# Many optimization methods have been proposed to solve inverse pro

Many optimization methods have been proposed to solve inverse problems, based on the estimation of deterministic and stochastic parameters. Among the deterministic methods, the Levenberg–Marquardt method has been used successfully in several

areas (Kanevce et al., 2005, Mejias et al., 2003 and Mendonça et al., 2005). Among the stochastic methods, the Differential click here Evolution method has been applied less frequently to inverse problems, but has been used by Kanevce et al., 2005, Mariani and Coelho, 2009a, Mariani and Coelho, 2009b, Mariani et al., 2008 and da Silva et al., 2009. Optimization methods for estimating parameter are used to estimate the diffusion coefficient as a function of the minimization of J by the sum of squared differences between the experimental moisture content and the moisture content computed with a diffusion model: equation(5) J=∑1n(Xexp−Xcomp)2where Xexp is the experimental moisture content and Xcomp is the computed moisture content. A set of moisture contents was obtained experimentally

at discrete times during the unsteady drying process. The literature uses different criteria to evaluate the quality of the fit obtained by the mathematical selleckchem model and optimization methods to simulate the experimental results. In this study, deviations between measured and simulated moisture content were calculated

using the coefficient of determination in successive trials, as follows: equation(6) R2=1−∑(Xexp−Xcomp)2∑(Xexp−X¯exp)2 The Differential Evolution and Levenberg–Marquardt methods were implemented. 3-oxoacyl-(acyl-carrier-protein) reductase Differential Evolution (DE) is an evolutionary algorithm proposed by Storn and Price (1995). Although DE shares similarities with other evolutionary algorithms (EA), it differs significantly in that the search process is guide based on information about the distance and direction of the current population. DE uses the differences between randomly selected vectors (individuals) as the source of random variations for a third vector (individual), referred to as the target vector. Trial solutions are generated by adding weighted difference vectors to the target vector. This process is referred to as the mutation operator in which the target vector is mutated. A crossover step is then applied to produce an offspring, which is only accepted if it improves the fitness of the parent individual. The basic DE algorithm is described in greater detail below with reference to the three evolution operators: mutation, crossover, and selection.