Finding and Proving the Optimum: Cooperative Stochastic and Deterministic Search

Abstract

In this article, we introduce a global cooperative approach between an Interval Branch and Bound Algorithm and an Evolutionary Algorithm, that takes advantage of both methods to optimize a function for which an inclusion function can be expressed. The Branch and Bound algorithm deletes whole blocks of the search space whereas the Evolutionary Algorithm looks for the optimum in the remaining space and sends to the IBBA the best evaluation found in order to improve its bound. The two algorithms run independently and update common information through shared memory. The cooperative algorithm prevents premature and local convergence of the evolutionary algorithm, while speeding up the convergence of the branch and bound algorithm. Moreover, the result found is the proved global optimum.