Optimal Shape Design for Heat Conduction Using Smoothed Fixed Grid Finite Element Method and Modified Firefly Algorithm

The present study is concerned with optimal shape determination of inhomogeneous and temperature dependent domains under steady state heat conduction. Such situations are important in many thermal design problems, especially in shape design of electronic components and chips. In the present paper, we formulate the shape optimization problem based on volume minimization of heat conductive material while limiting maximum temperature. The smoothed fixed grid finite element method which is a new approach based on the non-boundary-fitted meshes is used to obtain temperature field. The boundary parameterization technique using splines is also adopted to manipulate the shape variations. A modified version of the firefly algorithm which is a recently developed metaheuristic optimization technique is proposed as the optimizer. These modifications consist of adding memory, adding newborn fireflies and proposing a new updating formula. To evaluate the applicability of the proposed method five numerical examples are solved and the results are presented. Keywords– Shape optimization, nonlinear heat conduction, smoothed fixed grid finite element method, metaheuristic optimization, firefly algorithm