Optimization of the Human–Robot Collaborative Disassembly Process Using a Genetic Algorithm: Application to the Reconditioning of Electric Vehicle Batteries

Abstract

To achieve a complete circular economy for used electric vehicle batteries, it is essential to implement a disassembly step. Given the significant diversity of battery geometries and designs, a high degree of flexibility is required for automated disassembly processes. The incorporation of human–robot interaction provides a valuable degree of flexibility in the process workflow. However, human behavior is characterized by unpredictable timing and variable task durations, which add considerable complexity to process planning. Therefore, it is crucial to develop a robust strategy for coordinating human and robotic tasks to manage the scheduling of production activities efficiently. This study proposes a global optimization approach to the scheduling of production activities, which employs a genetic algorithm with the objective of minimizing the total production time while simultaneously reducing the idle time of both the human operator and robot. The proposed approach is concerned with optimizing the sequencing of disassembly tasks, considering both temporal and exclusion constraints, to guarantee that tasks deemed hazardous are not executed in the presence of a human. This approach is based on a two-level adaptation framework developed in RoboDK (Robot Development Kit, v5.4.3.22231, 2022, RoboDK Inc., Montréal, QC Canada). At the first level, offline optimization is performed using a genetic algorithm to determine the optimal task sequencing strategy. This stage anticipates human behavior by proposing disassembly sequences aligned with expected human availability. At the second level, an online reactive adjustment refines the plan in real time, adapting it to actual human interventions and compensating for deviations from initial forecasts. The effectiveness of this global optimization strategy is evaluated against a non-global approach, in which the problem is partitioned into independent subproblems solved separately and then integrated. The results demonstrate the efficacy of the proposed approach in comparison with a non-global approach, particularly in scenarios where humans arrive earlier than anticipated.

1. Introduction

In recent years, governments have paid increasing attention to the energy crisis and environmental protection, prompting many countries to prioritize investment and research in electric vehicles as part of their strategy for the future automotive market [1]. Consequently, the use of electric vehicles worldwide has grown considerably in recent years, as global sales are projected to increase from the current 1.1 million to 11 million in 2025 and 30 million by 2030 [2]. However, it has been reported that power batteries with less than 80% of their nominal capacity are no longer suitable for use [3], which could lead to the significant accumulation of batteries being used in the coming decades. The increasing number of batteries poses a significant threat to the environment, making their disassembly and recycling methods a research priority [4]. Promoting environmental protection and sustainable development is crucial for recycling batteries that contain toxic chemicals and high-value metals [5]. Numerous lithium-ion battery brands, models, and retirement states exist owing to variations in models and service procedures [4]. This diversity adds an extra layer of complexity that requires significant adaptability in the disassembly process, which can only be provided by human operators. Their ability to adapt to various specifications and carefully handle diverse components is crucial for effectively meeting the unique requirements of each battery model during the disassembly process. However, end-of-life products frequently contain numerous hazardous components (such as lithium batteries and circuit boards) that can considerably harm the human body and endanger life [6]. Specifically, end-of-life batteries from electric vehicles can retain residual current, causing temperatures to increase during the recycling process, which can lead to fires or explosive accidents [7]. Furthermore, disassembly tasks, which are often repetitive and strenuous, can expose workers to the risk of developing musculoskeletal disorders. This highlights the importance of collaborating with robots because they excel at handling repetitive, dangerous, and persistent tasks [8]. In this context, human–robot collaborative disassembly combines the adaptability, judgment, and perception of operators [9] with the high-speed, safe, and repeatable advantages of industrial robots [8]. However, the introduction of collaborative robots in the industry has naturally raised the question of how to effectively utilize both partners (robots and humans) to optimize production time while preventing the development of musculoskeletal disorders [10]. Notably, scheduling disassembly tasks significantly affects the recycling performance of used or discarded products [11]. This effect underscores the importance of carefully coordinating human–robot interactions, particularly in scenarios in which humans work alongside robots to perform shared tasks. Therefore, developing a strategy for effectively distributing and planning tasks between humans and robots is crucial for enhancing the efficiency of human–robot teams. The study of human–robot collaborative disassembly has attracted the interest of researchers [12]. The optimal scheduling of human and robotic tasks to maximize overall process efficiency within a shared workspace has been explored in various ways in the literature. Some researchers examined scheduling structures in which the time required for each agent to complete their tasks is treated as a constant [1,13,14]. However, this approach assumes a static production environment that does not reflect real-world conditions [10]. Production scheduling problems in real-world manufacturing environments are dynamic and stochastic [15], where random interruptions can disrupt the execution of a planned schedule. Indeed, in interactive mode, human behavior can vary for the same task. In real-world scenarios, scheduling systems function in dynamic and unpredictable environments where random interruptions can disrupt the execution of a planned schedule [15]. Furthermore, human interventions can exhibit random temporal variations, meaning that they may intervene at unpredictable times and for variable durations. To manage the stochasticity inherent in collaborative production facilities, a combination of proactive/predictive and reactive methods, based on the estimation of future performance, must be further exploited [16]. Therefore, a reactive adaptive strategy is proposed to adjust to the real availability of humans, considering the variability and unpredictability of their behavior, and to maintain the continuity of productivity via dynamic reprogramming [10]. For configurations where robot mode changes can occur owing to the presence or absence of a human in the collaborative cell and considering human tasks as known and fixed, no approach has been formulated for the structure scheduling necessary to adapt to any temporal variability of the human partner based solely on the rescheduling of the robot tasks. The only article [10] was mainly interested in cases where the human was considered completely uncontrollable by the robotic planner, which, in this case, was used as a subcomponent of the global planner. This problem was reformulated as a combination of the Traveling Salesman Problem (TSP) and Knapsack Problem (KP), and then solved via a partitioning approach that divides the problem into independent subproblems [10]. These subproblems were subsequently solved using dynamic programming before being combined to obtain an overall solution. However, solving this problem using this approach presents a risk of converging to a suboptimal solution. This raises the question of whether a global approach that considers the entire problem offers a better solution.

This study aims to optimize the disassembly process of electric batteries through a global optimization approach integrating human–robot collaboration (teamwork using tasks sharing without physical contact), while ensuring reliable and safe sharing of the common workspace. The major challenge is to accommodate this variability while optimizing the total production time and minimizing the periods of inactivity for human operators and robots. This study examines situations in which a human is considered a completely uncontrollable entity in the workspace. In this framework, human tasks are predefined and accompanied by specific time constraints in order to intervene in the workspace. This optimization approach is based on a two-level adaptation scheme. The first level, offline (predictive approach), is based on the expected availability times of human intervention to propose a task sequencing order with the aim of minimizing the total production time and inactivity periods of both human and robot. However, the actual behavior of humans may differ from predictions, making real-time adaptation necessary to adjust planning in the face of these contingencies, owing to the unpredictable nature of human behavior. The second level, the online (reactive) approach, is based on the real-time detection of human intervention, and dynamically adjusts the planning with respect to the initial predictions provided by the predictive approach. The results obtained from this global optimization approach are compared to those of a non-global approach, which divides the problem into several subproblems solved independently before being combined to generate a global solution [10]. Both global and non-global approaches were simulated in different scenarios, where the expected time differed from the “real” time. In addition, the predictive and reactive versions of these two optimization approaches were compared to measure their effectiveness in optimizing the disassembly process in the face of uncertainties related to the unpredictable behavior of the human operator.

Subsequently, we proposed three fundamental hypotheses based on this bibliographic study. The first hypothesis is that the global optimization approach is more efficient than dividing the problem into several independent subproblems. Each sub-solution may be locally optimal by dividing it into a complex problem. However, this does not guarantee that the resulting global solution is optimal. Interactions and interdependencies between subproblems can lead to inefficiencies and suboptimal solutions. The second hypothesis proposes that a reactive optimization approach can improve the predictive results based on anticipated human availability. By detecting the operator’s actual availability in real time, this approach allows the scheduler to better manage unexpected behaviors and reduce idle time for both humans and robots. Finally, the third hypothesis proposes that the results obtained by the global approach using a genetic algorithm and those of the non-global approach, based on the resolution of the TSP–KP (Traveling Salesman Problem and Knapsack Problem), will be equivalent on the reactive side through dynamic programming. Both methods can adapt their sequences to the operator’s actual availability despite employing different predictive planning strategies.

The main contribution of this study is the development of a global optimization approach to optimize the behavior of a robot, considering the variability of human intervention and the inability of the planner to control human behavior. The predictive offline solution obtained is then readjusted in a reactive manner online to scope for every human task time deviation during the normal production cycle. We defend this contribution based on an analysis of related works to examine previous studies in this area, which is presented in Section 2. Based on the suggested hypothesis, a methodology detailed in Section 3 is adopted and presented to define the objective function and associated constraints. A comparative analysis of the performance of the two optimization approaches is presented in Section 4, highlighting the significant differences in terms of methodology, efficiency, and results obtained. Section 5 presents an in-depth discussion of the results and limitations of the study. Finally, Section 6 concludes the paper and suggests avenues for future work.

2. Related Works

A circular economy is an environment-friendly economic model that prioritizes resource recycling. In this context, remanufacturing is essential to the circular economy as it enables the sustainable and efficient use of materials and energy in economic activities, thereby reducing their negative impact on the environment [12]. Disassembly is the first and most difficult process of product remanufacturing. Before executing the disassembly process, the generation of optimal disassembly sequences plays an important role in improving disassembly efficiency [17]. Therefore, quickly determining the optimal disassembly sequence to obtain the highest recycling value or disassembly efficiency for end-of-life products is one of the most important issue for enterprises [1]. Indeed, this process has emerged as a key research topic in recent decades to achieve successful remanufacturing [12]. There have been many investigations in this field, and several disassembly sequence planning methods have been developed [18].

The remanufacturing process, driven by human–robot collaboration (teamwork for optimal tasks sharing without physical contact) technology, is becoming an important carrier for the circular economy, contributing to economic development while significantly reducing environmental pressure [12].

The analysis highlighted that complete robotic disassembly remains difficult because of the inherent challenges that robots face in handling uncertainties. Although robots are effective for repetitive tasks and are used for disassembling electronic products [19], they require human assistance for more adaptable tasks. Therefore, Human–Robot Collaboration (HRC) addresses this issue by combining robotic efficiency with human flexibility, resulting in a more flexible and productive disassembly process [17]. The advent of collaborative robotics in industry has created closer collaboration between humans and robots. However, the introduction of robots into the industry has naturally raised the question of how to effectively use both partners (human and robot) to optimize production time while preventing the development of musculoskeletal disorders [10]. This has led to the need to optimally schedule human and robot tasks to be sufficiently robust to handle the variability induced by time-related operator errors caused by the inability to accurately forecast the stochastic nature of human behavior [10]. This problem has become a major research topic in recent decades, particularly in the context of improving the remanufacturing processes [6]. The solution to the disassembly sequence-planning problem is generally divided into two parts. Initially, a mathematical model was developed to represent the relationships between various components, which helps identify all potential disassembly sequences that complied with the required precedence constraints [1]. The constructed mathematical model is then used to determine all disassembly sequences that satisfy the disassembly precedence relationship. Subsequently, a range of algorithms is applied to the model to determine the optimal disassembly sequence that achieves the specified optimization goals within the solution space [1]. In the literature, a considerable number of studies have focused on the optimization of disassembly sequences. To better understand recent advances in the optimization of this process, a literature review was conducted. Particular attention has been paid to research focused on optimizing the disassembly process of electric batteries [1,8,10,20]. The focus has also been directed towards approaches exploring a collaborative mode of operation that combines human and robotic capabilities [4,6,21,22]. Different optimization algorithms have been developed to identify the most efficient disassembly sequences. Owing to the complexity of disassembly planning problems, which are classified as the hardest problems in Nondeterministic Polynomial time (NP-hard) [23], heuristic and metaheuristic approaches have been developed to provide rapid solutions for large-scale problems [8]. Various techniques have been explored, including the use of genetic algorithms [1,4,6,20], bee colony algorithms [11,24,25], ant colony algorithms [26,27,28], frog leap algorithms [29], discrete squirrel search algorithms [30], bald eagle search algorithms [31] and discrete gray wolf algorithms [32]. Compared to other metaheuristic algorithms, the genetic algorithm offers a wide range of applications, strong scalability, and a reduced risk of becoming trapped in local optima. It is also widely used to solve disassembly sequence planning problems [1].

The question of how to optimally coordinate human and robotic tasks to maximize overall efficiency within a shared workspace has been addressed in various ways in the literature. Some authors have explored planning structures in which the time required for each agent to complete tasks is constant [1,13,14]. However, this approach assumes a static production environment that does not reflect real-world conditions [10]. Planning systems operate in dynamic and uncertain environments where random disruptions can prevent the execution of a predefined schedule [15]. Other studies have adopted an approach that uses probability distribution. The article [33] proposed an optimization framework for planning disassembly sequences in the context of uncertainty by integrating human–robot collaborations. In this study [33], the disassembly time was considered as an uncertain parameter modeled by a beta distribution. However, regardless of the approach used, such a structure is ineffective in capturing the variability inherent to different agents, particularly those induced by a human partner [10]. Humans exhibit a higher rate of unforeseen failures than their robotic counterparts in collaborative tasks because of their susceptibility to spatial, temporal, and contextual errors [34]. To manage the stochasticity inherent in collaborative production facilities properly, a combination of proactive/predictive and reactive methods based on the estimation of future performance must be further exploited [16]. Therefore, a reactive adaptive strategy is proposed to adjust to the actual availabilities of humans, considering the variability and unpredictability of their behavior, and to maintain the continuity of productivity via dynamic rescheduling [10]. The article [35] presents an architecture for dynamic task scheduling. This method first identifies the group of tasks that should be executed based on the task priority order. After obtaining this prioritized group of tasks, a quality metric (a numerical value that indicates which agent is best suited to performing the task) is used to determine the agent to which each task should be assigned. Finally, real-time monitoring of the human agent is used to detect changes in its performance so that tasks can be transferred from one agent to another. However, this method considers the possibility of modifying human behavior [10]. Furthermore, considering the human as a fully controllable operator restricts its adaptive properties, which were initially sought as an asset for human–robot collaboration [36,37].

Table 1. Summary of scheduling approaches based on their ability to handle tasks time variability.

Article	Fixed Human Tasks	Human as Non-Controllable Agent	Non-Fixed Time Distribution	Constraints		Scheduling Approach		Global Problem Formulation
				Cooperation	Exclusion	Predictive	Reactive
Our Approach	X	X	X	X	X	X		X
[1]	X			X		X		X
[38]			X	X		X	X	X
[30]	X			X		X	X	X
[23]		X		X	X	X		X
[29]		X	X	X	X	X		X
[39]			X	X		X	X	X
[10]	X	X	X	X	X	X	X

summarizes the various methodologies studied in the literature based on specific criteria to contextualize the work carried out in this study with respect to existing approaches. These criteria include the presence of fixed tasks assigned to humans that cannot be altered and the unpredictability of human interventions within the shared workspace. The analysis also considers how the durations of human tasks are specifically characterized and whether they follow a stationary and fixed distribution. Additionally, it considers exclusion constraints, which prevent human presence during hazardous robotic operations, and cooperation constraints, which allow humans and robots to operate simultaneously in the same area. The evaluation also includes the development of proactive and reactive approaches using dynamic programming to dynamically adapt the scheduling plan in response to unpredictable variations in human behavior. Finally, this study examined whether a global or non-global approach has been adopted.

To complement the comparative analysis presented in Table 1, we briefly describe the main contributions and limitations of the referenced studies to better position our study. Article [1] addressed scheduling with fixed human tasks, and introduced exclusion constraints to ensure safety in a shared workspace. However, they did not consider the dynamic variability of human actions. By contrast, article [23] models humans as non-controllable agents and considers both cooperation and exclusion constraints. However, an adaptive scheduling strategy for coping with real-time uncertainties is lacking. Article [30,38] explored time variability through a reactive scheduling approach, although it accounted for neither the unpredictability of human interventions in the workspace nor explicitly modeled humans. In scenarios where human presence can influence robot behavior within a shared workspace, no specific method has been developed to adapt solely through robot task rescheduling to the temporal variability introduced by human collaborators [10]. Only the study presented in [10] considered human tasks as predefined, with strict temporal constraints governing their access to the workspace, while also treating their timing as subject to random fluctuations. The authors reformulate the problem as a combination of the Traveling Salesman Problem (TSP) and Knapsack Problem (KP) and address it using a non-global approach that decomposes the problem into independent subproblems. These subproblems are then solved using dynamic programming and are recommended to produce a global solution. However, such a non-global strategy carries the risk of converging suboptimal solutions. This raises the question of whether adopting a global optimization approach that considers the problem could yield better performance.

Our main contribution in comparison to the study in [10], which addressed the same type of problem, lies in the development of a global optimization strategy that explicitly incorporates the variability of human intervention to optimize robot behavior. This strategy followed a two-level adaptive framework. The first level is an offline predictive phase that uses the estimated human availability to generate an optimal disassembly sequence to minimize the total production time and idle periods for both humans and robots. The second level is an online reactive phase that dynamically adjusts the schedule in soft real time based on deviations from the expected human activity detected during execution. The online reactive phase is not synchronized with the robot controller and driver: the real-time nature of the reactive phase is based on the availability of the algorithm solution before the end of the previous solution executed by the robot. Our approach is primarily predictive: an initial disassembly sequence is generated based on the estimated arrival time of the human operator. This sequence serves as the baseline path for execution. During real-time execution, if there is a deviation between the predicted availability and the actual arrival time (e.g., the human is late or early), reactive adjustments are applied. These are not full re-executions of the genetic algorithm but rather local rescheduling strategies that modify the current disassembly path based on updated availability data.

3. Methodology

Industrial human–robot collaboration is characterized by the presence of two hybrid agents working towards a common goal. In this study, we consider a situation in which a human operator and a robot collaborate in a shared workspace to share tasks in a teamwork meaning. The layout of the disassembly line of the NISSAN Leaf battery using RoboDK (Robot Development Kit, v5.4.3.22231, 2022, RoboDK Inc., Montréal, (Québec,) Canada) is shown in Figure 1. The central problem of this study lies in the major challenges associated with optimizing the disassembly process of used products, with a specific focus on electric vehicle batteries. These challenges stem from the need to effectively manage the collaboration between human and robotic capabilities, considering the uncertainty surrounding the availability of human agents in a shared workspace and the duration of their presence. One of the predominant challenges in this context is managing the transition between the autonomous work of a robot and human integration into the collaborative disassembly process. This complexity can be exacerbated by the variability in the start times and execution durations of tasks performed by humans, while the robot must continue to operate without interruption. In this study, the robot began its work autonomously; however, at a certain point, the human must intervene to perform specific tasks such as removing electrical cables and battery management modules. However, the exact time required for human entry into a shared workspace remains uncertain. In the absence of a human, it is imperative to optimize the disassembly time by allowing the robot to continue with other tasks, because the goal is to find the optimal disassembly sequence while maximizing the robot’s utilization time. Even when a human enters, the robot can continue to perform certain tasks to minimize the total disassembly time. However, some tasks are incompatible with human presence, meaning that a robot cannot perform them when a human is present.

3.1. Disassembly Relationship Graph

To clearly express the disassembly precedence relationships between the components, an AND/OR graph was proposed. The disassembly graph presented in this study is composed of nodes representing various disassembly tasks and edges that define the precedence constraints between these tasks. According to the relevant disassembly information of Nissan Leaf Battery 2011, a graph model was established, as shown in Figure 2. This graph illustrates the steps required to disassemble the 2011 Nissan Leaf battery [10]. The different blocks on the graph represent specific subsections of the battery. Block 1 focuses on the initial steps required to remove the battery cover, whereas Block 2 details the procedures for removing the battery management system. Block 3, located above, contains instructions for extracting cells lateral to the robot, and tasks that can be performed in its presence. Block 4 covers the removal of cells from the left side and the operations that must be performed in the absence of a human operator to ensure safety. Finally, Block 5 includes instructions for extracting cells from the rear battery compartment.

Additionally, the graph uses color coding to distinguish between different types of tasks. The green nodes represent the tasks performed by the robot, whereas the blue nodes indicate tasks that require human intervention. Yellow nodes denote parallel tasks that can be performed simultaneously by both humans and robots. The red nodes indicate nonparallel tasks that must be performed when humans are not in the workspace for safety or ergonomic reasons.

The disassembly process consists of 33 sequential tasks numbered from 1 to 33, which correspond to the actions illustrated in Figure 2 and are detailed in

Table 2. Definition of the tasks Si for battery disassembly.

Tasks Group	Tasks	Definitions
1—Removing the battery cover (Ts1)	S1 to S3	Remove screws of the cover
	S5-S6	Extract cover
	S7	Human intervention to remove cables of the BMS (robot far from human)
	S8	Robot tool change
2—Removing the BMS (Battery Management System)	S9	Remove rear support block
3—Removing the cells located on the side of the robot at right (robot’s tasks that may be performed in parallel with operator)	S10 to S13	Move four right bloc supports (for each compartment)
	S14	Move right block electrical junction screws
	S21	Move right electrical junction block
	S22 to S25	Four right blocs removed (for each compartment)
4—Removing the cells that are situated at the closest possible distance to the operator at left (operator outside workspace for safety)	S15	Move left block electrical junction screws
	S16 to S19	Move four left bloc supports (for each compartment)
	S20	Move left electrical junction block
	S26 to S29	Four right blocs removed (for each compartment)
5—Extracting the cells in the battery compartment at the rear	S30–S33	Rear block electrical junction to remove (S30 screw, S31 block, S32 end moved, S33 back cover)

[10]. Each task was associated with a cost, defined as the time required to complete it, and expressed in minutes. In this formulation, it is assumed that the task execution times of the robot are constant and do not vary, even in the presence of a human partner within the shared workspace. These task durations were obtained directly from RoboDK simulation software, which estimates them based on the operational performance of the robot [10].

3.2. Mathematical Model

A feasible disassembly sequence must satisfy precedence constraints while avoiding conflicts among disassembly operations. The notations used to formulate the model are listed in Table 2. Before detailing the optimization algorithm developed, it is essential to present a mathematical formulation of the problem, where indices and parameters are presented in

Table 3. Description of the indices and parameters of the mathematical model.

Indices
i,j	Index of the disassembly task, i/j = 1, 2, ..., n
w	Index of the worker type, w ∈ W
W	Set of worker groups, W = [10]
Iw	Set of tasks to be performed by worker w
I	Set of all disassembly tasks performed by the set of workers W
Sets
P(i)	Set of predecessor tasks for task i, ∀ i ∈ Iw
E(i)	Set of tasks exclusive to human presence, ∀ i ∈ I_H
C(i)	Set of tasks that can be performed in the presence of a human, ∀ i ∈ I_H
Parameters
N	Total number of disassembly tasks
dij [min]	Execution time of task j started after task i
Tdp [min]	Expected human availability time required to be ready to work
Tdr [min]	Real human availability time
Tip [min]	Expected time for human intervention
Tir [min]	Real human work time intervention
Tih [min]	Human idle time
M	A very large coefficient used as a substitute for infinity
Cmax [min]	Total disassembly time

. This step defines the framework and guides the elaboration of the optimization approach used.

This paper introduces the following two matrices to express disassembly relations:

-Time matrix T = [t_ij]: This matrix specifies the time values associated with each arc of the graph, indicating the time required to transition from one task to another. Each element of the matrix T = [t_ij], located at the intersection of row i and column j, indicates the duration required to move from task i to task j, where an element t_ij represents the relationship of disassembly operations i and j.

-Precedence matrix: This matrix captures the dependencies between different disassembly tasks. This ensures that the prerequisites are met, thereby preventing situations in which a task depends on another task that has not yet been completed. In this matrix P = [p_ij], the elements at row i and column j indicate the indices of the tasks.

$$p_{ij}=\left\{\begin{array}{cc}1& \mathrm{i}\mathrm{f} \mathrm{o}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{a}\mathrm{t}\mathrm{i}\mathrm{o}\mathrm{n} i \mathrm{c}\mathrm{a}\mathrm{n} \mathrm{b}\mathrm{e} \mathrm{p}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e} j,\\ & and j \mathrm{c}\mathrm{a}\mathrm{n}\mathrm{n}\mathrm{o}\mathrm{t} \mathrm{b}\mathrm{e}\mathrm{p}\mathrm{e}\mathrm{r}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{m}\mathrm{e}\mathrm{d} \mathrm{b}\mathrm{e}\mathrm{f}\mathrm{o}\mathrm{r}\mathrm{e} i.\\ 0& \mathrm{otherwise}\end{array}\right.$$

(1)

-Exclusion set E: This set identifies tasks that cannot be performed simultaneously with task S7 conducted by a human due to safety or compatibility constraints. Tasks S16, S17, S18 and S19 belong to set E, meaning they must be performed either before the start of task S7 or after its completion. The values are defined as follows:

$$E=\left\{\mathrm{16,17,18,19}\right\}$$

(2)

-Cooperation set C: This set identifies tasks that can be performed in parallel with task S7 conducted by a human. Tasks S10, S11, S12, and S13 belong to set C. The values are defined as follows:

$$C=\left\{\mathrm{10,11,12,13}\right\}$$

(3)

The matrices and sets described above model the relationships between priority, exclusivity, and cooperation among the tasks in the disassembly sequence.

-Decision Variables:

To model the disassembly process, the following decision variables have been defined:

-

x_ij: A binary variable that equals 1 if task i is executed immediately before task j and 0 otherwise.

-

y_ij: A binary variable that equals 1 if task i is completed before the start of task j and 0 otherwise.

-

t_i^s: The start time of task i.

-

t_i^f: The finish time of task i.

Determining the total disassembly duration requires considering the finish time of the final task in the process, represented by task n + 1, as shown in Equation (4).

$$C_{max} = t_{n+1}^f$$

(4)

-Objectives and constraints:

The objectives of the mathematical model and the associated constraints are presented in this section. These equations define the criteria to be optimized and describe the relationships to be considered within the framework of the disassembly problem.

$$Min{C}_{max}$$

(5)

$$Tir=min{\sum }_{\left(i,j\right)\in I_R}(t_j^s-t_i^f)x_{ij}$$

(6)

$$Tih=min{\sum }_{i\in I_H}\left(t_i^s-\mathrm{T}\mathrm{d}\mathrm{p}\right)$$

(7)

$${\sum }_{j\in I_w}{x}_{ij}=1\forall i\in I_w$$

(8)

$${\sum }_{i\in I_w}{x}_{i,n+1}=1$$

(9)

$$t_j^f\ge t_j^s+d_{ij}\forall i,j\in I_w$$

(10)

$$t_j^f-M\left(1-x_{ij}\right)\le t_j^s\forall i,j\in I_w$$

(11)

$$t_i^s=\mathrm{m}\mathrm{a}\mathrm{x}(\mathrm{T}\mathrm{d}\mathrm{p},t_j^f)\forall i\in I_H,j\in I_R$$

(12)

$$t_i^f\le t_j^s+{M(1-y}_{ij})\forall i\in E(j)$$

(13)

$$t_j^f\le t_j^s+{M.y}_{ij}\forall i\in E(j)$$

(14)

$$t_j^f\le C_{max}$$

(15)

Equations (5)–(15) define the optimization model developed to enhance the efficiency of the disassembly process. The main objective of Equation (5) is to minimize the total disassembly time. To support this, two sub-objectives are introduced. Equation (6) minimizes the robot idle time (TsiR) by reducing the cumulative delays between the completion of one robot-assigned task and the start of the next task, thereby ensuring a more continuous use of the robot. Similarly, Equation (7) minimizes the human idle time (Tih) by penalizing the difference between the expected human availability time (Tdp) and the actual start time of the human-assigned tasks, thereby reducing unnecessary waiting periods. Constraints (8) and (9) ensure that each task has a unique predecessor and successor, except for the dummy start (task 0) and end (task n + 1). Constraint (10) ensures nonpreemption, requiring that once a task starts, it must be executed without interruption. Constraint (11) enforces the precedence relation: if task i precedes task j (i.e., xᵢⱼ = 1), then task i must be completed before task j begins (tᶠᵢ ≤ tˢⱼ); otherwise, if xᵢⱼ = 0, the constraint is neutralized using a sufficiently large constant M. Constraint (12) sets the start time of a human-executed task i as the maximum of the expected human availability time (Tdp) and finish time of the preceding robot task j. Therefore, (12) ensures that a human task starts only when two conditions are met: the human is available (estimated by Tdp) and the previous task is completed ($t_j^f$). Since the human arrival times are uncertain, the maximum of these two values is used to determine the actual start time. For example, if a human arrives earlier than expected (Tdp < $t_j^f$), the solution must wait for the previous task to complete. This reflects the realistic synchronization between human availability and system task flow.

Constraints (13) and (14) enforce mutual exclusion if two tasks i and j cannot overlap; then, their execution windows must not intersect. Specifically, if yᵢⱼ = 1, then tᶠᵢ ≤ tˢⱼ; if yⱼᵢ = 1, then tᶠⱼ ≤ tˢᵢ. In both cases, the constraint is deactivated when the binary variable equals zero, using the big-M method. Finally, constraint (15) ensures that the makespan (Cₘₐₓ) is greater than or equal to the latest finish time across all tasks, representing the total duration of the disassembly process.

3.3. Implementation of Genetic Algorithm

In this study, a genetic algorithm was employed to minimize the total disassembly time. The disassembly process for electric vehicle batteries is inherently complex due to the vast number of possible sequences combined with variability in battery design and conditions. In our study, while the Nissan Leaf battery serves as a use case, genetic algorithms prove highly effective for this type of optimization problem because they can efficiently handle its NP-hard nature by exploring a very large solution space.

Beyond sequence optimization, an important challenge we address in this study is the temporal variability of human intervention within the workspace. Genetic algorithms offer the flexibility to integrate such variability into the optimization process, ensuring that the global objectives are effectively balanced: minimizing the total production time while simultaneously reducing idle times for both the human operator and the robot. This capability makes GAs especially well suited for collaborative disassembly environments.

Through iterative selection, crossover, and mutation, genetic algorithms evolve towards better disassembly sequences across generations. This not only prevents premature convergence to local optima but also fosters the discovery of innovative and non-intuitive solutions. As a result, genetic algorithms constitute a powerful and versatile approach for sustainable product recovery and remanufacturing.

This model is inspired by the theory of natural evolution, and utilizes an initial random population to explore and exploit the solution space [40]. Each individual in a population represents a disassembly sequence. Each element of this sequence determines the order of task execution, and is configured to respect the precedence constraints established in the disassembly graph. The diagram in Figure 3 represents the various steps of the process from the generation of the initial population to the selection of the best solution, including the crucial steps of parent selection, crossover, mutation, and evaluation by the objective function.

The genetic algorithm relies on an iterative cycle of selection, crossover, mutation, and evaluation, which is repeated until a specific stopping condition is met. This stopping condition can be defined by a predetermined number of iterations or by reaching a specific level of “fitness” representing the quality of a solution relative to the defined evaluation criteria. The fitness function was specifically designed to address the disassembly problem under dynamic human–robot collaboration constraints. The mathematical model was implemented and solved using a genetic algorithm developed in Python (PyCharm, 2023 edition) and was integrated into RoboDK.

3.4. Methodological Differences Between the Global Genetic Algorithm and the Non-Global TSP–KP Approach

The genetic algorithm developed in this study adopts a global approach for the optimization of the disassembly process. This optimization approach simultaneously considers all tasks to be performed to optimize the disassembly sequence globally. This algorithm uses an initial population of solutions that evolves over generations through crossover and mutation operations. Each solution is evaluated using an objective function that considers precedence constraints, total time required to perform all tasks, and exclusivity and cooperation rules. Exclusivity rules prohibit the simultaneous execution of certain tasks by the robot and the human simultaneously owing to safety constraints, whereas cooperation rules favor the parallel execution of tasks that can be performed simultaneously without risk. This ensures that the generated solutions respect all the operational constraints of the disassembly process. In contrast, the non-global TSP–KP approach described in this paper [10] divides the optimization problem into several independent subproblems, each of which is optimized separately before being combined to obtain a global solution. The scheduling problem is reformulated as a combination of the traveling salesman problem (TSP) and 0/1 knapsack problem (KP) and then solved via dynamic programming. The tasks to be performed before human intervention (Ts1) were optimized in the first step. This sequence is formulated as a traveling salesman problem (TSP) without returning to the initial node, aiming to minimize the total travel time between tasks. Task (Ts2) refers to all tasks that can be added to the execution schedule of the robot before human intervention. These tasks are optimized using a knapsack (KP), which maximizes the value of the selected tasks under time constraints. In this step, non-parallel tasks were prioritized. Task (Ts3) refers to all operations that the robot must perform in the presence of a human operator. A knapsack problem (KP) was formulated to optimize these joint actions, considering the production time and precedence constraints. This step aims to prioritize parallel tasks while ensuring that all precedence constraints are respected. While (Ts4) refers to the tasks that must be performed after the human partner leaves the workspace, the parallel tasks not integrated in (Ts3) as well as the non-parallel tasks not integrated in (Ts2), including those remaining from the disassembly of the rear battery pack, are reformulated as a traveling salesman problem (TSP) to find the optimal sequence [10]. In summary, this approach divides the disassembly problem into several independent subproblems that are separately optimized before being combined to obtain a global solution.

3.5. Implementation of the Reactive Optimization Approach

The reactive optimization strategy continuously adapts the task schedule of the robot in response to the real-time availability of the human operator. The main challenge is to accommodate this variability while simultaneously minimizing the total production time and reducing idle periods for both agents. In contrast to the predictive optimization approach described in the previous section, the reactive method continuously updates the task schedule in real time according to the operator’s actual presence in the shared workspace. This adaptive method relies on the real-time detection of human availability, which may disrupt or override the initial plan generated by the predictive model. The optimization algorithm was tested in several scenarios in which the initially expected human availability was deliberately inaccurate, requiring the system to respond effectively to such discrepancies. To manage these deviations, the approach incorporates dynamic programming to handle unexpected events caused by human behavior. This enables the scheduler to respond adaptively to the differences between the predicted and observed availability times. Importantly, the reactive genetic algorithm builds upon the disassembly sequence proposed by the predictive model. In each work cycle, the human task duration and availability were predicted. This strategy is based on three successive update phases, each triggered by discrepancies between expected and actual human availability. Initially, if all tasks scheduled before human arrival have already been executed, the scheduler interprets this as an underestimation of the availability. It then assigns the robot the shortest available task, prioritizing those initially planned after the human intervention. If the operator is absent, the tasks from the collaborative phase are introduced. Conversely, when human availability is overestimated, some tasks may be interrupted to minimize the waiting time of the operator. The robot’s tasks can be performed in parallel with the presence of the human being rescheduled, either during or after collaboration, whereas non-parallel tasks are deferred until the human has left. Finally, after the human exits the workspace, the scheduler initiates a final reorganization phase to reintegrate previously unexecuted tasks.

4. Results

To present realistic results, the system was designed using RoboDK with the available design presented in [41]. This approach is based on a two-level adaptation framework. Section 4.1 presents the metrics used to compare the optimization approaches developed in Section 4.2. To evaluate and compare the efficiencies of the two optimization approaches for the disassembly process, we relied on the experimental data provided in

Table 4. Use cases results.

Use Case	Approach	Before Collaboration	During Collaboration	After Collaboration	Texh [min]	SoiH [min]	TsiR [min]	Tpro [min]
Case 1 (Tdp = 12, Tip = 3, Tdr = 14.813, Tir = 1)	NG-TSPKP	Ts1-S17-S18	S10-S13	S11-S12-S19-S16-Enf	1.048	0	3.028	66.477
	G-GA	Ts1-S18-S12	S13-S10-S11	S17-S19-S16-Enf	2.045	0	2.817	66.436
	R-TSPKP	Ts1-S17-S18-S19-S16-S11	S10	S12-S13-Enf	0	0.181	0.215	63.664
	R-GA	Ts1-S18-S17-S19-S16-S12-	S13	S10-S11-Enf	0	0.132	0	63.615
Case 2 (Tdp = 18, Tip = 7, Tdr = 10.81, Tir = 6)	NG-TSPKP	Ts1-S17-S18-S16-S19-S11-S10-S12	S13	Enf	0	5.991	4.742	68.401
	G-GA	Ts1-S17-S18-S19-S16	S13-S12-S10-S11	Enf	0	3.138	1.930	65.545
	R-TSPKP	Ts1-S17-S18	S13-S11-S10-S12	S16-S19-Enf	0	0.972	1.93	65.379
	R-GA	Ts1-S17-S18	S13-S12-S10-S11	S19-S16-Enf	0	1.041	1.93	65.545
Case 3 (Tdp = 10, Tip = 3, Tdr = 10.81, Tir = 2)	NG-TSPKP	Ts1	S10-S13	S11-S12-S17-S18-S19-S16-Enf	0.048	0	1	64.449
	G-GA	Ts1	S13-S12-S10	S17-S18-S19-S11-S16-Enf	1.045	0	0.831	64.467
	R-TSPKP	Ts1-S17	S10-S13	S11-S12-S18-S19-S16-Enf	0.048	0.167	0	63.636
	R-GA	Ts1-S17	S13-S12	S18-S19-S11-S16-S10-Enf	0	0.149	0	63.615
Case 4 (Tdp = 14, Tip = 4, Tdr = 11.81, Tir = 2)	NG-TSPKP	Ts1-S17-S18-S19-S16	S11-S10-S12	S13-Enf	1.022	1.969	0	63.449
	G-GA	Ts1-S17-S18-S19-S16	S13-S12-S10-S11	Enf	2.07	2.138	0	63.615
	R-TSPKP	Ts1-S17-S18-S19	S11-S10-S12	S13-S16-Enf	1.022	0.969	0	63.449
	R-GA	Ts1-S17-S18-S19	S13-S12-S10	S11-S16-Enf	1.022	1.038	0	63.615
Case 5 (Tdp = 15, Tip = 6, Tdr = 13.81, Tir = 2)	NG-TSPKP	Ts1-S17-S18-S19-S16-S11	S10-S12-S13	Enf	1.073	0.966	0	63.449
	G-GA	Ts1-S17-S18-S19-S16	S13-S12-S10-S11	Enf	2.07	0.138	0	63.615
	R-TSPKP	Ts1-S17-S18-S19-S16-S11	S10-S12	S13-Enf	0.025	0.966	0	63.449
	R-GA	Ts1-S17-S18-S19-S16-S11	S10-S12	S13-Enf	0.025	0.966	0	63.615
Case 6 (Tdp = 18, Tip = 8, Tdr = 11.81, Tir = 1)	NG-TSPKP	Ts1-S17-S18-S19-S16-S11-S10-S12	S13	Enf	0.048	4.991	0	63.449
	G-GA	Ts1-S17-S18-S19-S16	S13-S12-S10-S11	Enf	3.07	2.138	0	63.615
	R-TSPKP	Ts1-S17-S18-S19	S13	S10-S11-S12-S16-Enf	0.048	0.969	0	63.449
	R-GA	Ts1-S17-S18-S19	S13	S12-S10-S11-S16-Enf	0.048	1.038	0	63.615
Case 7 (Tdp = 12, Tip = 5, Tdr = 10.81, Tir = 1)	NG-TSPKP	Ts1-S17-S18	S11-S10-S12-S13	S19-S16-Enf	3.07	0.972	0	63.449
	G-GA	Ts1-S19-S16	S13-S12-S10-S11	S17-S18-Enf	3.07	1.166	0	63.615
	R-TSPKP	Ts1-S17-S18	S11-S10	S12-S13-S19-S16-Enf	0.997	0.972	0	63.449
	R-GA	Ts1-S19-S16	S11-S10	S17-S18-S12-S13-Enf	0.997	1.066	0	63.615
Case 8 (Tdp = 14, Tip = 9, Tdr = 15.81, Tir = 1)	NG-TSPKP	Ts1-S17-S18-S19-S16	S11-S10-S12-S13	Enf	3.07	0	2.031	65.480
	G-GA	Ts1-S17-S18-S19-S16	S13-S12-S10-S11	Enf	3.07	0	1.862	65.477
	R-TSPKP	Ts1-S17-S18-S19-S16-S11-S10	S12	S13-Enf	0.025	0.184	0.218	63.667
	R-GA	Ts1-S17-S18-S19-S16-S13-S12	S10	S11-Enf	0	0.135	0	63.615
Case 9 (Tdp = 16, Tip = 8, Tdr = 11.81, Tir = 6)	NG-TSPKP	Ts1-S18-S17-S19-S16-S11-S10	S12-S13	Enf	0	3.633	3.927	67.376
	G-GA	Ts1-S17-S18-S19-S16	S13-S12-S10-S11	Enf	0	2.138	1.93	65.545
	R-TSPKP	Ts1-S18-S17-S19	S11-S10-S12-S13	S16-Enf	0	0.969	1.93	65.379
	R-GA	Ts1-S17-S18-S19	S13-S12-S10-S11	S16-Enf	0	1.038	1.93	65.545
Case 10 (Tdp = 14, Tip = 8, Tdr = 11.81, Tir = 6)	NG-TSPKP	Ts1-S17-S18-S19-S16	S11-S10-S12-S13	Enf	0	1.969	1.93	65.379
	G-GA	Ts1-S17-S18-S19-S16	S13-S12-S10-S11	Enf	0	2.138	1.93	65.545
	R-TSPKP	Ts1-S17-S18-S19	S11-S10-S12-S13	S16-Enf	0	0.969	1.93	65.379
	R-GA	Ts1-S17-S18-S19	S13-S12-S10-S11	S16-Enf	0	1.038	1.93	65.545
Case 11 (Tdp = 17, Tip = 5, Tdr = 10.81, Tir = 1)	NG-TSPKP	Ts1-S17-S18-S19-S16-S11-S10-S12	S13	Enf	0.048	5.991	0	63.449
	G-GA	Ts1-S17-S18-S19-S16	S13-S12-S10-S11	Enf	3.07	3.138	0	63.615
	R-TSPKP	Ts1-S17-S18	S13	S11-S10-S19-S16-Enf	0.048	0.972	0	63.449
	R-GA	Ts1-S17-S18	S13	S12-S10-S11-S19-S16-Enf	0.048	1.041	0	63.615
Case 12 (Tdp = 14, Tip = 7, Tdr = 19.91, Tir = 2)	NG-TSPKP	Ts1-S17-S18-S19-S16	S11-S10-S12-S13	Enf	2.07	0	6.131	69.580
	G-GA	Ts1-S17-S18-S19-S16	S13-S12-S10-S11	Enf	2.07	0	5.962	69.577
	R-TSPKP	Ts1-S18-S17-S19-S16-S11-S10-S12-S13	N/A	Enf	0	0	2.061	67.510
	R-GA	Ts1-S17-S18-S19-S16-S13-S12-S10-S11	N/A	Enf	0	0	3.891	67.507
Case 13 (Tdp = 10, Tip = 5, Tdr = 10.81, Tir = 1)	NG-TSPKP	Ts1	S11-S10-S12-S13	S18-S17-S19-S16-Enf	3.07	0	1	64.449
	G-GA	Ts1	S11-S10-S12-S13	S17-S18-S19-S16-Enf	3.07	0	0.831	64.446
	R-TSPKP	Ts1-S17	S11-S10	S12-S13-S18-S19-S16-Enf	0.997	0.167	0.187	63.636
	R-GA	Ts1-S17	S11-S10	S18-S19-S16-S12-S13-Enf	0.997	0.149	0	63.615
Case 14 (Tdp = 16, Tip = 8, Tdr = 10.81, Tir = 1)	NG-TSPKP	Ts1-S17-S18-S19-S16-S11-S10	S12-S13	Enf	1.073	4.966	0	63.449
	G-GA	Ts1-S17-S18-S19-S16	S13-S12-S10-S11	Enf	3.07	3.138	0	63.615
	R-TSPKP	Ts1-S17-S18	S12	S11-S10-S13-S19-S16-Enf	0.025	0.972	0	63.449
	R-GA	Ts1-S17-S18	S13	S12-S10-S11-S18-S19-S16-Enf	0.048	1.041	0	63.615
Case 15 (Tdp = 14, Tip = 7, Tdr = 11.81, Tir = 5)	NG-TSPKP	Ts1-S17-S18-S19-S16	S11-S10-S12-S13	Enf	0	1.969	0.93	64.379
	G-GA	Ts1-S17-S18-S19-S16	S13-S12-S10-S11	Enf	0	2.138	0.93	64.545
	R-TSPKP	Ts1-S17-S18-S19	S11-S10-S12-S13	S16-Enf	0	0.969	0.93	64.379
	R-GA	Ts1-S17-S18-S19	S13-S12-S10-S11	S16-Enf	0	1.038	0.93	64.545
Case 16 (Tdp = 11, Tip = 5, Tdr = 10.81, Tir = 2)	NG-TSPKP	Ts1-S18	S11-S10-S12-S13	Enf	2.07	0	0.008	63.457
	G-GA	Ts1-S16	S11-S10-S12-S13	S17-S18-S19-Enf	2.07	0.169	0	63.615
	R-TSPKP	Ts1-S18-S17	S11-S10-S12	S13-S16-S19-Enf	1.02	0.972	0	63.449
	R-GA	Ts1-S16-S17	S11-S10-S12	S18-S19-S13-Enf	1.022	1.141	0	63.615
Case 17 (Tdp = 12, Tip = 8, Tdr = 15.81, Tir = 6.1)	NG-TSPKP	Ts1-S17-S18	S11-S10-S12-S13	S19-S16-Enf	2.03	0	4.028	69.507
	G-GA	Ts1-S19-S16	S13-S12-S10-S11	S17-S18-Enf	0	0	5.864	69.479
	R-TSPKP	Ts1-S17-S18-S19-S16-S11-S10	S13-S12	Enf	0	0.181	4.027	67.691
	R-GA	Ts1-S19-S16-S17-S18-S13-S12	S10-S11	Enf	0	0.135	4.027	67.670
Case 18 (Tdp = 11, Tip = 10, Tdr = 16.813, Tir = 11.1)	NG-TSPKP	Ts1-S18	S11-S10-S12-S13	S17-S19-S16-Enf	0	0	13.04	76.487
	G-GA	Ts1-S16	S13-S12-S10-S11	S17-S18-S19-Enf	0	0	12.864	76.479
	R-TSPKP	Ts1-S18-S17-S19-S16-S11-S10-S12	S13	Enf	0	0.186	10.050	73.696
	R-GA	Ts1-S16-S17-S18-S19-S11-S10-S12	S13	Enf	0	0.157	10.051	73.719
Case 19 (Tdp = 13, Tip = 8, Tdr = 10.813, Tir = 1)	NG-TSPKP	Ts1-S18-S17-S19	S11-S10-S12-S13	S16-Enf	3.07	1.969	0	63.449
	G-GA	Ts1-S18-S19-S16	S13-S12-S10-S11	S17-Enf	3.07	2.155	0	63.615
	R-TSPKP	Ts1-S17-S18	S11-S10	S12-S13-S19-S16-Enf	0.997	0.972	0	63.449
	R-GA	Ts1-S18-S19	S11-S10	S17-S12-S13-S16-Enf	0.997	1.055	0	63.615
Case 20 (Tdp = 20, Tip = 9, Tdr = 11.813, Tir = 1)	NG-TSPKP	Ts1-S17-S18-S19-S16-S11-S10-S12-S13	N/A	Enf	0	6.039	1	64.449
	G-GA	Ts1-S17-S18-S19-S16	S11-S10-S12-S13	Enf	3.07	2.135	0	63.615
	R-TSPKP	Ts1-S17-S18-S19	S11-S10	S12-S13-S16-Enf	0.997	0.969	0	63.449
	R-GA	Ts1-S17-S18-S19	S11-S10	S12-S13-S16-Enf	0.997	1.135	0	63.615

of the same study [10]. The first level, performed offline to anticipate human behavior, is presented in Section 4.3. The second level, performed online to dynamically adjust the plan in response to actual human interventions, is presented in Section 4.4. The results obtained from this global optimization approach are compared to those from the non-global strategy presented in Section 4.5.

4.1. Parameters and Comparison Metrics

Before presenting the results of the comparison between the two optimization approaches, it is essential to define the different parameters and task sets used, such as:

-Ts1: includes tasks that must be performed before the human partner is allowed to enter the workspace. Task set Ts1 was defined as follows: S1-S3-S2-S4-S5-S6-S8.

-Enf: includes tasks that must be performed after the human partner leaves the workspace. Task set Enf was defined as follows: S14-S15-S20-S21-S26-27-S28-S29-S22-S23-S24-S25-S30-S31-S9-S32-S33.

The genetic algorithm operates mainly on the flexible middle part between Ts1 and Enf, where the order of tasks can change depending on time constraints and human availability. The crossover and mutation operators are designed to maintain feasibility and help find the best disassembly schedule. Regarding the stopping condition, it is based on reaching a specific fitness level or a maximum number of generations.

Both optimization algorithms consider two key parameters: the expected time of availability for the human to enter the workspace and the expected duration of the intervention. However, the actual behavior of humans may not match the forecasts, which requires adapting the planning in response to these unforeseen events. In each case studied, the times and durations of actual human intervention were integrated into the simulation, and the optimization algorithm was evaluated based on real data in contrast to the forecasts. This allowed us to measure how the algorithm, designed based on expected times, behaves when faced with different real conditions. To conduct a comparative study between the two approaches, specific parameters are defined to verify the flexibility and adaptability of each approach.

For comparison purposes, the metrics presented below have been calculated:

-SoiH: Human worker activity time. Given their significant importance in industry, it is essential to minimize these periods of inactivity.

-TsiR: total robot inactivity time, referring to the extended time during which the robot is stopped.

-Tpro: total production time.

-Texh: time during which the robot continues to perform the task in the collaborative mode after the human leaves. This time was measured from the moment the human left the workspace until the end of the task.

The diagram in Figure 4 provides a visual analysis of the metrics employed to compare the two optimization strategies.

These metrics assess the differences between the planned schedule and the actual execution, considering human availability and intervention duration. These deviations are primarily due to the unpredictability of human actions, which impacts synchronization with the robot. In this example, the human idle time (SoiH) is zero because the human operator is immediately available without a waiting period. However, the delay caused by humans led to robot stoppage (TsiR), preventing the simultaneous start of tasks S13, S11, and S12 as initially planned. The robot had to wait for human arrival to begin these tasks. Furthermore, the Texh metric represents the time during which the robot continues to work collaboratively after a human exits the workspace. As the real human intervention time (Tir = 2) was shorter than the expected human intervention time (Tip = 3), tasks S13 and S11 were completed in the presence of humans. However, task S12, which was initially planned as a collaborative task, was partially completed without a human and its duration corresponded to that of Texh. Finally, human delay resulted in an extension of the total production time, T_pro, exceeding T_final, which represents the production duration initially planned in the predictive schedule.

4.2. Comparison Results of Two Optimization Approaches

To evaluate the performance of the developed genetic algorithm and the TSP–KP approach, which divides the problem into several independent subproblems, 20 case studies were analyzed and are presented in Table 4. These cases, also discussed in [10] using the same durations of the tasks of the disassembly graph, provide a basis for comparing the two optimization approaches. This comparison highlights the significant differences in methodology, flexibility, and results obtained by the two approaches at predictive and reactive levels.

In each case study, four distinct results were presented to compare the performances of the predictive and reactive approaches:

-NG-TSPKP represents the non-global TSP–KP approach, which divides the problem into several independent subproblems. This method is described in detail in [10].

-GGA: denotes the global approach utilizing a genetic algorithm for optimization, which is also discussed in the aforementioned article.

-R-TSPKP: reflects the reactive version of the TSP–KP approach, adapting disassembly sequences in real time based on actual human intervention times.

-R-GA: This presents the results of the reactive approach employing a genetic algorithm, allowing the dynamic adaptation of disassembly sequences in response to real-time human intervention.

These four approaches are compared to evaluate their effectiveness in human–robot collaboration contexts, considering variations in human intervention times and the necessity to adapt disassembly sequences accordingly.

4.3. Analysis of Predictive Approach Results

The global optimization approach is distinguished by the fact that it seeks to optimize the solution, considering all tasks and their interactions throughout the process, rather than dividing the problem into several specific subproblems. The genetic algorithm relies on the generation of an initial population of possible paths, followed by a series of mutations and crossovers to explore different task orders. This means that the algorithm evaluates and optimizes the order of all tasks together, verifying that the precedence rules are respected and that the global path minimizes the total execution time. The mutation and crossover operations in the algorithm are applied to the set of tasks of each proposed disassembly sequence. This contrasts with the non-global approach presented, which treats each segment of the problem independently [10]. In Case Study 2, the differences between the non-global TSP–KP and global genetic optimization approaches revealed distinct strategies for task optimization before human intervention and during collaboration. For comparative purposes, we focus on this specific case, as illustrated in Figure 5, based on the results presented in Table 4.

The TSP–KP approach formulates the problem using a model similar to the knapsack problem, in which each task is treated as an object to be added into a knapsack, represented here by the time available before human intervention. After completing the necessary tasks in set TS1 prior to human involvement, the non-global TSP–KP approach selects additional tasks to maximize time utilization without exceeding the planned availability of the human. This selection process results in only task S13 being available for execution in parallel with the human task. This planning optimizes the use of the available time by allowing the robot to complete the maximum number of tasks before the arrival of the human while adhering to predefined time constraints. However, if the human arrives earlier than expected, it can lead to an increase in human idle time because the human may have to wait for the robot to complete its scheduled tasks based on the predictive availability plan.

By contrast, the genetic approach employs a different strategy by prioritizing tasks that do not pose any risk to humans before collaboration, thereby optimizing the available time to perform all tasks in parallel during their presence, as shown in Figure 6.

This method significantly reduces the idle time of the robot compared with the TSP–KP approach and minimizes the human waiting time to access the workspace. Once non-parallel tasks are completed, both humans and robots can proceed with their tasks in parallel.

Consequently, the global genetic approach demonstrates superior optimization of the total production time compared with the non-global TSP–KP approach. This highlights the importance of integrating strategies that not only maximize task execution before collaboration but also ensure seamless parallelism during human–robot interaction to enhance overall efficiency.

After analyzing the optimization strategies of both approaches, the non-global TSP–KP and global genetic methods, the results from 20 comparative cases are presented for each metric. These plots provide a detailed view, enabling the analysis and interpretation of the observed discrepancies between the two optimization approaches at the predictive level for each specific case.

-

Collaborative Work Time Texh:

The metric Texh represents the duration during which the robot continues to operate in the collaborative mode after the human has left the workspace. As observed in Figure 7, the genetic algorithm consistently exhibits higher Texh values than the TSP–KP approach in cases 1, 3, 4, 5, 6, 11, 14, and 20. This increase in Texh occurred when the actual intervention time differed from the planned time. The genetic approach prioritizes the parallel execution of tasks between the human and robot to minimize the downtime and optimize the total production time. However, when the real intervention time Tir is shorter than the planned intervention time Tip, the robot continues to operate in the collaborative mode even after the human has exited the workspace. This behavior results in an elevated Texh value. A detailed analysis of these specific cases revealed that, in each instance, the actual intervention time was shorter than the planned time, as indicated in Table 4, thus explaining the observed increase in Texh with the genetic approach.

-

Human idle time:

As shown in Figure 8, the genetic algorithm demonstrates better optimization of this metric in Cases 2, 5, 6, 9, 14, and 20. In these instances, the actual availability time is shorter than the planned availability time, as indicated in Table 4. The genetic algorithm employs a distinct optimization strategy compared to the TSP–KP approach, aiming to maximize task execution as long as their inclusion remains within the planned availability time of the human.

This strategy explains the increase in human idle time SoiH with the TSP–KP approach, as humans are often forced to wait for the completion of tasks scheduled before their presence, according to the predictive plan.

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Robot idle time:

In Cases 2, 9, and 20, where a difference was observed between the two optimization approaches, the variation arose from the early arrival of the human operator. The global genetic approach prioritizes the execution of tasks that can be performed simultaneously in the presence of humans. When a human arrives earlier than planned, the robot continues to execute tasks scheduled by the predictive approach before human entry into the workspace. Once the human is allowed to enter, the robot operates seamlessly, completing tasks that can be performed in parallel with human presence. Conversely, the TSP–KP approach maximizes the utilization of the available time by performing tasks that are scheduled to wait for humans based on their planned availability. However, if the human arrives earlier than expected, the robot completes the set of tasks planned before the human enters and then idles, waiting for the human to complete the task. This results in a period of robot inactivity, because tasks that could have been executed during human presence have already been completed in their absence, such as described in Figure 9.

This explains the differences observed in the robot idle time between the two approaches: the non-global TSP–KP and global genetic approaches. In the TSP–KP approach, the robot often waits for the human after completing all possible tasks prior to their arrival. By contrast, the global genetic approach allows the robot to continue working in parallel with the human, thereby minimizing the idle time of the robot.

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Production time:

As observed in Figure 10, despite the different planning strategies between the two optimization approaches, the total production time remains largely comparable. However, in cases 2, 9, and 20, the genetic algorithm demonstrated superior performance when the human operator arrived earlier than planned. This improvement is attributed to the optimization of the robot idle time in these specific cases, which contributes to the enhanced overall production time optimization.

The first hypothesis suggests that optimization results can be improved using a global approach rather than a non-global method that decomposes the problem into several independent subproblems, as presented in [10]. A comparative analysis of certain case studies reveals that while the TSP–KP approach maximizes robot utilization time before human arrival, it may also result in extended idle periods for both the human and the robot in cases of early human arrival, an issue less pronounced with the global genetic algorithm. These findings partially validate the first hypothesis. Indeed, the global genetic approach demonstrated better optimization of the total production time and idle times in scenarios where humans intervened earlier than expected. However, when the actual human intervention time is shorter than anticipated, it can lead to extended collaborative work periods even after the human has left. These observations underscore the need to develop a reactive approach capable of dynamically readjusting task sequences in real-time to accommodate the unpredictable nature of human intervention.

4.4. Analysis of Reactive Approach Results

Although the global genetic approach has demonstrated superior optimization of production time and idle periods in scenarios involving early human intervention, it exhibits limitations when the human presence is shorter than anticipated. This situation can lead to extended collaborative work periods even after a human has departed, highlighting the necessity for a reactive approach capable of real-time adjustment of planning sequences to accommodate variations in human intervention. To address this requirement, the following section analyses the results obtained through the reactive approach designed to complement the predictive strategy. To evaluate the effectiveness of the reactive approach compared with the predictive approach, the percentage differences were calculated for each comparison metric using Equation (16).

$$Percentagediff.={\displaystyle \frac{Predictive time-Reactive time}{Predictive time}} \times 100\%$$

(16)

Subsequently, the average of these percentages was computed for each metric to provide an overall performance improvement for both the approaches in the developed genetic algorithm. The results are presented in

Table 5. Percentage Differences Between Predictive and Reactive Approaches.

Metric	Percentage Difference
Collaboration Time Texh	98.63%
Human Idle Time	93.15%
Robot Idle Time	69.58%
Production Time	2.07%

.

The reactive approach demonstrated significant improvements in most performance metrics. Notably, the collaborative work time without human presence (Texh) was reduced by 98.63%, indicating that dynamic sequence adjustments effectively minimized the tasks initially planned for human–robot collaboration. Upon detecting the departure of a human, the robot completes the ongoing non-preemptive task in the collaborative mode before transitioning to autonomous operation. Similarly, the human idle time decreased by 93.15% as the robot promptly concluded its current task upon detecting the human presence, allowing the human to engage without undue waiting. The robot idle time also saw a 69.58% reduction, reflecting enhanced synchronization with the actual human availability. Despite the different planning strategies of the predictive and reactive approaches, the total production time exhibits only a slight increase. This outcome is primarily influenced by the idle periods of the robots, which can occur because of delays in human availability or extended durations of human intervention. The reactive approach dynamically adjusts task sequences based on real-time human availability and assigns tasks to the robot to minimize idle time. These findings validate our second hypothesis. This optimization effectively reduced the inactivity of the robot, thereby slightly improving the total production time in specific scenarios.

4.5. Comparative Study of Two Optimization Approaches

This section presents a comparative analysis of two optimization strategies: the non-global approach, as detailed in reference [10], and the global approach developed within this research project, examined from a reactive perspective. The outcomes from 20 comparative case studies are illustrated to analyze and interpret the differences observed between the global genetic algorithm and the non-global TSP–KP approach in each specific scenario.

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Collaborative Work Time (Texh):

Figure 11 demonstrates that both optimization approaches yield similar results concerning collaborative work time (Texh) after the human exits the workspace. This similarity indicates that despite employing different predictive planning strategies, both the global genetic algorithm and non-global TSP–KP approach effectively adjust the robot’s operating mode based on the actual timing of human intervention. Upon detecting the departure of a human, both methods automatically switch the robot to the autonomous mode.

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Human idle time:

The comparative analysis depicted in Figure 12 reveals that both the global genetic algorithm and non-global TSP–KP approach yield remarkably similar results concerning human idle time (SoiH). This convergence suggests that despite employing different predictive optimization strategies, both methods effectively adjust their task sequences in real time based on the actual availability of the human operator. Consequently, they facilitate the timely entry of humans into the collaborative workspace to perform their tasks, thereby minimizing periods of inactivity.

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Robot idle time:

Interpreting this comparative curve in Figure 13 shows that the results are very similar for both optimization approaches, namely, the global genetic approach and the non-global TSP–KP approach, regarding the robot idle time (T_pro). This suggests that although the two methods adopt different optimization strategies (global genetic versus non-global TSP–KP) from a predictive perspective, they tend to achieve comparable results when dynamically adjusting their decisions based on actual human availability times.

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Production time:

As the robot idle time curves were equivalent, Figure 14 demonstrates that for most of the tested scenarios, both optimization approaches yield similar results in terms of production time. This indicates that, in these situations, both algorithms employed comparable scheduling strategies to optimize the production time. Consequently, these results support the third hypothesis, which posits that both approaches achieve similar outcomes through dynamic scheduling, which adjusts task sequences based on the actual availability of the human operator.

5. Discussion

The integration of collaborative robots into industrial settings has raised the question of how to effectively utilize both partners to optimize the total time of the disassembly process [10]. The global optimization approach aims to optimize the solution as a whole, considering all tasks and their interactions throughout the process rather than dividing the problem into multiple specific subproblems. The genetic algorithm operates by generating an initial population of possible task sequences, followed by a series of mutations and crossovers to explore various task orders. This means that the algorithm evaluates and optimizes the order of all tasks collectively, ensuring that the precedence rules are respected and that the global sequence minimizes the total execution time. Mutation and crossover operations were applied to all the tasks within each proposed disassembly sequence. This contrasts with the non-global approach presented in [10], which treats each segment of the problem independently. Based on the obtained results, this algorithm successfully optimized the task sequences by exploring all possible solutions to minimize the total disassembly time.

The first hypothesis posits that the optimization results can be improved using a global approach rather than a non-global approach that divides the problem into several independent subproblems. An analysis of certain comparative cases reveals that while the TSP–KP approach maximizes the robot utilization time before the human’s arrival, it can lead to extended idle periods for both the human and the robot in cases of early arrival, unlike the global genetic approach. This partially validates the first hypothesis. Specifically, the global genetic approach better optimized the total production time and reduced idle times in scenarios in which humans arrived earlier than expected. The improved performance of the genetic approach, especially when the human arrives earlier than expected, comes from its adaptive task allocation strategy. Instead of trying to fill the robot’s schedule as much as possible before the human arrives (as in the TSP–KP approach), the genetic algorithm intentionally delays some non-risky parallel tasks, keeping them available to be executed during human presence. This scheduling choice allows the system to immediately transition to collaborative work if the human arrives early instead of forcing them to wait for the robot to finish pre-planned tasks. As a result, both the human idle time and the total production time are reduced. By contrast, the TSP–KP strategy is based on a knapsack-like formulation. It selects tasks to maximize robot utilization before expected human arrival. It selects tasks based on predicted human availability, and selects tasks whose addition maximizes time utilization without exceeding the expected human availability. However, if this prediction is incorrect and the human intervenes too early, there is often nothing left to do but wait. The genetic algorithm avoids this by developing schedules that are resilient to uncertainty in the case of early arrival. However, when a human spends less time than anticipated, this can result in an increase in collaborative work time, even after the human leaves the workspace. These observations underscore the need to develop a reactive approach capable of dynamically readjusting task sequencing in real time to adapt to the changing dynamics of human intervention. The integration of a reactive approach that adjusts work sequences in real time based on the actual availability of the human operator is essential for optimizing the process.

The second hypothesis, which stipulated that the reactive approach would improve the optimization results by considering variations in actual human intervention times, was validated through the results obtained. The simulations showed a significant reduction in idle time for both the operator and the robot, confirming the effectiveness of the reactive approach.

Furthermore, the third hypothesis, which suggests that the results of the two approaches, global genetics and TSP–KP, would be equivalent because of dynamic programming, was confirmed. As indicated by the comparative curves, the two methods achieved similar results across the four metrics. The results of this study provide interesting perspectives for the optimization of collaborative processes in the fields of remanufacturing and disassembly. Future research could focus on integrating machine learning mechanisms to refine algorithm responsiveness based on the past behavior of human operators. This would further improve the prediction of human response times and anticipate unforeseen events with greater accuracy.

6. Conclusions and Future Work

Recent advances in robotics have significantly promoted the close collaboration between humans and robots in shared work environments. In particular, optimization of the electric vehicle battery disassembly process is crucial for improving the efficiency and profitability of this essential recycling step. Therefore, this study focuses on developing a global optimization approach to efficiently manage the variability of human interventions by integrating a genetic algorithm capable of adapting to unpredictable intervention times and durations. The first objective of this study was to formulate a global problem and solve it using an appropriate optimization algorithm. In this framework, the genetic algorithm proved to be relevant for dealing with dynamic and complex scenarios. Furthermore, the comparison between a global approach and a non-global approach based on the division of the problem into independent subproblems made it possible to partially validate the first hypothesis. A study of some specific cases showed that the global genetic approach optimizes production time and inactivity periods better, especially when human intervention occurs earlier than expected. However, an increase in the robot’s working time in collaborative mode after human exit was observed when the duration of human intervention was less than anticipated, highlighting the need for a dynamic approach that accounts for the unpredictability of human behavior in real time. To address this challenge, this study introduces a reactive scheduling approach designed to dynamically adjust disassembly sequences based on the actual availability of human operators. By complementing the predictive planning method, the reactive approach effectively addresses its limitations, leading to notable improvements in system performance. This validates the second hypothesis, confirming the efficacy of integrating reactive strategies into human–robot collaborative tasks. Furthermore, comparative analyses between the global genetic algorithm and the non-global TSP–KP method, both operating in reactive mode, revealed similar outcomes despite their differing initial predictive strategies. This observation supports the third hypothesis, suggesting that, while these approaches diverge in predictive planning, they converge towards comparable strategies when adapting to real-time human interventions.

This study has successfully demonstrated the efficacy of genetic algorithms in optimizing battery disassembly sequences, with a focus on time efficiency for both human and robotic operations. However, several critical avenues remain to be explored to enhance the industrial robustness and sustainability of the proposed framework. First, the current approach does not incorporate the energy consumption or throughput costs during disassembly. Integrating these metrics into the fitness function would enable more comprehensive optimization, particularly relevant for large-scale industrial applications where energy efficiency is a key concern. Second, although the genetic algorithm framework is inherently adaptable to various battery geometries and brands, this research has been limited to a single use case. Future studies should investigate a diverse taxonomy of battery designs from multiple manufacturers. This would involve constructing a scalable library of graph-based models to evaluate the adaptability of the algorithm across significant variations in the component layout, connection hierarchies, and structural geometries. To address the combinatorial complexity of disassembling multi-batteries, multi-humans, high-density, and multi-module battery packs, future efforts may explore parallel and distributed genetic algorithm implementations, such as the Island Model. These approaches can significantly accelerate the search for optimal disassembly plans while maintaining solution diversity. Moreover, the dynamic nature of disassembly environments, characterized by fluctuating labor costs, recycling market values, and operational conditions, suggests the need for real-time adaptive optimization. Hybrid approaches that combine genetic algorithms with online learning or reinforcement learning can enhance responsiveness to changing variables. Such systems can dynamically adjust the disassembly sequences based on real-time sensor data (e.g., thermal state and component degradation) or operational feedback (e.g., tool wear). Finally, expanding the optimization framework to support multi-objective optimization would allow for a balanced consideration of material recovery rates (in terms of both quality and volume), environmental impact (e.g., carbon footprint and hazardous waste generation), and the existing time and energy metrics. This would enable the generation of Pareto-optimal disassembly strategies that promote both operational efficiency and sustainable resource circulation.

7. Limit of the Study

This study presents a planning framework tailored for optimization problems involving human interventions at specific yet unpredictable times. The results demonstrate that both predictive and reactive implementations of the global genetic algorithm effectively optimize the disassembly process, accommodating the inherent unpredictability of human behavior. However, certain limitations warrant further discussion to enhance the robustness and applicability of these findings. The current model assumes a simplified operational environment with a single robot, conveyor, and battery, which may not fully represent the complexities of industrial settings that involve multiple robots, conveyors, or different battery geometries. Incorporating scenarios with multiple agents can provide insights into more adaptive solutions, particularly for managing idle times for both robots and humans. Additionally, the model does not account for the varying initial states of the disassembly process, such as partially disassembled batteries, which can significantly affect task sequencing and overall system performance. Future studies should explore these scenarios to assess the robustness of proposed solutions under diverse conditions. Moreover, this study considered only a single human intervention during the task scheduling. As battery technologies evolve, more complex scenarios may require multiple human interventions, which necessitates the integration of such dynamics into the planning framework. The variability in the robot execution speeds during collaborative tasks can also enhance the adaptability of the model. Finally, validating the proposed architecture in a real-world industrial context is crucial. Conducting user studies in a practical setting provides a comprehensive evaluation of their potential and effectiveness in real-world applications.

In summary, this research advances the field of human–robot collaborative disassembly processes by introducing a reactive planning approach that enhances the system performance and adaptability. This also lays the groundwork for future studies aimed at addressing the identified limitations and expanding the applicability of the proposed method.