Algorithms for Multi-objective Optimization Problems in Geodesy

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In geodesy, multi-objective optimization problems are ubiquitous. An example from project C1 are clustering and aggregation problems in cartography where one has to cluster areas and aggregate them into larger regions and there are multiple objectives one wants to optimize. Another example from project C2 comes from satellite radar altimetry of the sea surface where one wants to estimate both the sea surface height (SSH) and the significant wave height (SWH) from satellite data, which leads to a multi-objective shortest path problem.A common approach to handle multi-objective optimization problems is to combine the different criteria into a single objective by taking a weighted sum. This weighting is often artificial and can result in a loss of information. We will make use of the full potential of multi-objective optimization and study in particular the set of Pareto-optimal solutions. We will develop algorithms for efficiently computing or approximating this set for the problems mentioned above and other problems motivated by applications from geodesy. We will collaborate with A2,B1, B2, and C1 on multi-objective clustering and aggregation problems, with C1 and C2 on multi-objective triangulations, and with B2, C1, and C2 on multi-objective shortest path problems. Our algorithms will be analyzed theoretically but also implemented and tested in cooperation with projects C1 and C2 as well as B2. This will lead to both improved solutions in practice and novel theoretical results.