# Evaluation of Disassembling Process Inference Based on Positional Relations Matrix
## 4 Concluding Remarks  
Geometrical constraints among the constituent parts are a fundamental factor for the disassembly of systems consisting of a number of parts. We adopt the positional relations matrix of binary elements to describe the geometrical constraints. On the basis of the matrix, a disassembling process inference approach was developed in a general form. The approach can be applied to any disassembling problem expressed in terms of the positional relations matrix.  
In the current study, we have evaluated the proposed disassembling process inference approach based on two-dimensional disassembling problems, which were generated by a random number-based disassembling problem generation system. The disassembling problems adopted for the evaluation appear relatively simple because of their two-dimensionality; however, they exhibit a complicated nature comparable to practical problems in case of a sufficient number of constituent parts.  
From the viewpoint of the optimality of the results, the obtained disassembling processes based on the proposed inference approach were fairly appropriate; however, it was confirmed that the proposed inference approach does not always result in the optimal disassembling process. In the proposed approach, there actually is some arbitrariness in the marking process of impeding parts, as mentioned in Section 2.2.2. We are studying this point to improve the disassembling process to be generated. From the viewpoint of the computational cost, it was demonstrated that the proposed inference approach is quite practical and the computational cost is \(\mathcal{O}(N^{2})\), compared with the computational cost of  
Figure 4: Typical disassembling processes of a 40-part system based on the proposed approach.  
\(\mathcal{O}(N!)\) of the permutation approach that always gives the optimal results. We conclude that the proposed disassembling process inference approach based on the positional relations matrix is practical enough.  
The proposed disassembling process inference is expected to have a wide range of applicability because of the generality and extensibility of the positional relations matrix, as mentioned in Section 2.1. From the optimality viewpoint, it is considered to be possible to employ a criterion other than the number of disassembling moves for the target part, such as the required work time or the total mass of the disassembled parts, by customizing the selection from the possible candidate moves suggested in Section 2.2.2.  
The positional relations matrix is assumed to be constant in the current study. Dynamic impeding conditions--that is, impeding conditions among parts depending on the order of disassembling parts or so-called compound moves--cannot be dealt with. Mechanical conditions of such as supported or supporting parts are currently not taken into account either. Expanding the positional relations matrix to include intermediate states of part condition and introducing logical operation among the matrix elements to determine a part's propensity for disassembly are promising candidate topics to be undertaken. Such an extension of the disassembling process inference is also a topic that can be addressed in future work.  
Conceptualization, K.Y.; Methodology, K.H. and K.Y.; Software, K.H.; Writing--original draft, K.H.; Visualization, K.H. and K.Y.; Funding acquisition, K.Y. All authors have read and agreed to the published version of the manuscript.  
This research was supported by JSPS KAKENHI Grant Number JP 23K11719.  
Not applicable.  
The data presented in this study are generated by our original computer program that is not publicly available. The data as well as the computer program can be partially available on request from the corresponding author.  
The authors declare no conflicts of interest.