Lipschitz continuity and the termination of interval methods for global optimization

AbstractIn this paper, it is shown how the Lipschitz continuity of a global optimization problem's objective function influences the termination of a Hansen type method. The results concern applying different termination criteria to a Hansen method and retrieving more information than explicitly supplied by a certain criterion. A similar result for Moore-Skelboe methods arises, as a consequence

ANALISA METODE BRANCH AND BOUND UNTUK PROBLEMA PROGRAM INTEGER TAK LINIER (Literature Review)

In this paper, we analyze branch and bound methods for solving non linear integer programming problem. After solving a problem by ignoring the integrality requirements, this strategy is used to force the appropriate non-integer basic variables to move to their neighbourhood integer points

Experiments with hybrid Bernstein global optimization algorithm for the OPF problem in power systems

This paper presents an algorithm based on the Bernstein form of polynomials for solving the optimal power flow (OPF) problem in electrical power networks. The proposed algorithm combines local and global optimization methods and is therefore referred to as a `hybrid' Bernstein algorithm in the context of this work. The proposed algorithm is a branch-and-bound (B&B) procedure wherein a local search method is used to obtain a good upper bound on the global minimum at each branching node. Subsequently, the Bernstein form of polynomials is used to obtain a lower bound on the global minimum. The performance of the proposed algorithm is compared with the previously reported Bernstein algorithm to demonstrate its effi cacy in terms of the chosen performance metrics. Furthermore, the proposed algorithm is tested by solving the OPF problem for several benchmark IEEE power system examples and its performance is compared with generic global optimization solvers such as BARON and COUENNE. The test results demonstrate that the algorithm HBBB delivers satisfactory performance in terms of solution optimality.This research is supported by the National Research Foundation, Prime Ministers Office, Singapore, under its CREATE programme