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Mechanical Product Ecological Design Knowledge Reduction Based on Rough Set
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Procedia CIRP 00 (2017) Procedia CIRP 000–000 80 (2019) 33–38 www.elsevier.com/locate/procedia
26th 26th CIRP CIRP Life Life Cycle Cycle Engineering Engineering (LCE) (LCE) Conference Conference
Mechanical Ecological Design Knowledge Based Mechanical Product Product Ecological DesignMay Knowledge Reduction Based on on 28th CIRP Design Conference, 2018, Nantes, Reduction France Rough Set Rough Set A new methodology to analyze the functional and physical architecture of a, a a a Lei Zhang *, Zhifeng Jin , Yu Zheng , Rui Jiang a, a a *, Zhifeng oriented Jina, Yu Zheng , Rui Jiang existing products Lei forZhang an assembly product family identification a aSchool
of Mechanical Engineering, Hefei University of Technology, Hefei, 230009, China School of Mechanical Engineering, Hefei University of Technology, Hefei, 230009, China
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat *Corresponding author. Tel.: Supérieure +00-86-0551-62904875; fax: +00-86-0551-62904875. E-mail addresses: École Nationale d’Arts et Métiers, et Métiers ParisTech,E-mail LCFCaddresses: EA 4495, [email protected] [email protected] Rue Augustin Fresnel, Metz 57078, France *Corresponding author. Tel.: +00-86-0551-62904875; fax: Arts +00-86-0551-62904875.
* Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]
Abstract Abstract In the process of product design, the knowledge of product ecological design is growing with the increasing of environmental requirements of In the process of product design, the knowledge of product ecological design is growing with the increasing of environmental requirements of Abstract product. In the process of knowledge acquisition of product ecological design, massive redundant or insignificant design data will affect product. In the process of knowledge acquisition of product ecological design, massive redundant or insignificant design data will affect designers’ efficiency, and it is necessary to reduce these data. In this paper, taking the automobile reducer as an example, the ontology designers’ efficiency, and it is necessary to reduce these data. variety In this and paper, taking the isautomobile reducer as an example, the Inexpression today’s business thethe trend towards more product customization unbroken. Duefrom to this theontology need the of model isenvironment, established for ecological design knowledge needed in the design process. Starting the development, rough set knowledge, expression model is established for systems the ecological design knowledge neededproducts in the design process. StartingTo from the rough set knowledge, the agile and reconfigurable production emerged to cope with various and product families. design and optimize production rough set theory is applied to reduce the attributes and remove the redundancy. Finally, the accurate data which meets the design requirements rough set is applied tothe reduce the attributes and remove the redundancy. Finally, accurate data which meets design requirements systems as theory well choose optimal product analysis methods arethe needed. Indeed, most of the the known methods aim to is obtained, and as thetodesign efficiency and product precisionmatches, are improved. is obtained, and the design efficiency and precision are level. improved. analyze a product or one product family on the physical Different product families, however, may differ largely in terms of the number and © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license © 2019 The Authors. Published Published by Elsevier B.V. This is is an an open open access access article under under the CC CC BY-NC-ND BY-NC-ND license nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production © 2019 The Authors. by Elsevier B.V. This article the license (http://creativecommons.org/licenses/by-nc-nd/3.0/). (http://creativecommons.org/licenses/by-nc-nd/3.0/). system. A new methodology is proposed to analyze existing products in CIRP view of their functional and physical architecture. The aim is to cluster (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the scientific committee of the 26th Life Cycle Engineering (LCE) Conference. Peer-review responsibility of committee of 26th CIRPof Life Cycleassembly Engineering (LCE) Conference. Peer-review under responsibility of the the scientific scientific committee of the the 26th CIRP Life Cycle Engineering Conference. these productsunder in new assembly oriented product families for the optimization existing lines(LCE) and the creation of future reconfigurable assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and Keywords: Ecological design; Attribute reduction; Ontology model; Rough set AttributeMoreover, reduction; Ontology Roughand set physical architecture graph (HyFPAG) is the output which depicts the a Keywords: functionalEcological analysis design; is performed. a hybridmodel; functional similarity between product families by providing design support to both, production system planners and product designers. An illustrative example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. regarding different classification 1. Introduction theoretic Introduction theoretic rough rough set set models models regarding different classification ©1.2017 The Authors. Published by Elsevier B.V. properties, which provides aa new properties, which provides new insight insight into into the the problem problem Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.
Rough set of Rough set theory theory [1,2] [1,2] is is aa mathematical mathematical theory theory of attribute attribute reduction. reduction. Ren Ren et et al. al. [4] [4] studied studied the the attribute attribute proposed by the Polish mathematician Pawlak in 1982 reductions of three-way concept lattices in order Keywords: Family identification proposedAssembly; by the Design Polishmethod; mathematician Pawlak in 1982 reductions of three-way concept lattices in order to to make make which the which is is used used to to research research inaccurate inaccurate and and incomplete incomplete data. data. the data data easily easily be be understood understood and and proposed proposed four four kinds kinds of of Attribute reduction reduction is is aa core core issue issue in in rough attribute Attribute rough set set theory. theory. attribute reductions reductions which which embody embody different different characteristics characteristics General speaking, of General speaking, the the information information in in the the knowledge knowledge base base is is of aa formal formal context context and and can can be be used used in in different different occasions. occasions. equally important, and there is redundancy, which is not Xie et al. [5] introduced the concept of 1.not Introduction of the product range and characteristics manufactured and/or not equally important, and there is redundancy, which is not Xie et al. [5] introduced the concept of an an inconsistency inconsistency conducive to making correct and concise decisions. In the degree in an incomplete decision system and prove that assembled in this system. In this context, the main challenge in conducive to making correct and concise decisions. In the degree in an incomplete decision system and prove that the the rough set theory, aiming at information system, by attribute reduction based on the inconsistency degree Due to the fast development in the domain of modelling and analysis is now not only to cope with single rough set theory, aiming at information system, by attribute reduction based on the inconsistency degree is is eliminating redundant attributes and keeping the equivalent to based on three communication and an ongoing trend of digitization and products, a limited existingregion. productAnd families, eliminating redundant attributes and keeping the equivalent to that thatproduct based range on the theorpositive positive region. And three classification ability the classification strategies of degree for dynamic digitalization, enterprises are facing important butupdate also to be able to analyze and to compare products define classification manufacturing ability unchanged, unchanged, the reduced reduced classification update strategies of inconsistency inconsistency degree for to dynamic or decision rules are obtained. incomplete decision systems are also provided. Zheng challenges in today’s market environments: a continuing new product families. It can be observed that classical existing or decision rules are obtained. incomplete decision systems are also provided. Zheng et et al. al. Currently, scholars at home and abroad have done [6] proposed an effective enhancement for improving tendency towards reduction of product development times and product families are regrouped in function of clients or features. Currently, scholars at home and abroad have done [6] proposed an effective enhancement for improving the the extensive research on design attribute attribute significance based heuristic attribute reduction shortened In of addition, is anreduction. increasing However, oriented product families are hardly to find. extensive product researchlifecycles. on the the issue issue of design there attribute reduction. attributeassembly significance based heuristic attribute reduction Yao et al. [3] addressed attribute reduction in decisionmethods, which providing a means of effectively achieving demand of customization, being at the same time in a global On the product family level, products differ mainly in two Yao et al. [3] addressed attribute reduction in decisionmethods, which providing a means of effectively achieving competition with competitors all over the world. This trend, main characteristics: (i) the number of components and (ii) the which is inducing the development from macro to micro type of components (e.g. mechanical, electrical, electronical). 2212-8271 results © 2019 The Published Elsevier B.V. is an open access article under the CC BY-NC-ND license markets, in Authors. diminished lot by due toThis augmenting Classical methodologies considering mainly single products 2212-8271 © 2019 The Authors. Published bysizes Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). (http://creativecommons.org/licenses/by-nc-nd/3.0/). product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the Peer-review under responsibility of the scientific committee of the 26th CIRP Life Cycle Engineering (LCE) Conference. Peer-review under responsibility of thevariety scientificas committee oftothebe 26th CIRP Life Cycle Engineering (LCE) Conference. To cope with this augmenting well as able to product structure on a physical level (components level) which doi:10.1016/j.procir.2017.04.009 doi:10.1016/j.procir.2017.04.009 identify possible optimization potentials in the existing causes difficulties regarding an efficient definition and production system, it is important to have a precise knowledge comparison of different product families. Addressing this 2212-8271 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) 2212-8271 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of scientific the scientific committee theCIRP 26thDesign CIRP Conference Life Cycle 2018. Engineering (LCE) Conference. Peer-review under responsibility of the committee of the of 28th 10.1016/j.procir.2019.01.030
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the optimal reduction for the dependence based and consistency based heuristic reduction algorithms. Jing et al. [7] presented the incremental algorithms for attribute reduction based on the calculated knowledge granularity when multiple attributes are added to the decision system. Min et al. [8] proposed a partial-complete searching technique for ACO and design the APC algorithm. Fan et al. [9] introduced a new neighborhood rough set model, named max-decision neighborhood rough set model. An attribute reduction algorithm is designed based on the model. Wei et al. [10] proposed a discernibility matrix based incremental attribute reduction algorithm and developed an incremental attribute reduction algorithm based on the discernibility matrix of a compact decision table. Teng et al. [11] analyzed the limitations of existing attribute reduction algorithms and proposed a novel measure of attribute quality, called the relative discernibility degree based on the discernibility. Liu et al. [12] proposed the concepts of lth decision class lower approximation reduction, lth decision class reduction, and lth decision class β-reduction for decision tables, then provided their corresponding reduction algorithms via discernibility matrices. Qian et al. [13] proposed several parallel attribute reduction algorithms. Jing et al. [14] proposed a generalized indiscernibility reduction model(GIRM) and a concept of the granular structure in GIRM, which is a quantitative measurement induced from multiple indiscernibility relations and which can be used to represent the computation cost of varied models. The current research mainly focuses on the reduction of general design knowledge, without taking into account the ecological mechanical products design knowledge which is complex, multi-disciplinary and discrete. In the process of mechanical product design, the factors such as function, performance, economy and environmental impact should be considered comprehensively. There is redundancy between these factors. How to reduce the attributes of the mechanical products ecological design knowledge is an urgent problem to be solved. Genetic algorithm is an adaptive global optimization probabilistic search algorithm which simulates the genetic and evolutionary processes of organisms in natural environment. It was first proposed by Professor Holland of the University of Michigan in the United States. Its search method is not a single direction or structure. It takes multiple individuals as possible solutions and considers the global scope of search space. As a result, the genetic algorithm has a strong global search ability and can find the global optimal solution in a relatively short time. 2. Expression of ecological design knowledge for mechanical products Knowledge ontology [15] is a standardized description of the relationship between domain concepts and concepts. This description is standardized, explicit, formal and shared. Explicit means a clear definition of the types of concepts adopted and constraints applied to them. Enterprises often improve their product design ability through collaboration.
On the one hand, owing to the confusion of various related knowledge, ontology technology can easily organize it and greatly improve the utilization efficiency of design knowledge; on the other hand, from the perspective of enterprise design tasks, they generally have multiple attributes such as multiple objectives, multiple constraints, and multiple contents. Multiple attributes can also be organized by the concept expression ability of ontology. Therefore, this article uses ontology to establish knowledge expression model of mechanical product design. Ecological design knowledge is produced in the process of product ecological design. It is the analysis and summary of product life cycle design content. According to the characteristics of product ecological design, based on ontology, product ecological design knowledge is divided into three categories: product design basic knowledge, product design environment attribute knowledge and product design post-processing knowledge. The ontology of product ecological design knowledge can be expressed as: B= {BK, EK, RK}. Among them, BK represents the product design basic knowledge, mainly including type and material; EK represents the product design environment attribute knowledge; product design environment attribute knowledge has a wide range of concepts, mainly including lubrication, heat dissipation, power and emission; RK represents the product design post-processing knowledge, mainly including maintenance, disassembly and recovery. Based on the whole life cycle of product ecological design, the knowledge ontology expression model of product ecological design is established based on the automobile reducer, as shown in Fig. 1. Type Product design basic knowledge Material
Lubrication Ontology expression of product ecological design knowledge
Product design environment attribute knowledge
Heat dissipation
Power
Emission
Recovery
Product design postprocessing knowledge
Maintenance
Disassembly
Fig. 1. Ontology expression model for ecological design knowledge of automobile reducer.
3. Basic concepts 3.1 Rough set theory The characteristics of rough set theory are: prior
Lei Zhang et al. / Procedia CIRP 80 (2019) 33–38 Lei Zhang/ Procedia CIRP 00 (2019) 000–000
knowledge is not needed except the data set to be processed; it can deal with the uncertainty and inaccuracy of knowledge, and it is an objective method of data reasoning. 3.2 Information system The information system can be represented by a sequence of four elements: IS= (U, A, Va, fa). Where U is domain, representing a set of finite object sets U= {x1, x2, …, x3}; A=C∪D represents a finite set of attributes, including conditional attributes and decision attributes, A= {a1, a2,…,a3}. Va is the range of attribute a. The information function fa: U→Va is defined for each attribute. The information system can be described by a two-dimensional information table. Each row in the table represents an object in U, and each column represents an attribute in A. Each element in the table represents the value of the attribute, that is, the value of information function fa. 3.3 Indistinguishable relationship For any attribute set B⊂A, the indistinguishable relationship Ind(B) is defined as: ∃xi, xj∈U, ∀b∈B, if b(xi) = b(xj), the objects xi, xj are indistinguishable for the attribute set B. The equivalent class of Ind(B) is called the basic set in B, which represents the minimum set of indistinguishable objects, and embodies the highest discrimination ability of the information system. The objects in every equivalence class are not distinguishable under the attribute set B. For any object xi, the equivalence class of xi in Ind(B) is denoted as [xi]Ind(B). The symbol U/A represents the set of all the equivalence relations of objects in U based on the equivalence relation A. It can be seen that Ind(B) is also an equivalence relation in domain U, which form a division U/ Ind(B) of domain U. 3.4 Independence ∀ai ∈ A, if Ind(A)=Ind(A-{ai}), ai is redundant. Otherwise, ai is independent or necessary. ∀ai∈A, if ai∈A, ai is independent, then A is also independent. 3.5 Attribute core and reduction Core and reduction are two basic concepts of rough set theory. When the attribute set B is independent, B⊂A and Ind(B)=Ind(A), then B is the reduction of A. Obviously, the reduction of A is often not unique, and it is recorded as red(A). The collection of all attributes that cannot be omitted is called the core of A. There is a connection between core and reduction: Core(A)=∩red(A). The core has two main functions: (1) Being the basis for the calculation of the reduction; (2) Being the necessary attributes in the information system. 4. Attribute reduction genetic algorithm Reduction genetic algorithm is a way to find minimum
35 3
relative reduction when solving the decision problems. Minimum relative reduction contains the least set of attributes in all relative reductions. For information system, because knowledge reduction set is often more than one, the less the attributes that needed to be considered, the easier it is to handle the information system. Finding minimum relative reduction is of great importance to decision making. The combination of genetic algorithm and rough set often obtain better results. 4.1 Encoding method How to code is the first problem when reducing attribute with genetic algorithm. Considering the practical characteristics of attribute reduction, a fixed-length binary string is usually used to represent individuals in a population whose alleles consist of a set of binary symbols {0,1}. The set of conditional attributes is C={c1,c2,…,cn}, the conditional attribute space KC can be projected into the chromosome of the genetic algorithm. Chromosomes are binary strings of length n, each bit corresponds to a conditional attribute. If a bit has a value of 1, the bit selects its corresponding conditional attribute; if a bit has a value of 0, it does not select its corresponding conditional attribute. Therefore, each chromosome individual corresponds to a subset of attributes in the conditional attribute space. The composition of the chromosome is shown in Table 1. The table shows the case where n=9, and the attribute subset corresponding to the chromosome is {a2, a4, a7}. Table 1. The composition of the chromosome. C1
C2
C3
C4
C5
C6
C7
C8
C9
0
1
0
1
0
0
1
0
0
4.2 The design of fitness function Appropriate evaluation of individuals will lead to good search results. Individual evaluation is accomplished by a fitness function, and fitness function is the only deterministic index for individual evaluation, which can control the evolution of chromosomes toward minimal reduction. Therefore, the design of fitness function directly determines the evolution of population. According to the actual situation of reduction, the fitness function is defined as equation (1):
F ( x) = 1 − card ( x) / n +
card ( Rx ) card ( RC )
(1)
The function consists of two parts. The first part is defined as f(x)=1-card(x)/n, representing the objective function. Where, n represents the length of the conditional attribute set, card(x) represents the number of 1 in an individual, that is, the number of conditional attributes contained in it. The meaning of f(x) is the ratio of the attributes which is not included in the individual x. If the number of attributes in x is smaller, the value of f(x) is
36 4
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larger. The second part is defined as P(x) =card(Rx)/card(Rc), which indicates the dependence of decision attribute D on conditional attribute C. Card(Rx) represents the number of objects that can be distinguished by the corresponding conditional attributes of individual x. Card(Rc) represents the number of objects that the conditional attribute C can distinguish. The bigger the value of P(x), the stronger the decision-making ability of the condition attribute x has. When the value is 1, the decisionmaking information is completely determined by the condition information. Solving the minimum relative reduction in the knowledge expression system is to find the least reduction of the conditional attributes under the condition of keeping the overall decision attribute dependency unchanged, and the fitness function constructed in this paper can meet the requirements from these two aspects. 4.3 Selecting Selecting refers to the selection of a good individual from a randomly generated population that makes it possible for the parent to generate a next generation population. The process of eliminating the fittest by genetic algorithm is selection, and the criterion of selection is individual fitness. The paper chooses fitness ratio selection method. The specific implementation process is as follows: (1) Calculating the total fitness of all individuals; (2) The ratio of individual fitness to total fitness is calculated, which is the probability that each individual is inherited into the next generation. (3) The simulated roulette is used to determine the number of times each individual is selected. 4.4 Crossover After selecting the next generation of parents, it is necessary to reorganize and generate new individuals. The crossover operation is carried out between two individuals. Two new individuals are obtained by exchanging part of the information of two individuals. Together with the selection operation, it is ensured that the population evolves in the desired direction. In this paper, single-point crossover is used to randomly pair the individuals in the group. 4.5 Mutation Mutation refers to the process of reversing a selected gene and forming a new individual. In genetic algorithms, an important stage is to complete individual mutation at a very low rate. The mutation operation is performed bitwise, that is, a certain bit of an individual code is mutated. The purpose of the mutation is to maintain the diversity of individuals and to avoid the search process converge too quickly to a local optimal solution. The paper adopts basic bit mutation. For each specified mutation point, the gene bit corresponding to the attribute in the core does not mutate, and the other bits perform the reversal operation, thereby a
new individual is generated. In order to ensure that the individual does not make a big difference with the parent, the mutation probability is generally small to ensure the stability of the population development. 4.6 Preserving the optimal individual Individuals with the greatest fitness in each generation are copied to the next generation of populations. This method can ensure that the characteristics of each generation of optimal individuals rise monotonously when the algorithm is executed, and the algorithm can be converged. 4.7 Terminating algorithm If the fitness of the optimal individuals in the continuous t generation is no longer rose, then the algorithm is terminated. 5. Executing reduction genetic algorithm Input: An information system IS= (U, A, Va, fa). Where, A=C ∪ D, C is the conditional attribute, D is decision attribute. Output: An attribute reduction R of the information system. The basic process is as follows: (1) The initial population consisting of 24 binary bit strings with length of 9 was randomly generated, the corresponding bit attribute is selected to be assigned a value of 1, and if it is not selected, the value is assigned to 0; (2) After calculating the dependence and fitness, the individual is selected by the simulated roulette operation according to the probability that each individual is selected; (3) Crossing. Crossover rate Pc is 0.7; (4) Mutation. Mutation rate Pm is 0.03; (5) Preserving the best individual; (6) The fitness values of the optimal individuals in the continuous t generation are no longer increased, and then the computation is terminated. 6. Algorithm example Automobile reducer is a common mechanical product. As an important transmission component, it is one of the most critical parts of the automobile. Therefore, in the process of its eco-design, it is necessary to consider the impact of each link on its ecological performance, whether in material selection, energy saving, consumption reduction or disassembly and recycling. This paper takes the automobile reducer as an example to reduce the attributes that affect the ecological design of the automobile reducer. Table 2 is an information system for data about automobile reducer, in which domain U= {1,2,...,24}, condition attribute set C ={type, material, lubrication, heat dissipation, power, discharge, recovery, maintenance,
Lei Zhang et al. / Procedia CIRP 80 (2019) 33–38 Lei Zhang/ Procedia CIRP 00 (2019) 000–000
disassembly}, decision attribute D ={ecological performance}. The parameters are set as follows: terminate algebra m=30, Pc=0.7, Pm=0.03. Table 3 is the result of algorithm calculation. The results show the number of iterations, the optimal individuals of each generation, the fitness of the optimal individual and the total fitness. In this example, the optimal individuals appeared in the 12th generation and remained unchanged for 18 consecutive generations. The composition of the optimal chromosome is shown in the Table 4. The result of relative attribute
37 5
reduction is {material, power, emission, disassembly}. After obtaining these attributes which have great influence on the Eco-design of the reducer, designers can consider the Eco-design of the reducer from these aspects first. Table 4. The composition of the optimal chromosome. C1
C2
C3
C4
C5
C6
C7
C8
C9
0
1
0
0
1
1
0
0
1
Table 2. An information system for data on automobile reducer. U Domain
C1 Type
C2 Material
C3 Lubrication
C4 Heat dissipation
C5 Power
C6 Emission
C7 Recovery
C8 Maintenance
C9 Disassembly
D Ecological performance
1
1
2
2
1
3
2
3
1
2
2
2
2
4
1
2
4
2
2
1
1
2
3
1
3
3
2
3
1
3
1
1
1
4
2
1
3
1
1
2
1
2
2
3
5
1
3
3
2
2
2
2
2
1
2
6
3
2
1
1
3
1
2
1
3
2
7
2
2
2
1
4
1
1
1
1
1
8
1
1
2
1
2
3
1
1
1
2
9
2
4
2
2
1
1
3
1
2
1
10 11 12 13 14 15 16 17 18 19 20 21 22 23
2 3 1 2 1 3 1 2 1 3 2 1 1 1
2 2 3 4 1 3 2 3 2 4 1 2 1 1
1 1 1 1 2 1 1 2 2 2 1 2 2 3
2 2 1 2 2 1 1 1 2 1 2 2 1 2
1 3 2 4 3 2 1 3 2 4 1 2 3 2
3 2 3 1 1 3 2 1 1 1 2 3 2 3
3 3 2 2 2 3 2 3 2 2 1 3 2 2
2 1 1 2 2 2 1 1 2 2 2 1 2 2
1 2 2 2 3 1 2 3 2 1 2 3 2 2
2 3 1 2 3 3 1 1 2 3 1 2 2 3
24
2
4
1
2
1
1
1
2
1
1
Table 3. The result of algorithm calculation. Number of iterations
Optimal individual
Fitness
Total fitness
1
010111011
0.772148
15.4415932
2
010111011
0.772148
13.1756165
3
010111011
0.772148
17.531552
4
010111011
0.772148
17.115346
5
010111011
0.771148
14.452263
6
010111011
0.772148
15.444623
7
010111011
0.772148
15.697356
8
010111001
0.963159
18.954665
9
010111001
0.963159
19.753549
10
010111001
0.963159
17.689242
11
010111001
0.963159
17.584362
12
010011001
1.038314
25.874848
13
010011001
1.038314
23.124522
14
010011001
1.038314
24.123368
15
010011001
1.038314
26.212234
16
010011001
1.038314
25.634413
Lei Zhang et al. / Procedia CIRP 80 (2019) 33–38 Lei Zhang/ Procedia CIRP 00 (2019) 000–000
38 6
17
010011001
1.038314
18
010011001
1.038314
22.566458
19
010011001
1.038314
19.563149
20
010011001
1.038314
17.693478
21
010011001
1.038314
24.834896
22
010011001
1.038314
19.675521
23
010011001
1.038314
25.334156
24
010011001
1.038314
22.321114
25
010011001
1.038314
21.565478
26
010011001
1.038314
26.496178
27
010011001
1.038314
20.661783
28
010011001
1.038314
16.784924
29
010011001
1.038314
23.479354
30
010011001
7. Conclusion (1) Based on rough set theory, the operation basis of attribute reduction algorithm is calculated. (2) A rough set attribute reduction algorithm based on genetic algorithm is proposed, which enhances the ability of local search while maintaining the global optimization characteristics of the algorithm. (3) Taking the automobile reducer as an example, the feasibility and efficiency of the algorithm are verified, especially when the data scale is large, the calculation time is saved more. (4) Future work will focus on improving genetic algorithm, combining genetic algorithm with other optimization algorithms, constructing hybrid genetic algorithm, or using parallel genetic algorithm. Acknowledgements This study is supported by the National Natural Science Foundation of China (Grant No. 51775162). We highly appreciate the assistance of all colleagues in the Institute of Green Design and Manufacturing Engineering at Hefei University of Technology. Reference [1] Pawlak Z. Rough set[J]. International Journal of Computer & Information Sciences, 1982, 11(5). [2] Jerzy W. Grzymała-Busse, Zdzisław Pawlak, Roman Słowiński, et al. Rough set[J]. Communications of the Acm, 1995, 38(11):800-805.
25.156354
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26th 26th CIRP CIRP Life Life Cycle Cycle Engineering Engineering (LCE) (LCE) Conference Conference
Mechanical Ecological Design Knowledge Based Mechanical Product Product Ecological DesignMay Knowledge Reduction Based on on 28th CIRP Design Conference, 2018, Nantes, Reduction France Rough Set Rough Set A new methodology to analyze the functional and physical architecture of a, a a a Lei Zhang *, Zhifeng Jin , Yu Zheng , Rui Jiang a, a a *, Zhifeng oriented Jina, Yu Zheng , Rui Jiang existing products Lei forZhang an assembly product family identification a aSchool
of Mechanical Engineering, Hefei University of Technology, Hefei, 230009, China School of Mechanical Engineering, Hefei University of Technology, Hefei, 230009, China
Paul Stief *, Jean-Yves Dantan, Alain Etienne, Ali Siadat *Corresponding author. Tel.: Supérieure +00-86-0551-62904875; fax: +00-86-0551-62904875. E-mail addresses: École Nationale d’Arts et Métiers, et Métiers ParisTech,E-mail LCFCaddresses: EA 4495, [email protected] [email protected] Rue Augustin Fresnel, Metz 57078, France *Corresponding author. Tel.: +00-86-0551-62904875; fax: Arts +00-86-0551-62904875.
* Corresponding author. Tel.: +33 3 87 37 54 30; E-mail address: [email protected]
Abstract Abstract In the process of product design, the knowledge of product ecological design is growing with the increasing of environmental requirements of In the process of product design, the knowledge of product ecological design is growing with the increasing of environmental requirements of Abstract product. In the process of knowledge acquisition of product ecological design, massive redundant or insignificant design data will affect product. In the process of knowledge acquisition of product ecological design, massive redundant or insignificant design data will affect designers’ efficiency, and it is necessary to reduce these data. In this paper, taking the automobile reducer as an example, the ontology designers’ efficiency, and it is necessary to reduce these data. variety In this and paper, taking the isautomobile reducer as an example, the Inexpression today’s business thethe trend towards more product customization unbroken. Duefrom to this theontology need the of model isenvironment, established for ecological design knowledge needed in the design process. Starting the development, rough set knowledge, expression model is established for systems the ecological design knowledge neededproducts in the design process. StartingTo from the rough set knowledge, the agile and reconfigurable production emerged to cope with various and product families. design and optimize production rough set theory is applied to reduce the attributes and remove the redundancy. Finally, the accurate data which meets the design requirements rough set is applied tothe reduce the attributes and remove the redundancy. Finally, accurate data which meets design requirements systems as theory well choose optimal product analysis methods arethe needed. Indeed, most of the the known methods aim to is obtained, and as thetodesign efficiency and product precisionmatches, are improved. is obtained, and the design efficiency and precision are level. improved. analyze a product or one product family on the physical Different product families, however, may differ largely in terms of the number and © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license © 2019 The Authors. Published Published by Elsevier B.V. This is is an an open open access access article under under the CC CC BY-NC-ND BY-NC-ND license nature of components. This fact impedes an efficient comparison and choice of appropriate product family combinations for the production © 2019 The Authors. by Elsevier B.V. This article the license (http://creativecommons.org/licenses/by-nc-nd/3.0/). (http://creativecommons.org/licenses/by-nc-nd/3.0/). system. A new methodology is proposed to analyze existing products in CIRP view of their functional and physical architecture. The aim is to cluster (http://creativecommons.org/licenses/by-nc-nd/3.0/) Peer-review under responsibility of the scientific committee of the 26th Life Cycle Engineering (LCE) Conference. Peer-review responsibility of committee of 26th CIRPof Life Cycleassembly Engineering (LCE) Conference. Peer-review under responsibility of the the scientific scientific committee of the the 26th CIRP Life Cycle Engineering Conference. these productsunder in new assembly oriented product families for the optimization existing lines(LCE) and the creation of future reconfigurable assembly systems. Based on Datum Flow Chain, the physical structure of the products is analyzed. Functional subassemblies are identified, and Keywords: Ecological design; Attribute reduction; Ontology model; Rough set AttributeMoreover, reduction; Ontology Roughand set physical architecture graph (HyFPAG) is the output which depicts the a Keywords: functionalEcological analysis design; is performed. a hybridmodel; functional similarity between product families by providing design support to both, production system planners and product designers. An illustrative example of a nail-clipper is used to explain the proposed methodology. An industrial case study on two product families of steering columns of thyssenkrupp Presta France is then carried out to give a first industrial evaluation of the proposed approach. regarding different classification 1. Introduction theoretic Introduction theoretic rough rough set set models models regarding different classification ©1.2017 The Authors. Published by Elsevier B.V. properties, which provides aa new properties, which provides new insight insight into into the the problem problem Peer-review under responsibility of the scientific committee of the 28th CIRP Design Conference 2018.
Rough set of Rough set theory theory [1,2] [1,2] is is aa mathematical mathematical theory theory of attribute attribute reduction. reduction. Ren Ren et et al. al. [4] [4] studied studied the the attribute attribute proposed by the Polish mathematician Pawlak in 1982 reductions of three-way concept lattices in order Keywords: Family identification proposedAssembly; by the Design Polishmethod; mathematician Pawlak in 1982 reductions of three-way concept lattices in order to to make make which the which is is used used to to research research inaccurate inaccurate and and incomplete incomplete data. data. the data data easily easily be be understood understood and and proposed proposed four four kinds kinds of of Attribute reduction reduction is is aa core core issue issue in in rough attribute Attribute rough set set theory. theory. attribute reductions reductions which which embody embody different different characteristics characteristics General speaking, of General speaking, the the information information in in the the knowledge knowledge base base is is of aa formal formal context context and and can can be be used used in in different different occasions. occasions. equally important, and there is redundancy, which is not Xie et al. [5] introduced the concept of 1.not Introduction of the product range and characteristics manufactured and/or not equally important, and there is redundancy, which is not Xie et al. [5] introduced the concept of an an inconsistency inconsistency conducive to making correct and concise decisions. In the degree in an incomplete decision system and prove that assembled in this system. In this context, the main challenge in conducive to making correct and concise decisions. In the degree in an incomplete decision system and prove that the the rough set theory, aiming at information system, by attribute reduction based on the inconsistency degree Due to the fast development in the domain of modelling and analysis is now not only to cope with single rough set theory, aiming at information system, by attribute reduction based on the inconsistency degree is is eliminating redundant attributes and keeping the equivalent to based on three communication and an ongoing trend of digitization and products, a limited existingregion. productAnd families, eliminating redundant attributes and keeping the equivalent to that thatproduct based range on the theorpositive positive region. And three classification ability the classification strategies of degree for dynamic digitalization, enterprises are facing important butupdate also to be able to analyze and to compare products define classification manufacturing ability unchanged, unchanged, the reduced reduced classification update strategies of inconsistency inconsistency degree for to dynamic or decision rules are obtained. incomplete decision systems are also provided. Zheng challenges in today’s market environments: a continuing new product families. It can be observed that classical existing or decision rules are obtained. incomplete decision systems are also provided. Zheng et et al. al. Currently, scholars at home and abroad have done [6] proposed an effective enhancement for improving tendency towards reduction of product development times and product families are regrouped in function of clients or features. Currently, scholars at home and abroad have done [6] proposed an effective enhancement for improving the the extensive research on design attribute attribute significance based heuristic attribute reduction shortened In of addition, is anreduction. increasing However, oriented product families are hardly to find. extensive product researchlifecycles. on the the issue issue of design there attribute reduction. attributeassembly significance based heuristic attribute reduction Yao et al. [3] addressed attribute reduction in decisionmethods, which providing a means of effectively achieving demand of customization, being at the same time in a global On the product family level, products differ mainly in two Yao et al. [3] addressed attribute reduction in decisionmethods, which providing a means of effectively achieving competition with competitors all over the world. This trend, main characteristics: (i) the number of components and (ii) the which is inducing the development from macro to micro type of components (e.g. mechanical, electrical, electronical). 2212-8271 results © 2019 The Published Elsevier B.V. is an open access article under the CC BY-NC-ND license markets, in Authors. diminished lot by due toThis augmenting Classical methodologies considering mainly single products 2212-8271 © 2019 The Authors. Published bysizes Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/). (http://creativecommons.org/licenses/by-nc-nd/3.0/). product varieties (high-volume to low-volume production) [1]. or solitary, already existing product families analyze the Peer-review under responsibility of the scientific committee of the 26th CIRP Life Cycle Engineering (LCE) Conference. Peer-review under responsibility of thevariety scientificas committee oftothebe 26th CIRP Life Cycle Engineering (LCE) Conference. To cope with this augmenting well as able to product structure on a physical level (components level) which doi:10.1016/j.procir.2017.04.009 doi:10.1016/j.procir.2017.04.009 identify possible optimization potentials in the existing causes difficulties regarding an efficient definition and production system, it is important to have a precise knowledge comparison of different product families. Addressing this 2212-8271 © 2019 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/) 2212-8271 © 2017 The Authors. Published by Elsevier B.V. Peer-review under responsibility of scientific the scientific committee theCIRP 26thDesign CIRP Conference Life Cycle 2018. Engineering (LCE) Conference. Peer-review under responsibility of the committee of the of 28th 10.1016/j.procir.2019.01.030
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the optimal reduction for the dependence based and consistency based heuristic reduction algorithms. Jing et al. [7] presented the incremental algorithms for attribute reduction based on the calculated knowledge granularity when multiple attributes are added to the decision system. Min et al. [8] proposed a partial-complete searching technique for ACO and design the APC algorithm. Fan et al. [9] introduced a new neighborhood rough set model, named max-decision neighborhood rough set model. An attribute reduction algorithm is designed based on the model. Wei et al. [10] proposed a discernibility matrix based incremental attribute reduction algorithm and developed an incremental attribute reduction algorithm based on the discernibility matrix of a compact decision table. Teng et al. [11] analyzed the limitations of existing attribute reduction algorithms and proposed a novel measure of attribute quality, called the relative discernibility degree based on the discernibility. Liu et al. [12] proposed the concepts of lth decision class lower approximation reduction, lth decision class reduction, and lth decision class β-reduction for decision tables, then provided their corresponding reduction algorithms via discernibility matrices. Qian et al. [13] proposed several parallel attribute reduction algorithms. Jing et al. [14] proposed a generalized indiscernibility reduction model(GIRM) and a concept of the granular structure in GIRM, which is a quantitative measurement induced from multiple indiscernibility relations and which can be used to represent the computation cost of varied models. The current research mainly focuses on the reduction of general design knowledge, without taking into account the ecological mechanical products design knowledge which is complex, multi-disciplinary and discrete. In the process of mechanical product design, the factors such as function, performance, economy and environmental impact should be considered comprehensively. There is redundancy between these factors. How to reduce the attributes of the mechanical products ecological design knowledge is an urgent problem to be solved. Genetic algorithm is an adaptive global optimization probabilistic search algorithm which simulates the genetic and evolutionary processes of organisms in natural environment. It was first proposed by Professor Holland of the University of Michigan in the United States. Its search method is not a single direction or structure. It takes multiple individuals as possible solutions and considers the global scope of search space. As a result, the genetic algorithm has a strong global search ability and can find the global optimal solution in a relatively short time. 2. Expression of ecological design knowledge for mechanical products Knowledge ontology [15] is a standardized description of the relationship between domain concepts and concepts. This description is standardized, explicit, formal and shared. Explicit means a clear definition of the types of concepts adopted and constraints applied to them. Enterprises often improve their product design ability through collaboration.
On the one hand, owing to the confusion of various related knowledge, ontology technology can easily organize it and greatly improve the utilization efficiency of design knowledge; on the other hand, from the perspective of enterprise design tasks, they generally have multiple attributes such as multiple objectives, multiple constraints, and multiple contents. Multiple attributes can also be organized by the concept expression ability of ontology. Therefore, this article uses ontology to establish knowledge expression model of mechanical product design. Ecological design knowledge is produced in the process of product ecological design. It is the analysis and summary of product life cycle design content. According to the characteristics of product ecological design, based on ontology, product ecological design knowledge is divided into three categories: product design basic knowledge, product design environment attribute knowledge and product design post-processing knowledge. The ontology of product ecological design knowledge can be expressed as: B= {BK, EK, RK}. Among them, BK represents the product design basic knowledge, mainly including type and material; EK represents the product design environment attribute knowledge; product design environment attribute knowledge has a wide range of concepts, mainly including lubrication, heat dissipation, power and emission; RK represents the product design post-processing knowledge, mainly including maintenance, disassembly and recovery. Based on the whole life cycle of product ecological design, the knowledge ontology expression model of product ecological design is established based on the automobile reducer, as shown in Fig. 1. Type Product design basic knowledge Material
Lubrication Ontology expression of product ecological design knowledge
Product design environment attribute knowledge
Heat dissipation
Power
Emission
Recovery
Product design postprocessing knowledge
Maintenance
Disassembly
Fig. 1. Ontology expression model for ecological design knowledge of automobile reducer.
3. Basic concepts 3.1 Rough set theory The characteristics of rough set theory are: prior
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knowledge is not needed except the data set to be processed; it can deal with the uncertainty and inaccuracy of knowledge, and it is an objective method of data reasoning. 3.2 Information system The information system can be represented by a sequence of four elements: IS= (U, A, Va, fa). Where U is domain, representing a set of finite object sets U= {x1, x2, …, x3}; A=C∪D represents a finite set of attributes, including conditional attributes and decision attributes, A= {a1, a2,…,a3}. Va is the range of attribute a. The information function fa: U→Va is defined for each attribute. The information system can be described by a two-dimensional information table. Each row in the table represents an object in U, and each column represents an attribute in A. Each element in the table represents the value of the attribute, that is, the value of information function fa. 3.3 Indistinguishable relationship For any attribute set B⊂A, the indistinguishable relationship Ind(B) is defined as: ∃xi, xj∈U, ∀b∈B, if b(xi) = b(xj), the objects xi, xj are indistinguishable for the attribute set B. The equivalent class of Ind(B) is called the basic set in B, which represents the minimum set of indistinguishable objects, and embodies the highest discrimination ability of the information system. The objects in every equivalence class are not distinguishable under the attribute set B. For any object xi, the equivalence class of xi in Ind(B) is denoted as [xi]Ind(B). The symbol U/A represents the set of all the equivalence relations of objects in U based on the equivalence relation A. It can be seen that Ind(B) is also an equivalence relation in domain U, which form a division U/ Ind(B) of domain U. 3.4 Independence ∀ai ∈ A, if Ind(A)=Ind(A-{ai}), ai is redundant. Otherwise, ai is independent or necessary. ∀ai∈A, if ai∈A, ai is independent, then A is also independent. 3.5 Attribute core and reduction Core and reduction are two basic concepts of rough set theory. When the attribute set B is independent, B⊂A and Ind(B)=Ind(A), then B is the reduction of A. Obviously, the reduction of A is often not unique, and it is recorded as red(A). The collection of all attributes that cannot be omitted is called the core of A. There is a connection between core and reduction: Core(A)=∩red(A). The core has two main functions: (1) Being the basis for the calculation of the reduction; (2) Being the necessary attributes in the information system. 4. Attribute reduction genetic algorithm Reduction genetic algorithm is a way to find minimum
35 3
relative reduction when solving the decision problems. Minimum relative reduction contains the least set of attributes in all relative reductions. For information system, because knowledge reduction set is often more than one, the less the attributes that needed to be considered, the easier it is to handle the information system. Finding minimum relative reduction is of great importance to decision making. The combination of genetic algorithm and rough set often obtain better results. 4.1 Encoding method How to code is the first problem when reducing attribute with genetic algorithm. Considering the practical characteristics of attribute reduction, a fixed-length binary string is usually used to represent individuals in a population whose alleles consist of a set of binary symbols {0,1}. The set of conditional attributes is C={c1,c2,…,cn}, the conditional attribute space KC can be projected into the chromosome of the genetic algorithm. Chromosomes are binary strings of length n, each bit corresponds to a conditional attribute. If a bit has a value of 1, the bit selects its corresponding conditional attribute; if a bit has a value of 0, it does not select its corresponding conditional attribute. Therefore, each chromosome individual corresponds to a subset of attributes in the conditional attribute space. The composition of the chromosome is shown in Table 1. The table shows the case where n=9, and the attribute subset corresponding to the chromosome is {a2, a4, a7}. Table 1. The composition of the chromosome. C1
C2
C3
C4
C5
C6
C7
C8
C9
0
1
0
1
0
0
1
0
0
4.2 The design of fitness function Appropriate evaluation of individuals will lead to good search results. Individual evaluation is accomplished by a fitness function, and fitness function is the only deterministic index for individual evaluation, which can control the evolution of chromosomes toward minimal reduction. Therefore, the design of fitness function directly determines the evolution of population. According to the actual situation of reduction, the fitness function is defined as equation (1):
F ( x) = 1 − card ( x) / n +
card ( Rx ) card ( RC )
(1)
The function consists of two parts. The first part is defined as f(x)=1-card(x)/n, representing the objective function. Where, n represents the length of the conditional attribute set, card(x) represents the number of 1 in an individual, that is, the number of conditional attributes contained in it. The meaning of f(x) is the ratio of the attributes which is not included in the individual x. If the number of attributes in x is smaller, the value of f(x) is
36 4
Lei Zhang et al. / Procedia CIRP 80 (2019) 33–38 Lei Zhang/ Procedia CIRP 00 (2019) 000–000
larger. The second part is defined as P(x) =card(Rx)/card(Rc), which indicates the dependence of decision attribute D on conditional attribute C. Card(Rx) represents the number of objects that can be distinguished by the corresponding conditional attributes of individual x. Card(Rc) represents the number of objects that the conditional attribute C can distinguish. The bigger the value of P(x), the stronger the decision-making ability of the condition attribute x has. When the value is 1, the decisionmaking information is completely determined by the condition information. Solving the minimum relative reduction in the knowledge expression system is to find the least reduction of the conditional attributes under the condition of keeping the overall decision attribute dependency unchanged, and the fitness function constructed in this paper can meet the requirements from these two aspects. 4.3 Selecting Selecting refers to the selection of a good individual from a randomly generated population that makes it possible for the parent to generate a next generation population. The process of eliminating the fittest by genetic algorithm is selection, and the criterion of selection is individual fitness. The paper chooses fitness ratio selection method. The specific implementation process is as follows: (1) Calculating the total fitness of all individuals; (2) The ratio of individual fitness to total fitness is calculated, which is the probability that each individual is inherited into the next generation. (3) The simulated roulette is used to determine the number of times each individual is selected. 4.4 Crossover After selecting the next generation of parents, it is necessary to reorganize and generate new individuals. The crossover operation is carried out between two individuals. Two new individuals are obtained by exchanging part of the information of two individuals. Together with the selection operation, it is ensured that the population evolves in the desired direction. In this paper, single-point crossover is used to randomly pair the individuals in the group. 4.5 Mutation Mutation refers to the process of reversing a selected gene and forming a new individual. In genetic algorithms, an important stage is to complete individual mutation at a very low rate. The mutation operation is performed bitwise, that is, a certain bit of an individual code is mutated. The purpose of the mutation is to maintain the diversity of individuals and to avoid the search process converge too quickly to a local optimal solution. The paper adopts basic bit mutation. For each specified mutation point, the gene bit corresponding to the attribute in the core does not mutate, and the other bits perform the reversal operation, thereby a
new individual is generated. In order to ensure that the individual does not make a big difference with the parent, the mutation probability is generally small to ensure the stability of the population development. 4.6 Preserving the optimal individual Individuals with the greatest fitness in each generation are copied to the next generation of populations. This method can ensure that the characteristics of each generation of optimal individuals rise monotonously when the algorithm is executed, and the algorithm can be converged. 4.7 Terminating algorithm If the fitness of the optimal individuals in the continuous t generation is no longer rose, then the algorithm is terminated. 5. Executing reduction genetic algorithm Input: An information system IS= (U, A, Va, fa). Where, A=C ∪ D, C is the conditional attribute, D is decision attribute. Output: An attribute reduction R of the information system. The basic process is as follows: (1) The initial population consisting of 24 binary bit strings with length of 9 was randomly generated, the corresponding bit attribute is selected to be assigned a value of 1, and if it is not selected, the value is assigned to 0; (2) After calculating the dependence and fitness, the individual is selected by the simulated roulette operation according to the probability that each individual is selected; (3) Crossing. Crossover rate Pc is 0.7; (4) Mutation. Mutation rate Pm is 0.03; (5) Preserving the best individual; (6) The fitness values of the optimal individuals in the continuous t generation are no longer increased, and then the computation is terminated. 6. Algorithm example Automobile reducer is a common mechanical product. As an important transmission component, it is one of the most critical parts of the automobile. Therefore, in the process of its eco-design, it is necessary to consider the impact of each link on its ecological performance, whether in material selection, energy saving, consumption reduction or disassembly and recycling. This paper takes the automobile reducer as an example to reduce the attributes that affect the ecological design of the automobile reducer. Table 2 is an information system for data about automobile reducer, in which domain U= {1,2,...,24}, condition attribute set C ={type, material, lubrication, heat dissipation, power, discharge, recovery, maintenance,
Lei Zhang et al. / Procedia CIRP 80 (2019) 33–38 Lei Zhang/ Procedia CIRP 00 (2019) 000–000
disassembly}, decision attribute D ={ecological performance}. The parameters are set as follows: terminate algebra m=30, Pc=0.7, Pm=0.03. Table 3 is the result of algorithm calculation. The results show the number of iterations, the optimal individuals of each generation, the fitness of the optimal individual and the total fitness. In this example, the optimal individuals appeared in the 12th generation and remained unchanged for 18 consecutive generations. The composition of the optimal chromosome is shown in the Table 4. The result of relative attribute
37 5
reduction is {material, power, emission, disassembly}. After obtaining these attributes which have great influence on the Eco-design of the reducer, designers can consider the Eco-design of the reducer from these aspects first. Table 4. The composition of the optimal chromosome. C1
C2
C3
C4
C5
C6
C7
C8
C9
0
1
0
0
1
1
0
0
1
Table 2. An information system for data on automobile reducer. U Domain
C1 Type
C2 Material
C3 Lubrication
C4 Heat dissipation
C5 Power
C6 Emission
C7 Recovery
C8 Maintenance
C9 Disassembly
D Ecological performance
1
1
2
2
1
3
2
3
1
2
2
2
2
4
1
2
4
2
2
1
1
2
3
1
3
3
2
3
1
3
1
1
1
4
2
1
3
1
1
2
1
2
2
3
5
1
3
3
2
2
2
2
2
1
2
6
3
2
1
1
3
1
2
1
3
2
7
2
2
2
1
4
1
1
1
1
1
8
1
1
2
1
2
3
1
1
1
2
9
2
4
2
2
1
1
3
1
2
1
10 11 12 13 14 15 16 17 18 19 20 21 22 23
2 3 1 2 1 3 1 2 1 3 2 1 1 1
2 2 3 4 1 3 2 3 2 4 1 2 1 1
1 1 1 1 2 1 1 2 2 2 1 2 2 3
2 2 1 2 2 1 1 1 2 1 2 2 1 2
1 3 2 4 3 2 1 3 2 4 1 2 3 2
3 2 3 1 1 3 2 1 1 1 2 3 2 3
3 3 2 2 2 3 2 3 2 2 1 3 2 2
2 1 1 2 2 2 1 1 2 2 2 1 2 2
1 2 2 2 3 1 2 3 2 1 2 3 2 2
2 3 1 2 3 3 1 1 2 3 1 2 2 3
24
2
4
1
2
1
1
1
2
1
1
Table 3. The result of algorithm calculation. Number of iterations
Optimal individual
Fitness
Total fitness
1
010111011
0.772148
15.4415932
2
010111011
0.772148
13.1756165
3
010111011
0.772148
17.531552
4
010111011
0.772148
17.115346
5
010111011
0.771148
14.452263
6
010111011
0.772148
15.444623
7
010111011
0.772148
15.697356
8
010111001
0.963159
18.954665
9
010111001
0.963159
19.753549
10
010111001
0.963159
17.689242
11
010111001
0.963159
17.584362
12
010011001
1.038314
25.874848
13
010011001
1.038314
23.124522
14
010011001
1.038314
24.123368
15
010011001
1.038314
26.212234
16
010011001
1.038314
25.634413
Lei Zhang et al. / Procedia CIRP 80 (2019) 33–38 Lei Zhang/ Procedia CIRP 00 (2019) 000–000
38 6
17
010011001
1.038314
18
010011001
1.038314
22.566458
19
010011001
1.038314
19.563149
20
010011001
1.038314
17.693478
21
010011001
1.038314
24.834896
22
010011001
1.038314
19.675521
23
010011001
1.038314
25.334156
24
010011001
1.038314
22.321114
25
010011001
1.038314
21.565478
26
010011001
1.038314
26.496178
27
010011001
1.038314
20.661783
28
010011001
1.038314
16.784924
29
010011001
1.038314
23.479354
30
010011001
7. Conclusion (1) Based on rough set theory, the operation basis of attribute reduction algorithm is calculated. (2) A rough set attribute reduction algorithm based on genetic algorithm is proposed, which enhances the ability of local search while maintaining the global optimization characteristics of the algorithm. (3) Taking the automobile reducer as an example, the feasibility and efficiency of the algorithm are verified, especially when the data scale is large, the calculation time is saved more. (4) Future work will focus on improving genetic algorithm, combining genetic algorithm with other optimization algorithms, constructing hybrid genetic algorithm, or using parallel genetic algorithm. Acknowledgements This study is supported by the National Natural Science Foundation of China (Grant No. 51775162). We highly appreciate the assistance of all colleagues in the Institute of Green Design and Manufacturing Engineering at Hefei University of Technology. Reference [1] Pawlak Z. Rough set[J]. International Journal of Computer & Information Sciences, 1982, 11(5). [2] Jerzy W. Grzymała-Busse, Zdzisław Pawlak, Roman Słowiński, et al. Rough set[J]. Communications of the Acm, 1995, 38(11):800-805.
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