RESULTS AND DISCUSSION

RESULTS AND DISCUSSION

6.1 INTRODUCTION

The cell formation problem determines the decomposition of the manufacturing cells of a production system. Machines are assigned to the cells to process one or more part families so that each cell operated independently and the inter-cellular movements minimized. Group Technology is the part of manufacturing cell formation to attain the best performance like reduced cell formation problem. One application of GT is in cellular manufacturing (CM), which aims to decompose a manufacturing system into manufacturing cells where different machines are aggregated into cells and operate on a part family. The chapter evolves the results and discussion about the manufacturing cell formation to attained through metaheuristic algorithms like Discrete Cauchy Mutation Algorithm with Salp Swarm Algorithm, Monarch Butterfly Optimization with Firefly algorithm, and Modified Adaptive Resonance Theory (MART1) Neural Network Algorithm. In this chapter, the result of the manufacturing cell formation discussed and the algorithms perform effectively.

6.2 PERFORMANCE ANALYSIS

The result section examined the validation result for benchmark problems. Here, we select a diverse problem size, for example, small size problems and significant size problems. The proposed technique is actualized in MATLAB programming with the most recent version of 2016a and completed in the processor of Intel center i5 with 8 RAM. The parameters required to run the algorithm are population size, number of generations, the number of iterations, hybrid, and mutation probabilities. These parameters have an essential job in the presentation of the DCMA-SSA. The proposed hybrid algorithm accomplishes ideal solutions which have minimum cell load variation and minimum intercellular movements. Table 6.1 shows the parameters used in DCMA.

Table 6.1 Parameters used in DCMA

Table 6.2 represents the intercellular movements for small-sized benchmark problems.

Table 6.2 Intercellular movements for small-sized benchmark problems

The parameter that utilized for approving DCMA-SSA given as pursues:

Table 6.3 represents the intercellular movements for small-sized benchmark problems.

Table 6.3 Intercellular movements for small-sized benchmark problems

Table 6.4 shows the Cell load variation for small-sized benchmark problems.

Table 6.4 Cell load variation for small-sized benchmark problems

Table 6.5 Intercellular movements for large-sized benchmark problems

Table 6.5 illustrates the intercellular movements for large-sized benchmark problems. Table 6.6 represents the cell load variation for large-sized benchmark problems.

Table 6.6 Cell load variation for large-sized benchmark problems

Table 6.2, 6.3 shows the performance of the proposed approach based on small-sized benchmark problems. Here we noted the intercellular movements and cell load variation for ten benchmark problems. The proposed result compared with EA, SSA, and DCMA. The computational time for each benchmark problem is analyzed. From the result compared to all the benchmark problems, the intercellular movements and cell load variation of the solution reached by the proposed method is optimal than that of existing algorithms (EA, SSA, and DCMA) (Goncalves and Resende 2004). Here, the minimum value of intercellular movements reached in problems 2, 1, 3, and 5; in cell load variation, the minimum amount achieves in the CFP as problems 2, 6, 7, 10, and 3. Moreover, the computational time for the validation process analyzed for the proposed hybrid algorithm (DCMA-SSA); the proposed method reduced the computational time. Table 6.4, 6.5, shows the performance of the validation result based on large-sized benchmark problems. In these types of issues, problem number 2 gives an optimal solution with less amount of computational time. In the validation part, the population of the DCMA-SSA expands if the CFP size increased. The use of DCMA-SSA will discover the local and global optimum effectively and simultaneously.

Figure 6.1 Objectives based on iterations for benchmark problem (8 x 20) through like as 6.1 (a) Intercellular movements 6.1 (b) Cell Load Variation (CLV).

Figure 6.2 Fitness function based on generations

Figure 6.2 shows the performance of fitness function based on iterations for benchmark problem 8 x 20. The convergence graph compares the proposed method into existing algorithms EA, GA. Here we take 100 iterations for the analysis; for the comparison of all the three optimization techniques proposed, DCMA gives an optimal solution, i.e., minimum fitness values. The result depicts that the effectiveness of the algorithm decides the number of machines and parts into several cells. Similarly, CLV also varies based on the iteration for problem size (8 x 20). DCMA produces minimum CLV compared to the existing one. It achieves the optimal fitness in the 80th iteration. To minimize the intercellular movements can be made by optimal material transfer within the cells based on the function of the machines. Cell load variation depicts the system imbalance, to minimize these over-allocating problems, we have to choose the optimal machine loads that can decrease the pressure of loads.

Figure 6.3 shows the fitness function based on several generations. If machines grouped into the same cells, copy one of the parents as one child; another child is created randomly with the initialization operation. And then break out from the crossover operator; according to our test, we find that the repetitions of the same individual with better fitness will be overfull as the generations grow, and those excess repetitions will induce trapping into local optima. The best fitness means the optimal solution achieved and the average fitness shows the solution with nearby optima moreover the worst fitness means the solution with maximum fitness. The graph performs the best fitness value as the minimum and shows the average and worst fitness values. Our method is capable of dealing with CFP more efficiently and flexibly without predetermining the number of cells.

Figure 6.3 Computational time analysis 6.3 (a) analysis for small-sized problems 6.3 (b) analysis for large-sized problems

Figure 6.4 Computational time analysis by comparing existing techniques

Figure 6.3 and 6.4 shows the computational time analysis for small and large-sized benchmark problems. The computational time may vary based on the benchmark problem size. Here, we take different sized benchmark problems to find the objectives. All the above figure shows the computational time for each benchmark problems concerning the proposed hybrid approach. Significant problems get more running time compared to small-sized problems. Figure 6 shows the computational time for all the benchmark problems and also examines the proposed DCMA-SSA model into existing techniques’ like CSA, GLCA, TS-GA. Compared to the existing algorithm proposed algorithm finds the objective in minimum computational time with an optimal solution.

6.3 PERFORMANCE ANALYSIS

The proposed CFP with an optimization method for accomplishing the optimal solution is finished by utilizing MATLAB software variant 2016a most recent form in a system having 8 GB RAM with a 64-bit operating system having i5 processor. The performance of the hybrid algorithm MBO-FF systematically evaluated in comparison with other existing methods on standard benchmark testing problems. All these data are available for downloading from the http://opt-hub.com/problems/cfp hub.

Table 6.7 Comparison of performance measures of the proposed model to other algorithms.

Table 6.7 represents the comparison of performance measures of the proposed model to other algorithms.

6.3.1 Performance evaluation

Table 4.1 depicts the comparison of the proposed model to other algorithms with computational results. Here, the performances of CFP for twenty benchmark problems are analyzed and are named as A1, A2 … up to A20. In this table, M signifies the machines; P identifies Parts, and C indicates Cell.

The G.E, C.E, M.U, and percentage of EE compared with every problem. The evaluation of the proposed MBO-FF compared with the existing techniques such as Dragonfly-Fruit Fly Algorithm (DF-FFA). The MBO-FF attains optimal value, and it reaches the global optimum solution based on increasing the efficiency, efficacy, and machine utilization and reducing the exceptional elements. The performance of the proposed algorithm MBO-FF evaluated 20 different benchmark test problems taken from the literature.

Table 4.2 depicts the sources and sizes for these problems. For every problem source number of machines, parts, cells, grouping efficacy, cell efficiency, machine utilization, and percentage of exceptional elements and the best cell size obtained. Also, this table reported the computational time required to get the best solution for each problem source by the proposed approach.

The grouping efficacy of the solutions obtained by the MBO-FF is as good as the best solution available in the literature. Our solution is better than that of all the 20 methods. Therefore, the proposed method outperforms all the other methods. The cell efficiency of the solutions obtained by the MBO-FF is superior to the 17 ways out of 20 methods. Therefore, the proposed method performs well. The performance on machine utilization attained by the MBO-FF is shown improvement in 18 methods out of 20 ways.

The percentage of exceptional elements by the proposed MBO-FF model outperforms on 7 methods and equivalent to the remaining 13 problems taken from the 20 methods as the best solution available in the literature.

Based on the performance measures such as grouping efficacy, cell efficiency, machine utilization, and percentage of exceptional elements, the MBO-FF shows best performs.

6.5 (a) G.E evaluation

6.5 (b) M.U evaluation

6.5 (c) C.E analysis

6.5 (d) Percentage of EE analysis

Figure 6.5 Performance evaluation of MBO-FF

Figure 6.5 shows the convergence graph representation of all the performance parameters compared with different techniques. The G.E., M.U., C.E., and percentage of E.E. attained for varying iterations.

It denotes that increasing iterations will improve the optimal solution. That means for significant sized problems; the result can be confirmed optimal. Comparing the effects of different techniques is a difficult task, but the convergence graph illustrates that the optimal solution achieved in MBO-FF than DF-FFA.

6.3.2 Comparison evaluation

Figure 6.6 shows the comparative analysis of performance parameters based on the five sample benchmark problems such as King (A1), Waghodekar and Sahu (A2), Seifoddini (A3), Kusiak and Cho (A4) and Kusiak and Chow (A5), DF-FFA and the proposed MBO-FF. Here, Actual value refers to the experimental values of the above mentioned existing techniques.

The Grouping Efficacy for MBO-FF values of A1-85.96, A2-77.45, A3-83.95, A4-89.45, and A5-64.12 is higher than the actual costs of A1-82.3, A2-69.5, A3-80.85, A4-79.17, and A5-60.87. The benchmark problem works under the basis of the cell forming of particular parts working in machines. On cell efficiency and Machine utilization, the proposed algorithm MBO-FF scores maximum performance, as shown in figure 3.

The Percentage of Exceptional Elements for MBO-FF values of A1- 0, A2-12.5, A3-12.5, A4-24.6, and A5-23 are the minimum of the actual costs of A1- 0, A2-12.5, A3-12.5, A4-25 and A5-23.7.

This study concludes that M.U, G.E, and C.E achieves maximum value in the proposed model, i.e., maximum G.E. reaches 93.66%, C.E. as 91.54%, M.U as 92.85%, and minimum in the percentage of EE as 0 and 0.7. The proposed model achieves an optimal result in CFP.

Figure 6.6 (a)

Figure 6.6 (b)

Figure 6.6 (c)

Figure 6.6 (d)

Figure 6.6 Comparison analysis a) G.E comparison b) C.E comparison c) M.U analysis d) Percentage of E.E comparison analysis.

Figure 6.6 illustrates the comparison analysis a) G.E comparison b) C.E comparison c) M.U analysis d) Percentage of E.E comparison analysis.

6.4 PERFORMANCE ANALYSIS

6.4.1 For PMIM CF

For CF, using MART1 was tested with different benchmark datasets, which collected from the literature. In all the tested problems, the ρ value is taken as 0.1. The results compared with the different CF approaches with various performance measures.

The datasets already tested for the vigilance parameter selection. The comparative results shown in Table 6.8. For the first two datasets, the MART1 results are equal to the solutions. For the dataset 3 and 4 E are similar, the MART1 grouping efficiency is high when compared to the grouping efficiency. For all other datasets, the E is low, and η is high when compared to the values of E and η.

Table 6.8 Comparison of results with Chandrasekharan and Rajagopalan (1989)

6.4.2 For CF with Production Factors

The first dataset of NBIM adapted from Peker and Kara (2004). They tested their Fuzzy ART network approach by using 7 X 7 NBIM. The same problem considered for the evaluation of the MART1. First of all, the NBIM converted into a PMIM, and it is given as input to the MART1 CF network to get the final output of grouped parts and machines. Then the NBIM CF procedure is followed, and the final output obtained. The OFV (i.e., the sum of exceptional value) is 2.4. The result is identical to the Peker, and Kara (2004) results.

The next NBIM data taken from Vohra et al. (1990). They used machining time NBIM of size 7 X 7. Vohra et al. tested the dataset with a constraint of two and three cells, and their objective function is to minimize the total machining times of the inter-cellular movement. For two cells, the MART1 result shown in Table 6.9. The MART1 considered for the minimization of exceptional elements and minimization of total inter-cellular machining time. In the MART1, the number of a unique component is 1, and the entire inter-cellular movement is 8. But Vohra et al. (1990) used a network approach, and their number of an exceptional element is three, and their total inter-cellular machining time is only 4. Vohra et al. (1990) are not considering the minimization of extraordinary items.

Table 6.9 Result for Vohra et al. (1990) NBIM problem

For three cells, the MART1 number of an exceptional element is two, and the total inter-cellular machining time is 14. But Vohra et al. (1990) give only 9 total inter-cellular machining time, and the number of an exceptional element is 4.

             The next dataset is OSIM. The dataset taken from Suresh et al. (1999). They used 15 X 15 OSIM. The OSIM is converted into a PMIM, and it is given as input to the MART1, and the final output is grouped machines and parts. Based on the output, the inter-cell move matrix obtained by using the equation (5.1), and the MART1 with production factors procedures followed. The result is identical to the Suresh et al. (1999) result.

The next two OSIM data adapted from Nair and Narendran (1998). The size of the first dataset is 7 X 7. The result is identical to the Nair and Narendran (1998) findings. They used the CASE algorithm. The second Nair and Narendran (1998) dataset is 20 X 20, and the number of groups is 3. The MART1 result is identical to Nair and Narendran (1998).

The next dataset is an operational sequence with a production volume dataset, which adapted from Youk Yung Won and Kun Chang Lee (2002). The operation sequences and production volumes for the parts shown in Table 6.10.

Table 6.10 Operation sequences with the production volume problem

The table converted into PMIM, and it given as input to the MART1 network and the final output grouped machines and parts. The inter-cell flows calculated by using equation (5.2). The MART1 with production factor steps followed, and the final output is identical to the Youk Yung Won and Kun Chang Lee (2001) solution.

6.4 SUMMARY

            In this chapter, the performance of results executed practically. The effective Cauchy Mutation Algorithm with Salp Swarm Algorithm, Monarch Butterfly Optimization with Firefly algorithm, and Modified Adaptive Resonance Theory (MART1) Neural Network Algorithm to perform the better manufacturing cell formation process. The way of processing results evolves better cell formation to reduces the inter-cell movements, load variation, operation sequence, etc., for the given period.

CHAPTER 7

CONCLUSION

7.1 CONCLUSION

The cell formation problem is related to one of the primary aims of Group Technology (GT): to decompose the manufacturing system into manufacturing cell formation that is as independent as possible. The manufacturing cell formation problem is NP-hard. So, the nonheuristic methods cannot address issues of typical industrial dimensions because they would require outrageous amounts of computing time. The meta-heuristic algorithms can perform an active manufacturing cell formation. The results examined the validation results for benchmark problems. The proposed technique is actualized in MATLAB programming with the most recent version and completed in the processor of Intel center i5 with 8 RAM. The parameters required to run the algorithm are population size, number of generations, the number of iterations, hybrid, and mutation probabilities.

In the first stage of the work, the proposed Discrete Cauchy Mutation Algorithm (DCMA) Salp Swarm Algorithm (SSA). The aim of this algorithm that reduced the number of intercellular movements and also minimized the cell load variation for the given period. Genetic Algorithm related to the updated model DCMA-SSA. The performance of the hybrid algorithm is purposely assessing in comparison with other existing techniques on standard benchmark testing problems. The proposed hybrid technique gives an optimal solution which empowers ideal fitness for every benchmark problems such as minimum intercellular movements and minimum cell load variation.

In the second stage of the work, the Monarch Butterfly Optimization with Firefly algorithm used to solve the multi-objective cell formation problem. This algorithm is competent to investigate the search space viably and recognize the global optimal within a short measure of time. The quality of best solutions attained and firefly is united to solve the large-size cell formation problem. The performance measurement determines the result in terms of percentage, such as exceptional elements (EE), machine utilization (MU), grouping efficacy (GE), and cell efficiency (CE).

In the third stage of the work, the Modified Adaptive Resonance Theory (MART1) Neural Network Algorithm. The MART1 gives PF and MC and the number of exceptional elements with the constant vigilance parameter. This MART1 deals with non-binary data to enhance the operation sequences and production volume with the maximization of the grouping efficiency. Finally, the above algorithms solved the inefficiency of the existing cell formation methodologies. The results showed better manufacturing cell formation throughout the various kind of meta-heuristic algorithms used.