A meta‐heuristic approach for supporting adaptive disassembly sequencing using a multi‐objective concept

Abstract

One of the key features of environmentally conscious manufacturing has been the efforts to promote product recycling and remanufacturing. Efficient material re‐utilisation through product disassembly to retrieve the desired parts and/or subassemblies is one rational approach. This is because it can promote the conservation of both material and energy resources whilst concurrently reducing environmental impact. However, because manufactured products may be made from many components, disassembly load becomes a critical factor that may obstruct the recovery of materials. Accordingly, it is essential to develop a practical method for deriving a disassembly plan to decrease such load, and to endow a certain value to the product at the end of its life cycle. With this understanding, the authors have developed a practical procedure to produce an adaptive disassembly strategy. The authors have applied a meta‐heuristic method known as genetic programming (GP) as a search engine to derive the adaptive disassembly sequence together with a multi‐objective optimisation method termed MOON^2R. The authors have also proposed a hierarchical sequencing method to cope with large/complex products and added several ideas to increase the applicability associated with the interests in disassembly of hazardous and/or valuable parts, and alternative disassembly actions. Through numerical experiments, the authors examined the effectiveness of the proposed approach by showing its support for relevant planning and design decisions for product recycling and remanufacturing from various viewpoints.

Keywords:

• DfD
• eco‐design
• material re‐utilisation
• multi‐objective optimisation method
• genetic programming

1. Introduction

Considerable effort is being devoted to the demonstration of new ideas that reflect environmental consciousness in manufacturing activities (sustainable technology). For example, life cycle assessment (LCA) is standardised in the ISO‐14000 series and applied widely to various industries. Further support for sustainability has been the provision of an information infrastructure for integrating decision aids for life cycle engineering in an extensive and understandable manner (Naka et al. 2000, Shimizu et al. 2001, Shimizu et al. 2002, Shimizu et al. 2005).

In addition to these studies, the retrieval of desired parts and/or subassemblies from spent products is becoming increasingly popular as a rational way for efficient material re‐utilisation. This approach can promote material and energy resource conservation while concurrently reducing environmental impacts. However, because many modern industrial products are assembled from several parts made of different materials, disassembly load becomes a key factor that may obstruct recovery of such valuable materials. Accordingly, an adequate disassembly plan should be sought to decrease disassembly load and to increase a product's value at the end of its life cycle. Moreover, since such effort induces awareness about life cycle cost, there is keen interest in developing reverse engineering that makes the disassembly task easier as well as more complete, e.g. design for disassembly (DfD).

From this understanding, the authors have, in this paper, extended previous studies (Shimizu et al. 2004, 2007) to cope with the problem in a comprehensive way. The authors have proposed an adaptive disassembly sequencing method using multi‐objective optimisation and a hierarchical procedure for solving large‐scale problems. The authors are also interested in the disassembly problem associated with hazardous and/or valuable parts and multiple disassembly actions. Such a combination of ideas has not been considered in previous studies due to the extreme difficulty in solving the resulting optimisation problem. After briefly reviewing previous studies, the authors describe their proposed ideas in detail before validating their effectiveness through illustrative examples.

Nomenclature

Table

aij	output value of RBFN or scale of preference of the i‐trial to the j
D	set of disassembly action
f ^i	i‐th trial solution in adaptive optimisation problem
F	score for evaluating DfD
F’	fitness value
L	level in disassembly tree
N	numbers of objective function
p	parameter controlling type of value function
U(•)	implied value function of virtual DM
v, w	binary values associated with existence of violation and premium
VRBF ( f ( x ), f ^R )	value function modelled using RBFN
α, β	constants appearing in Equation (2)
λ i	weighting coefficient of the i‐th objective function

2. Previous studies and prototype development

Several studies have been conducted on the disassembly sequencing problem (Navinchandra 1991, Beasley and Martin 1993, Zussman et al. 1994, Penev and de Ron 1996, Xirouchakis and Kiritsis 1997, Moore et al. 1998, Srinivasan and Gadh 1998, Gungor and Gupta 2001, Lambert and Gupta 2005). In addition to these single‐objective approaches, a multi‐objective optimisation model was proposed by Kongar and Gupta (2002) who derived a disassembly order by using integer goal programming. However, most of these studies considered the state of the art, and did not demonstrate practical applications.

In contrast, Dini et al. (2001) who generated all feasible disassembly sequences in a manner correlated with CAD information developed a practical system. Nishi and Hiroshige (2004) developed commercial software that sums the disassembly time and cost of every part of the product from a database and proposed a metric to evaluate the disassembly sequencing. Knoth et al. (2001) discuss the use of automation for the disassembly of electronic equipment. However, neither of these studies was concerned with the optimisation of the disassembly process.

Since the disassembly optimisation problem belongs to an NP‐hard class, due to the permutation nature of sequencing, its solution becomes extremely difficult especially with an increase in the number of parts. In partial attempts to cope with this problem, some authors applied genetic algorithms (GA) to derive the optimal disassembly sequence (Seo et al. 2001, Li et al. 2005). They defined the chromosome simply by the sequence of disassembly actions with the aid of graphical representation where the disassembly configuration is imbedded a priori in an expedient manner. However, since the disassembly sequence can be represented more conveniently as a list of functions (disassembly actions) and terminals (parts), we can express the sequence more straightforwardly by a tree structure. For example, Figure 1 shows that if d1 and d2 mean disassembly actions, such as ‘unscrew’ and ‘snap‐off’ respectively, and p1 is a set of screws; the first action will be removal of the screws. The remainder will be disassembled by ‘snap off’ and that will be followed by the further disassembly actions (d3–d5) to retrieve every part (p2–p6) in turn. Hence, we applied a metaheuristic method known as generic programming (GP) (Koza 1992), as this was considered the most relevant; and developed a prototype system to derive the optimal disassembly sequence (Shimizu et al. 2007). Although such efforts have improved the practicality, there are still problems to resolve before a practical solution can be found for real‐world applications.

Figure 1 Illustration of a disassembly sequence tree.

In this paper, we will apply our existing understanding of the factors associated with the problem formulation. With regard to the available parts for material re‐utilisation, we will take account of the condition of the parts and societal needs for recycling and/or reuse. We should make our strategic decision on the value and classification of parts to be retrieved based on the movement of markets and environmental legislation (Burke et al. 1992). Our consideration will also be affected by the idea of planning for disassembly (Ishii et al. 1994, Johnson and Wang 1995, Zeid et al. 1997), as this is essential for deciding the unit of disassembly, the objective function and its evaluation. Regarding the selection of available disassembly actions for the target product, we may encounter a similar problem. Since these issues are very problem‐specific in their nature, we assume that such decisions have been made properly elsewhere. However, our approach is still effective since we provide a flexible approach that makes it possible to cope readily with every case, i.e. it is possible to arbitrarily add/delete appropriate options according to the situation.

To summarise this section, the present study contributes to the development of a practical optimisation method for disassembly sequencing. It adopts the natural representation of the disassembly sequence that makes it possible to apply a more suitable solution method, like GP, rather than methods such as GA. In particular, the study seeks to increase the adaptability of the previous prototype development. For this purpose, we use adaptive decision‐making as this is essential for a socio‐technical system like re‐manufacturing, and propose a method for handling such a large size problem for which meta‐heuristic approaches are generally weak. Moreover, we consider some measures that have rarely been studied, although they are relevant to practical problems.

3. Adaptive disassembly sequence planning using multi‐objective genetic programming

3.1 Multi‐objective optimisation method termed MOON^2R

For adaptive optimisation or optimisation with varying relative importance between the objectives, depending on the decision maker (DM), we represent the formulation as a multi‐objective optimisation, which is described generally as follows:

where x denotes a decision variable vector; X is a feasible region; and f is an objective function vector for which some elements conflict and are incommensurate with each other.

To overcome some of the disadvantages of the conventional methods of the multi‐objective optimisation problem (MOP), we previously developed a method named MOON^2R (Shimizu and Kawada 2002, Shimizu et al. 2004). Its procedure begins by identifying an overall value function that integrates each objective function using a neural network such as the radial basis function network (RBFN) (Orr 1996). Training data for RBFN are gathered through a pair‐wise comparison regarding the relative preference of the DM. That is, for a pair ( f ⁱ , f ^j ), DM is asked to reply which he/she likes, and by how much, using linguistic statements such as those in the analytic hierarchy process (AHP) (Saaty 1980). After completing such pair‐wise comparisons for every pair of trial solutions, we can obtain a pair‐wise comparison matrix whose i–j element a_ij represents the degree of preference of f ^j compared with f ⁱ . After training, we can derive the RBFN that can map the input vector ( f ⁱ , f ^j ) to a scalar a_ij . Writing such mapping as V_RBF ( f ⁱ , f ^j ) = a_ij , we should note that the following relation holds: if V_RBF ( f ⁱ , f ^j )≻ V_RBF ( f ^k , f ^j ) then f ⁱ ≻ f ^k where ≻ denotes a binary relation representing ‘preferable to’. Consequently, we can rank the preference of any solutions from the output value calculated by fixing one of the input vectors at an appropriate reference, say f^R . It is equivalent to say that we can view the thus derived V_RBF ( f ( x ), f ^R ) as a value function that can evaluate cardinally any decision variable vector x . That means we can re‐describe the original problem as (p.2):

As long as we can evaluate V_RBF , we can solve (p.2) effectively by selecting the most appropriate method, i.e. GP in the present case.

3.2 An approach for GP application

Genetic programming is a branch of GA that works best for those problems that require the most efficient solution when there is a large list of variables. It creates a computation scheme as the solution, i.e. compositions of functions and terminals of the problem, whereas GA produces a string of numbers that represent values for decision variables. A typical GP algorithm is composed using similar steps to those used in GA. Below, we explain GP focussing on the major modified elements that we present for consideration.

According to the introduction of alternative disassembly actions, we modified the coding from those presented previously. For example, assuming the disassembly action d1 has another choice D1, we code the chromosome as a string shown in Figure 2.

Figure 2 An extended coding of chromosome for multiple disassembly actions.

Figure 3 An additional mutation dealing with multiple disassembly actions.

We applied a roulette strategy together with elitism as the reproduction rule. Regarding the crossover and mutation, we applied these on the basis of a sub‐tree structure. Under certain conditions, a crossover and two kinds of mutation are defined (Shimizu et al. 2004, 2007). In this work, we have added a new mutation only applicable to the non‐terminal nodes with the multiple disassembly actions. For example, let us assume that the non‐terminal node d1 with multiple disassembly alternative actions has become a mutation locus; a pair of the terminal nodes diverging from d1 is p1 and p3; and the alternative of d1 is D1. Then this operation is applied as follows (see also Figure 3):

Step 1: Take a pair of the terminal nodes {p1, p3} that diverge from the non‐terminal node d1 to which multiple disassembly actions are permitted. Select the pair randomly when there are multiple such pairs.

Step 2: As sub‐tree A, mark {p2} that is diverged from the common non‐terminal node d2 to p1, and {d4, p4, d5, p5, p6} as sub‐tree B by applying the same idea for p3.

Step 3: Exchange sub‐tree B with p1 (or A with p3).

Step 4: Exchange d1 and d3 so that d1 may become the non‐terminal node of p1 and p3.

Step 5: Select an arbitrary disassembly action for d1 from the remaining alternatives, i.e. D1 presently.

To define the fitness of GP, we considered disassembly time and cost. The disassembly time (cost) is evaluated by the sum of the set‐up time (set‐up cost) for every disassembly action and time (cost) depending on the part number. These are common factors for evaluating the disassembly decision, and their relative importance may change depending on the target product and according to the circumstances of the reverse engineering market.

Compared with the previous formulation, whose objective function was given by the weighted sum of the disassembly time and cost, we can consider the problem more adaptively by formulating it as an MOP. By applying a method like MOON^2R, we can readily evaluate the sequence based on the multiple attributes just from the output value of RBFN as mentioned already. First, we define the score F using Equation (1).

The expression ‘a_xR ’, (x = {i, nad or uto}) denotes a preference value of x compared with the reference f ^R . That is, they mean the outputs of RBFN for the i‐th trial, nadir and utopia solutions, respectively.

Using this defined score, we ascribe fitness using Equation (2). Therefore, we consider premium disassembly, in which particular parts are to be retrieved at the earliest stage of the disassembly sequence. Parts that are expensive but fragile or parts that are harmful when destroyed accidentally are such examples.

where v_i represents a binary value that takes 1 if the i‐th disassembly action would violate the priority and otherwise 0. Summation is taken over the whole set of disassembly actions D. Hence this term acts as a penalty against the inhibited sequences. Also w_i denotes a binary value that takes 1 if the premium parts might be involved in the feasible sequence and otherwise 0. Moreover, coefficient α and β denote certain constants and L is the level where the violation or the premium has appeared in the disassembly tree. The more often, and the shallower the level that those extra disassemblies may occur, the more the fitness F′ will be affected.

3.3 A hierarchical approach

As the number of parts increases, the possible combinations of disassembly sequence will expand incredibly rapidly. In such a case, it becomes almost impossible to obtain a result within a permissible time even by using approximated approaches. To cope with this ‘curse of dimension’, we note the following features that are common to current manufacturing practice:

1. A sub‐component is produced as a single integrated unit in terms of the functional roles and structural conditions (module).

2. Each module can be disassembled from the others by certain simple disassembly operations. The module appears almost independent within the whole configuration, or there usually exist only a few connections that combine the modules, e.g. hinge, slot, etc.

Consequently, we have given a hierarchical procedure as follows (see also Figure 4). First, decide the disassembly sequence of the parts that comprise each module at the lower level. Then, letting the disassembly time and cost obtained there be the time and cost necessary to disassemble the module, search the sequence among the modules using them at the upper level. If the physical priority might be violated at the lower level, it is reported to the upper level to penalise the disassembly sequence of the module according to its level. Similarly, the premium disassembly is reported to give a reward for it. Thus, the disassembly sequence for the module (upper level) will take place only after the evaluation of its parts (lower level). These procedures are repeated until; finally, we can expect to obtain almost the best result with a reasonable computation effort.

This procedure is summarised as follows:

Step 1: Divide the product components into the modules or sub‐components connecting the modules.

Step 2: Derive an initial set of sequences regarding the modules at random.

Step 3: Search the disassembly sequence of the parts that compose each module individually.

Step 4: The above result is viewed as the disassembly time and cost of each module. Violations and premiums should be reported to the upper level. From these, the present set is to be evaluated.

Step 5: Another set of module disassembly sequences is generated by the GP algorithm.

Step 6: If a certain convergence criterion has been satisfied, then stop. Otherwise go back to Step 3.

4. Illustrative example

We validated the effectiveness of the proposed approach through numerical experiments with example products. We show two cases, each of which highlights the effect of multiple disassembly actions with the premium evaluation and the adaptive optimisation associated with the hierarchical approach.

Table 1. Configuration data for a fluorescent light stand.

Part number	Part name	Quantity	Category	Prior part number*
1	Lamp shade	1	Reuse	6,11
2	Fluorescent tube	1	Treat	None
3	Lamp socket	2	Reuse	2
4	Supporting rod	1	Unit	6,11,12
5	Upper cover	1	Reuse	4,10,12
6	Stem cable	1	Disposal	3,8
7	Under cover	1	Reuse	10
8	Circuit switch	1	Treat	7
9	Power code	1	Disposal	None
10	Screw	2	Material	None
11	Connector	1	Disposal	2
12	Connector	1	Disposal	7
*parts that must be disassembled before this part.

Table 2. A matrix representing the connection relation.

	1	2	3	4	5	6	7	8	9	10	11	12
1		0	1	1	0	1	0	0	0	0	2	0
2			1	0	0	0	0	0	0	0	0	0
3				0	0	13	0	0	0	0	0	0
4					1	1	0	0	0	0	2	2
5						0	1	0	0	2	0	2
6							0	23	0	0	0	0
7								2	1	2	0	0
8									23	0	0	0
9										0	0	0
10											0	0
11												0
12

The first case study was conducted by taking a fluorescent light stand composed of 12 parts, some of which can be disassembled by multiple actions (see Figure 5). Data in Table 1 show part number, part name, quantity, category of dealings after disassembly1, and those part numbers requiring prioritised retrieval (physical priority). On the other hand, Table 2 represents the connection (disassembly) relation2 between the parts where: zero means no connection (‘Free’); one means ‘Remove’; two means ‘Turn’; three means ‘Cut’; and double figures denote ‘possible multiple candidates’; for example, the number 13 indicates that either ‘Remove’ or ‘Cut’ can be selected as the possible disassembly action. Here, we define the overall objective function Equatiion (3) as the weighted sum of each objective function as before (Shimizu et al. 2007).

where nadir (superscript n), and utopia (superscript u) values of Time and Cost are given as Timeⁿ  = 100, Time^u  = 50 [min], Costⁿ  = 3000, Cost^u  = 1500 [Yen], respectively. We set these so that λ₁ = λ₂ = 0.5. On the other hand, parameters of GP were set as: population size = 100; total generation = 500; crossover rate = 0.75; and mutation rate = 0.25.

Figure 4 A scheme of hierarchical approach for a large‐scale problem.

Figure 5 Parts configuration of fluorescent light stand.

As shown in Table 3, we can ascertain that the extended coding and proposed mutation successfully derives the results that outperformed the conventional one obtained without the alternative disassembly actions and the premium effect (β = 0). Thus the proposed approach can accelerate the earlier disassembly for every valuable part (reusable parts) except for the under cover. Finally, we know that the reward from the premium disassemblies is realised at the expense of disassembly cost.

Table 3. Validation for the premium disassembly.

		Conventional	Proposed
Equation (2) as α = 0.5		60.7 (β = 0)	64.5 (β = 0.2)
• Disassembly time [min]		88	84
• Disassembly cost [Yen]		1540	1545
Disassembly Level	[lamp shade]	11	9
	[lamp socket]	8	3
	[upper‐cover]	11	10
	[under‐cover]	4	5

Regarding the search by GP, we observed the profile of convergence and the distribution of fitness at the final stage, and confirmed the good and proper convergence properties. Figure 6 shows a snapshot of the output graphic user interface (GUI) where the premium disassembly (reusable parts) is highlighted using ellipses in the left hand side of the display field. Locations of multiple disassembly action are highlighted using underlines. The unemployed action thereat is shown in the parenthesis in the same row. Moreover, a few numeric values are summarised in the right hand side field.

Figure 6 Output GUI for the fluorescent light stand. Number in Table1 corresponds to the number in the parenthesis [ ] augmented manually for convenience to translate the Japanese characters.

The second case study considered the disassembly planning for a refrigerator composed of 22 modules and totally deployed into 133 parts or sub‐assemblies. To cope with such a large number of parts, we applied the hierarchical approach mentioned in Section 3.3. The configuration data regarding the refrigerator modules are described in Table 4, similar to Table 1. Therefore, the sub‐quantity column represents the number of parts involved within the module; and every module has similar configuration data to those given in Table 1. For examples, Tables 5, 6 and 7 show the scheme of disassembly actions, configuration data and connection relation for the cooling unit, respectively. We considered that the Freon in the cooling unit and the lubricants in the cooling device should be preferentially retrieved at the earlier stage because of their associated environmental problems. We therefore augmented new disassembly actions like ‘discharge‐gas d4’ in Tables 5 and 7 for the cooling unit, and ‘discharge‐oil’ for the lubricant in the cooling device.

Table 4. Configuration data for the refrigerator module.

Module number	Module name	Quantity	Sub‐quantity	Category	Prior module number
1	Chiller door	1	10	Unit	5,17
2	Crisper door	1	12	Unit	None
3	Freezer door (upper)	1	12	Unit	None
4	Freezer door (lower)	1	12	Unit	None
5	Hinge	1	3	Connector	17
6	Chiller's interior component	1	11	Unit	None
7	Crisper's interior component	1	5	Unit	2
8	Freezer's interior component	1	5	Unit	3,4
9	Functional part	1	11	Unit	19
10	Electrical part and electronic part	1	4	Treat	9,18
11	Cooling unit	1	8	Treat	8,9,19,21
12	Interior and exterior auxiliary part	1	6	Unit	2,3,4,7,8
13	Bach part component	1	7	Unit	9,14,19,22
14	Cooling device	1	9	Treat	8,9,19,21
15	Inner box	1	4	Reuse	6,7,8,11,12,20,21
16	Outside box	1	8	Unit	Except for 16
17	Screw for chiller's door	2	1	Connector	None
18	Screw for electrical and electronic part	2	1	Connector	None
19	Screw for functional component	16	1	Connector	None
20	Screw for inner box	32	1	Connector	None
21	Screw for cooling device	4	1	Connector	None
22	Screw for bach part component	2	1	Connector	None

Table 5. Disassembly actions of cooling unit.

ID	Code	Branch number	Action
d0	Free	2	No action
d1	Remove	2	Strip down
d2	Turn	2	Screw off
d3	Cut	2	Cut off
d4	Discharge	2	Discharge gas

Furthermore, the objective functions for the adaptive disassembly are described as follows:

where Time^u (Cost^u ) and Timeⁿ (Costⁿ ) denote the utopia and nadir values of Time(Cost).

Table 6. Configuration data for the cooling unit.

Number	Part name	Quantity	Category	Prior part number
1	Compressor matrials	1	Unit	8
2	Condenser materials	1	Unit	8
3	Fan motor	1	Treat	1,2,8
4	Fan	1	Reuse	None
5	Starter	1	Treat	None
6	Over‐load relay	1	Disposal	3,5
7	Compressor base	1	Reuse	1,2,3,5,8
8	Coolant	1	Treat	None

Table 7. Connection relation for the cooling unit.

	1	2	3	4	5	6	7	8
1		1	23	0	0	23	2	4
2			23	0	0	23	2	0
3				2	12	1	0	0
4					0	0	0	0
5						1	1	0
6							3	0
7								0
8

For the numerical experiment, we assumed a virtual DM whose embedded preference can be given by linear and quadratic value functions described by Equation (4), and that his/her degree of preference in the pair‐wise comparison is supposed to be given numerically by Equation (5).

where and denote a utopia and nadir values of f_i (x), {i = 1 (Time), 2 (Cost)} respectively. Moreover, N is a number of objective functions, λ _i a weighting coefficient of the i‐th objective function, and p a parameter deciding a type of norm.

where K is the total number of trial solutions employed in the pair‐wise comparison.

We set GP parameters such as population size = 100, maximum generation = 5000, cross‐over rate = 0.75, and mutation rate = 0.35. The utopia and nadir values are given as Timeⁿ  = 2000 [min], Time^u  = 400 [min], Costⁿ  = 37,500 [Yen], and Cost^u  = 15,000 [Yen], respectively. We randomly generated four additional trial solutions ( f ⁱ , i = 1,2,…,4) within the region surrounded by the nadir and the utopia.

Table 8 shows the pair‐wise comparison matrix derived from Equations (4) and (5) when p = 1 in Equation (4). Each value in the Table denotes the evaluated value generated by Equation (5). It represents the degree of preference of the i‐th trial solution to the j‐th using the metrics ranging from 1/9 to 9, the same as those for AHP. The larger it is, the more preferable it is for the DM. This matrix provides data to identify the value function V _RBF that enables us to apply the GP similarly to the previous study (Shimizu et al. 2007).

Table 8. A pair‐wise comparison matrix (p = 1).

	f ^u	f ^1	f ^2	f ^3	f ^4	f ^n
f ^u	1	1.6	2.7	4.0	7.4	9
f ^1		1	2.1	3.4	6.7	8.4
f ^2			1	2.4	4.3	5.9
f ^3				1	5.7	7.3
f ^4					1	2.6
f ^n						1

Table 9. Comparison of lower level results.

Module number	Value function (p = 1)		Value function (p = 2)
	Disassembly time [min]	Disassembly cost [Yen]	Disassembly time [min]	Disassembly cost [Yen]
1	35	1745	37	1745
2	45	2100	43	2090
3	44	2055	43.5	2080
4	44.5	2100	42	2075
5	3	130	3	130
6	20.5	427	19.5	410
7	9	240	9	240
8	5	120	5	120
9	18.5	735	21	785
10	5.5	380	5.5	380
11	36	1420	33	1460
12	12.5	120	14.5	120
13	16	550	16	550
14	29.5	1195	31.5	1225
15	25	430	25	430
16	32	1470	31	1470
17	1	5	1	5
18	1	5	1	5
19	1	5	1	5
20	1	5	1	5
21	1	5	1	5
22	1	5	1	5

Table 9 shows the evaluation of the lower level disassembly at the final (optimal) stage for the linear and quadratic value functions.

The final results are summarised in Table 10. Therefore, ‘Score’ denotes the value given by Equation (1) or the result of the best adjustment between the normalised cost and time, and ‘Best generation’, the generation where the best fitness value was obtained in the course of the search by GP. The ‘Penalty status’ section indicates the number of violations regarding the physical priority for disassembly and its penalty value respectively. Moreover, ‘Premium value’ corresponds to a value‐added evaluation that is obtained by subtracting F from F′. We know that the results are feasible (no penalty) and the premium disassembly appears but differs slightly depending upon the value function types. This means any DM with various value systems can engage in the adaptive decision making just through the pair‐wise comparison when MOON^2R is applied.

Figure 7 A part of GUI for the resulting sequence whenp = 1. Number in Table 4 corresponds to the number in the parenthesis [ ] augmented manually for convenience to translate the Japanese characters.

Figure 8 Output GUI for cooling unit of refrigerator. Number in Table6 corresponds to the number in the parenthesis [ ] augmented manually for convenience to translate the Japanese characters.

A left hand side part of Japanese GUI when p = 1 is shown in Figure 7. These upper‐level disassembly sequences of the module are further extended to show the lower‐level sequences of parts by clicking each module icon in the prototype system. For example, Figure 8 shows a sub tree of sequence for the cooling unit.

Profile of convergence is shown in Figure 9, and distributions of population at the final stage are illustrated both for fitness or evaluated value of Equation (2) and F of Equation (1), respectively in Figure 10 where the transverse indicates each individual. They validate the sufficient convergence of GP schematically, that is, fast convergence (Figure 9) and high rate of individual with the larger fitness value at the final stage in Figure 10.

Table 10. Comparison of results for the refrigerator.

	p = 1	p = 2
Score	93.31	94.1
Time [min]	441	452
Cost [Yen]	17,897	17,220
Best generation	1508	3505
CPU time [min]*	36.5	34.8
	Penalty status
No. of violation	0	0
∑αvi /L in Equation (2)	0	0
	Value‐added status
Premium value	3.93	7.4
∑βwi /L in Equation (2)	0.013	0.017
*Performed under PC: Pentium 2.8 GHz, 512 MB, OS: Windows XP, and Programming language: Java.

Figure 9 Convergence propfile of GP.

Figure 10 Distribution of population at the final stage.

5. Conclusions

We have paid our attention to product recycling and remanufacturing as a key issue for environmentally conscious manufacturing, and improved a prototype system that can provide an adaptive disassembly strategy for DfD. We applied GP in MOON^2R to derive the disassembly sequence for this purpose. Furthermore, we proposed a hierarchical sequencing method to cope with large‐complex products and added several ideas to increase the applicability.

The effectiveness of the proposed approach was examined through numerical experiments. Results obtained from the system show that it is possible to make relevant planning and design decisions about product recycling and remanufacturing from various viewpoints, e.g. validity of product recycling, layout of disassembly plant, and ideas for new green design.

Further studies should consider the incorporation of environmental factors within the evaluation. That will link a multi‐objective optimisation through trade‐off analysis between economic and environmental factors. It would also be interesting to integrate a procedure that can automatically retrieve set‐up information, such as physical priority, on the disassembly sequence into the system in terms of geometry of the parts configuration from CAD data system, for example.

Notes

1. In this example, we classified the retrievable units into several categories, i.e. unit made of uniform material (material), complex unit (unit), reusable complex unit (reuse), unit that requires a certain treatment before disposal (treat), part hard to destroy (destroy), and disposable unit (disposal).

2. We considered presently five disassembly actions, i.e. no action (Free), snap off (Remove), screw off (Screw), turn off (Turn) and cut off (Cut).