Global optimization of thermal conductivity using stochastic algorithms

Abstract

In this article, the performance of a self-organizing migration algorithm (SOMA), a new stochastic optimization algorithm, has been compared with a genetic algorithm with floating-point representation (GAF) and differential evolution (DE) for an engineering application. This application is the estimation of the apparent thermal conductivity of foods at freezing temperature using an inverse method. Assuming two piecewise functions for apparent thermal conductivity in function of the temperature data, the heat diffusion equation was solved to estimate the unknown variables of inverse problem. The thermal conductivity is continuously adjusted by three approaches of stochastic optimization algorithms, used to minimize a performance criterion based on error information for the inverse problem. The variables that provide the best fitness between the experimental and predicted time-temperature curves at centre of the food under freezing conditions were obtained. Moreover, a statistical analysis showed the agreement between reported and estimated curves. In this application domain, the SOMA and DE approaches outperform the GAF.Nomenclature c random value in GAF c p specific heat (J kg À1 C À1 ) CR crossover or recombination rate in DE DE differential evolutionf objective function f m mutation factor in DE g parameter in SOMA GAF genetic algorithm with floating-point representation h heat transfer coefficient (W m À2 C À1 )H volumetric specific enthalpy (J m À3 ) IHTP inverse heat transfer problem k thermal conductivity (W m À1 C À1 ) L half length in x direction (m) m difference between leader and start position of individual in SOMA N size population (individuals); number of samples N (0,1) random number with Gaussian distribution, zero mean and variance one PRT parameter in range [0,1] in SOMA PRT ! perturbation vector in SOMA rnd random number generation r vector candidate solution in SOMA R 2 Pearson multiple correlation coefficient index SOMA self-organizing migration algorithm t coordinate in freezing time (s) T theoretical temperature ( C) experimental temperature ( C) u trial vector in DE x vector solution z mutant vector in DE Greek symbols step length used in BFGS evaluated by Armijo or index for indicates vectors in DE recombination mechanism in DE " tolerance value density (kg m À3 ) index that indicates the method for selecting of the parent chromosome in DE Át temporal mesh step (s) Áx spatial mesh step (m) Subscripts i index represents mesh interval or individuals for optimization algorithms j index represents time interval or dimensions problem space l leader in SOMA max maximum n dimension of the vector solution n pop size population r 1 , r 2 , r 3 integers used in DE 0 initial 1 ambient 512 V.C. Mariani and L. dos Santos Coelho Superscripts ct generations counter L lower boundary tt time indicator U upper boundary * reference which corresponds to null enthalpy

Mass transfer during the osmotic dehydration of West Indian cherry

“…Among the deterministic methods, the LevenbergeMarquardt method has been used successfully in several areas (Kanevce, Kanevce, & Dulikravich, 2005;Mejias, Orlande, & Özisik, 2003;Mendonça, Filho, & Silva, 2005). Among the stochastic methods, the Differential 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, Lima, and Coelho (2008); da Silva, da Silva, and Mariani (2009).…”

Identification of time-dependent coefficients of heat transfer by the method of suboptimal stage-by-stage optimization

“…Recently, a Bayesian statistical inference method [10,11] is actively applied to solution of IHCP. We should mention also hybrid methods which combine algorithms of artificial neuron networks, genetic algorithms and procedures of annealing simulation [12,13].…”