# Evaluation of Disassembling Process Inference Based on Positional Relations Matrix
## 3 Evaluating Disassembling Process Inference  
In order to evaluate the performance and efficiency of the disassembling process inference developed in Section 2.2, we employ a disassembling-problem generation system [18]. The system is able to generate two-dimensional block-pattern-based disassembling problems consisting of any number of parts. The approach is based on a weighted random walk; that is, it places parts consisting of four to six square blocks at empty cells in the course of the walk. The point is that the direction of the walk has a weak tendency towards the origin in order to keep the state of aggregation as an assembled system. Figures 2 and 3 show examples of randomly generated disassembling problems of 12 parts and their obtained disassembling processes. The red parts are the target part and the parts to be disassembled; the arrows in the parts indicate the disassembly moves. Figures 2b and 3b are the optimal disassembling processes of minimum moves obtained by  
the permutation approach indicated in Section 2.3. Figures 2c and 3c are the disassembling processes obtained by the proposed disassembling process inference. The disassembling processes shown in Figure 2b,c are the same; however, the disassembling processes shown in Figure 3b,c are different. These results show that the proposed disassembling process inference is not guaranteed to generate the optimal disassembling process. We evaluate the computational cost for disassembling process inference in terms of the number of evaluations of elements of the positional relations matrix. Comparing the numbers of evaluations required to obtain the results shown in Figure 2b (\(3.8\times 10^{9}\)) and Figure 2c (730) as well as Figure 3b (\(2.6\times 10^{9}\)) and Figure 3c (960), it is demonstrated that the computational cost by means of the proposed approach is considerably less than the computational cost by means of the permutation approach. On the basis of 20 randomly generated disassembling problems of 12 parts, the average numbers of disassembly moves are 2.70 by means of the permutation approach and 3.15 by means of the proposed inference approach. Fifteen of the twenty results (75%) are of the same numbers of moves for both permutation and the inference approaches in this case; however, there is one result that the inference approach gives seven moves while the optimal result has only three moves. Figure 2: Disassembling process generation example (1). Table 1 shows the averaged computational costs of the proposed disassembling process inference for the generated disassembling problems of various numbers of parts. The results indicate that the computational cost of the proposed inference approach is less than \(\mathcal{O}(N^{2})\) for the \(N\)-part problem. Compared with the computational cost \(\mathcal{O}(N! )\) for \(N\)-part problem of the permutation approach, the proposed inference approach is considered to be practical enough from this point of view. Figure 4 shows typical examples of a disassembling process for a 40-part system based on the proposed inference approach. Figure 3(a) shows an appropriate disassembling process; however, the result shown in Figure 3(b) seems fairly redundant. On the basis of the obtained disassembling process shown in Figure 3(b), we can see the possibility of a disassembling process of two fewer steps without the disassembly moves of the top and the bottom parts, by assuming the leftward move to all the parts to be disassembled. This result also demonstrates that the proposed inference approach does not always generate the optimal disassembling process. It should be noted, however, that the permutation approach cannot be applied to a disassembling problem of this number of parts because of the computational cost of \(\mathcal{O}(N! )\).