Finally, we examine the computational performance of the proposed algorithm on various test problems that cover most of the difficulties encountered in global optimization. The other updates a search tree that represents a hierarchical structure of subdivided subspaces during the solution process. One involves subdivision into mutually disjoint subspaces and computation of their bound information, both of which are accomplished by using B-spline hypervolumes. The algorithm includes two procedures that are performed iteratively until all stopping conditions are satisfied. We then describe a proposed algorithm for finding global solutions approximately within a prescribed tolerance. For these schemes, we first introduce a B-spline hypervolume to approximate an objective function defined in a design space, where the approximation is based on Latin-hypercube sampling points. The key components of the branch-and-bound, a well-known algorithm paradigm for global optimization, are a subdivision scheme and a bound calculation scheme. ![]() This paper presents a B-spline-based branch-and-bound algorithm for unconstrained global optimization.
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