On the arithmetic of infinity oriented implementation of the multi-objective P-algorithm

Abstract

The single-objective P-algorithm is a global optimization algorithm based on a statistical mod- el of objective functions and the axiomatic theory of rational decisions. It has been proven quite suitable for optimization of black-box expensive functions. Recently the P-algorithm has been generalized to multi-objective optimization. In the present paper, the implementation of that algorithm is considered using the new computing paradigm of the arithmetic of infinity. A strong homogeneity of the multi-objective P-algorithm is proven, thus enabling rather a simple application of the algorithm to the problems involving infinities and infinitesimals.