Difference between revisions of "GLBSOLVE (analysis)"

Revision as of 15:25, 4 April 2013

GLBSOLVE algorithm

A deterministic global optimization method¹. It is a version of the DIRECT algorithm² that handles nonlinear and integer constraints. The first step in the DIRECT algorithm is to transform the search space to be the unit hypercube. The function is then sampled at the center-point of this cube. Computing the function value at the center-point instead of doing it at the vertices is an advantage when dealing with problems in higher dimensions. The hypercube is then divided into smaller hyperrectangles whose center- points are also sampled. Instead of using a Lipschitz constant when determining the rectangles to sample next, DIRECT identifies a set of potentially optimal rectangles in each iteration. All potentially optimal rectangles are further divided into smaller rectangles whose center-points are sampled. When no Lipschitz constant is used, there is no natural way of defining convergence (except when the optimal function value is known as in the test problems). Instead, the procedure described above is performed for a predefined number of iterations.

Note that this solver does not support parameters constraints.

References

1. M Björkman and K Holmström, "Global Optimization Using the DIRECT Algorithm in Matlab". AMO, vol. 1, #2, pp. 17-37, 1999.
2. DR Jones, "DIRECT global optimization algorithm". Encyclopedia of optimization, pp. 431-440, 2001.