Parallel cell mapping for unconstrained multi-objective optimization problems

Abstract

Recently, the cell mapping techniques, originally designed for the global analysis of dynamical systems, have been proposed as a numerical tool to thoroughly investigate multi-objective optimization problems. These methods, however, suffer the drawback that they are restricted to low-dimensional problems, say n ≤ 5 decision variables. The reason is that algorithms of this kind operate on a certain discretization on the entire search space resulting in a cost that is exponential to n. As a possible remedy we propose in this paper to use a parallel implementation of the cell mapping strategy. We will make use of Graphics Processing Units (GPUs) which allow for comfortable speedups in particular for problems that are costly to evaluate since cell mapping techniques are highly parallelizable.We will test our methods on several widely used benchmark models with n = 10 decision variables and make some comparisons to the sequential version of the cell mapping technique.