General Limits in Black-Box Optimization

Abstract

We already observed that evolutionary algorithms are usually thought of as general problem solvers. This implies that they are designed according to a general idea of how search should be implemented. In the case of evolutionary algorithms this idea stems from an understanding of natural evolution. More importantly, they are not designed in a way tailored toward a specific kind of optimization problem. We call this way of doing optimization while being in this sense oblivious to the concrete problem instance at hand black-box optimization. In this chapter we make precise what we mean when talking of black-box optimization. This allows us to recognize general limitations on the performance of any algorithm tackling the problem of black-box optimization. On one hand this helps us to get a clearer picture of what we can and cannot expect from evolutionary algorithms. On the other hand it even yields practically useful lower bounds on the performance of evolutionary algorithms. This is surprising good news since we consider a very general framework without concrete references to evolutionary algorithms that covers an enormous array of optimization algorithms.