Complex method for nonlinear constrained multi-criteria (multi-objective function) optimization of thermal processing

ne goal in a multi-objective function optimization problem is to optimize the several objective functions simultaneously. ne complex method is a powerful algorithm to find the optimum of a general nonlinear function within a constrained region. The objective of this study was to apply the complex method to two different shapes (a sphere and a finite cylinder) subjected to the same thermal processing boundary conditions to find a variable process temperature profile (decision variable) to maximize the volume-average retention of thiamine. A process temperature range of 5 to 150C was used as an explicit constraint. Implicit constraints were center temperature and accumulated center lethality of the sphere and the finite cylinder. The objective functions for both shapes were combined into a single one using a weighting method. Then, the previously developed complex algorithm was applied using Lexicographic Ordering to order the objective functions with respect to their significance. The results were reported as optimum variable process temperature profiles using the given geometries and objective functions. The thiamine retentions were also compared with a constant process temperature process, and 3.0% 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 multi-criteria thermal processing problems.