A new global optimization algorithm for process design: its application to thermal desalination processes Original Research Article

A new deterministic algorithm [1] to solve a nonconvex, nonlinear optimization problem (a desalination process model) to global optimality is presented. The algorithm optimization was applied to the simplified model developed previously by Mussati et al. [2,3]. The objective was to determine the optimal process design and operating conditions for a given water production. Although the model for the desaltor was derived from a simplified hypothesis, it considers all the most important aspects of the process. The model takes into account the evaporator geometric design (height, length and width of stages), number of tubes in the pre-heater, boiling point elevation, among other. The resulting mathematical model contains inherently nonlinear and nonconvex constraints. The proposed iterative algorithm is deterministic, and it attains finite ε-convergence to the global optimum through the successive subdivision of the original region and the subsequent solution of nonconvex optimization problems. A bound reduction technique is performed in order to accelerate the algorithm convergence. The global optimal solutions obtained by the algorithm provide preliminary designs for the process. Moreover, these solutions are used as a starting point to solve more complex models efficiently [3]. Different case studies are presented and discussed in order to illustrate the methodology and computational performance.