Branch and probability bound methods in multi-objective optimization

An approach to non-convex multi-objective optimization problems is considered where only the values of objective functions are required by the algorithm. The proposed approach is a generalization of the probabilistic branch-and-bound approach well applicable to complicated problems of single-objective global optimization. In the present paper the concept of probabilistic branch-and-bound based multi-objective optimization algorithms is discussed, and some illustrations are presented

A lower bound on convergence rates of nonadaptive algorithms for univariate optimization with noise

Global optimization, Wiener process, Noisy information,

Subdivision, Sampling, and Initialization Strategies for Simplical Branch and Bound in Global Optimization

AbstractWe consider the problem of optimizing a Lipshitzian function. The branch and bound technique is a well-known solution method, and the key components for this are the subdivision scheme, the bound calculation scheme, and the initialization. For Lipschitzian optimization, the bound calculations are based on the sampling of function values.We propose a branch and bound algorithm based on regular simplexes. Initially, the domain in question is covered with regular simplexes, and our subdivision scheme maintains this property. The bound calculation becomes both simple and efficient, and we describe two schemes for sampling points of the function: midpoint sampling and vertex sampling.The convergence of the algorithm is proved, and numerical results are presented for the two dimensional case, for which also a special initial covering is presented