An Improved Interval Global Optimization Algorithm Using Higher-order Inclusion Function Forms

We propose an improved algorithm for unconstrained global optimization in the framework of the Moore–Skelboe algorithm of interval analysis (H. Ratschek and J. Rokne, New computer methods for global optimization, Wiley, New York, 1988). The proposed algorithm is an improvement over the one recently proposed in P.S.V. Nataraj and K. Kotecha, (J. Global Optimization, 24 (2002) 417). A novel and powerful feature of the proposed algorithm is that it uses a variety of inclusion function forms for the objective function – the simple natural inclusion, the Taylor model (M. Berz and G. Hoffstatter, Reliable Computing, 4 (1998) 83), and the combined Taylor–Bernstein form (P.S.V. Nataraj and K. Kotecha, Reliable Computing, in press). Several improvements are also proposed for the combined Taylor–Bernstein form. The performance of the proposed algorithm is numerically tested and compared with those of existing algorithms on 11 benchmark examples. The results of the tests show the proposed algorithm to be overall considerably superior to the rest, in terms of the various performance metrics chosen for comparison.