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Challenging optimization problems, which elude acceptable solution viaconventional calculus methods, arise commonly in different areas of industrialdesign and practice. Hard optimization problems are those who manifest thefollowing behavior: a) high number of independent input variables; b) verycomplex or irregular multi-modal fitness; c) computational expensive fitnessevaluation. This paper will focus on some theoretical issues that have strongimplications for practice. I will stress how an interpretation of the No FreeLunch theorem leads naturally to a general Bayesian optimization framework. Thechoice of a prior over the space of functions is a critical and inevitable stepin every black-box optimization.

No Free Lunch Theorem and Bayesian probability theory: two sides of the same coin. Some implications for black-box optimization and metaheuristics