Nature inspired optimization methods: how ants, bees, cuckoos and other friends may improve the work of mathematicians

In the present era, which is characterized by an unprecedented deluge of data, coming by many diversified sources, classical optimization methods often are not able to reach the target of finding "the best solution" to a mathematical problem. In this context, methods which imitate natural phenomena, and in particular animal behavior, have proven to be more effective and to some extent, more easily applicable to a wide range of optimization problems. These methods essentially are based on the self organization of swarms or populations of individuals, who keep some individual freedom, but have a tendency to "follow the best" in the group, which is a behavior very frequently observed in animal and even human societies. The interaction of biologists, ecologists and social scientists with mathematicians, who have been able to capture the main traits of the evolutionary success of a species or society and to reuse, interpret and embed them into an algorithm, has brought to the definition of a family of nature-inspired optimization methods, which since some years contribute in a fundamental way to the innovation of many productive and social processes.