Extensions of a Multistart Clustering Algorithm for Constrained Global Optimization Problems

Abstract

Here, we consider the solution of constrained global optimization problems, such as those arising from the fields of chemical and biosystems engineering. These problems are frequently formulated (or can be transformed to) nonlinear programming problems (NLPs) subject to differential−algebraic equations (DAEs). In this work, we extend a popular multistart clustering algorithm for solving these problems, incorporating new key features including an efficient mechanism for handling constraints and a robust derivative-free local solver. The performance of this new method is evaluated by solving a collection of test problems, including several challenging case studies from the (bio)process engineering area.

The GLOBAL optimization method revisited

“…the difficult one addressed in [9]). Still we are also working on the extension of the algorithm to constrained problems [22].…”

Improved placement of local solver launch points for large-scale global optimization

“…One of the main issues for clustering is: what constitutes a cluster? For global optimization software that seeks basins of attraction, cluster definitions are commonly based on the relative spatial locations and objective values of the points [85].…”

“…GLOBALm is a recently proposed multistart clustering algorithm for constrained global optimization problems [85]. The method consists of a global phase and a local phase.…”

“…Finally, due to the random assignment of the initial points there is no guarantee that the variable space will be adequately explored. Improved versions of the multistart method exist, for instance, MSNLP [56] and GLOBALm [85]. These algorithms employ techniques including advanced sampling, acceptance and rejection, and clustering methods in order increase the effectiveness of the multistart method.…”

Global optimization algorithms for bound constrained problems

“…According to our experiences, this approach can be successful in most of the cases encountered (see Csendes et al [31]). There is also an extension of the algorithm to constrained problems in Sendín et al [105].…”