Arbitrary function optimisation with metaheuristics
No free lunch theorems for optimisation suggest that empirical studies on benchmarking problems are pointless, or even cast negative doubts, when algorithms are being applied to other problems not clearly related to the previous ones. Roughly speaking, reported empirical results are not just the result of algorithms performances, but the benchmark used therein as well; and consequently, recommending one algorithm over another for solving a new problem might be always disputable. In this work, we propose an empirical framework, arbitrary function optimisation framework, that allows researchers to formulate conclusions independent of the benchmark problems that were actually addressed, as long as the context of the problem class is mentioned. Experiments on sufficiently general scenarios are reported with the aim of assessing this independence. Additionally, this article presents, to the best of our knowledge, the first thorough empirical study on the no free lunch theorems, which is possible thanks to the application of the proposed methodology, and whose main result is that no free lunch theorems unlikely hold on the set of binary real-world problems. In particular, it is shown that exploiting reasonable heuristics becomes more beneficial than random search when dealing with binary real-world applications.
no free lunch theorems empirical studies real-world problems general-purpose algorithms unbiased results