Towards a More Practically Sound Formulation of Dynamic Problems and Performance Evaluation of Dynamic Search Methods

The commonly used methodology for the simulation of dynamic problems formulates them as intervals of static problems, in which the change occurs between two successive intervals. This study proposes a more practically sound formulation of steadily changing dynamic problems, a class of dynamic problems in which the problem landscape continuously, but smoothly, changes over time. The new formulation provides more flexibility for a dynamic optimizer to choose the trade-off between the change frequency and the change severity while the change rate is prescribed by the actual problem. Besides, this study introduces a novel performance indicator for dynamic optimization methods. Unlike conventional ones, this indicator considers the real-time change in the actual problem during a time step and the period in which the best solution should be implemented. The practical importance of this formulation and the proposed performance indicator are studied on a few carefully designed controlled experiments. Subsequently, more comprehensive numerical simulations are performed to investigate the dependency of the optimal change frequency on the employed prediction method and test problem.