Abstract
Robust optimization over time is a new approach to solving dynamic optimization problems. It aims to maximize the time within which a solution remains to be acceptable in a changing environment. Since switching solutions often incurs cost in many real-world applications, it is essential for decision makers to take into account the trade-off between robustness and the switching cost in deciding whether the solution currently in use should be switched to a new solution when an environmental change occurs. This paper proposes a generic multi-objective optimization framework for robust optimization over time that simultaneously maximizes the robustness and minimizes the switching cost. An instantiation of the framework is also implemented, where a multi-objective particle swarm optimization algorithm is adopted as the optimizer and the cost for switching a solution is defined to be the difference in the decision space between the solution used in the previous environment and the one in the current environment. In addition, performance indicators are defined to quantitatively evaluate the performance of the proposed algorithm. Empirical studies are carried out on a number of benchmark problems to analyze the influence of the parameters on the behavior of the algorithm. Our results demonstrate that the proposed algorithm is able to find trade-off solutions between the robustness over time and switching cost in a dynamic environment. Finally, the performance of the algorithm is analyzed in terms of the performance indicators, confirming the effectiveness of the proposed framework in minimizing the switching cost in dynamic environments.