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

Figures & data

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

Figure 1 Illustration of a disassembly sequence tree.

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

Figure 3 An additional mutation dealing with multiple disassembly actions.

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

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

Figure 5 Parts configuration of fluorescent light stand.

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

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.

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

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

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

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.

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.