Prediction of foods freezing and thawing times: Artificial neural networks and genetic algorithm approach S.M. Gon ˜i a,b,c , S. Oddone d , J.A. Segura b , R.H. Mascheroni a,c, * , V.O. Salvadori a,c a CIDCA, Facultad de Ciencias Exactas, UNLP – CONICET, La Plata, Argentina b Departamento de Ciencia y Tecnologı ´a, UNQ, Bernal, Argentina c MODIAL – Depto. Ing. Quı ´mica – Facultad de Ingenierı ´a, UNLP, La Plata, Argentina d Facultad de Ingenierı ´a y Ciencias Exactas, UADE, Buenos Aires, Argentina Received 22 December 2006; received in revised form 15 March 2007; accepted 1 May 2007 Available online 13 May 2007 Abstract In this work a feedforward neural network, trained and validated using experimental values of freezing and thawing times of foods and test substances of different geometries, is developed. A total of 796 experimental times of both processes were collected from reported works. The database used covered a wide range of operative conditions as well as size, shape and type of material. The input layer had seven elements: shape factor, characteristic dimension, Biot number, thermal diffusivity, initial, ambient and final temperatures. The out- put layer had one element: the process time. The total number of hidden layers and the number of neurons in each hidden layer were chosen by trial and error. For each topology, a simple based genetic algorithm search technique was applied to obtain the initial training parameters of the neural network that improve its generalization capacity. Three particular networks were evaluated: one for freezing times, another one for thawing times, and a third one for both freezing and thawing times. The final topologies has one or two hidden layers with 4 nodes in each one. Our results show that the neural network had an average absolute relative error of less than 10%, sug- gesting that ANN provide a simple and accurate prediction method for freezing and thawing times, valid for wide ranges of food types, sizes, shapes and working conditions. Ó 2007 Elsevier Ltd. All rights reserved. Keywords: Freezing time; Thawing time; Food; Artificial neural network 1. Introduction One of the main interests of design engineers and equip- ment users is to be able to count on simple and accurate prediction methods for the simulation of the process they are dealing with, mainly for the calculation of process times as a function of material characteristics and operating con- ditions. Particularly, freezing is an important operation in food preservation, for it involves millions of tons of food per year (Pierce, 2002). That is why there is a continuous interest in improving and simplifying prediction methods of food freezing and thawing times (Delgado and Sun, 2001). Detailed modeling of heat transfer in freezing or thaw- ing of foods leads to strongly nonlinear differential bal- ances, due to the rapid variation of the thermal properties with temperature in the freezing range (Sanz, Domı ´nguez, and Mascheroni, 1987). Generally, the bal- ance to be solved is (Eq. (1)): oT ot ¼ rðaðrT ÞÞ; oT o ~ n ¼ BiðT s  T a Þ; 8 > < > : ð1Þ where the Laplacian $ can have one, two or three compo- nents, depending on whether the heat transfer is 0260-8774/$ - see front matter Ó 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jfoodeng.2007.05.006 * Corresponding author. Address: CIDCA – Facultad de Ciencias Exactas, UNLP and CONICET, La Plata, Argentina. Tel./fax: +54 221 425 4853. E-mail address: rhmasche@ing.unlp.edu.ar (R.H. Mascheroni). www.elsevier.com/locate/jfoodeng Journal of Food Engineering 84 (2008) 164–178