3.2.2. Evaluation Method

The performance of the disassembly strategies, coded in chromosomes, has to be evaluated using an objective function, which depends on several parameters. Thereby, different evaluation criteria can be involved, such as the economic and social performance or the environmental impacts. In this paper, we focus on the economic performance of the disassembly strategies by implementing the following objective function to maximize the economic profit (see Equation (2)).

$$\mathbf{y} = \left(\sum\_{\mathbf{i}=1}^{\text{DL}} \mathbf{R} \mathbf{V}\_{\mathbf{i},\mathbf{j}} - \mathbf{R} \mathbf{C}\_{\mathbf{i},\mathbf{j}} - \mathbf{O} \mathbf{C}\_{\mathbf{i},\mathbf{j}} - \mathbf{F} \cdot \mathbf{D} \mathbf{T}\_{\mathbf{i},\mathbf{j}}\right) + \left(\mathbf{q} \cdot \sum\_{\mathbf{i}=\text{DL}+1}^{\text{n}} \mathbf{R} \mathbf{V}\_{\mathbf{i},\mathbf{4}} - \mathbf{R} \mathbf{C}\_{\mathbf{i},\mathbf{4}}\right) \tag{2}$$

y: Economic profit

i: Index of components

j: Circular economy strategy

DL: Disassembly depth

RVi,j: Revenues from component i while applying the circular economy strategy j

RCi,j: Recovery costs for component i to apply the circular economy strategy j, for example, costs of cleaning, further mechanical treatment, replacement of elements, pyrometallurgical and hydrometallurgical treatment, etc.

OCi,j: Overhead costs for component i to apply the circular economy strategy j

F: Machine and personnel hourly rate for the disassembly process

DTi,j: Disassembly time of component i while applying the circular economy strategy j

q: Value reduction factor for the achievable yield from recycling in case of incomplete disassembly

n: Number of components.

It is assumed that the revenues, recovery costs, and overhead cost depend on the selected circular economy strategy. This also applies to the disassembly times because, in the case of recycling, disassembly operations can be performed faster due to destructive disassembly techniques.

#### 3.2.3. Selection and Crossover

During the selection phase, parents are selected based on their fitness value. The candidates with higher fitness will subsequently mate to produce new generations. In the literature, there are several selection procedures. Ke et al. [12] used the roulette wheel selection method to select the fittest disassembly sequences for EVBs. In this work, a tournament selection technique is used. In a tournament, each chromosome competes twice against two random other chromosomes. The winners move into a mating pool consisting of parents of the same size as the initial population.

Afterward, the crossover phase takes place, usually with high probability (Pc). During this phase, children representing new solutions are generated using the genetic material of two parents. In the context of the disassembly planning task in this paper, it is essential to ensure that the created chromosomes during the crossover phase represent feasible solutions by not violating the precedence relationships and the condition constraints. Therefore, the precedence preservative crossover method described in [27] was chosen and adapted to the characteristics of our chromosome structure. Thereby, two parents generate

two children whose chromosome structure is determined by two randomly generated masks. The first child is recombined by using mask 1, and the second one by mask 2. The chromosomes of the children are built up step by step. If the used mask has the value 1 at position i, parent 1 is used to specify the gene i of the child. Here, the leftmost element of parent 1 will be deleted from both parents and placed in the position i of the child. Otherwise, parent 2 is used to define the gene i. Figure 7 shows two possible disassembly sequences of the theoretical product presented in Figure 8, as well as two randomly generated masks, which were used to create new feasible disassembly sequences. The section of the chromosome, representing the circular economy strategies, is recombined simultaneously with the disassembly sequence using the same masks. However, the masks do not play any role in the definition of the disassembly depth. Here, child 1 gets the disassembly depth from parent 1 and child 2 from parent 2.

**Figure 7.** Using randomly generated masks to produce new feasible disassembly sequences during the crossover phase of the genetic algorithm.

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**Figure 8.** Structure of the chromosomes of the initial population.

#### 3.2.4. Mutation

The mutation phase plays a crucial role in enhancing the quality of the solution. It increases the diversity in a population and the possibility of discovering new candidates with high performance [27]. In addition, mutation increases the robustness of genetic algorithms concerning local optima [15]. In the context of disassembly planning, the feasibility of mutated solutions must be guaranteed. In this work, the disassembly strategy involves three decisions: the disassembly sequence, the circular economy strategies, and the disassembly depth. Therefore, we chose a three-step mutation by applying the swap mutation method to sections 1 and 2 of the chromosome, representing the disassembly sequence and the circular economy strategies, respectively, and a random resetting of the third chromosome section describing the disassembly depth.


Figure 9 shows an exemplary execution of the three-step mutation based on a disassembly strategy of the theoretical product presented in Figure 7. During the first step, the fifth and last genes of the first section, as well as the corresponding circular economy strategies, were changed. The mutation is accepted because the disassembly sequence 1-2-3-5-4-6 is feasible. The mutation in step 2 is rejected because part 3 cannot be reused (see condition vector S in Figure 7). The mutation during the last step consists of substracting 16.7% of the total number of components (one part).

**Figure 9.** Three-step mutation in the chromosome sections of the defined theoretical product: (**a**) step 1: swap mutation in the disassembly sequence and the corresponding circular economy strategies; (**b**) step 2: swap mutation in the circular economy strategies; (**c**) step 3: random resetting mutation of the gene representing the disassembly depth DL (DL = DL ± random x; x ∈ [0, 20% · n]; DL ∈ [0, n]; n: number of components).
