Radial basis function approximations to polynomials
Numerical analysis 1987
Voronoi diagrams—a survey of a fundamental geometric data structure
ACM Computing Surveys (CSUR)
Convergence qualification of adaptive partition algorithms in global optimization
Mathematical Programming: Series A and B
Lipschitzian optimization without the Lipschitz constant
Journal of Optimization Theory and Applications
A comparison of sequential Delaunay triangulation algorithms
Proceedings of the eleventh annual symposium on Computational geometry
Evolutionary algorithms in theory and practice: evolution strategies, evolutionary programming, genetic algorithms
Genetic algorithms + data structures = evolution programs (3rd ed.)
Genetic algorithms + data structures = evolution programs (3rd ed.)
The quickhull algorithm for convex hulls
ACM Transactions on Mathematical Software (TOMS)
Experiments with new stochastic global optimization search techniques
Computers and Operations Research
Numerical Optimization of Computer Models
Numerical Optimization of Computer Models
Stochastic Global Optimization: Problem Classes and Solution Techniques
Journal of Global Optimization
Global Optimization by Multilevel Coordinate Search
Journal of Global Optimization
Parallel Simulated Annealing Algorithms in Global Optimization
Journal of Global Optimization
A Radial Basis Function Method for Global Optimization
Journal of Global Optimization
A Taxonomy of Global Optimization Methods Based on Response Surfaces
Journal of Global Optimization
A note on the use of a fuzzy approach in adaptive partitioning algorithms for global optimization
IEEE Transactions on Fuzzy Systems
Hi-index | 7.29 |
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 new partitions. 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.