Abstract
Hierarchical optimization problems such as (generalized) semi-infinite optimization problems and bilevel problems appear in various disciplines of process systems engineering, such as flexibility analysis or parameter estimation. Adaptive discretization-based algorithms are a family of methods to solve these problems. In these methods, the original problem is decomposed into subproblems, which are solved with a standard optimization solver and then refined iteratively. Several related algorithms have been published. Until recently, computational studies have typically been performed using publication-specific implementations and benchmark problems. We recently published a software package - libDIPS - comprising existing adaptive discretization-based algorithms and a library of test problems for comparison. Several of the algorithms implemented in libDIPS exhibit strong parallelization potential in their algorithmic steps: In the algorithms of Mitsos [Optimization 60:1291-1308 (2011)] and Mitsos and Tsoukalas [J Glob Optim 61:1-17 (2015)], the upper- and lower-bounding procedures are independent. In the algorithm of Tsoukalas and Rustem [Optim Lett 5:705-716 (2011)], several objective function values can be probed independently for feasibility. However, algorithm statements in the literature typically only consider serial execution of the algorithm steps. While parallelization of the used subsolver is already possible in libDIPS, leveraging parallelization in the algorithmic steps has not been investigated until now. In this contribution, we present an overview of libDIPS and introduce our parallelized implementations of several existing algorithms. We investigate the effect of parallelization at the algorithm-level compared to parallelization within the subsolver. Furthermore, we propose two improvements to speed up the solution process of the algorithms compared to their original publications. Results are presented for the existing library of test problems collected from literature.