No Free Lunch Theorems: Limitations and Perspectives of Metaheuristics

The No Free Lunch (NFL) theorems for search and optimization are reviewed and their implications for the design of metaheuristics are discussed. The theorems state that any two search or optimization algorithms are equivalent when their performance is averaged across all possible problems and even over subsets of problems fulfilling certain constraints. The NFL results show that if there is no assumption regarding the relation between visited and unseen search points, efficient search and optimization is impossible. There is no well performing universal metaheuristic, but the heuristics must be tailored to the problem class at hand using prior knowledge. In practice, it is not likely that the preconditions of the NFL theorems are fulfilled for a problem class and thus differences between algorithms exist. Therefore, tailored algorithms can exploit structure underlying the optimization problem. Given full knowledge about the problem class, it is in theory possible to construct an optimal algorithm.