TRIOPT: a triangulation-based partitioning algorithm for global optimization

Abstract

We propose a triangulation-based partitioning algorithm,TRIOPT, for solving low-dimensional bound-constrained black box global optimization problems. The method starts by forming a Delaunay triangulation of a given set of samples in the feasible domain, and then, it assesses the simplices (partitions) obtained for re-partitioning. Function values at the vertices of each partition are mapped into the zero one interval by a nonlinear transformation function and their aggregate entropy is calculated. Based on this entropy, partitions that hold a promise of containing the global optimum are re-partitioned according to different triangular splitting strategies, forming newpartitions. These strategies are efficient in terms of the number of new function evaluations required per new partition. A novelty in the search scheme proposed here is that once a partition narrows down to a small size, its vertices are eliminated from the available sample set. This changes global information on the best solution and triggers a re-calculation of transformed values. Hence, revised entropies change the direction of the search to new areas. The latter scheme leads to a dynamic parallel search policy which is based on an entropy cut. The tree adopts flexible breadth depending on the status of the search. In the experimental results it is demonstrated that TRIOPTs performance is compatible and often better than that of a well-known response surface methodology and two other efficient black box partitioning approaches proposed for global optimization.