={\displaystyle \sum _{m=1}^J{y}_{jm}},\hspace{1em}j=1,2,\dots ,J,$$

(10)

$${\displaystyle \sum _{j=1}^J{y}_{jm}}\le 1,\hspace{1em}m=1,2,\dots ,J,$$

(11)

$${\displaystyle \sum _{j=1}^J{W}_j{T}_j{x}_j+{\displaystyle \sum _{j=1}^J{\displaystyle \sum _{k=1}^J{\displaystyle \sum _{m=1}^{J-1}{h}_{jk}{y}_{jm}{y}_{k,m+1}}\le Q}}},$$

(12)

$${\mathrm{x}}_j,y_{jm}\in \left\{0,1\right\},\hspace{1em}j,k=1,2,\dots ,J.$$

(13)

4. Improved MOPSO-GA Algorithm

The IRAO model proposed in this paper simultaneously optimizes the three objectives of profit, energy consumption, and risk, so the calculation is complicated, and the optimal solution is difficult to obtain. Multi-objective particle swarm (MOPSO) is a kind of evolutionary calculation algorithm used to solve the problem of multi-objective optimization. It has the advantages of fast convergence, is easy to use, and has fewer parameters, but it usually tends to search solution space in the global range; less attention is paid to local search, especially if the solution space is large or complex, which may lead the algorithm into a local optimal solution. Therefore, in this paper, a modified MOPSO-GA algorithm is proposed to optimize and solve the established IRA-DSP model. The algorithm flow is shown in Figure 1.

The algorithm first constructs the external archive set via non-dominant sorting and then iteratively optimizes the current population using particle swarm optimization, while combining the selection, crossover, and variation operation of the genetic algorithm to increase the diversity of the population simultaneously. During the iterative process, the external set of archives and the current contemporary optimal solutions are dynamically updated to guarantee the global search capability of the algorithm. Finally, by reaching the set number of iterations, the excellent non-dominant solution set is obtained as the output result of the algorithm. The running parameters of the algorithm are as follows: random number seed: 1; number of leading solution sets: $n=200$; maximum number of iterations: $n=200$; cross probability: $p1=0.5$; variation rate $p2=1$; inertia weights take $0.4\sim 0.9$; individual learning factor: $c1=0.8$; and social learning factor $c2=1$.

4.1. Initialize the Population Based on the Prior Knowledge

Population initialization is a crucial step in swarm optimization algorithms, directly influencing the convergence speed and the quality of the final solution. In the absence of relevant prior knowledge, random initialization is often used to generate the initial population. While random initialization ensures a uniform distribution of the initial population in the solution space, it can affect the convergence speed of the algorithm. To generate a more optimal initial population for a more efficient exploration of the solution space, this paper proposes generating initial solutions based on the internal structure and disassembly rules of battery dismantling. Assuming that the battery has a total of N detachable components, each component is numbered, and the disassembly sequence is represented by a one-dimensional array. Feasible solutions are generated according to the existing prior knowledge, using an array structure for encoding. The calculation formula for generating feasible solutions is as follows:

$$x=shuffle ([x_0]),$$

(14)

where the operation involves shuffling the array.

4.2. The Pivotal Incorporation of Genetic Operators

4.2.1. Tournament Selection

Genetic algorithms are adept at discerning and propagating individuals with superior fitness values, which, in this study, is quantified by “total tardiness”, thereby facilitating the evolution of the fittest population. The selection mechanism employed in this research utilizes a tournament selection strategy, which is systematically executed as follows: Initially, two individuals from the population, distinguished by their unique fitness values, are randomly selected. Subsequently, a random number $r$ is generated within the interval [0, 1]. This number dictates the selection of the offspring; if $r$ is less than the established selection probability $ps$, the individual with the higher fitness is advanced to the next generation, thereby reinforcing the genetic contribution of the fitter individuals. Should $r$ exceed $ps$, the selection favors the individual with the lower fitness, deliberately incorporating an element of stochasticity that enriches the genetic diversity of the population. This process is iteratively applied until the contingent of new offspring corresponds with the desired population size. Importantly, the tournament selection in this paper incorporates a selection method with replacement, ensuring that while striving to select superior individuals, the diversity of the population is preserved, which is imperative for the exploration of a broad solution space and the avoidance of premature convergence.

4.2.2. Partially Matched Crossover

In genetic algorithms, the crossover operation aims to generate new offspring individuals by exchanging and combining genetic information from two parent individuals. However, in the battery disassembly sequence planning problem, each battery component is dismantled only once, requiring that no duplicate genes appear in the chromosome representation. Therefore, this study selects the partially matched crossover (PMX) to better avoid generating invalid offspring individuals while preserving some of the favorable characteristics of the parent individuals.

PMX is similar to two-point crossover, where two crossover points are randomly selected to define the crossover region. After executing the crossover, it is typically observed that two invalid chromosomes are produced, with some genes appearing duplicated. To repair the chromosomes, a matching relationship for each chromosome is established within the crossover region. This matching relationship is then applied to the duplicated genes outside the crossover region, effectively eliminating conflicts. The specific implementation process is described as follows:

• Step 1: Randomly select the starting and ending positions of several genes in a pair of chromosomes (parents), ensuring that the selected positions are identical in both chromosomes. As in Figure 2, the orange color is the selected gene.

• Step 2: Swap the positions of these two sets of genes. As in Figure 3, the orange regions are the exchanged gene fragments.

Figure 3. Gene swapping.

Figure 3. Gene swapping.

• Step 3: Perform conflict detection and establish a mapping relationship based on the swapped gene sets. As illustrated, taking the mapping relationship 4-3-2 as an example, we can see that there are two gene 2s in offspring 2 from the second step’s result. These are then transformed into gene 2 using the mapping relationship. The process is repeated until there are no conflicts. Finally, all conflicting genes will undergo mapping to ensure that the newly formed pair of offspring chromosomes has no conflicts. The mapping relationship is shown in Figure 4.

Figure 4. Conflict detection.

Figure 4. Conflict detection.

• Step 4: Produce two offspring as shown in Figure 5.

Figure 5. Offspring.

Figure 5. Offspring.

4.2.3. Uniform Gaussian Mixture Mutation

The objective of the mutation operation in genetic algorithms is to maintain the diversity of the population particles. Mutation can prevent offspring particles from becoming overly similar to parent particles, thus avoiding falling into local optima. To enhance the global search capability of the algorithm and increase the diversity of the population, this paper introduces a mutation method that combines uniform distribution and Gaussian distribution. The reference formula is as follows:

$${\mathrm{x}}_i=\left\{\begin{array}{c}r\times (U_i-L_i)\\ rand\mathrm{n}()\end{array}\right.\begin{array}{c},\\ ,\end{array}\begin{array}{c}\mathrm{r}\le 0.3\\ others\end{array}.$$

(15)

$\mathrm{x}$ is a given individual, containing a series of genetic values; ${\mathrm{x}}_i$ is the ith genetic value in the individual; $\mathrm{r}$ is a random number uniformly distributed within the interval $[0,1]$; $\mathrm{z}$ is a random number drawn from a standard normal distribution; and $L_{\mathrm{i}}$ and $U_{\mathrm{i}}$ are the lower and upper bounds of the ith gene, used to limit the range of the mutated genetic value.

5. Case Study Analysis

To validate the effectiveness of the constructed IRA-DSP model and demonstrate the superiority of the improved MOPSO-GA algorithm in solving optimization problems, this paper selects the Guangqi LB7A-FX1 power battery as a dismantling case for analysis. All algorithms are programmed and implemented on MATLAB-R2022a software, using a computer with an Intel (R) Core (TM) i7-8750H CPU @ 2.20 GHz.

5.1. Data and Parameter Settings

The disassembly component information provided in this paper is entirely based on the disassembly information sheets and disassembly guidance manuals furnished by the battery manufacturer, ensuring both authority and professionalism. The various data points referenced in this paper have been drawn from the actual recycling prices of various sub-components under current market conditions, which are sourced from real-time market transaction data and professional assessments within the battery recycling industry. This aims to provide readers with practical references regarding the costs of battery recycling. The 3D model of the power battery is shown in Figure 6. Some unnecessary sub-assemblies are removed, and fasteners and their respective sub-assemblies are abstracted into a single entity to simplify the model. The detailed reference information for the simplified sub-assemblies and their recycling benefits is provided in

Table 1. The information for the simplified sub-assemblies and their recycling benefits.

Number	Battery Sub-Assembly	Profit (Yuan)
1	Module upper shell bolt	5
2	Module upper shell rivets	0
3	Battery top-shell sealant	0
4	Battery upper shell	75
5	Fire bolt	4
6	Total bus of negative electrode	0
7	The left bus	−5
8	The right bus	−5
9	Positive pole total bus	0
10	Mode side terminal buckle	2
11	Module bracket nut	5
12	Other components of the battery pack lower shell except the module	7850
13	Module bracket bolt	5
14	SBM bolt	10
15	Card grasp	1
16	Articulate hook	2
17	Upper cover of the battery cell module	20
18	Positive electrode IC pull loop	1
19	Battery cell module bolt	2
20	Battery cell module bottom cover	20
21	Negative electrode IC pull loop	0
22	3 of side cover plate	2
23	Negative electrode confluence	30
24	Radiator and monomer	10,873
25	Battery cell module enclosure	121

.

Based on the estimated battery recycling process in an actual factory, detailed reference data for disassembly tasks, including their respective durations, costs, power requirements, and safety-level compensation coefficients, are presented in

Table 2. Disassembling operation.

Number	Disassembling Operation	Time (min)	Prime Cost (Yuan)	Energy Consumption (w)
1	Remove the battery shell bolts	2	3	60
2	Remove the battery upper shell rivet	2	2	60
3	Remove the battery top shell sealant	2	5.2	30
4	Remove the upper shell of the battery	1.5	2	0
5	Remove the fire protection cover bolts	4.95	5.2	15
6	Remove the negative electrode main bus	2	1.25	15
7	Place the left insulation tool, remove the left bus, and recover the insulation tool on the left	3.25	1.3	10
8	Place the right insulation tool, remove the right bus, and recycle the right insulation tool of the appliance	3.25	1.3	10
9	The positive pole main bus is removed	2.52	1.35	15
10	Remove the module side terminal fasteners	3	4.5	20
11	Remove the module support nut	2	2.9	20
12	Remove the module and the lower shell of the battery pack with the module disassembly tool, and place the repair car	2.2	2.8	10
13	Remove the module support bolts	4.25	1.675	220
14	The SBM bolts are removed	0.65	0.125	17
15	Remove the clamp	1.5	1.25	0
16	Remove the hinged hook	2	2.8	0
17	Remove the upper cover of the battery cell module	2	2.5	0
18	Disconnect the positive terminal’s integrated circuit pull tab	4.88	2.3	20
19	Remove the bolt	1	1	5
20	Remove the bottom cover	1	2	0
21	Cut off the negative electrode IC pull loop	2.85	1	30
22	Cut off the latching claws of the engagement parts at 3 locations on the side cover	0.8	0.15	30
23	Lift off a negative polar junction row	1	1	0
24	Remove the heat sink plate and the monomer	0.55	0.125	0

. Utilizing general disassembly operation experience, an initial assessment of the risk coefficients for these tasks (ranging from 0 to 5, with 0 indicating almost no risk and 5 indicating the highest risk) is conducted. An extended risk coefficient-based component prioritization graph is then plotted, as shown in Figure 7. The number above the circle represents the risk factor of the component.

5.2. Interpretation of Result

Solving the RIA-DSP model through MOPSO and the modified MOPSO-GA algorithm, we output the optimal non-dominant solution set of the two algorithms, as shown in Figure 8; the squares represent the MOPSO algorithm, and the circles represent the modified MOPSO-GA algorithm. In order to show the disassembly scheme more clearly,

Table 3. Decomposition sequence plan for different target solutions.

Target	MOPSO	Improved MOPSO-GA
The highest profit	1→3→2→4→11→10→9→5→6→ 7→8→12→14→15→13→16→17→ 18→22→19→21→20→23→24	3→1→2→4→10→9→5→6→11 →8→7→12→14→16→15→13→ 17→18→21→22→19→20→23→24
The lowest energy consumption	3→2→1→4→10→6→7→11→5→ 9→8→12→13→15→16→14→17→ 22→21→23→18→19→20→24	3→2→1→4→11→10→6→9→5 →8→7→12→13→16→14→15→ 17→21→22→23→18→19→20→24
The lowest risk	1→2→3→4→9→10→5→6→7→ 8→11→12→16→14→13→15→17 →18→19→21→20→22→23→24	1→2→3→4→5→10→11→6→7→ 9→8→12→13→14→15→16→17 →22→21→23→18→19→20→24
The compromise plan	3→2→1→4→11→10→9→6→7→ 5→8→12→13→16→14→15→17 →22→18→19→21→20→23→24	3→2→1→4→11→5→9→6→10 →7→8→12→15→13→14→16→ 17→22→21→23→18→19→20→24

presents the disassembly sequence obtained by the two algorithms for different targets (arrows point to the direction of operation execution), and the corresponding indicators of different schemes are shown in

Table 4. Target values for different disassembly sequences.

Algorithm	Plan	Profit (Yuan)	Energy Consumption (w)	Risk Index
MOPSO	The highest profit	18,798.275	1856.2	115
	The lowest energy consumption	18,778.275	1835.2	103.5
	The lowest risk	18,782.275	1845.2	71.5
	The compromise plan	18,787.275	1840.2	115
MOPSO-GA	The highest profit	18,800.275	1852.2	91.5
	The lowest energy consumption	18,786.275	1834.2	95.5
	The lowest risk	18,784.275	1858.2	65.5
	The compromise plan	18,788.275	1847.2	81.5

.

When considering different objectives of maximizing profit, minimizing energy consumption, and minimizing risk, the model endeavors to avoid operational transformations with high costs, high energy consumption, and high risks, respectively, in order to plan the optimal disassembly sequence. Specifically, the highest profit achieved is 18,800.275 yuan, the lowest energy consumption recorded is 1834.2 W, and the minimum risk index obtained is 65.5. The key advantage of the IRA-DSP model lies in its capability to comprehensively consider the three objectives of energy consumption, profit, and risk, while aiming to concurrently mitigate operational transformations with high energy consumption, high costs, and high risks, thereby formulating a compromise disassembly sequence scheme. For instance, the compromise scheme obtained through the improved MOPSO-GA algorithm, although having a profit that is 13 yuan less than the highest-profit disassembly scheme, saves 10 W in energy consumption and reduces the risk by approximately 20%.

5.3. Test Contrast

5.3.1. Comparative Analysis of Models

To validate the effectiveness of the risk perception of the proposed model, a disassembly sequence planning (DSP) model, without considering operational transformation risk, was introduced. The risk indices of the compromise solutions obtained using the improved MOPSO-GA are presented in

Table 5. Compromise solutions and risk indices for different models.

Model Types	Title 2	Risk Index
DSP	3→1→2→4→11→10→9→5→6→8→7→12→16→14→15→13→17→21→22→23→18→19→20→24	92
IRA-DSP	3→2→1→4→11→5→9→6→10→7→8→12→15→13→14→16→17→22→21→23→18→19→20→24	81.5

. The risk index of the DSP compromise solution is higher than the IRA-DSP compromise solution by 10.5, indicating an approximately 12.88% higher hazard level. The results demonstrate that the risk function introduced in the IRA-DSP model is effective. For high-risk battery components, the model is able to ensure the continuous disassembly of adjacent components to the greatest extent possible, thereby avoiding disassembly sequences with high risk indices. This effectively enhances the safety and efficiency of the disassembly process.

5.3.2. Algorithmic Comparative Analysis

In the experiment, the MOPSO algorithm took 5.9369 s to solve the problem, while the improved MOPSO-GA (Genetic Algorithm) took 4.6589 s. Based on the results of the IRA-DSP model, the improved MOPSO-GA achieved a 2 yuan increase in maximum profit, a 1 W reduction in minimum energy consumption, and a 6-point decrease in risk index compared to MOPSO. In the discounted scenario, the profit was increased by 1 yuan, the risk index was lowered by 30, and the energy consumption was higher by 7 w. The improved MOPSO-GA demonstrates significantly better performance than MOPSO.

To further validate the superiority of the improved MOPSO-GA in solving the IRA-DSP model, this paper compares the two algorithms from four perspectives: population distribution, iterative optimization process, the number of Pareto-front solutions, and hypervolume (HV). Figure 9 depicts the population distributions of the two algorithms. The crossover and mutation operations of the improved MOPSO-GA increase the diversity of the population, avoid premature convergence, and result in a more extensive and uniform population distribution. The iterative optimization comparison process between the two algorithms is illustrated in Figure 10. The iterative optimization process of the improved MOPSO-GA is generally more stable and sustainable, converging to better solutions faster compared to the original MOPSO.

HV is an essential metric for evaluating the performance of multi-objective optimization algorithms, representing the volume covered by the solution set in the objective space.

A larger HV value typically implies that the algorithm is able to find more and more widely distributed optimal solutions. Let the non-dominated solution set obtained by the algorithm be the reference point corresponding to the true Pareto front, which is often a vector formed by the maximum values of each objective. Then, the hypervolume of the non-dominated solution set to the true Pareto front, i.e., the HV metric, is specifically calculated as follows:

$$HV(X,P)=\underset{x\in X}{\overset{X}{\cup }}v(x,P)$$

(16)

where HV represents the hypervolume of the space formed between the solutions in the non-dominated solution set and the reference point. Specifically, it is the volume of the hypercube constructed with the diagonal line connecting the solution and the reference point. The number of frontier solutions and the HV performance metrics during the iterative process of the two algorithms are shown in Figure 11. Under the premise of retaining only the top 200 feasible solutions, the modified MOPSO-GA algorithm reduces the solution time compared to the traditional MOPSO algorithm by 27.43%, while the speed of finding feasible solutions increases by 68.64%. In the 100th generation of optimization, the hypervolume of the modified MOPSO-GA is approximately seven times better than that of MOPSO.

6. Conclusions

This study successfully developed and validated an IRA-DSP (integrated recycling and disassembly sequence planning) model based on an extended component priority graph, targeting the disassembly planning issue of retired electric vehicle batteries. The model employs an improved MOPSO-GA algorithm to seek the optimal disassembly sequence. Through a case study, we demonstrated that the IRA-DSP model not only comprehensively considers the costs and energy consumption during disassembly but also effectively avoids high-risk operations, thus ensuring the safety of the disassembly process.

The proposed method integrates a risk assessment mechanism to enhance the safety of the disassembly process and employs a multi-objective optimization strategy to ensure a balanced economic, environmental, and safety target. The introduction of the improved MOPSO-GA algorithm significantly improves the efficiency and feasibility of the solutions. Additionally, the case study driven by actual data enhances the practical applicability of the method, bringing significant economic and environmental benefits to waste battery disassembly and recycling enterprise, which helps reduce operational risks and promote the healthy development of the industry.

The risk coefficient assessment in this study is based on general disassembly operation experience, not specific to a certain battery type or disassembly environment, providing a flexible framework for practical applications. In future work, we plan to integrate this method into the manufacturing execution system (MES), design a user-friendly interface for inputting relevant basic data, and provide customized disassembly guidance through the system, further enhancing the intelligence of the disassembly process.