New performance indicators for robust optimization over time

A new approach to solving dynamic optimization problems (DOPs), called robust optimization over time (ROOT) has recently been suggested and a number of optimization algorithms for finding ROOT solutions have been developed. These algorithms typically rely on the predicted fitness in the new environment to determine the robustness of a solution, which may be considerably different from the true robustness due to the errors in fitness prediction. Consequently, performance comparison based on the predicted fitness may be also misleading. In this paper, we propose a new formulation of the performance measures for quantitatively evaluate the performance of optimization algorithms for finding robust solutions over time, assuming that the actual optimal solution of the problem is known. We empirically verify the proposed performance measures by analyzing the robust optimal solutions obtained in two recently reported ROOT evolutionary algorithms. Our results indicate that the proposed performance measures are able to provide an effective means for performance comparison of ROOT algorithms.