Parallel Triangulated Partitioning for Black Box Optimization

Abstract

We propose a parallel triangulation based partitioning algorithm (TRIOPT) for solving low dimensional bound-constrained black box global optimization problems. Black box optimization problems are important in engineering design where restricted numbers of input-output pairs are provided as data. Optimization is carried out over sparse data in the absence of a formal mathematical relationship among inputs and outputs. In such settings, function evaluations become expensive, because system performance assessment might be conducted via simulation studies or physical experiments. Thus, the optimal solution should be found in a minimal number of function evaluations. In TRIOPT, input-output pairs are treated as samples located in the search domain and search space coverage is obtained over these samples by triangulation. This produces an initial partition of the domain. Thereafter, each simplex is assessed for re-partitioning in parallel. In this assessment, performance values at the vertices are transformed and mapped to [0,1] interval using a non-linear transformation function with dynamic parameters. Transformed values are then aggregated into a group measure upon which the decision for re-partitioning is taken. Simplices whose group measures overcome a given threshold value are re-partitioned in parallel. Here, the performance of TRIOPT is measured on several applications from different fields and compared with powerful partitioning techniques such as LGO, DIRECT, and MCS.