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

- Stochastic and deterministic black-box global optimization methods are considered in the paper.
- The problem of their numerical comparison is examined.
- A new methodology called operational zones is proposed for a reliable comparison and an intuitive visualization of numerical results obtained by stochastic and deterministic global optimization algorithms.
- Several widely used metaheuristic global optimization methods (as genetic, differential evolution, particle swarm optimization, artificial bee colony, and firefly algorithms) are compared with Lipschitz deterministic methods by using operational zones.

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.