Disassembly sequence planning using a Simplified Teaching–Learning-Based Optimization algorithm☆
Introduction
Mass-customized productions, technology updating and shortening lifespan of products in modern societies have resulted in generation of enormous amount of waste products like Waste Electrical and Electronic Equipment (WEEE). Developing technical solutions for sustainable recovery of waste products becomes a global trend. End-of-life recovery options include part reuse, remanufacturing, material recycling, energy recovery and disposal. As shown in Fig. 1, disassembly, which is a systematic method for separating a product into its constituent components and subassemblies [1], is a critical stage for end-of-life recovery. Finding an optimum or near optimum disassembly sequence is crucial to increasing the efficiency of the disassembly process.
Disassembly Sequence Planning (DSP) determines the order in which components are removed from products aiming at minimizing the disassembly time or cost, while considering the disassembly direction, disassembly method, and other attributes of components. DSP has been proved as a NP-hard problem [2] and has been becoming an important but still a challenging research topic in recent years. In the previous research, heuristics and meta-heuristics were used to find near optimum or optimum solutions and generate cost-effective and feasible disassembly sequences. Heuristics include rule-based recursive method [3], graph-based heuristic approach [4], etc. Meta-heuristics, which have been widely applied for solving such problems as well, include Genetic Algorithm (GA) [5], [6], [7], [8], [9], [10], [11], Particle Swarm Optimization (PSO) [12], [13], [14], [15], [16], [17], Ant Colony Optimization (ACO) [18], [19], [20], Greedy Randomized Adaptive Search Procedure (GRASP) [21], [22], [23], etc. However, the controlling parameters in the above meta-heuristics need to be tuned, such as crossover rate and mutation probability in GA, inertia weight and two acceleration constants in PSO, two weights for path selection and evaporation rate in ACO, and window size in GRASP, etc. This characteristic makes the above meta-heuristics not adaptive and robust enough for various situations.
A new population-based evolutional algorithm named Teaching–Learning-Based Optimization (TLBO) algorithm, which was originally introduced by Rao, et al. in 2012 [24], [25], has been successfully applied to continuous non-linear large scale problems [26], [27] including mechanical design optimization [25], parameter optimization of machining processes [28], [29], [30], high dimensional real parameter optimization [31], economic emission load dispatch [32], etc. Unlike the above optimization techniques, the TLBO algorithm does not require any algorithm parameters (except population size and iteration times) to be tuned and outperforms some of the well-known meta-heuristics regarding constrained benchmark functions, constrained mechanical design, and continuous non-linear numerical optimization problems [24].
However, the TLBO algorithm is not suitable for solving the DSP problems directly as it was designed for continuous optimization problems while the DSP problems are discrete combinatorial optimization problems with complex disassembly precedence constraints. In continuous problems, a solution is a vector of design variables, each of which belongs to a continuous rang. Sequencing the components in a product for disassembly planning is a typical DSP problem. In this problem, a solution can be represented as a permutation of integers, which are the serial numbers of components in a product. For this DSP problem, the solution space is not continuous and TLBO is unable to be applied directly. Meanwhile, a directly discretized TLBO algorithm could not be a good choice for the above DSP problem either. In a DSP problem, the search space for an optimal solution is growing exponentially according to the number of components in the product, while the disassembly constraints could be complex. These characteristics cause that there are few feasible solutions in the population by using a random solution generation method embedded in TLBO. Furthermore, disassembly precedence constraints cannot be preserved simply using an arithmetic operation method during the evolutions towards optimization, which leads to few feasible solutions in the offspring. Hence, the directly discretized TLBO algorithm can hardly converge and solve the DSP problem effectively.
In order to solve the DSP problems more efficiently, this paper proposes a new optimization algorithm named Simplified Teaching–Learning-Based Optimization (STLBO) algorithm. The STLBO algorithm inherits the main idea of the teaching–learning-based evolutionary mechanism so as to take the merits of the TLBO algorithm. Three new operators, including a Feasible Solution Generator (FSG), a Teaching Phase Operator (TPO) and a Learning Phase Operator (LPO), have been designed and incorporated into the algorithm so as to make the algorithm applicable for DSP problems with complex constraints. In the meantime, the complex and multidimensional matrix computation used to modify solutions in the TLBO algorithm is simplified to a precedence preservation crossover operation in the STLBO algorithm. The detecting of feasibilities of new generated solutions would be also avoided. With the designed operators, STLBO can converge faster in the optimization or search process with higher accuracy so as to eventually improve the disassembly efficiency as well as reducing disassembly cost.
The rest of the paper is organized as follows: In Section 2, the proposed STLBO algorithm for DSP problems is presented in detail. Section 3 demonstrates the performance of STLBO algorithm through numerical experiments and benchmark tests with case studies of waste product disassembly planning. Finally, conclusions are drawn in Section 4.
Section snippets
STLBO algorithm for DSP problems
This section presents the STLBO algorithm developed for DSP problems in detail. Firstly, the TLBO algorithm is introduced briefly. And then, the framework of the STLBO algorithm is described. Subsequently, three key operators implemented in STLBO algorithm are presented in detail with illustrative examples of disassembly of waste products. Lastly, the comparison analysis of STLBO algorithm with other optimization algorithms is given and the implementation steps of STLBO algorithm for the DSP
Experimental studies
In order to test the performance of the STLBO algorithm and conduct a further comparative study, two kinds of disassembly sequence planning problems are described and used for testing. In both problems, the case of complete disassembly of wasted products is considered and it assumes that the structure of waste products and disassembly precedence constraints are known. Two types of representation methods of disassembly precedence constraints and the corresponding methods for generating a
Conclusions
This paper proposes a novel STLBO algorithm for solving DSP problems. The STLBO algorithm is divided into two phase: teaching phase and learning phase. And three new key operators are presented: FSG, TPO and LPO. The developed STLBO algorithm is a discrete and population-based optimization algorithm with a new teaching–learning-based evolutionary mechanism. The characteristics and advantages of the developed STLBO are summarized as follows:
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The STLBO algorithm is specially designed for DSP
Acknowledgements
This research is carried out as a part of GREENet project which was supported by a Marie Curie International Research Staff Exchange Scheme Fellowship within the 7th European Community Framework Programme under Grant Agreement No. 269122. The paper reflects only the author’s views and that the Union is not liable for any use that may be made of the information contained therein. This research work is also supported by the Special Funds for the Scientific and Technological Cooperation with EU
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Handled by C.-H. Chen.