Operational zones for comparing metaheuristic and deterministic one-dimensional global optimization algorithms

Univariate continuous global optimization problems are considered in this paper. Several widely used multidimensional metaheuristic global optimization methods-genetic algorithm, differential evolution, particle swarm optimization, artificial bee colony algorithm, and firefly algorithm-are adapted to the univariate case and compared with three Lipschitz global optimization algorithms. For this purpose, it has been introduced a methodology allowing one to compare stochastic methods with deterministic ones by using operational characteristics originally proposed for working with deterministic algorithms only. As a result, a visual comparison of methods having different nature on classes of randomly generated test functions becomes possible. A detailed description of the new methodology for comparing, called "operational zones", is given and results of wide numerical experiments with five metaheuristics and three Lipschitz algorithms are reported.