Decision-making and multi-objectivization for cost sensitive robust optimization over time

Abstract

Most existing research on dynamic optimization focuses on tracking the moving global optimum (TMO). Recently, a new paradigm for handling dynamic optimization, known as robust optimal over time (ROOT), has been proposed to avoid frequent changes in the optimal solutions. To explicitly minimize the costs incurred in switching solutions, a multi-objective ROOT algorithm has also been suggested. In practice, however, only one Pareto optimal solution can be adopted when the environment changes. To automate the decision-making process, this paper proposes a new approach that combines a ROOT/SCII algorithm with a policy to handle dynamic optimization problems. In the proposed approach, ROOT/SCII is used to simultaneously maximize the robustness and minimize the costs of switching solutions, and the policy is used to select a solution from the obtained Pareto set to be used in the new environment. In addition, multi-objectivization is introduced to enhance the efficiency in search for Pareto optimal solutions trading off between the robustness over time and the switching costs for the high dimension of decision space. Simulation results demonstrate that multi-objectivization is effective and the proposed approach is able to find a sequence of preferred solutions guided by the policy, considerably reducing the total switching costs while satisfying the user’s robustness requirement, and outperforming TMO and ROOT in terms of switching cost minimization.