Differential Evolution with Dynamic Adaptation of Mutation Factor Applied to Inverse Heat Transfer Problem

In this paper a Modified Differential Evolution (MDE) is proposed and its performance for solving the inverse heat transfer problem is compared with Genetic Algorithm with Floating-point representation (GAF) and classical Differential Evolution (DE). The inverse analysis of heat transfer has some practical applications, for example, the estimation of radioactive and thermal properties, such as the conductivity of material with and without the temperatures dependence of diffusive processes. The inverse problems are usually formulated as optimization problems and the main objective becomes the minimization of a cost function. MDE adapts a concept originally proposed in particle swarm optimization design for the dynamic adaptation of mutation factor. Using a piecewise function for apparent thermal conductivity as a function of the temperature data, the heat transfer equation is able to estimate the unknown variables of the inverse problem. The variables that provide the beast least squares fit between the experimental and predicted time-temperatures curves were obtained. Numerical results for inverse heat transfer problem demonstrated the applicability and efficiency of the MDE algorithm. In this application, MDE approach outperforms the GAF and DE best solutions.