Constrained Global Optimization: Multiprocessor Approach

A collection of global optimization algorithms employing different types of a priory and accumulated information to boost the search for global optimum is presented in [1–4]. These schemes may easily be used as constituents for building some more sophisticated combined procedures that could be effectively acceler-ated being run on multiprocessor systems. Some of these possibilities are listed below. If φ(y) is a Lipschitzian function defined on the N-dimensional hypercube D then the N-dimensional global optimization problem by applying a Peano space-filling curve y(x) can be reduced to a one-dimensional problem of minimizing φ(y(x)) over the interval [0, 1]. The reduced problem can be then solved by efficient algorithms [1, sec. 8.1]. Some of these algorithms allow effective paral-lelization [1, sec. 9.1–9.3]. Approximation techniques for computing y(x) are also available [1, sec. 8.2]. To accelerate the search, a set of space-filling curves can be used [1, sec. 10.1] together with a smart parallel implementation [1, sec. 10.3]. Multi-dimensional global optimization problems with multiextremal partially defined constraints can also be reduced to a one-dimensional unconstrained prob-lem [1, sec. 8.3] that can be then solved by the algorithm [4] allowing an effective parallelization, as well