Different approaches for the solution of a backward heat conduction problem

This work presents a comparison of three different techniques to solve the inverse heat conduction problem involving the estimation of the unknown initial condition for a one-dimensional slab, whose solution is obtained through minimization of a known functional form. The following techniques are employed to solve the inverse problem: the conjugate gradient method with the adjoint equation, regularized solution using a quasi-Newton method, and regularized solution via genetic algorithm (GA) method. For the first one, a general form to compute the gradient of the functional form (considering the time and space domains) is presented, and for the GA method a new genetic operator named epidemical is applied.