Disassembly Sequence Planning for Green Remanufacturing Using an Improved Whale Optimisation Algorithm

: Currently, practical optimisation models and intelligent solution algorithms for solving disassembly sequence planning are attracting more and more attention. Based on the importance of energy efﬁciency in product disassembly and the trend toward green remanufacturing, this paper proposes a new optimisation model for the energy-efﬁcient disassembly sequence planning. The minimum energy consumption is used as the evaluation criterion for disassembly efﬁciency, so as to minimise the energy consumption during the dismantling process. As the proposed model is a complex optimization problem, called NP-hard, this study develops a new extension of the whale optimisation algorithm to allow it to solve discrete problems. The whale optimisation algorithm is a recently developed and successful meta-heuristic algorithm inspired by the behaviour of whales rounding up their prey. We have improved the whale optimisation algorithm for predation behaviour and added a local search strategy to improve its performance. The proposed algorithm is validated with a worm reducer example and compared with other state-of-the-art and recent metaheuristics. Finally, the results conﬁrm the high solution quality and efﬁciency of the proposed improved whale algorithm.


Introduction
The growth of manufacturing uses a large number of energy resources.It generates many end-of-life products, such as electronics, vehicles, and industrial equipment, often containing valuable components and materials that can be reused or recycled [1].Recycling these products helps reduce the extraction of raw materials and energy consumption and promotes sustainable manufacturing.Disassembly is a necessary process in the remanufacturing of end-of-life products.The components' disassembly sequence directly impacts disassembly efficiency and recycling effectiveness.Thus, the disassembly sequence scheme is critical to recycling end-of-life products.An optimal or near-optimal disassembly solution should be determined to maximise the value recovery of end-of-life products [2].This decision process is known as disassembly sequence planning (DSP).Disassembly sequence planning is an essential part of the product disassembly research.In the disassembly sequence planning problem, there are three core issues:

•
Modelling of product disassembly information.

•
Solution strategies for the disassembly sequence.
• Evaluation and optimisation of the disassembly sequence.
Considering the impact of energy efficiency on DSP, this work is one of the first studies dedicated to energy-efficient DSP to minimise the energy consumption generated during disassembly operations.As a complex optimisation problem known as NP-hard [3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22], no single optimisation algorithm can solve all the latest issues, according to the non-free lunch theory of optimisation problems [23].The main contribution of this paper is to propose an improved metaheuristic algorithm based on the whale optimisation algorithm, a recently developed and successful metaheuristic method inspired by the hunting behaviour of humpback whales, i.e., encircling prey, foaming net attack, and searching for predation operations.It is clear from the literature analysis that this metaheuristic algorithm has not been applied to solve DSP problems before.In this paper, we used it and compared it with existing techniques and other metaheuristic algorithms that are more recent.
The rest of the paper is organised as follows.Section 2 is a literature review of recent studies in the field of DSP.Section 3 describes the construction of the disassembly model.Section 4 describes the improved whale optimisation algorithm.Section 5 provides an extensive case study to verify the feasibility of our proposed method and a comparative analysis with other methods.The final section summarises the full text, including our findings, limitations, and an analysis of future research directions for the DSP problem.

Literature Review
With the development of green remanufacturing, DSP is attracting more and more attention.Early research on the DSP focused on graph theory [3].Henriound et al. describe the links between product structures using association graphs [4].Lambert uses a graphical approach based on AND/OR graphs to produce optimal disassembly sequences [5].Tian et al. combine conflict matrices and AOG graphs to make them more widely applicable [6].Huang et al. improve the disassembly matrix model by using it to obtain disassembly sequences quickly and efficiently [7].Mitrouchev et al. produce disassembly hybrid graphs after grading product parts to exclude parts that do not need to be disassembled, improving disassembly efficiency [8].Smith and Chen plan the disassembly of products based on specific rules [9].
However, as product manufacturing processes become more complex, they contain more and more parts.DSP evolves into an NP-hard combinatorial optimisation problem [10], prompting the use of intelligent optimisation methods with high solution speed and easy parameter tuning [11].Rickli and Camelio discuss the DSP problem, considering cost, revenue, and environmental impacts, and propose an improved genetic algorithm that effectively improves the efficiency of the solution search [12].Liu et al. obtain the optimal disassembly sequence with an improved maximum minimal ant system (MMAS) [13].Kheder et al. compare the differences between ant colony and genetic algorithms for the DSP problem [14].Tseng et al. apply five different ant colony algorithms to the DSP problem [15].Hwai-En Tseng et al. propose a flatworm algorithm to solve demolition sequence planning problems.Test results demonstrate that their new flatworm algorithm outperforms two genetic and ant colony algorithms regarding solution quality [16].Tian et al. improve the multi-criteria decision-making method by combining fuzzy AHP and fuzzy G-TOPSIS to provide a new idea for evaluating automotive parts remanufacturing [17].Wang et al. propose a disassembly sequence planning model considering energy consumption and solve it with an improved artificial bee colony algorithm [18].Yang et al. study and analyse the DSP problem for used agricultural machines and propose a multiobjective disassembly line balancing fruit fly optimisation algorithm [19].Parsa et al. define a new optimisation parameter approach for disassembly methods and requirements of the same used product in different states [20].Bentaha et al. develop a decision tool for deciding on the best disassembly solution and depth in the case of end-of-life product quality changes [21].Babbitt et al. collect quality information on the primary materials and components contained in a wide range of used electronics and build a complete database of the bill of materials (BOM) data for the disassembly and recycling of used electronics [22].
The first finding from the literature review was that few energy-efficient DSP models had been formulated in the literature.Another result is that although many metaheuristics (e.g., ABC, ACO, and GA) have been applied to solve DSP problems; the whale optimisation algorithm (WOA), a recently developed metaheuristic, has never been used in this research area.WOA was inspired by whales by Mirjalili et al. [24] and is based on simulating the predatory behaviour of humpback whales in nature by search, encirclement, chase, and attack processes to optimise tracking.The WOA has been successfully applied to a variety of optimisation problems with various improvements.Ma et al. propose an improved multithreshold image segmentation method based on the whale optimisation algorithm (RV-WOA) using the inter-class variance (Otsu method) as the objective function [25].Kaur et al. introduce chaos theory into the WOA optimisation process and considered various chaos mapping WOA (CWOA) methods to adjust the main parameters [26].Nadimi-Shahraki et al. propose an enhanced whale optimisation algorithm based on a pooling mechanism and three efficient search strategies (migration, preferential selection, and enrichment of prey enclosures) to detect coronavirus disease 2019 (COVID-19) disease, and the algorithm is proved to be highly efficient in searching the problem space and selecting the most efficient features [27].To address the problem that WOA tends to converge prematurely, Tong et al. design a hybrid WOA algorithm framework with learning and complementary fusion properties, combining WOA with complementary feature operators to improve its detection capability [28].To overcome the shortcomings of the WOA algorithm, an improved WOA algorithm (OCDWOA) was proposed by Liang et al.The four leading operators of the opposition-based learning method, non-linear parameter design, densitypeak clustering strategy, and differential evolution, were introduced in OCDWOA to enhance the search performance of WOA and apply it to seismic inversion problems [29].
In these areas, WOA has demonstrated its good stability and search capability [30].To our knowledge, there are no studies on applying WOA to DSP problems.WOA is robust, has easily tuneable parameters, and has powerful search capabilities.After testing WOA on our energy-efficient DSP model, we found that it can significantly improve disassembly efficiency and promote green remanufacturing.This paper proposes an improved WOA (IWOA), defining encoding methods incorporating DSP problem features to discrete its continuous search space.Two new strategies for whale predation prey are introduced to improve the quality and diversity of the solution sequence.A new local search strategy is proposed to improve the algorithm's accuracy.Finally, the effectiveness and practicality of the algorithm are investigated with an example of a worm-gear reducer.

Disassembly Hybrid Graph
To describe the connection and priority constraints between the various parts of the product, a hybrid disassembly graph is chosen to represent the product disassembly model [31].The disassembly hybrid graph describes the contact and constraint relationships between the parts and consists of several nodes, undirected edges, and directed edges combined according to certain rules.The basic product disassembly hybrid graph by the ternary group said, which is shown in Equation (1).
where G is a hybrid graph; V is a node, a product part or subassembly; if the product has n parts, then V = [v1, v2, vn]; E is an undirected edge; D is a directed edge.Figure 1 shows a hybrid disassembly graph for a product.The numbers in the circles represent the parts to be disassembled; the solid arrows E represent the direct existence of a priority constraint relationship between the two disassembly tasks; the task at the beginning of the arrow is the task immediately preceding the task at the end of the arrow, and the solid line D indicates the direct existence of a contact relationship between the two tasks.
where G is a hybrid graph; V is a node, a product part or subassembly; if the product has n parts, then V = [v1, v2, vn]; E is an undirected edge; D is a directed edge.Figure 1 shows a hybrid disassembly graph for a product.The numbers in the circles represent the parts to be disassembled; the solid arrows E represent the direct existence of a priority constraint relationship between the two disassembly tasks; the task at the beginning of the arrow is the task immediately preceding the task at the end of the arrow, and the solid line D indicates the direct existence of a contact relationship between the two tasks.To facilitate the disassembly analysis, the set of undirected edges E and the set of directed edges D are represented by the connection matrix C and the priority constraint matrix P. C corresponds to {V, E} and P to {V, D} [14].
when there is direct contact between parts i and part j.Cij = 0 when they are not in direct contact or when i = j.For example, in Figure 1, there is a direct contact relationship between disassembly task 4 and disassembly task 6, so C46 = 1 when part i is the immediately preceding task of part j; otherwise Pij = 0.For example, in Figure 1, disassembly task 5 needs to be performed before disassembly task 6, so P56 = 1.
A disassembly sequence requires that the part currently being disassembled must be available for disassembly.A detachable part is not subject to the priority constraints of other parts, i.e., it satisfies: and is only connected to one of the other parts, i.e., satisfied: To facilitate the disassembly analysis, the set of undirected edges E and the set of directed edges D are represented by the connection matrix C and the priority constraint matrix P. C corresponds to {V, E} and P to {V, D} [14].
when there is direct contact between parts i and part j.C ij = 0 when they are not in direct contact or when i = j.For example, in Figure 1, there is a direct contact relationship between disassembly task 4 and disassembly task 6, so C 46 = 1.
P ij = 1 when part i is the immediately preceding task of part j; otherwise P ij = 0.For example, in Figure 1, disassembly task 5 needs to be performed before disassembly task 6, so P 56 = 1.
A disassembly sequence requires that the part currently being disassembled must be available for disassembly.A detachable part is not subject to the priority constraints of other parts, i.e., it satisfies: and is only connected to one of the other parts, i.e., satisfied: The method for generating the disassembly sequence can be obtained based on the priority constraint matrix and the connection matrix.First, find the rows in the matrix that are disassemblable, select one of them at random and disassemble the part represented by that row; then, set all the columns corresponding to that row in the matrix to zero and remove that row; after that, repeat the above steps until both matrices are empty to generate a feasible disassembly sequence.

Proposed DSP Formulation
Past research on the DSP problem has focused on minimizing disassembly costs and disassembly time.This paper uses the energy consumption generated during disassembly as the evaluation criterion for disassembly efficiency [31].The dimensions of the standard energy consumption unified objective function for the disassembly tool and direction change are set, and the following mathematical model is constructed by combining the characteristics of the DSP problem.
where F is the energy consumption generated during disassembly, and e t is the energy consumption caused by a change in the disassembly tool, with a weighting factor of w t , if the disassembly tool is changed, t ij = 1, otherwise t ij = 0. e d is the energy consumption caused by a change in the disassembly direction, with a weighting factor of w d .If the disassembly direction is changed, d ij = 1, otherwise d ij = 0. e i is the energy consumption generated by the disassembly part itself, with a weighting factor of w i , g m is the difficulty of the disassembly task, and L is the fixed energy consumption generated during disassembly.

Original WOA
In the traditional WOA, which contains several stages of encircling prey, spiral bubbles, and finding prey, the search process starts with an initial set of random solutions (candidate solutions), which are then updated according to optimisation rules until the end conditions are satisfied [30].
The WOA algorithm assumes that the optimal solution is the location of the target prey and that other individual whales will attempt to update and proxy the relative position.The expression is shown in Equation (5).
where X* (t) is the optimal solution position; X(t) is the current position; t is the number of iterations; A and C are the adjustment coefficients, and A and C are denoted as: where: rand 1 and rand 2 are random real numbers in (0,1); a is a decreasing factor from 2 to 0. a is denoted as: where: Maxiter is the maximum number of population iterations.
The WOA algorithm divides the bubble net attack into a shrink-wrap mechanism and a spiral update mechanism.The shrink-wrap mechanism is shown in Equation ( 6), and the spiral update mechanism is shown in Equation (10).
cos θ(2πl) (10) where: l is the (−1, 1) random number, b is a constant indicating the logarithmic spiral shape, and D q is the distance between the whale and its prey, and the expression for D q is shown in Equation (11).
It is assumed that humpback whales when hunting target prey, choose by a 50% probability whether to contract the encirclement or spiral update mechanism to update the position.The specific expression is: cos θ(2πl), p 0.5 (12) Processes 2022, 10, 1998 Humpback whales can search randomly for targets within their range, as expressed in Equation (13).
where: X m (t) is the random position of the whale.

Improved WOA
We take the following steps to develop our proposed IWOA based on these WOA concepts and combine them with an integer encoding approach to make it suitable for the DSP problem: Step 1: Initialise the disassembly sequence.DSP is a discrete optimisation problem where the initial disassembly sequence must satisfy the disassembly ability of each part [32].The initial disassembly sequence is obtained according to the previous section's proposed method.After the initial disassembly sequence is generated, the corresponding sequence of each initial disassembly sequence is generated, such as a disassembly sequence with n parts, whose corresponding sequence is n minus its task number plus 1, after which the initial sequence and its corresponding sequence are mixed to select the initial population.Figure 2 shows a disassembly task with a total number of parts of 6.
the position.The specific expression is: Humpback whales can search randomly for targets within their range, as expressed in Equation (13).
where: Xm (t) is the random position of the whale.

Improved WOA
We take the following steps to develop our proposed IWOA based on these WOA concepts and combine them with an integer encoding approach to make it suitable for the DSP problem: Step 1: Initialise the disassembly sequence DSP is a discrete optimisation problem where the initial disassembly sequence must satisfy the disassembly ability of each part [32].The initial disassembly sequence is obtained according to the previous section's proposed method.After the initial disassembly sequence is generated, the corresponding sequence of each initial disassembly sequence is generated, such as a disassembly sequence with n parts, whose corresponding sequence is n minus its task number plus 1, after which the initial sequence and its corresponding sequence are mixed to select the initial population.Figure 2 shows a disassembly task with a total number of parts of 6. Step 2: Determining the head whale The best-adapted disassembly sequence from the initial population was selected as the head whale, after which the head whale was used for a subsequent attack and hunting.Step 2: Determining the head whale.The best-adapted disassembly sequence from the initial population was selected as the head whale, after which the head whale was used for a subsequent attack and hunting.
Step 3: Foaming net attack.This step redefines the way how the whale attacks its prey, updating the disassembly scheme with a new contractive approach and spiral position according to the characteristics of the DSP problem."a" (a decreases linearly from 2 to 0 inches) is introduced [24], as shown in Equation (9).Depending on the value of "a", the whale will choose one of the hunting methods.
The new disassembly sequence is formed by fusing the disassembly sequence X that needs to be updated with the head whale, selecting two points in the head whale and dividing it into three segments, choosing to take the middle segment as part of the updated disassembly sequence, and its left and right segments in reverse order of their position in X, as shown in Figure 3.
Processes 2022, 10, x FOR PEER REVIEW 7 of 16 Step 3: Foaming net attack This step redefines the way how the whale attacks its prey, updating the disassembly scheme with a new contractive approach and spiral position according to the characteristics of the DSP problem."a" (a decreases linearly from 2 to 0 inches) is introduced [24], as shown in Equation (9).Depending on the value of "a", the whale will choose one of the hunting methods.1) Shrink-wrapped approach.
The new disassembly sequence is formed by fusing the disassembly sequence X that needs to be updated with the head whale, selecting two points in the head whale and dividing it into three segments, choosing to take the middle segment as part of the updated disassembly sequence, and its left and right segments in reverse order of their position in X, as shown in Figure 3. 2) Spiral position updates.
As shown in Figure 4, a consecutive segment is selected in the disassembly sequence to be updated, another row is chosen randomly in the population, and a straight segment is also randomly selected in that sequence, after which the two schemes are each combined (2) Spiral position updates.
As shown in Figure 4, a consecutive segment is selected in the disassembly sequence to be updated, another row is chosen randomly in the population, and a straight segment is also randomly selected in that sequence, after which the two schemes are each combined into one continuous section to form the new disassembly sequence.2) Spiral position updates.
As shown in Figure 4, a consecutive segment is selected in the disassem to be updated, another row is chosen randomly in the population, and a stra is also randomly selected in that sequence, after which the two schemes are ea into one continuous section to form the new disassembly sequence.When |a| ≥ 1, the shrink-wrap method is selected to update the disassem When |a| < 1, the spiral position update is chosen to update the disassembly original scheme is replaced if the new updated scheme is more adaptive tha scheme.
Step 4: Search for predators The traditional whale predation approach is changed to a local search p prove the algorithm's accuracy.The optimal disassembly solution and the la disassembly solution for each population are searched, the existing disassem is compared with the resulting new disassembly solution, and the better s lected.Our proposed local search method randomly selects four points in sequence and performs an arbitrary swap of these four points, as shown in F When |a| ≥ 1, the shrink-wrap method is selected to update the disassembly scheme.When |a| < 1, the spiral position update is chosen to update the disassembly scheme.The original scheme is replaced if the new updated scheme is more adaptive than the original scheme.
Step 4: Search for predators.The traditional whale predation approach is changed to a local search process to improve the algorithm's accuracy.The optimal disassembly solution and the last ten percent disassembly solution for each population are searched, the existing disassembly solution is compared with the resulting new disassembly solution, and the better solution is selected.Our proposed local search method randomly selects four points in the solution sequence and performs an arbitrary swap of these four points, as shown in Figure 5. Step 5: Check the disassembly sequence The updated disassembly sequence requires them to be checked for starting with the first position in the sequence.If the disassembly task repre position can be completed, the next task is checked for removability, and i completed, one of the completable tasks is randomly selected to replace it, next task is checked for executability.The above operation is repeated unti meets the disassembly requirements.
Figure 6 illustrates the flow of our IOWA.Step 5: Check the disassembly sequence.
The updated disassembly sequence requires them to be checked for removability, starting with the first position in the sequence.If the disassembly task represented by this position can be completed, the next task is checked for removability, and if it cannot be completed, one of the completable tasks is randomly selected to replace it, and then the next task is checked for executability.The above operation is repeated until the last task meets the disassembly requirements.
Figure 6 illustrates the flow of our IOWA.
starting with the first position in the sequence.If the disassembly task represented by this position can be completed, the next task is checked for removability, and if it cannot be completed, one of the completable tasks is randomly selected to replace it, and then the next task is checked for executability.The above operation is repeated until the last task meets the disassembly requirements.Figure 6 illustrates the flow of our IOWA.

Discussion and Results
Here, we first analyse the application of the optimisation model and solution algorithm to a wide range of instances.To run the tests and algorithms, all code was written in MATLAB with an Intel(R) Core (TM) i7-10850H CPU @ 2.70GHz, 2712 Mhz,6 cores, and 12 logic processors for the operating system.

A Case Study for Our Model
To verify the accuracy and applicability of the proposed algorithm, the disassembly sequence of the worm reducer disassembly line is solved [19].The worm reducer is shown in Figure 7 According to the product priority constraint and connection relationship, the disassembly hybrid graph of the worm reducer can be obtained, as shown in Figure 8.The original disassembly information of the worm reducer components is shown in Table 1.

Discussion and Results
Here, we first analyse the application of the optimisation model and solution algorithm to a wide range of instances.To run the tests and algorithms, all code was written in MATLAB software with an Intel(R) Core (TM) i7-10850H CPU @ 2.70GHz, 2712 Mhz, 6 cores, and 12 logic processors for the operating system.

A Case Study for Our Model
To verify the accuracy and applicability of the proposed algorithm, the disassembly sequence of the worm reducer disassembly line is solved [19].The worm reducer is shown in Figure 7 According to the product priority constraint and connection relationship, the disassembly hybrid graph of the worm reducer can be obtained, as shown in Figure 8.The original disassembly information of the worm reducer components is shown in Table 1.It should be noted that we have set wt = 0.8, wd = 0.8, wi = 1, et = 3, ed = 5, l = 50.In combination with the information in Table 1, the solution for the disassembly sequence of the worm gear disassembly line can be executed by the developed method steps.

Comparison with Other Algorithms
To verify the effectiveness of the algorithm, the turbo reducer disassembly sequence was solved using IWOA, Genetic Algorithm (GA), Artificial Bee Colony Algorithm (ABC), and Artificial Fish Swarm Algorithm (AFSA) with initial populations of 5, 15, and 30, respectively.Since all the metaheuristics worked randomly, each algorithm was run 15 times to obtain reliable results.The parameters were set the same as in the previous section, and the number of iterations was 200.The statistical test results are shown in Figures 9-11  It should be noted that we have set w t = 0.8, w d = 0.8, w i = 1, e t = 3, e d = 5, l = 50.In combination with the information in Table 1, the solution for the disassembly sequence of the worm gear disassembly line can be executed by the developed method steps.

Comparison with Other Algorithms
To verify the effectiveness of the algorithm, the turbo reducer disassembly sequence was solved using IWOA, Genetic Algorithm (GA), Artificial Bee Colony Algorithm (ABC), and Artificial Fish Swarm Algorithm (AFSA) with initial populations of 5, 15, and 30, respectively.Since all the metaheuristics worked randomly, each algorithm was run 15 times to obtain reliable results.The parameters were set the same as in the previous section, the worm gear disassembly line can be executed by the developed method steps.

Comparison with Other Algorithms
To verify the effectiveness of the algorithm, the turbo reducer disassembly sequence was solved using IWOA, Genetic Algorithm (GA), Artificial Bee Colony Algorithm (ABC), and Artificial Fish Swarm Algorithm (AFSA) with initial populations of 5, 15, and 30, respectively.Since all the metaheuristics worked randomly, each algorithm was run 15 times to obtain reliable results.The parameters were set the same as in the previous section, and the number of iterations was 200.The statistical test results are shown in            As can be observed from Figures 9-11, when the initial population size is small, AFSA has the best solution quality and convergence of results, and IWOA is in the middle level among the four algorithms.Still, as the population size increases, the quality of results and convergence of IWOA exceeds the other three algorithms.Three experiments were conducted with multiple sets of parameters and averaged to analyse the convergence behaviour and avoid the influence of specific parameters.The results are shown in Table 2, and other parameters were the same as in the previous section.As can be observed from Figures 9-11, when the initial population size is small, AFSA has the best solution quality and convergence of results, and IWOA is in the middle level among the four algorithms.Still, as the population size increases, the quality of results and convergence of IWOA exceeds the other three algorithms.Three experiments were conducted with multiple sets of parameters and averaged to analyse the convergence behaviour and avoid the influence of specific parameters.The results are shown in Table 2, and other parameters were the same as in the previous section.As can be observed from Figures 9-11, when the initial population size is small, AFSA has the best solution quality and convergence of results, and IWOA is in the middle level among the four algorithms.Still, as the population size increases, the quality of results and convergence of IWOA exceeds the other three algorithms.show the time required to solve this problem.IWOA is relatively superior compared to the three different algorithms.
Three experiments were conducted with multiple sets of parameters and averaged to analyse the convergence behaviour and avoid the influence of specific parameters.The results are shown in Table 2, and other parameters were the same as in the previous section.Table 2 shows the good convergence and solution quality of IWOA.Compared with the other three algorithms, IWOA has a good balance.The reason is that, as the population size increases, our proposed initial disassembly sequence and corresponding disassembly sequence generation methods allow for higher initial population quality, and the two whale blistering net attacks we set up can both capture the advantages of the current optimal disassembly sequence and enhance the diversity of disassembly sequences to be optimised.The local search strategy further improves the accuracy of the IWOA, accompanied by fewer parameters, and the efficiency of the IWOA is somewhat guaranteed.Table 3 shows the running results of the four algorithms when the initial population is 50, and the number of iterations is 200.

Conclusions and Future Works
In this paper, we propose a minimum energy consumption optimisation model for disassembly sequences, by which the energy consumption generated during disassembly can be effectively reduced.To solve the model, we propose a new extension of the whale optimisation algorithm.This new algorithm overcomes the drawback that the traditional whale optimisation algorithm cannot solve discrete combinatorial optimisation problems, redefines whale attack and capture operations, and proposes two whale attack methods and a local search strategy, which effectively improves the accuracy of the algorithm.In order to generate feasible disassembly sequences and improve their quality, a disassembly sequence and its corresponding sequence generation and verification method are proposed.Finally, the problem of the disassembly sequence of the turbo reducer is solved.Compared with existing algorithms, the algorithm is able to better balance the quality of its solution and the solution time when solving the disassembly sequence planning problem and is more suitable for complex and variable situations in actual disassembly.
Planning the disassembly sequence is critical for reducing the pollution and promoting resource reuse [33].Although this paper analyses an energy-efficient DSP using a modified WOA, there are still many research directions that can be pursued in depth, such as multi-product disassembly, coordinated robotic disassembly and disassembly sequence planning with multiple uncertainty conditions.The use of multi-criteria decision-making techniques [34][35][36][37][38][39][40], deep learning [41], and research and analysis of models [42,43] and algorithms that are more relevant to operational processes [44][45][46][47][48][49] is a feasible approach.
, and the program run times are shown in Figures 12-14.
and the number of iterations was 200.The statistical test results are shown in Figures 9-11, and the program run times are shown in Figures 12-14.
, and the program run times are shown in Figures 12-14.

Figure 9 .
Figure 9. Box plot of run results when the population is 5.

Figure 9 . 16 Figure 10 .
Figure 9. Box plot of run results when the population is 5. Processes 2022, 10, x FOR PEER REVIEW 11 of 16

Figure 11 .
Figure 11.Box plot of run results when the population is 30.

Figure 10 . 16 Figure 10 .
Figure 10.Box plot of run results when the population is 15.

Figure 11 .
Figure 11.Box plot of run results when the population is 30.

Figure 11 .
Figure 11.Box plot of run results when the population is 30.

Figure 11 .
Figure 11.Box plot of run results when the population is 30.

Figure 12 .
Figure 12.Running time box plot when the population is 5.

Figure 12 . 16 Figure 13 .
Figure 12.Running time box plot when the population is 5. Processes 2022, 10, x FOR PEER REVIEW 12 of 16

Figure 14 .
Figure 14.Running time box plot when the population is 30.
show the time required to solve this problem.IWOA is relatively superior compared to the three different algorithms.

Figure 13 . 16 Figure 13 .
Figure 13.Running time box plot when the population is 15.

Figure 14 .
Figure 14.Running time box plot when the population is 30.
show the time required to solve this problem.IWOA is relatively superior compared to the three different algorithms.

Figure 14 .
Figure 14.Running time box plot when the population is 30.

Author
Contributions: Conceptualization, Methodology and Software, D.Y.; Data Curation, Writing and Original Draft Preparation, X.Z.; Visualization and Investigation, G.T., Z.L. and Z.J.; Supervision, G.T. and T.Q.; Software and Validation, C.Z.All authors have read and agreed to the published version of the manuscript.

Table 1 .
Parts of worm reducer.

Table 1 .
Parts of worm reducer.

Table 2 .
Algorithm convergence comparison with multiple sets of parameters.