• First chromosome section

A precedence-matrix (P) is used to derive feasible disassembly sequences. It describes the order of precedence of the disassembly steps and can be obtained from carrying out manual disassembly experiments or by using the computer-aided design (CAD) models of the product to be disassembled [28]. Another approach to determining possible precedence relationships in an automatic way based on computer vision was presented in [13]. This can avoid the disadvantages of the two mentioned methods: while manual pre-processing is error-prone and time-consuming, pre-processing using CAD data is often inaccurate. This is because CAD models can rarely still reliably describe the product at their EoL

phase, for example, due to corrosion or changes that have been applied to the product during the usage phase. We used the disassembly precedence graph (DPG) to generate the P matrix for the use case in this paper. It allows a simple one-to-one comparison of all components. If a component i is the predecessor of the component j, the value Pij gets the value 1, otherwise 0. The numerical method to derive feasible disassembly sequences from the P matrix is illustrated in Figure 5.

**Figure 4.** Disassembly strategy optimizer using a genetic algorithm.

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**Figure 5.** Method to generate feasible disassembly sequences from a given precedence matrix.

• Second chromosome section

The transfer of battery components into a circular economy takes place via the implementation of circular economy strategies. Here, there are different strategies, which mainly differ in preparing the components and the application field. The waste hierarchy of the European Commission contains five priorities [29]. In this work, we focus on the priorities on the top, as they should be preferred in a circular economy. The highest one is prevention, for example, by extending the life of products through predictive maintenance or simple repair operations. The second priority is repair for reuse, followed by recycling. These priorities can be achieved by applying diverse circularity strategies. Potting et al. [30] identified ten strategies and divided them into three categories: (1) smarter product use and manufacture, (2) extend lifespan of product and its parts, and (3) useful application of materials. Here, we consider only the strategies, which can be applied at the EoL phase. Circularity solutions during the stages of design, manufacturing, and use are ignored. In this scope, the EoL strategies can be reduced to four strategies: reuse, remanufacturing, repurposing, and recycling. The integration of these strategies in the waste hierarchy and the material flows after their application are illustrated in Figure 6. In the literature, different definitions can be found for these strategies [24]. In this paper, we adopt the definitions of Potting et al. [30]. Reuse means the utilization of a discarded battery or a set of its components by another user in the automotive field. Remanufacturing is the treatment of battery parts so that they can at least meet the requirements of newly manufactured products and their utilization for the manufacturing of EVBs. If the battery or its parts are reconditioned and used in another application field, such as stationary energy storage, this is called repurposing. Recycling is the recovery of materials. In this case, pure and high-quality materials for use in the automotive sector should be targeted.

Figure 6 shows that disassembly is of central importance for the implementation of all these circularity strategies. The components of the EVBs can be allocated to different strategies depending on their condition. However, the selection of the optimal circular economy strategy does not depend exclusively on this. Other factors, such as the disassembly costs and the market constraints, such as the potential revenues, also play an important role. Therefore, we consider the selection of the EoL strategy as a part of the disassembly planning. This paper assumes that the feasibility of a circular economy strategy for a given component depends on its condition. That is why the second section of the chromosome must fulfill the condition constraints defined by a condition vector S containing the feasible circular economy strategies CESi for every component i—see Equation (1). Here, the priority of the circular economy strategies is taken into account. If a component i is in excellent condition, it can be allocated to all strategies (reuse, remanufacturing, repurposing, and recycling). In this case, CESi is assigned the value 1. If CESi equals 2, the reuse option will be excluded. Part i can be neither reused nor remanufactured if CESi equals 3. CESi is assigned the value 4 if recycling is the only possible recovery option.

$$\mathbf{S} = \begin{pmatrix} \text{CES}\_1 \\ \dots \\ \text{CES}\_n \end{pmatrix}; \text{CES}\_i \in \{1; 2; 3; 4\} \tag{1}$$

**Figure 6.** Overview about the considered end-of-life strategies.

The S vector cannot just be seen as a collection of testing results. Other factors can play a role in determining the potentially possible circular economy strategies for the different battery parts, such as the employees' experience in the disassembly factory. Testing results include the state of health (SoH) and state of charge (SoC) of battery cells and modules and additional parameters for the rest of the components.

• Third chromosome section

This section consists of a single gene and is used to define the disassembly depth. An EVB could be entirely disassembled by separating all its parts. However, this approach is neither economically nor environmentally practical in an industrial context [16]. Therefore, EVBs are more likely to be subject to incomplete disassembly. Here, there are two methods to perform incomplete disassembly: (1) the selective method and (2) the unrestricted method. The selective method means that specific components are selected to be disassembled. Subsequently, the disassembly planner needs to calculate a strategy for the optimal extraction of these parts. Here, the high-value strategy and the high-impact strategy can be distinguished [31]. For EVBs, the removal of the modules could present a high-value disassembly strategy. The high-impact strategy applies when, for example, a module with safety risks is identified and has to be replaced before reusing the battery. In contrast, no target components are selected in the unrestricted incomplete disassembly. The disassembly planner can freely calculate the optimal disassembly strategy based on an objective function. This method is considered in this paper. Thereby, the gene representing

the disassembly depth is randomly generated with values between 0 (no disassembly) and the maximum number of components n while generating the initial population.

In Fehler! Verweisquelle konnte nicht gefunden werden, a disassembly precedence graph of a theoretical product, the associated precedence matrix, and the entire structure of a possible chromosome depending on a given condition vector are presented. In this case, one feasible disassembly sequence is 1-2-3-5-6-4, possible circular economy strategies at the component level are 1-2-4-1-2-4, and the disassembly is complete, since the last gene matches the component number.
