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108Proceeding of the 4 rd International Symposium“NEW RESEARCH IN BIOTECHNOLOGY” USAMV Bucharest, Romania, 20112.2.3. An evolutionary method for process optimizationFor problems involving optimization of a process where variables model can varyover time (or any other independent variables such as distance) turn to an evolutionaryprogram [6]. For example, heat or chill food processing, efficiency and resulting productquality are dependent on the time-temperature regime. The method is based on randomtemperature regimes. Each of these regimes (also called members of the population)consists of a vector ( )1,...,nX X X whose components depend on the (constant) equalt ,... t , t t t− = + , ( ) i 1,∀ = n , the temperature values at times areintervals of time 1 n i 1 idetermined by the linear interpolation or using Lagrange polynomial.Starting from two random vectors and using a mathematical formula we obtain thefollowing vector-temperature (this step is called a generation reproductive stage). Then, twovectors are taken at random from those indicated. The "less competent" (for therefrigeration process- the highest temperature) of them is eliminated.This process of elimination provides vectors temperature range finding "fit" for theprocess considered. The algorithm is repeated until it reaches a satisfactory regime existingin the population until they can get improvements for a pre-specified number of cycles.3. RESULTS AND DISCUSSIONS3.1. Optimize defrosting meat blocksThe problem of optimization of complete thawing meat blocks, considering thetemperature fluctuation in a certain period of time, was solved by applying the evolutionarymethod above, after having first found the following:- Using a conventional technique of numerical analysis, the calculus of finite differences,we can determine the temperature at different points of the food.- If we consider the temperature variations in the block of meat to be thawed are highbecause the edges and corners are heated more quickly and if we consider the deviationsdue to random errors of measurement or recording, we believe that stochastic modeling isthe most appropriate method to optimize this process.- The meat blocks are represented by a plate 160 mm thick; initial temperature of -20 ° C,heat transfer coefficient is 20 W/m2 K and the time available for thawing 24 hours.- We assume that the temperature varies, but because of design restrictions vaporizerchamber cannot exceed 30°C, graphical representation of this temperature is a polygonalline with a slope change every three hours.- The objective function we want to determine is the extent to which the minimum surfacetemperature exceeds 7 ° C and is characterized mathematically by:f( T ) ⎤2∫ ⎡⎣max 0,s7 ⎦,= −WhereT Sis the surface temperature.- The cost of thawing is given by the penalty function:( )g = max 0, TP− TC
Proceeding of the 4 rd International Symposium“NEW RESEARCH IN BIOTECHNOLOGY” USAMV Bucharest, Romania, 2011WhereT Cis the temperature in any point of the block of meat and TPis the temperature inthe center. We want to determinemin f( + cg )c is the coefficient of penalty cost.To ensure that the packaging is completely thawed, choose a high cost factor, forexample. To determine the optimal solution, it is necessary to achieve a number of differentsimulations (between 500 and 1000). Starting from the maximum value of 30 ° C airtemperature drops to 24-23 ° C, then at 20 ° C and finally at 8 ° C. This process keeps thesurface temperature to no more than about 13 ° C, while the center is thawed in 24 hours.The results obtained with the evolutionary method have the next graphical representation:Fig.1 Optimized thawing process for meat blocks.3.2. Optimization of beef carcass chilling (microbial constrains)We propose to model a system to cool the temperature of a foot deep beef carcasse,such as the potential microbial (E. coli) growth on the surface of the foot should not exceedthree generations and at the same time to obtain maximum tenderness of the meat. Heattransfer coefficient is assumed to be 20 W/m2K and initial temperature 40 ° C. The airtemperature ranges from 15 ° C and -10 ° C because of regulations and design restrictions.The problem was proposed and analyzed by Q. Tuan Pham and S. Lovatt [4]. Themathematical model corresponding to E.coli growth rate (Gill, 1993), indicates bothnecessary intervals beef carcass cooling according to different values of temperature andmicrobial growth rate (in E.coli generations per hour).109
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