Post-Optimality Pareto-Robustness Analysis of an Earth-Observation Satellite Mission

In this paper a methodology for post-optimality studies to assess the robustness of the Pareto-optimal solutions, computed with a multi-objective optimization algorithm, is presented. The proposed Pareto-Robust Optimization Approach (PROA) is based on factorial design for sampling the design region in the neighborhood of the Pareto-optimal solutions. It allows for estimating a metric for the Pareto-Robustness and contributes to improving convergence of the known Pareto-front towards the true Pareto-front. Further, the sensitivity of the performance (the objectives of the analysis) to the dispersion of the design variables is analyzed using variance decomposition techniques. The shape of the design space is studied using the response surfaces method without additional computational cost. The proposed approach is applied to three validation test cases and to the design of a satellite Earth-observation mission for disaster monitoring. The results show that PROA can correctly detect Pareto-robust solutions on the Pareto front and that it provides additional Pareto-optimal solutions at the same time, eventually improving the original known Pareto front. Further, PROA shows its potentialities in effectively narrowing the search-space to only one limited portion. In the case of the Earth-observation mission, the study demonstrates the possibility to enable and promote trade-offs amongst the engineering-team members to obtain an effective decision-making process. The solution identified as the most Pareto-robust one can be considered quite uncommon, but still very reasonable due to the assumptions, presenting a satellite in a non sun-synchronous Medium Earth Orbit.