Proof. Lets assume that there are two nodes u and v in depth d for which the calculated lower bound is optimal, and u is visited first among all nodes in depth d with optimal lower bound. This implies that the lower bound of v is not smaller than the lower bound of u. A best-first search Branch-and-Bound algorithm only visits nodes with lower bounds not greater than the global minimum. It follo...

We investigate unconstrained optimization with an objective function that has an unknown and possibly large number of local minima. By varying the selection and termination criteria, we obtain several variants of the Moore-Skelboe algorithm for distinct tasks in nonconvex global optimization. All of these terminate after having found the best answer that is possible, given the precision of the ...

This paper presents a convergence proof of the adaptive tabu search (ATS) algorithms. The proof consists of two parts, i.e. convergence proof of all interested solutions in a finite search space, and that of searching processes of the ATS algorithms to the global minimum. With the proposed definitions and theorems, the proofs show that the ATS algorithms based on a random process have finite co...