A genetic algorithm for product disassembly sequence planning
Introduction
Product's disassembly/recycle design is one of the most important issues in product green design. As Gupta [11] pointed out, “product disassembly sequence is the main engine of disassembly planning system”.
Disassembly sequence generation problem involves the generation of one or more feasible sequences to disassemble a product successfully. Traditionally, researches on disassembly planning have often made use of graph-models to represent product architecture, collect and store relevant product information, such as adjacency graph or adjacency matrix, AND/OR graph and precedence graph [4], [12], [7], [20], [14]. Main contents of these researches are:
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How to construct the graph model to represent product architecture.
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How to handle the graph and generate disassembly sequence solution(s).
Adjacency graph (or adjacency matrix) is often used to represent the connecting relationships between components of a product. AND/OR graph, in essence, describes all of its possible disassembly sequences by simulating components’ disassembly/assembly operations. Precedence graph shows the constraint relationships among these components. Thus, feasible or optimal disassembly sequences could be deduced from these constraint relationships.
Disassembly sequence planning problem is a NP-hard combinatorial optimization problem [18]. Generally, with the increase of components in product, the computational complexity of searching for optimal disassembly sequence in a large solution space will increase more quickly. Therefore, traditional methods cannot solve this problem effectively—that is, avoid the combinatorial explosion. Consequently, metaheuristic methods are often used to find out optimal solutions at a high efficiency [6], [15].
Several examples of metaheuristic applications in assembly/disassembly sequencing have been introduced [16], such as expert systems, simulated annealing, Petri nets and neural networks. In particular, genetic algorithm (GA) is often used, for its capability to evolve toward optimal solution without processing all the alternatives. Lazzerini et al. [17], in their GA method for assembly planning, encoded chromosome with three parts: disassembly sequence of components, directions of disassembly operations and used gripper. Kongar and Gupta [15] also proposed a genetic algorithm for disassembly process planning. A little different from Dini's encoding method, the representation of a chromosome (solution) consists of three parts of equal length, sequences of components, operations’ directions and the methodology (destructive method or not). This encoding method was also used by Galantucci et al. for his fuzzy logic and genetic algorithms (2004) [9].
As the above-mentioned methods, much information of constraint relationships and disassembling operations is included in chromosome as genes. But these researchers failed to explain how to obtain relevant information/data to construct solutions space before genetic search. Furthermore, with the increase of components number, the solutions space will be very, very huge. And it may make the search process less efficient to find out optimal solution.
The research work presented in this paper, by converting disassembly sequence planning problem into a searching problem on an information-enhanced graph, uses genetic algorithm to search for good disassembly solutions.
The rest of this paper is organized as follows. Section 2 provides a detailed description of the disassembly feasibility information graph (DFIG), and discusses the idea of converting disassembly sequence planning problem into a simple path searching problem. In Section 3, a GA-based algorithm is presented to solve this problem. All key parts of the proposed algorithm, including encoding of chromosome, genetic operators and fitness function, are introduced. Finally, Section 4 describes briefly an application case.
Section snippets
DFIG model
Firstly, we give the definition of DFIG, which is designed to represent product's disassembly operations (sequences) information. And Fig. 1 illustrates the DFIG of a product with five components.
Definition. Let G={V, W, D} be a simple non-negative weight, directed graph, and meanwhile:
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G has a root node, start point.
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Vertices set is V={Vi | i∈M}, where M is the number of vertices, D is directed edges set and W is the set of weights loaded on related edges.
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Ω={ai | i∈N} represents all components
Genetic algorithm
As is known today, genetic algorithm (GA) was first described by John Holland in the 1960s and 1970s. It is currently a prominent and widely used model [5], [10], for solving combinatorial optimization problems.
When GA is used in engineering applications, the following steps are often very important:
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Encode problem into proper chromosome.
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Define fitness function to evaluate the performance of chromosome (solution).
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Genetic operators: crossover, mutation and selection.
Encoding of chromosome
Chromosomal encoding is a way
A case study and results
We have developed a software system based on the above methods. It is designed, developed and tested as a sub-system of PTC Pro/Engineer Wildfire [13] (Pro/Engineer is PTC's integrated 3D product design software, which is one of most famous software for product design and development in manufacturing). By this system, product is displayed as a 3D model to facilitate the visualization of disassembly process.
A hypothetical product, formed by 30 parts, has been used to evaluate the performance of
Conclusions
Disassembly & recycle research is an important field of Environmentally Conscious Manufacturing, in recent years. The Disassembly Feasibility Information Graph (DFIG) proposed in this paper, by simulating product's disassembly operations, can represent product's disassembly solutions and store relevant information, and therefore, we can map disassembly sequence planning problem onto DFIG model as an optimal path searching problem. This conversion offers a concise and powerful model to use
Wang Hui is currently a Ph.D. candidate in the Department of Precision Instruments and Mechanology, Tsinghua University, PR China. He received B.Eng and M.Sc. in 2000 and 2003, respectively, from Northwestern Polytechnical University, Xi’an. His main research interests include assembly/disassembly planning, green design, and heuristic methods.
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Wang Hui is currently a Ph.D. candidate in the Department of Precision Instruments and Mechanology, Tsinghua University, PR China. He received B.Eng and M.Sc. in 2000 and 2003, respectively, from Northwestern Polytechnical University, Xi’an. His main research interests include assembly/disassembly planning, green design, and heuristic methods.
Xiang Dong received his Ph.D. from Chongqing University. Now he is an associate professor in the Department of Precision Instruments and Mechanology of Tsinghua University. His main research interests include design for environment, cleaner production and recycling technology of e-wastes.
Duang Guanghong is a professor in the Department of Precision Instruments and Mechanology. He is also the Director of Research and a senior member of CASME. His current research interests include CAD/CAM, green manufacturing, advanced manufacturing machine and NC technology.