Statistical Models Based Algorithms

Multi-objective optimization problems with expensive objective functionsexpensive function are typical in engineering design, where time-consuming computations are involved for modeling technological processes. Frequently, the available software implements an algorithm to compute the values of objective functions, but neither details of implementation nor analytical properties of the objective functions are known. Nevertheless, the continuity of the objective functions can be normally assumed. The complexity of the computational model implies not only the expensiveness of the objective function but also the uncertainty in its properties, so that other analytical properties of f(x), besides the continuity, cannot be substantiated. Such unfavorable, from the optimization point of view, properties of f(x) as non-differentiability, non-convexity, and multimodality cannot be excluded. Difficulties of the black-boxblack-box global optimization of expensive functions are well known from the experience gained in the single-objective case.