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

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 others. The resulting mathematical model contains inherently nonlinear and nonconvex constraints. The proposed iterative algorithm is deterministic, and it attains finite g-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.

A new deterministic global optimization algorithm has been successfully applied to different case studies. It was possible to solve different problems for global optimality using a simplified model for the design of a multi-stage flash evaporator. The objective function determines the optimal process design and operating conditions for a given water production. These simplified models consider the most important aspects of the process (boiling point elevation, number of tubes, geometric design of evaporator, among others). Therefore, global optimal solutions provide adequate approximate solutions for preliminary design or an accurate starting point for solving more complex models for the problem since these solutions are good preliminary designs and global solutions for a good simplified model.