## 5 Conclusions  
In this study, the MIGA-based approximate optimizations using three types of meta-models were performed for the weight minimization design of the A60 BPP with the characteristics of discrete design variables. The three types of meta-models were applied to the approximate optimization in the fire resistance design of A60 BPP, and the most adequate meta-model was also explored. From the results of the transient heat transfer analysis, it was found that the temperature results of the newly devised A60 BPP satisfied the fire resistance temperature limit for the A60 class apparatus specified in the FTP code. The results of the transient heat transfer analysis were verified via the actual fire test, according to both the FTP code and international fire resistance test procedure specified in ISO. It was found that both the temperature measurement results and their variation characteristics from the transient heat transfer analysis were coincident with the verification test. Since the transient heat transfer analysis method adopted in this study was confirmed to be suitable for the evaluation of the fire resistance performance of the A60 BPP, both the meta-model generation and the approximate optimization based on the transient heat transfer analysis were performed for the minimum weight design of the A60 BPP. The DOE method was applied to generate the meta-models to be used for the approximate optimization, and the verified the transient heat transfer analysis models and their results were integrated into the design matrix of DOE. The length, diameter, and material type of A60 BPP, and the insulation density were included in the design variables with the discretized specifications that can be actually manufactured. Regarding the evaluation of the output responses such as the objective function and the constraint, the A60 BPP weight was applied as the objective function, and the constraints were considered the fire resistance temperature regulated in the FTP code, productivity, and cost, respectively. A total of 54 full-factorial experiments were generated to consider all the results of the objective functions and the constraints that occur due to the level of variation of the design variables. From the DOE results, Kriging, RSM, and RBFN were generated. The \(R^{2}\) values of all the generated meta-models for output responses represented 0.96 or higher on average. Among the meta-models, it was found that the RBFN was able to explore the design space of the A60 BPP with the highest accuracy, while the Kriging showed the lowest overall accuracy. In order to minimize the weight of the A60 BPP subject to the constraints, the approximate optimization with the discrete design variables was carried out by using the MIGA technique and the meta-models. The approximate optimization problem was formulated such that the discrete design variables were determined by minimizing the weight of the A60 BPP subject to the constraints of fire resistance, i.e., temperature, productivity, and cost. From the results of approximation optimization, the A60 BPP weight was reduced more than 23%, compared to the initial design while satisfying all the limit values of constraints. The approximate optimization result using the RBFN meta-model represented the highest accuracy because the approximate results of the constraints were coincident with the actual calculation results. In the case of applying Kriging and RSM meta-models, the weight was reduced up to 23.5%, but the approximation accuracy results of the fire test temperature constraint were inferior to the results of the case in which the RBFN meta-model was applied. From the approximate accuracy of constraints and the convergence results of the objective function, it was confirmed that the case of applying the RBFN meta-model was the most effective method in the approximate optimization with the discrete design variables for the fire resistance design of A60 BPP. Conceptualization, C.Y.S. ; methodology, C.Y.S. ; software, W.C.P. ; validation, C.Y.S. ; formal analysis, W.C.P.