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The problem of computing the set of Pareto-optimal solutions has been studied for a variety of multiobjective optimization problems. For many such problems, algorithms are known that compute the Pareto set in (weak) output-polynomial time. These algorithms are often based on dynamic programming and by weak output-polynomial time, we mean that the running time depends polynomially on the size of the Pareto set but also on the sizes of the Pareto sets of the subproblems that occur in the dynamic program. For some problems, like the multiobjective minimum spanning tree problem, such algorithms are not known to exist and for other problems, like multiobjective versions of many NP-hard problems, such algorithms cannot exist, unless 𝒫 = 𝒩𝒫. Dynamic programming over tree decompositions is a common technique in parameterized algorithms. In this paper, we study whether this technique can also be applied to compute Pareto sets of multiobjective optimization problems. We first derive an algorithm to compute the Pareto set for the multicriteria s-t cut problem and show how this result can be applied to a polygon aggregation problem arising in cartography that has recently been introduced by Rottmann et al. (GIScience 2021). We also show how to apply these techniques to also compute the Pareto set of the multiobjective minimum spanning tree problem and for the multiobjective TSP. The running time of our algorithms is O(f(w)⋅poly(n,p_{max})), where f is some function in the treewidth w, n is the input size, and p_{max} is an upper bound on the size of the Pareto sets of the subproblems that occur in the dynamic program. Finally, we present an experimental evaluation of computing Pareto sets on real-world instances of polygon aggregation problems. For this matter we devised a task-specific data structure that allows for efficient storage and modification of large sets of Pareto-optimal solutions. Throughout the implementation process, we incorporated several improved strategies and heuristics that significantly reduced both runtime and memory usage, enabling us to solve instances with treewidth of up to 22 within reasonable amount of time. Moreover, we conducted a preprocessing study to compare different tree decompositions in terms of their estimated overall runtime.