제국주의 경쟁 알고리즘을 이용한 구조최적화

Abstract

This thesis proposes a new method for topology optimization (TO), shape optimization (SO), and topological shape optimization (TSO) using the imperialist competitive algorithm (ICA). The ICA is a meta-heuristic method that is a socio-politically inspired optimization strategy; the algorithm mainly operates the social-political process of imperialism and imperialistic competition. In the present study, in order to apply for structural optimization, some modifications on the original ICA were performed to improve the capacities of the method. In particular, the solutions should be calculated in the discretized domain for structural optimization; however, the ICA operates only continuous (real) search space. From that reason, a variable called the “Elements Search Space” (ESS) which discretizes the search space was applied and the ESS was updated until the volume constraint is satisfied or initialized until the convergence criteria are satisfied. In addition, a parametric study for the algorithmic parameters was performed by an analysis of variance (ANOVA) and two major parameters were selected, namely, the assimilation coefficient and the number of decades. The proper values of algorithmic parameters were examined by the genetic algorithm (GA), providing robustness to the optimized results. In the SO method using the ICA, the solutions in the boundary design domain should be considered. Therefore, the Euclidean distance transform of binary image, which is a derived representation of an element state (void/solid) was implemented to obtain the boundary elements. The ESS was updated by boundary elements in each iteration and the reduction of the design variables improved the convergence rate and the CPU time. In the TSO method using the ICA, the solutions in the boundary design domain should be considered differently. In order to naturally create the holes and simultaneously optimize the boundary elements, a variable called the “Boundary Elements Range” (BER) which changes the boundary range was applied. The BER, which is calculated by stability, restricts and causes the variance of the boundary region. From the results, the number of the elements to be searched decreased from the overall design domain, while the convergence rate and CPU time improved in the optimization. To verify the effectiveness of the suggested method using the ICA, examples for structural optimization were provided to compare with those of the structural optimization method based on the BB-BC, HS, ABCA, and BESO methods or the discrete LSM. Our results suggest that the proposed algorithm was successfully applied to the TO, SO, and TSO methods and those results show that structural optimization using ICA provides a robust optimum design, a fast convergence rate, and a stable optimization process.