13-4 |
Thermal processing: A constrained non-linear multi-objective function optimization problem |
F. ERDOGDU, Food Engineering Dept., Mersin Univ., Ciftlikkoy-Mersin, 33342, Turkey and M. O. Balaban, Food Science & Human Nutrition Dept., Univ. of Florida, Gainesville, FL 32611. Optimization for more than one shape in thermal processing results in a multi-objective constrained optimization problem. Then, the goal becomes to optimize the objective functions for each shape simultaneously. Complex method is a powerful algorithm to find the optimum of a general non-linear function within a constrained region. The objective of this study was to apply the complex method to two different shapes to find a variable retort temperature profile to maximize the volume-average retention of thiamine during thermal processing. The model system consisted of a sphere (2r=30 mm) and a finite cylinder (2r=30 mm, 2l=60mm). A process temperature range of 5-150 C was used as one explicit constraint, that the process temperature had to reach 5 C at the end was another. The implicit constraints were the center temperature reached at the end of the processing, and the accumulated center lethality. The objective functions were the volume average retention of thiamine in each shape, and the decision variable was the variable process temperature profiles. The two objective functions were combined into a single one using the weighting method, associating each function with a real normalized weighted coefficient. Then, the complex algorithm was applied using Lexicographic Ordering method to prevent the violation of any constraint. The results were reported as optimum variable temperature profiles using the given geometries, objective functions and constraints. Process temperature profiles for the given double geometry system together with their thiamine retentions were presented. The thiamine retentions were also compared with a constant process temperature process, and 3.5% increase was obtained in the combined objective function. The results showed that the complex method can be successfully used to predict the optimum variable process temperature profiles in thermal processing for a multi-shape, multi-objective function optimization problem.
Session 13, Food Engineering: Thermal processes
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