Metaheuristic vs. deterministic global optimization algorithms: The univariate case

Many practical problems involve the search for the global extremum in the space of the system parameters. The functions to be optimized are often highly multiextremal, black-box with unknown analytical representations, and hard to evaluate even in the case of one parameter to be adjusted in the presence of non-linear constraints. The interest of both the stochastic (in particular, metaheuristic) and mathematical programming (in particular, deterministic) communities to the comparison of metaheuristic and deterministic classes of methods is well recognized. Although both the communities have a huge number of journal and proceedings papers, a few of them are really dedicated to a systematic comparison of the methods belonging to these two classes. This paper meets the requirement of such a comparison between nature-inspired metaheuristic and deterministic algorithms (more than 125000 launches of the methods have been performed) and presents an attempt (beneficial to practical fields including engineering design) to bring together two rather disjoint communities of metaheuristic and mathematical programming researchers and applied users.